WO2018021966A2 - Hot-carrier solar cell, and method to form the same - Google Patents

Hot-carrier solar cell, and method to form the same Download PDF

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WO2018021966A2
WO2018021966A2 PCT/SG2017/050365 SG2017050365W WO2018021966A2 WO 2018021966 A2 WO2018021966 A2 WO 2018021966A2 SG 2017050365 W SG2017050365 W SG 2017050365W WO 2018021966 A2 WO2018021966 A2 WO 2018021966A2
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hot
carrier
ncs
nanocrystals
energy
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PCT/SG2017/050365
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French (fr)
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WO2018021966A3 (en
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Tze Chien Sum
Mingjie LI
Subodh Gautam Mhaisalkar
Nripan Mathews
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Nanyang Technological University
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Priority to CN201780037453.3A priority Critical patent/CN109804479B/en
Publication of WO2018021966A2 publication Critical patent/WO2018021966A2/en
Publication of WO2018021966A3 publication Critical patent/WO2018021966A3/en

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    • H—ELECTRICITY
    • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10K—ORGANIC ELECTRIC SOLID-STATE DEVICES
    • H10K30/00—Organic devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation
    • H10K30/20—Organic devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation comprising organic-organic junctions, e.g. donor-acceptor junctions
    • H10K30/211—Organic devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation comprising organic-organic junctions, e.g. donor-acceptor junctions comprising multiple junctions, e.g. double heterojunctions
    • H—ELECTRICITY
    • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10K—ORGANIC ELECTRIC SOLID-STATE DEVICES
    • H10K85/00—Organic materials used in the body or electrodes of devices covered by this subclass
    • H10K85/50—Organic perovskites; Hybrid organic-inorganic perovskites [HOIP], e.g. CH3NH3PbI3
    • H—ELECTRICITY
    • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10K—ORGANIC ELECTRIC SOLID-STATE DEVICES
    • H10K30/00—Organic devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation
    • H10K30/50—Photovoltaic [PV] devices
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/549—Organic PV cells

Definitions

  • Various aspects of this disclosure relate to hot-carrier solar cells. Various aspects of this disclosure relate to methods of forming hot-carrier solar cells.
  • Various embodiments may provide a hot-carrier solar cell.
  • the solar cell may include a nanocrystal containing layer containing or including one or more nanocrystals, each of the one or more nanocrystals including a halide perovskite material.
  • the hot-carrier solar cell may also include a first electrode in contact with a first side of the nanocrystal containing layer.
  • the hot-carrier solar cell may further include a second electrode in contact with a second side of the nanocrystal containing layer opposite to the first side.
  • the nanocrystal containing layer may have a thickness of less than 100 nm.
  • Various embodiments may provide a method to form a hot-carrier solar cell.
  • the method may include providing or forming the nanocrystal containing layer including one or more nanocrystals (as described herein), each of the one or more nanocrystals including a halide perovskite material.
  • the method may also include forming a first electrode so that the first electrode is in contact with a first side of the nanocrystal containing layer.
  • the method may further include forming a second electrode so that the second electrode is in contact with a second side of the nanocrystal containing layer opposite to the first side.
  • the nanocrystal containing layer may have a thickness of less than 100 nm.
  • FIG. 1 shows a general illustration of a nanocrystal according to various embodiments.
  • FIG. 2 shows a general illustration of a hot-carrier solar cell according to various embodiments.
  • FIG. 3 is a schematic showing a method of forming a nanocrystal according to various embodiments.
  • FIG. 4 is a schematic showing a method of forming a hot-carrier solar cell according to various embodiments.
  • FIG. 5 is a schematic showing hot-carrier cooling with (a) intraband Auger-type energy transfer, (b) phonon-bottleneck effect and (c) interband Auger processes in semiconductor nanocrystals.
  • FIG. 6 shows representative transmission electron microscopy (TEM) images of methylammonium lead bromide perovskite (MAPbBr 3 ) nanocrystals (NCs) with relatively (a) small, (c) medium and (e) large sizes according to various embodiments and the respective size histograms (b, d, f) on their right.
  • the size distribution may be modeled with a Gaussian distribution.
  • FIG. 7 shows (a) top-view and (b) side-view scanning electron microscopy (SEM) images of methylammonium lead bromide (MAPbBr 3 ) bulk-film.
  • FIG. 8 shows (a) a plot of photoluminescence (PL) intensity (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating photoluminescence (PL) spectra of methylammonium lead bromide perovskite (MAPbBr 3 ) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (b) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating ultraviolet-visible (UV-vis) absorption spectra of methylammonium lead bromide perovskite (MAPbBr 3 ) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (c) a plot of energy of Is exciton, E ls (in electron volts or eV) as a function of average nanocrystal radius
  • FIG. 9A shows pseudo color transient absorption (TA) plot (upper panel, time (in picoseconds or ps) as a function of energy (in electron volts or eV)) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV)) for medium methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) (radii -4-5 nm) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal, ⁇ Vo> -0.1 (average carrier density per nanocrystal volume, n 0avg ⁇ 2.6 x 10 17 cm ⁇ 3 ) and high pump fluence (right panel) with ⁇ Vo> -2.5 (n 0avg ⁇ 6.5x 10 18 cm “3 ).
  • TA medium methylammonium lead bromide
  • FIG. 9B shows pseudo color representation (upper panel, time (in picoseconds or ps) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV)) for MAPbBr 3 bulk-film at low pump fluence (left panel) with initially generated carrier density no -2.1 x 10 17 cm 3 and high pump fluence (right panel) with no -1.5 x 10 19 cm 3 .
  • TA transient absorption
  • FIG. 10 shows plots of time (in picoseconds or ps) as a function of energy (electron volts or eV) showing pseudocolor transient absorption (TA) spectra (time in picoseconds or ps as a function of energy in electron volts or eV) for (a) small and (b) large sized methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal ⁇ No> -0.1 and high pump fluence (right panel) with ⁇ Vo> -2.5 following 3.1 eV photoexcitation.
  • TA pseudocolor transient absorption
  • FIG. 11 illustrates (a) a plot of normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV) showing normalized TA spectra at different short time delays of medium sized methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments in toluene with average generated electron-hole pair per nanocrystal, ⁇ No> ⁇ 0.1 (following 3.1 eV photoexcitation) and (b) the un-normalized transient absorption (TA) spectra of (a).
  • MAPbBr 3 NCs medium sized methylammonium lead bromide perovskite nanocrystals
  • FIG. 14 shows a table comparing properties of methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments, methylammonium lead bromide perovskite bulk films, and other materials reported in literature.
  • MAPbBr 3 NCs methylammonium lead bromide perovskite nanocrystals
  • FIG. 15 show plots of carrier temperatures (in Kelvins or K) as a function of time delay (picoseconds or ps) for three different sized methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments and bulk-film (a) at low pump fluence (corresponding to ⁇ No> -0.1 in NCs and no -2.1 x 10 17 cm 3 in bulk-film) and (b) at high pump fluence (corresponding to ⁇ Vo> -2.5 in NCs and no -1.5 x 10 19 cm 3 in bulk- film) following 3.1 eV photoexcitation.
  • MAPbBr 3 NCs methylammonium lead bromide perovskite nanocrystals
  • FIG. 16 illustrates plots of normalized transmittance change ⁇ / ⁇ as a function of time (picoseconds or ps) showing normalized photobleaching dynamics probed at the band edges of methylammonium lead bromide (a) bulk-film, (b) small nanocrystals (NCs) according to various embodiments, (c) medium nanocrystals (NCs) according to various embodiments, and (d) large nanocrystals (NCs) according to various embodiments, in solution with high and low pump fluence respectively, as well as (e) comparison of transient absorption (TA) dynamics for medium nanocrystals (NCs) according to various embodiments in solution and spin-coated nanocrystals (NCs) film according to various embodiments, and (f) pump- fluence-dependent bleaching dynamics probed at the band edge of small methylammonium lead bromide nanocrystals (NCs) according to various embodiments in solution.
  • TA transient absorption
  • FIG. 17 shows (a) a plot of energy loss rate (electron volts per picosecond eV ps "1 ) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate of hot-carriers as a function of carrier temperature T for methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments with ⁇ No> -0.1 and methylammonium lead bromide perovskite (MAPbBr 3 ) bulk-film with no -2.1 x 10 17 cm “3 , (b) a plot of normalized transmittance change ⁇ / ⁇ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band-edge for colloidal methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments and bulk-film at low carrier density, and (c) a plot of rise time
  • FIG. 18 is a plot of Raman intensity (in arbitrary units or a.u.) as a function of wavenumbers (in per centimeter or cm "1 ) showing room temperature Raman spectrum of as-prepared methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments drop-cast on glass substrate.
  • MAPbBr 3 NCs as-prepared methylammonium lead bromide perovskite nanocrystals
  • FIG. 19 shows (a) a plot of normalized transmittance change ⁇ / ⁇ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band edge for colloidal CdSe NCs with different diameters (shown in legend) at low pump fluence, and (b) plots of time (in picoseconds or ps) as a function of energy (in electron volts or eV) illustrating low pump fluence with initially generated ⁇ No> -0.1 (left) and high pump fluence with ⁇ No> -2.5 (right).
  • the phtotoexcitation energy is 3.1 eV.
  • FIG. 20 shows (a) a plot of energy loss rate (in electron volts per picosecond or eV ps "1 ) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate vs carrier temperature T c for methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments with ⁇ Vo> -2.5 and MAPbBr 3 bulk-film with no -1.5 x 10 19 cm “3 , (b) a plot of lifetime (in picoseconds or ps) as a function of nanocrystal volume (in cubic nanometer or nm 3 ) illustrating Auger recombination lifetimes and hot-carrier cooling time vs perovskite nanocrystal (NC) volume according to various embodiments, and (c) a plot of normalized hot carrier concentration ti ot as a function of time (in picoseconds or ps) showing normalized hot-carrier
  • FIG. 21 is a plot of energy loss rate (electron volts per picosecond or eV ps "1 ) as a function of carrier temperature (in Kelvins or K) showing energy loss rate of hot-carriers as a function of carrier temperature T c for methylammonium lead bromide (MAPbBr 3 ) bulk-film at low and high carrier densities.
  • eV ps "1 energy loss rate
  • FIG. 22 shows plots of photoelectron intensity (counts per second or cts/s) as a function of energy (in electron volts or eV) showing the ultraviolet photoelectron spectroscopy (UPS) spectrum of (a) 1,2-ethanedithiol (EDT)-treated and (b) post-annealed EDT-treated methylammonium lead bromide (MAPbBr 3 ) nanocrystals (NCs) films according to various embodiments, and (c) 7-diphenyl-l, 10-phenanthroline (Bphen) film on indium tin oxide (ITO) substrates.
  • UPS ultraviolet photoelectron spectroscopy
  • FIG. 23A is a flat-band energy diagram (vertical axis in electron volts or eV) to illustrate hot- electron extraction from perovskite nanocrystals according to various embodiments to 7- diphenyl- l,10-phenanthroline (Bphen) with competing hot-electron cooling pathways.
  • FIG. 23B shows an atomic force microscopy (AFM) image of 1,2-ethanedithiol (EDT)- treated nanocrystal (NC) film according to various embodiments.
  • AFM atomic force microscopy
  • FIG. 23C is a scanning electron microscopy (SEM) image of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments.
  • SEM scanning electron microscopy
  • FIG. 23D is a plot of normalized transmittance change ( ⁇ / ⁇ ) as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for about 35 nm thick of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film with (continuous lines) / without (dashed lines) 7-diphenyl- l,10-phenanthroline (Bphen) according to various embodiments following 3.1 eV photoexcitation with ⁇ No> around 0.1.
  • TA transient absorption
  • FIG. 23E is a plot of hot-carrier temperature (in Kelvins or K) as a function of delay time (in picoseconds or ps) for 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film and 1,2- ethanedithiol (EDT)-treated nanocrystal (NC) film /7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments at different pump fluences.
  • K hot-carrier temperature
  • FIG. 23F is a plot of extraction efficiency ?/hot (in percent or %) as a function of hot-electron excess energy (in electron volts or eV) showing pump energy dependence of the hot-electron extraction efficiencies in about 35 nm-thick 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl- l,10-phenanthroline (Bphen) bilayer according to various embodiments.
  • EDT 1,2-ethanedithiol
  • NC nanocrystal
  • Bphen 7-diphenyl- l,10-phenanthroline
  • 23G is a plot of extraction efficiency rjhot (in percent or %) as a function of thickness (in nanometres or nm) showing perovskite film thickness dependence of the hot electron extraction efficiencies upon 3.1 eV pump energy excitation for 1,2-ethanedithiol (EDT)- treated nanocrystal (NC)/ 7-diphenyl- l,10-phenanthroline (Bphen) bilayer according to various embodiments and bulk-film/7-diphenyl- l, 10-phenanthroline (Bphen) bilayer.
  • EDT 1,2-ethanedithiol
  • NC nanocrystal
  • Bphen 7-diphenyl- l,10-phenanthroline bilayer
  • Bphen bulk-film/7-diphenyl- l, 10-phenanthroline
  • FIG. 24 shows (a) plot of transmittance (in arbitrary units or a.u.) as a function of wavenumber (in per centimeter or cm "1 ) showing the attenuated total reflection- fourier transform infrared (ATR-FTIR) spectra of as-prepared methylammonium lead bromide nanocrystals (MAPbBr 3 NCs), 1,2-ethanedithiol (EDT)-treated nanocrystals (EDT-NCs) and 70 °C annealed 1,2-ethanedithiol nanocrystals (Ann-EDT-NCs) according to various embodiments, and plots of photoemission intensities (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing sulfur (S) 2p X-ray photoelectron spectroscopy (XPS) spectra of (b) non-annealed and (c) 70 °C post-annealed 1,2- ethan
  • FIG. 25 shows (a) atomic form microscopy (AFM) image of un-treated medium methylammonium lead bromide nanocrystals (MAPbBr 3 NCs) film according to various embodiments, and (b) representative transmission electron microscopy (TEM) image of 1,2- ethanedithiol -treated methylammonium lead bromide nanocrystals (EDT-treated MAPbBr 3 NCs) according to various embodiments.
  • AFM atomic form microscopy
  • MAPbBr 3 NCs un-treated medium methylammonium lead bromide nanocrystals
  • TEM transmission electron microscopy
  • FIG. 26 shows pseudocolor transient absorption (TA) spectra for (a) medium methylammonium lead bromide nanocrystals (MAPbBr 3 NCs) film according to various embodiments, (b) 1,2-ethanedithiol -treated nanocrystals (EDT-treated NCs) film according to various embodiments, and (c) on 1,2-ethanedithiol-treated nanocrystals film/7-diphenyl- 1,10-phenanthroline (EDT-treated NCs film/Bphen) bilayer according to various embodiments at low pump fluence (left panel) with initially generated ⁇ No> -0.1 and high pump fluence (right panel) with ⁇ Vo> -2.5.
  • TA pseudocolor transient absorption
  • FIG. 27 shows energy diagrams (y axis: energy in electron volts or eV) showing flat-band energy level alignment as determined from the ultraviolet photoelectron spectroscopy (UPS) and ultraviolet-visible (UV-VIS) spectroscopy measurements for non-annealed, annealed 1,2- ethanedithiol -nanocrystals (EDT-NCs) films and 7-diphenyl-l, 10-phenanthroline (Bphen) according to various embodiments - illustrated for the case of hot-electron extractions.
  • UPS ultraviolet photoelectron spectroscopy
  • UV-VIS ultraviolet-visible
  • FIG. 28 shows (a) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) showing linear absorption spectra of Bphen film on glass; (b) plot of normalized negative transmittance change - ⁇ / ⁇ as a function of wavelength (in nanometer or nm) showing negative transient absorbance spectra of 7-diphenyl- l,10-phenanthroline (Bphen) (300 nm pump with intensity of 20 ⁇ cm "2 , 400 nm pump with intensity of 40 ⁇ cm "2 ), perovskites nanocrystals (NCs) (400 nm pump with intensity of 15 ⁇ cm-2) according to various embodiments and 1,2-ethanedithiol nanocrystals / 7-diphenyl-l ,10-phenanthroline (EDT-NCs/Bphen) (400 nm pump with intensity of 15 ⁇ cm-2) according to various embodiments at 2 ps after excitation
  • FIG. 29 are plots of normalized transmittance change ⁇ / ⁇ as a function of time (in picoseconds or ps) showing normalized band-edge bleaching dynamics of 1,2-ethanedithiol- treated nanocrystals (EDT-NCs) film according to various embodiments and 1,2- ethanedithiol-treated nanocrystals / 7-diphenyl- l,10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments under (a) low ( ⁇ No> ⁇ 0. l) and (b) high ( ⁇ No> -2.5) pump fluence with 3.1 eV photoexcitation.
  • EDT-NCs 1,2-ethanedithiol- treated nanocrystals
  • Bphen 7-diphenyl- l,10-phenanthroline
  • FIG. 30A is a plot of normalized transmittance change ⁇ / ⁇ as a function of energy (electron volts or eV) showing normalized transient absorption spectra for annealed 1,2-ethanedithiol treated (EDT-treated) medium methylammonium lead bromide nanocrystals (MAPbBr 3 NCs) film with (continuous lines) and without (dashed lines) 7-diphenyl- l, 10-phenanthroline (Bphen) extraction layers according to various embodiments at low fluence with ⁇ No> - 0.1.
  • FIG. 30B is a plot of carrier temperature (in Kelvins or K) as a function of time (in picoseconds or ps) showing extracted hot-carrier temperature as a function of delay time for two samples according to various embodiments.
  • FIG. 30C is a plot of normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for methylammonium lead bromide (MAPbBr 3 ) bulk-film (-240 nm thick) with (lines) and without (dashes) 7-diphenyl- l,10-phenanthroline (Bphen) extraction layers at low pump fluence with 2x 10 17 cm "3 .
  • TA transient absorption
  • FIG. 30D shows a plot of carrier temperature (in Kelvins or K) as a function of time delay (in picoseconds or ps) for two samples according to various embodiments.
  • FIG. 31 shows cross-sectional scanning electron microscopy (SEM) images of 1,2- ethanedithiol-treated nanocrystals (EDT-NCs film) with different thickness according to various embodiments.
  • Embodiments described in the context of one of the methods or nanocrystals/solar cells/devices is analogously valid for the other methods or nanocrystals/solar cells/devices.
  • embodiments described in the context of a method are analogously valid for nanocrystals/solar cell/device, and vice versa.
  • the word “over” used with regards to a deposited material formed “over” a side or surface may be used herein to mean that the deposited material may be formed “directly on”, e.g. in direct contact with, the implied side or surface.
  • the word “over” used with regards to a deposited material formed “over” a side or surface may also be used herein to mean that the deposited material may be formed "indirectly on” the implied side or surface with one or more additional layers being arranged between the implied side or surface and the deposited material.
  • a first layer “over” a second layer may refer to the first layer directly on the second layer, or that the first layer and the second layer are separated by one or more intervening layers.
  • the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements.
  • FIG. 1 shows a general illustration of a nanocrystal 100 according to various embodiments.
  • the nanocrystal 100 may include a halide perovskite material.
  • the nanocrystal may have a diameter having a value selected from a range of 1 nm to 100 nm, e.g. of 4 nm to 14 nm or 4 nm to 13 nm.
  • a radius of the nanocrystal may be any one value selected from 0.5 nm to 50 nm, e.g. from 2 nm to 7 nm.
  • the expressions "from X to Y" or "a range of X to Y” may refer to a range including the values of X and Y, in addition to all values between X and Y.
  • Various embodiments may slow down the hot-carrier cooling processes through the phonon bottleneck effect or interband Auger process (which is also known as Auger heating).
  • Various embodiments may be employed in solar cells, which may overcome the SQ-limit by harvesting the excess energy from above-bandgap photons, thus improving efficiency.
  • NCs inorganic semiconductor nanocrystals
  • hot- carrier harvesting in these inorganic semiconductor nanocrystals are compromised by highly competitive relaxation pathways (e.g. , intraband Auger process, defects) that overwhelm their phonon bottlenecks.
  • Kilina et al. Quantum Zero Effect Rationalizes The Phonon Bottleneck In Semiconductor Quantum Dots", Physical Review Letters 110, 180404, p. 1 - 6, 2013
  • Kilina et al. Quantum Zero Effect Rationalizes The Phonon Bottleneck In Semiconductor Quantum Dots
  • Kilina et al. (“Quantum Zero Effect Rationalizes The Phonon Bottleneck In Semiconductor Quantum Dots", Physical Review Letters 110, 180404, p. 1 - 6, 2013) reports that the effect of phonon bottleneck in cadmium selenide (CdSe) quantum dots remains elusive due to Auger processes and structural defects.
  • CdSe cadmium selenide
  • colloidal halide perovskite NCs may transcend these limitations.
  • the halide perovskite NCs may exhibit ⁇ 2 orders longer hot- carrier cooling times and ⁇ 4 times higher hot-carrier temperatures than their bulk-film counterparts.
  • hot-carrier cooling mediated by a phonon bottleneck may surprisingly be slower in smaller NCs (in contrast to conventional NCs in which cooling time decreases as size decreases).
  • Auger heating may dominate hot-carrier cooling, which is slower in larger NCs (hitherto unobserved in conventional NCs).
  • the inventors demonstrate efficient room temperature hot-electrons extraction (up to -83%) by an energy- selective electron extraction layer from surface-treated perovskite NCs thin films within 1 picosecond (ps). These insights may allow fresh approaches for extremely thin absorber and/or concentrator-type hot-carrier solar cells.
  • the halide perovskite material may be represented by the general formula AMX 3 , where A may be a monopositive organic or inorganic cation (e.g. an organic group or organic cation or a metal cation or element), or a mixture of organic and/or inorganic cations, M may be a divalent metal cation or element, and X may be a halogen anion or element.
  • A may be a monopositive organic or inorganic cation (e.g. an organic group or organic cation or a metal cation or element), or a mixture of organic and/or inorganic cations
  • M may be a divalent metal cation or element
  • X may be a halogen anion or element.
  • MA may refer to methylammonium (CH 3 NH 3 )
  • the divalent cation may be Pb 2+ , Sn 2+ .
  • M may be lead (Pb) or tin (Sn).
  • the halide perovskite material may include one or more halide anions selected from a group consisting of ⁇ , CI " and Br " .
  • X 3 may be I 3 , Cl 3 , Br 3 , or a combination thereof (e.g. Cl 2 Br).
  • the halide perovskite material may include an organic ammonium cation.
  • the organic ammonium cation A may be selected from a group consisting of an ammonium cation, a hydroxylammonium cation, a methylammonium cation (MA + ), a hydrazinium cation, an azetidinium cation, a formamidinium cation (FA + ), an imidazolium cation, a dimethylammonium cation, an ethylammonium cation, a phenethylammonium cation, a guanidinium cation, and combinations thereof.
  • the organic ammonium cation may be a cation with formula CnEhn+i NH 3 + where 2 ⁇ n ⁇ 20.
  • A may be CnEhn+i NH 3 .
  • the halide perovskite material may include a metal cation such as cesium ion (Cs + ).
  • the nanocrystal 100 may exhibit a hot-carrier cooling lifetime of any value of at least 0.5 ps, e.g. from 0.5 ps to 40 ps.
  • the hot-carrier cooling lifetime may be defined as the time interval from pulse excitation till the cooling of hot-carriers to 600K.
  • FIG. 2 shows a general illustration of a hot-carrier solar cell 200 according to various embodiments.
  • the solar cell 200 may include a nanocrystal containing layer 202 containing or including one or more nanocrystals (as described herein), each of the one or more nanocrystals including a halide perovskite material.
  • the hot-carrier solar cell 200 may also include a first electrode 204 in contact with a first side of the nanocrystal containing layer 202.
  • the hot-carrier solar cell 200 may further include a second electrode 206 in contact with a second side of the nanocrystal containing layer opposite to the first side.
  • the nanocrystal containing layer 202 may have a thickness of less than 100 nm.
  • the solar cell 200 may include a nanocrystal containing layer 202 which contains one or more nanocrystals.
  • the layer 202 may be sandwiched by electrodes 204, 206.
  • the nanocrystal containing layer 202 may also be referred to as the absorbing layer or hot-carrier absorber.
  • the thickness of the layer 202 may be less than the hot-carrier diffusion length so that hot carriers can be extracted by the electrodes 204, 206 before cooling.
  • the hot-carrier solar cell 200 may receive incoming light (from the sun) and may be configured to generate electrical energy based on the solar energy from the incoming light.
  • the hot-carrier solar cell 200 may further include an optical arrangement configured to direct solar energy (from the sun) to the nanocrystal containing layer 202.
  • the hot-carrier solar cell 200 may be a concentrator hot carrier solar cell.
  • the optical arrangement may include one or more optical elements to direct solar energy to the nanocrystal containing layer 202.
  • the one or more optical elements may be or may include optical lenses and/or mirrors. Hot-carrier cooling may be become slower with increasing photoexcited charge carrier density at higher pump fluence.
  • the hot-carrier cooling lifetime may exceed 30 ps (compared to 1.5 ps in bulk film), which may be due to Auger-heating effect in the quantum confined system.
  • These features may be favorable for application of concentrator solar cells which are operated at higher power density by focusing light to a spot of the photovoltaic cell.
  • the hot-carrier lifetime in perovskite NCs may be longer at high pump fluence.
  • These features may be favorable for application of concentrator hot carrier solar cells, which may be operated at higher illumination (about or exceeding 1000 suns) using hot-carrier absorbers.
  • the hot-carrier solar cell 200 may be a single-junction solar cell. In various alternate embodiments, the hot-carrier solar cell 200 may be a multi- junction solar cell.
  • the first electrode 204 may be or may include a hot- electron extraction layer.
  • the first electrode 204 may be or may include a n-type layer.
  • the n-type layer or hot-electron extraction layer may include any one material selected from a group consisting of titanium oxide, zinc oxide, phenyl-C61 -butyric acid methyl ester (PCBM), 4,7-diphenyl-l,10-phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4- biphenylyl)-5-phenyl- 1 ,3 ,4-oxadiazole (PBD), 2,2',2"-( 1 ,3 ,5-benzinetriyl)-tris( 1 -phenyl- 1 -H- benzimidazole) (TPBI), poly(9,9-dioctylfluorene) (F8), and bathocuproine (BCP).
  • PCBM phenyl-C61 -butyric acid methyl ester
  • Bphen 4,7-dip
  • the first electrode 204 may be an energy selective contact configured to allow electrons having excess energies at or above a predetermined value to pass through, and further configured to reflect electrons having excess energies below the predetermined value back to the nanocrystal containing layer 202.
  • excess energies may refer to energy of the electrons beyond the conduction band minimum of the nanocrystal containing layer 202.
  • the predetermined value of excess energy may be any value selected from a range of around 0.1 eV to 2 eV.
  • the second electrode 206 may be or may include a hot- hole extraction layer.
  • the second electrode 206 may be or may include a p-type layer.
  • the second electrode 206 may be an energy selective contact configured to allow holes having excess energies at or above a predetermined value to pass through, and further configured to reflect holes having excess energies below the predetermined value back to the nanocrystal containing layer 202.
  • excess energies may refer to energy of the holes beyond the valence band maximum of the nanocrystal containing layer 202.
  • the predetermined value of excess energy may be any value selected from a range from around 0.1 eV to 2 eV.
  • the second electrode 206 may include a molecular semiconductor material.
  • the p-type layer or hot-hole extraction layer may include any one material selected from a group consisting of 2,2' ,7,7'- tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'-spirobifluorene (spiro-OMeTAD), poly(3- hexylthiophene-2,5-diyl) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS), and poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine) (TFB).
  • spiro-OMeTAD poly(3- hexylthiophene-2,5-diyl)
  • P3HT poly(3,4-ethylenedioxythiophene) polystyrene sulfonate
  • the one or more nanocrystals exhibit a hot-carrier cooling lifetime of at least 0.5 ps, e.g. above 30 ps.
  • a radius of each of the one or more nanocrystals is any one value selected from 0.5 nm to 50 nm, e.g. 2 nm to 7 nm.
  • the halide perovskite material may be an organic- inorganic halide perovskite material, such as MAPbI 3 , MAPbBr 3 , MAPbBr 2 I, FAPbI 3 , FAi- yCs y PbI 3 , or Cs x (MAi-yFAy)i-xPb(Ii-zBr z ) 3 (where each of x, y or z may be any value selected from a range of 0 to 1).
  • the halide perovskite material may be an inorganic halide perovskite material such as CsSnI 3 or CsPbI 3 .
  • Extraction of hot-carriers may be required to be very fast to limit energy loss; where the competition is between extraction rate and cooling rate rather than recombination rate.
  • the one or more nanocrystals may be treated with 1,2- ethanedithiol (EDT).
  • Bphen may be selected as the hot-electron extraction material because this molecular semiconductor has a high electron mobility and a higher lowest unoccupied molecular orbital (LUMO) than the conduction band minimum (CBM) of the EDT-treated NC's.
  • EDT treatment may be used to substitute the long and highly insulating oleic acid ligands that is present on the as- prepared NC surfaces with thiolate for more effective electronic coupling with Bphen and within NCs films.
  • FIG. 3 is a schematic 300 showing a method of forming a nanocrystal according to various embodiments.
  • the method may include, in 302, using a solution-based process to form the nanocrystal including a halide perovskite material.
  • the nanocrystal may have a diameter having a value selected from a range of 1 nm to 100 nm, e.g. of 4 nm to 14 nm.
  • the solution-based process may include mixing a plurality of precursors with a solvent to form a precursor solution.
  • the plurality of precursors may include an organic ammonium halide.
  • the solution-based process may further include adding one or more ligands and/or one or more surfactants to the precursor solution.
  • methylammonium bromide (MABr, with MA representing methyammonium) may be mixed with lead bromide (PbBr 2 ) in a solvent of dimethyformamide (DMF) to form an initial precursor solution.
  • Oleyamine (OAm) and oleic acid (OAc) may be added to the DMF solvent to form a final precursor solution for forming methylammonium lead bromide perovskite nanocrystals.
  • the solution-based process may further include heating a further solvent.
  • the further solvent may be heated to a predetermined temperature, e.g. 60 °C.
  • the solution based process may additionally include mixing the precursor solution with the heated further solvent under stirring to form the nanocrystal.
  • the further solvent may be toluene.
  • FIG. 4 is a schematic 400 showing a method of forming a hot-carrier solar cell according to various embodiments.
  • the method may include, in 402, providing or forming the nanocrystal containing layer including one or more nanocrystals (as described herein), each of the one or more nanocrystals including a halide perovskite material.
  • the method may also include, in 404, forming a first electrode so that the first electrode is in contact with a first side of the nanocrystal containing layer.
  • the method may further include, in 406, forming a second electrode so that the second electrode is in contact with a second side of the nanocrystal containing layer opposite to the first side.
  • the nanocrystal containing layer may have a thickness of less than 100 nm.
  • the solar cell may include a nanocrystal containing layer containing one or more nanocrystals as described herein and electrodes.
  • the method steps shown in FIG. 4 may not necessarily be in sequence.
  • the first electrode may be formed, before forming the nanocrystal containing layer.
  • the method may further include forming an optical arrangement configured to direct solar energy to the nanocrystal containing layer.
  • the optical arrangement may include one or more optical elements configured to direct solar energy to the nanocrystal containing layer.
  • the one or more optical elements may be or may include optical lenses and/or mirrors.
  • the first electrode 204 may be or may include a hot- electron extraction layer.
  • the first electrode 204 may be or may include a n-type layer.
  • the n-type layer or hot-electron extraction layer may include any one material selected from a group consisting of titanium oxide, zinc oxide, phenyl-C61 -butyric acid methyl ester (PCBM), 4,7-diphenyl-l,10-phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4- biphenylyl)-5-phenyl-l,3,4-oxadiazole (PBD), 2, 2',2"-(l,3,5-benzinetriyl)-tris(l-phenyl-l-H- benzimidazole) (TPBI), poly(9,9-dioctylfluorene) (F8), and bathocuproine (BCP).
  • PCBM phenyl-C61 -butyric acid methyl ester
  • Bphen 4,7-diphenyl-l,10-
  • the first electrode 204 may be an energy selective contact configured to allow electrons having excess energies at or above a predetermined value to pass through, and further configured to reflect electrons having excess energies below the predetermined value back to the nanocrystal containing layer 202.
  • excess energies may refer to energy of the electrons beyond the conduction band minimum of the nanocrystal containing layer 202.
  • the predetermined value of excess energy may be any value selected from a range of around 0.1 to 2 eV.
  • the second electrode 206 may be or may include a hot- hole extraction layer.
  • the second electrode 206 may be or may include a p-type layer.
  • the second electrode 206 may be an energy selective contact configured to allow holes having excess energies at or above a predetermined value to pass through, and further configured to reflect holes having excess energies below the predetermined value back to the nanocrystal containing layer 202.
  • excess energies may refer to energy of the holes beyond the valence band maximum of the nanocrystal containing layer 202.
  • the predetermined value of excess energy may be any value selected from a range of around 0.1 to 2 eV.
  • the second electrode 206 may include a molecular semiconductor material.
  • the p-type layer or hot-hole extraction layer may include any one material selected from a group consisting of 2,2',7,7'- tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'-spirobifluorene (spiro-OMeTAD), poly(3- hexylthiophene-2,5-diyl) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS), and poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine) (TFB).
  • spiro-OMeTAD poly(3- hexylthiophene-2,5-diyl)
  • P3HT poly(3,4-ethylenedioxythiophene) polystyrene sulfonate
  • the one or more nanocrystals exhibit a hot-carrier cooling lifetime of at least 0.5 ps, e.g. above 30 ps.
  • a radius of each of the one or more nanocrystals is any one value selected from 0.5 nm to 50 nm, e.g. 2 nm to 7 nm.
  • the halide perovskite material may be an organic- inorganic halide perovskite material, such as MAPbI 3 , MAPbBr 3 , MAPbBr 2 I, FAPbI 3 , FAi- yCs y PbI 3 , or Cs x (MAi-yFAy)i-xPb(Ii-zBr z ) 3 (where each of x, y or z may be any value selected from a range from 0 to 1).
  • the halide perovskite material may be an inorganic halide perovskite material such as CsSnI 3 or CsPbI 3 .
  • MAPbBr 3 methylammonium lead bromide perovskite nanocrystals
  • the hot-carrier cooling may be dramatically slower than the perovskite bulk-films.
  • the hot-carrier cooling time may be increased to 30 ps (or above) in MAPbBr 3 NCs which is ⁇ 2 orders slower than their bulk-film counterparts under comparable photoexcitation conditions.
  • the hot-carrier temperature of the MAPbBr 3 NCs is 4 times larger than their bulk-film counterparts under comparable photoexcitation conditions.
  • Controlling hot-carrier cooling dynamics may be challenging but critical for improving the performance of many semiconductor photonic and electronic devices.
  • the hot-carrier cooling time/rate may depend both on the volume and carrier densities.
  • the hot-carrier cooling in the NCs may be modulated by varying the size of NCs.
  • the hot-carrier cooling rate may be lower in smaller sized NCs due to confinement induced phonon bottleneck effect.
  • MAPbBr 3 perovskites NCs
  • other perovskites NCs with substitution of organic component and/or the metal element such as MAPbI 3 , MAPbBr x Ii- x (x is the ratio of Br/(Br + I), which is determined by the contents of Br and I in the precursors during synthesis), CsSnI 3 , CsPbI 3 , FAPbI 3 .
  • NCs may allow a wide choice of hot-carrier absorbers with different bandgaps. Moreover, after the surface chemical treatment, the hot electrons from NCs thin film may be efficiently injected (up to -83%) into electron extraction layers within ⁇ 1 ps. These insights may enable fresh approaches for hot-carrier and concentrator-type perovskite NC photovoltaic s.
  • Various embodiments may relate to the fabrication of the low temperature solution processed organic-inorganic perovskite nanocrystals, the observation of slow hot-carrier cooling, and/or the potential application of these nanocrystals for hot-carrier solar cells and concentrator hot-carrier solar cells.
  • concentrator hot-carrier solar cell may use focusing lenses or curved mirrors to focus the sunlight by a factor of between 300 to 1000 times onto a small cell area.
  • a concentrator cell may therefore operate at much higher light-generated current densities than the normal hot- carrier solar cell. The higher injection densities may induce the higher hot-carrier temperature and longer hot-carrier lifetimes, which may further increase the efficiencies of hot-carrier solar cells.
  • the nanocrystals may be fabricated using a low temperature solution processed approach in atmosphere.
  • traditional Si-based solar cells are usually produced at elevated temperatures and using high vacuum growth techniques that require significant infrastructural investments.
  • Hot-carrier cooling may be critical in many photonic and electronic devices.
  • a solution processable material may have much greater versatility than traditional material for integration with existing silicon based technologies. It can be applied to a much wider range of device designs and substrates by simply spin-coating, dip-coating or drop-casting.
  • Solution processed organic-inorganic perovskite nanocrystals may provide simple and inexpensive alternatives of material for potential photovoltaic applications as compared to traditionally silicon thin film produced with expensive gas-phase methods.
  • the low temperature of processing may also enable integration of these materials into flexible substrates.
  • the perovskites NCs may have much slower hot-carrier cooling as compared with that of current perovskites thin films used as absorbers in solar-cells which permit the efficient hot-carrier extraction. These features may be beneficial for the achievement of hot- carrier solar cell.
  • the hot-carrier cooling time/rate may also be tuned by modifying NC size.
  • Various embodiments may find wide use in the application area of photovoltaics as absorption materials, such as NCs- sensitized nanocrystalline T1O2 solar cells, concentrator solar cells, NCs-conducting polymer blend solar cells, p-i-n array solar cells and/or concentrator solar cells.
  • FIG. 5 is a schematic 500 showing hot-carrier cooling with Auger processes in semiconductor nanocrystals.
  • hot-carrier cooling is made possible via intraband Auger- type energy transfer.
  • a hot electron (dot) may be cooled by Auger-type energy transfer to densely spaced hole states (e.g. , CdSe NCs), then the hot holes (circle) can relax rapidly via a cascade of single phonon emissions (arrows);
  • (c) shows, hot-carrier re-excitation by interband Auger-recombination of carriers at band edges, also called Auger-heating.
  • FIG. 6 shows representative transmission electron microscopy (TEM) images of methylammonium lead bromide perovskite (MAPbBr 3 ) nanocrystals (NCs) with relatively (a) small, (c) medium and (e) large sizes according to various embodiments and the respective size histograms (b, d, f) on their right.
  • the size distribution may be modeled with a Gaussian distribution.
  • FIG. 7 shows (a) top-view and (b) side-view scanning electron microscopy (SEM) images of methylammonium lead bromide (MAPbBr 3 ) bulk-film.
  • SEM scanning electron microscopy
  • FIG. 8 shows (a) a plot of photoluminescence (PL) intensity (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating photoluminescence (PL) spectra of methylammonium lead bromide perovskite (MAPbBr 3 ) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (b) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating ultraviolet-visible (UV-vis) absorption spectra of methylammonium lead bromide perovskite (MAPbBr 3 ) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (c) a plot of energy of Is exciton, E ls (in electron volts or eV) as a function of average nanoc
  • results reveal that the weakly confined MAPbBr 3 NCs (FIG. 8) are very promising hot-carrier absorber materials as they possess much higher hot-carrier temperatures and longer cooling times (as compared to typical perovskite bulk-films under comparable photoexcitation conditions). This may be attributed to their intrinsic phonon bottleneck and Auger-heating effects at low and high carrier densities, respectively. Importantly, the hot- carriers may be efficiently extracted from MAPbBr 3 NC thin films at room temperature by using a molecular semiconductor as an energy selective contact. [0079] FIG.
  • FIG. 9A shows pseudo color transient absorption (TA) plot (upper panel, time (in picoseconds or ps) as a function of energy (in electron volts or eV)) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV)) for medium methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) (radii -4-5 nm) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal, ⁇ Vo> -0.1 (average carrier density per nanocrystal volume, n 0avg ⁇ 2.6 x 10 17 cm ⁇ 3 ) and high pump fluence (right panel) with ⁇ No> -2.5 (n 0avg ⁇ 6.5x 10 18 cm ⁇ 3 ).
  • TA medium methylammonium lead bromide
  • FIG. 9B shows pseudo color representation (upper panel, time (in picoseconds or ps) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV)) for MAPbBr 3 bulk-film at low pump fluence (left panel) with initially generated carrier density no -2.1 x 10 17 cm 3 and high pump fluence (right panel) with no -1.5 x 10 19 cm 3 .
  • TA transient absorption
  • FIGS. 9A-B show a comparison of the pseudo color TA plots and TA spectra of the medium MAPbBr 3 NCs (radius -4.5 nm) against MAPbBr 3 bulk-film at low and high pump fluence, respectively.
  • the plots/spectra display a prominent photo-bleaching (PB) peak with a high energy tail near the bandgap because of the state- filling effects. Similar results were also observed in the small and large NCs.
  • PB photo-bleaching
  • FIG. 10 shows plots of time (in picoseconds or ps) as a function of energy (electron volts or eV) showing pseudocolor transient absorption (TA) spectra (time in picoseconds or ps as a function of energy in electron volts or eV) for (a) small and (b) large sized methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal ⁇ No> -0.1 and high pump fluence (right panel) with ⁇ Vo> -2.5 following 3.1 eV photoexcitation.
  • TA pseudocolor transient absorption
  • the high energy tails of the PB peak originate from the rapid distribution of initial non-equilibrium carriers into a Fermi-Dirac distribution via elastic scatterings (including electron-hole scattering at low pump fluence and carrier-carrier scattering at high pump fluence) that can be characterized by a carrier temperature T .
  • T can thus be extracted by fitting the high-energy tail of the TA spectra with a simple Maxwell- Boltzmann function of exp(Ef - E/KB 7 ), where KB is the Boltzmann's constant and Ef is the quasi-Fermi energy.
  • the discrete energy levels can be approximately treated as a continuum in the case where thermal energy k ⁇ T » energy level spacing AE.
  • the perovskites NCs may be in the weak confinement regime with energy levels that are more closely spaced.
  • the TA spectra may be collected from an ensemble of NCs whose size distribution may cause inhomogeneous broadening, (i.e., overlapping TA spectrum from single NC). All these properties rightly lead to a continuous TA spectrum from the NCs ensemble to resemble that of the bulk materials.
  • the high- energy tail of the NCs' TA spectra may also be described by a Maxwell-Boltzmann distribution. The representative fits of the high-energy tails and non-normalized TA spectra are presented in FIG. 11.
  • FIG. 11 illustrates (a) a plot of normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV) showing normalized TA spectra at different short time delays of medium sized methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments in toluene with average generated electron-hole pair per nanocrystal, ⁇ Vo> ⁇ 0.1 (following 3.1 eV photoexcitation) and (b) the un-normalized transient absorption (TA) spectra of (a).
  • the solid black lines in (a) fit to the high-energy tails using the Maxwell-Boltzmann distribution function.
  • the analysis and interpretation of the TA spectra of halide perovskites are well- documented in the literature.
  • the TA spectra of MAPbBr 3 perovskites (bulk and nanocrystals) are similar with that of previous studies.
  • the positive TA peak (at -2.3 eV as shown in FIG. 11) arose from ground states bleaching (GSB) due to the state-filling of the carriers at the band edge.
  • GSB ground states bleaching
  • the first slope i.e. , the steeper one closer to the GSB peak
  • the second gentler slope of the high energy tail e.g. , start at -2.5 eV in FIG.
  • the negative part (photoinduced absorption) of this high energy side is caused by the photoinduced change of the imaginary part of the refractive index; while the negative part of the low energy side of the GSB is attributed to bandgap renormalization.
  • Hot-carrier temperature T is extracted by fitting the high-energy tail of the TA spectra with a Maxwell-Boltzmann function.
  • the Fermi-Dirac distribution function can be approximately described with an exponential - i.e. , a Maxwell- Boltzmann distribution:
  • PL
  • ⁇ of NCs can be obtained by fitting the data with equation of 1— e ⁇ Ja (solid lines). The fitted ⁇ are 8.5+0.5xl0 "15 , 3.2+0.2xl0 "14 and 6.8+0.3xl0 "14 cm 2 from small to large NCs, respectively.
  • the maximum T at the excitation onset with ⁇ No> -0.1 may be around 1700 K, which is about four times higher than that for the bulk-film sample with comparable carrier densities. The smaller T in the latter may be attributed to arise from the ultrafast cooling of hot-carriers, which had occurred on a timescale much shorter than the temporal resolution of the TA measurements.
  • hot-carrier cooling times due to several factors: (i) the pump energy (i.e., carriers' excess energy - typically, higher excess energies lead to longer hot carrier lifetimes); (ii) the initial hot-carrier densities (i.e., higher carrier densities usually lead to longer hot carrier lifetimes); and/or (iii) the energy loss rate at a specific hot-carrier temperature (i.e., generally, lower hot carrier temperatures yield smaller energy loss rates).
  • pump energy i.e., carriers' excess energy - typically, higher excess energies lead to longer hot carrier lifetimes
  • initial hot-carrier densities i.e., higher carrier densities usually lead to longer hot carrier lifetimes
  • the energy loss rate at a specific hot-carrier temperature i.e., generally, lower hot carrier temperatures yield smaller energy loss rates.
  • the hot-carrier cooling lifetime as described herein may be defined as the time interval from pulse excitation till the cooling of hot-carriers to 600 K. This temperature is used as the benchmark because previous theoretical calculations have shown that for T > 600 K, there may still be an appreciable hot-carrier conversion efficiency (i.e., > 40%) over a wide range of absorber bandgaps.
  • the hot-carrier cooling lifetime may be defined as the time interval from pulse excitation till the cooling of hot- carriers to 600K. 600K may be used as the benchmark because previous theoretical calculations have shown that for T > 600 K, there may still be an appreciable hot-carrier conversion efficiency (i.e., > 40%) over a wide range of absorber bandgaps.
  • TA refers to "Transient Absorption”
  • TRPL refers to "time-resolved photoluminescence".
  • FIG. 15 show plots of carrier temperatures (in Kelvins or K) as a function of time delay (picoseconds or ps) for three different sized methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments and bulk-film (a) at low pump fluence (corresponding to ⁇ No> -0.1 in NCs and no -2.1 x 10 17 cm 3 in bulk-film) and (b) at high pump fluence (corresponding to ⁇ Vo> -2.5 in NCs and no -1.5 x 10 19 cm 3 in bulk- film) following 3.1 eV photoexcitation.
  • MAPbBr 3 NCs methylammonium lead bromide perovskite nanocrystals
  • the lifetime of large NCs may be around 40x longer than that for the bulk-film sample, where the bulk film was excited at almost one order higher carrier density of 1.5 x 10 19 cm "3 .
  • the hot-carrier cooling lifetimes can be as long as -32 ps (FIG. 15) for large NCs with ⁇ N 0 > - 2.5 (or n 0 av g of - 3.5 x 10 18 cm "3 ).
  • the hot-carrier cooling lifetimes of the MAPbBr 3 NCs may be much longer than those reported for other semiconductor bulk and nano materials.
  • the reported cooling lifetime is -2 ps with carrier densities of -6.0 x 10 18 cm “ 3 and excess energies of 1.7 eV; and for CdSe nanorods, the reported cooling lifetime is -0.8 ps with carrier densities of -5.5 x 10 18 cm “3 and excess energies of 1.1 eV.
  • the MAPbBr 3 NCs may compare very favorably with much longer lifetimes of 18 ps, excited with much lower excess energies of -0.7 eV at comparable carrier densities of 6.5 x 10 18 cm "3 .
  • FIG. 16 illustrates plots of normalized transmittance change ⁇ / ⁇ as a function of time (picoseconds or ps) showing normalized photobleaching dynamics probed at the band edges of methylammonium lead bromide (a) bulk-film, (b) small nanocrystals (NCs) according to various embodiments, (c) medium nanocrystals (NCs) according to various embodiments, and (d) large nanocrystals (NCs) according to various embodiments, in solution with high and low pump fluence respectively, as well as (e) comparison of transient absorption (TA) dynamics for medium nanocrystals (NCs) according to various embodiments in solution and spin-coated nanocrystals (NCs) film according to various embodiments, and (f) pump-fluence-dependent bleaching dynamics probed at the band edge of small methylammonium lead bromide nanocrystals (NCs) according to various embodiments in solution.
  • the inset of (f) in FIG. 16 shows the extracted Auger
  • the hot-carrier relaxation mechanism at low pump excitation may therefore be representative of the material's intrinsic properties and may not be influenced by extrinsic effects such as the multi-particle Auger-recombination.
  • FIG. 17 shows (a) a plot of energy loss rate (electron volts per picosecond eV ps "1 ) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate of hot-carriers as a function of carrier temperature T for methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments with ⁇ No> -0.1 and methylammonium lead bromide perovskite (MAPbBr 3 ) bulk-film with no -2.1 x 10 17 cm “3 , (b) a plot of normalized transmittance change ⁇ / ⁇ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band-edge for colloidal methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according
  • FIG. 18 is a plot of Raman intensity (in arbitrary units or a.u.) as a function of wavenumbers (in per centimeter or cm "1 ) showing room temperature Raman spectrum of as-prepared methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments drop-cast on glass substrate. The peaks originate from LO phonons. From the Raman measurement shown in FIG.
  • the available phonon modes for hot-carrier cooling in MAPbBr 3 NCs are located at around -150 cm “1 (assigned to the stretching of the Pb-Br bonds) and 300 cm “1 (which could be from the second-order of 150 cm “1 and/or the torsional mode of MA cations), respectively.
  • Solid lines in FIG. 17(a) represent the numerical fits with LO-phonon model.
  • the arrow indicates the maximum T obtained for the bulk-film.
  • the inset in FIG. 17(a) shows the representative TEM images of small (S), medium (M) and large (L) perovskites NCs.
  • Solid lines in FIG. 17(b) are the single exponential fits.
  • Inset in FIG. 17(b) shows a schematic of the phonon bottleneck induced slow hot-carrier cooling in symmetric conduction and valence bands with discrete energy levels.
  • the energy loss rates per carrier J t may slowly decrease within the range of 0.6-0.3 eV ps "1 until T c reaches -700 K (FIG. 17(a)), below which J r plunges by several orders of magnitude until the T approaches the lattice temperature.
  • Such cooling trend is similar to that for the bulk-film sample as well as in other bulk inorganic semiconductors and nanostructures.
  • the initial rapid cooling i.e., higher cooling rate
  • the initial J t for small NCs is smaller than the large NCs by a factor -2 (indicating a weaker carrier-phonon interaction in the former).
  • the subsequent slower cooling of the hot-carriers closing to the band-edges is determined by the thermal equilibration between longitudinal optical phonons (LO phonons) and acoustic phonons.
  • the energy loss rate was fitted by using a LO-phonon interaction model (see below under LO-phonon model), the fitted TLO (characteristic LO-phonon decay time) increases with reducing NCs dimensionality (see FIG. 17(a)), which may provide direct evidence of the reduction in the optical phonon relaxation by the quantum confinement. This is a characteristic of the phonon bottleneck effect, which thus retards the hot-carriers cooling.
  • the NCs are in the weak confinement regime with confinement energy around -15- 60 meV, several early theoretical papers had shown that even in this weak confinement regime where the level spacing is only a few meV, the carrier relaxation mediated by phonon interactions can still be dramatically hindered.
  • the band-edge bleach buildup approach was also used to elucidate the hot-carrier cooling properties.
  • an alternative method is to probe the intraband relaxation of the photoexcited carriers high above the band-edge. This can be achieved through monitoring the buildup of the band-edge bleach as the recombination of the band- edge carriers ( ⁇ ns) is much slower than its intraband relaxation process (from several to tens of ps).
  • This latter approach is commonly used for investigating the hot-carrier dynamics in strongly confined quantum colloidal semiconductor NCs given the overlapping PB bands from the discrete energy levels make resolving their hot-carrier distribution extremely challenging.
  • the latter approach may be applied for a fair comparison of the hot-carrier cooling of perovskites NCs with that of conventional inorganic semiconductor NCs (e.g., CdSe NCs).
  • FIG. 17(b) shows the normalized TA spectra of the perovskite samples probed at their band-edge PB peaks following photoexcitation with similar excess energies at low carrier densities.
  • Each buildup process is fitted with a single-exponential growth function to yield a rise time (T r i se ).
  • the rise of the band-edge bleach occurs at sub-ps timescale that becomes slower with decreasing NC size, consistent with the smaller J r and slower hot-carrier temperature decay (FIG. 15) for smaller perovskites NCs.
  • the trend exhibited by the perovskite NCs is completely opposite to that for CdSe NCs (spanning the strong to weak quantum confinement regimes - FIG. 17(c) and FIG. 19).
  • FIG. 19 shows (a) a plot of normalized transmittance change ⁇ / ⁇ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band edge for colloidal CdSe NCs with different diameters (shown in legend) at low pump fluence, and (b) plots of time (in picoseconds or ps) as a function of energy (in electron volts or eV) illustrating low pump fluence with initially generated ⁇ No> -0.1 (left) and high pump fluence with ⁇ No> -2.5 (right).
  • the phtotoexcitation energy is 3.1 eV.
  • Solid lines in FIG. 19 (a) are the single exponential growth fitting curves.
  • the inset in FIG. 19(a) schematically shows the hot-carrier cooling process via Auger-type energy transfer.
  • the perovskite NCs rise times may also be much longer.
  • the faster hot-carrier cooling with decreasing CdSe NCs is consistent with previous reports, which is attributed to an Auger-type energy transfer from the hot electrons to the dense hole states. Results clearly show that such Auger-transfer mechanism present in conventional inorganic semiconductor NCs may be naturally suppressed in perovskites NCs.
  • FIG. 20 shows (a) a plot of energy loss rate (in electron volts per picosecond or eV ps -1 ) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate vs carrier temperature T for methylammonium lead bromide perovskite nanocrystals (MAPbBr 3 NCs) according to various embodiments with ⁇ No> -2.5 and MAPbBr 3 bulk-film with no -1.5 x 10 19 cm “3 , (b) a plot of lifetime (in picoseconds or ps) as a function of nanocrystal volume (in cubic nanometer or nm 3 ) illustrating Auger recombination lifetimes and hot-carrier cooling time vs perovskite nanocrystal (NC) volume according to various embodiments, and (c) a plot of normalized hot carrier concentration Hhot as a function of
  • the solid line in FIG. 20(a) represents the LO-phonon model at low carrier densities.
  • the dashed lines in FIG. 20(b) are guides to the eye showing the scaling of the lifetimes with the square root of nanocrystal (NC) volume, while the inset illustrates the hot-carrier re-excitation by Auger-recombination of carriers at band-edge (also known as Auger-heating), and the error bars represent standard errors.
  • Solid lines in FIG. 20(c) are bi-exponential decay fits. Photoexcitation energy for FIG. 20 (a) - (c) is 3.1 eV. The bulk film is about 240 nm thick.
  • FIG. 20(a) shows contrasting trends of energy loss rates vs carrier temperature between the three-different sized NCs (at ⁇ No> -2.5) and the bulk-film sample (at no - 1.5xl0 19 cm "3 ).
  • the initial hot-carrier cooling governed by the carrier- LO-phonon interactions may be nearly independent of carrier densities. This can be concluded from: (i) the almost identical initial fast decay of T at different carrier densities (FIG. 12), and (ii) the similar initial energy loss rate at high carrier temperatures for both low and high carrier densities (FIG. 17(a) and FIG. 20(a)).
  • the elongation of hot-carrier lifetime FIG.
  • Equation 21 is a plot of energy loss rate (electron volts per picosecond or eV ps "1 ) as a function of carrier temperature (in Kelvins or K) showing energy loss rate of hot-carriers as a function of carrier temperature T for methylammonium lead bromide (MAPbBr 3 ) bulk-film at low and high carrier densities.
  • Solid lines represent the fits numerically fitted with Equation (3) (shown below under section on "LO-phonon model”).
  • the fitted LO-phonon lifetime TLO and acoustic temperature T d are 150 + 20, 280 + 20 fs, and 305 + 10 and 350 + 10 K with low and high carrier densities, respectively.
  • FIG. 20(c) shows that the calculated concentration ( «hot (t)) of hot-carriers for different sized NCs relaxes bi-exponentially with a fast decay occurring within 1 ps and a slower decay of several tens of ps - similar to the behavior of the hot-carrier temperatures (FIG. 12 and FIG. 15).
  • the fast decay may be attributed to the carrier-LO-phonon interactions.
  • the fitted slow decay lifetimes of nhot (t) are well-matched with the 1/3 relation of their Auger lifetime TAug (i.e., Thot ⁇ TAug/3 - FIG. 20(b), see also below under "Auger-heating model" section).
  • the slower decay lifetime for the small NCs is fitted to be -12 ps, which is very close to 1/3 of its ⁇ 3 ⁇ 4 of 38 ps.
  • the excellent agreement between the experimental data and our simple model that includes Auger effects may strongly substantiate the dominant Auger heating contribution in further retarding the hot- carrier cooling at high carrier densities.
  • Auger induced hot-carrier cooling lifetime may be sublinearly dependent on the NC volume (FIG. 20(b)).
  • Auger heating causes a slowdown of the hot- carrier cooling rate favorable for hot-carrier extraction, it should also be noted that Auger effects may conversely reduce the carrier densities. It may therefore be necessary to balance the hot-carrier lifetime and carrier losses in the application of concentrator-type hot-carrier solar cells at high pump fluence.
  • FIG. 22 shows plots of photoelectron intensity (counts per second or cts/s) as a function of energy (in electron volts or eV) showing the ultraviolet photoelectron spectroscopy (UPS) spectrum of (a) 1,2-ethanedithiol (EDT)-treated and (b) post-annealed EDT-treated methylammonium lead bromide (MAPbBr 3 ) nanocrystals (NCs) films according to various embodiments, and (c) 7-diphenyl-l,10-phenanthroline (Bphen) film on indium tin oxide (ITO) substrates.
  • UPS ultraviolet photoelectron spectroscopy
  • the valence band maximum may be determined by linear extrapolation of the leading edge of the valence band to the background intensity, which is 1.9 + 0.1, 2.3 + 0.1 and 2.9 + 0.1 eV for FIG. 22 (a) -(c), respectively.
  • Bphen may be selected as the hot-electron extraction material because this molecular semiconductor has a high electron mobility and possess a higher lowest unoccupied molecular orbital (LUMO) than the conduction band minimum (CBM) of our EDT-treated NCs (see FIG. 22 for UPS measurements), implying only hot-carriers with sufficient excess energies above band-edge can be injected into Bphen (see FIG. 23A).
  • LUMO lowest unoccupied molecular orbital
  • CBM conduction band minimum
  • FIG. 23 A is a flat-band energy diagram (vertical axis in electron volts or eV) to illustrate hot-electron extraction from perovskite nanocrystals according to various embodiments to 7-diphenyl-l,10-phenanthroline (Bphen) with competing hot-electron cooling pathways.
  • Conduction band minimum (CBM) or LUMO levels
  • VBM valence band minimum
  • HOMO highest occupied molecular orbital
  • FIG. 23B shows an atomic force microscopy (AFM) image of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film according to various embodiments.
  • FIG. 23C is a scanning electron microscopy (SEM) image of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl- l, 10-phenanthroline (Bphen) bilayer according to various embodiments.
  • the scale bar is 100 nm.
  • FIG. 23D is a plot of normalized transmittance change ( ⁇ / ⁇ ) as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for about 35 nm thick of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film with (continuous lines) / without (dashed lines) 7-diphenyl- l,10-phenanthroline (Bphen) according to various embodiments following 3.1 eV photoexcitation with ⁇ No> around 0.1.
  • Inset of FIG. 23D shows the un-normalized transient absorption (TA) spectra at 0.8 ps.
  • 23E is a plot of hot-carrier temperature (in Kelvins or K) as a function of delay time (in picoseconds or ps) for 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film and 1,2-ethanedithiol (EDT)- treated nanocrystal (NC) film /7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments at different pump fluences. Dotted arrows show the decrease of the initial hot-carrier temperatures after adding the Bphen layer, indicating effective hot-electron extraction.
  • K hot-carrier temperature
  • FIG. 23F is a plot of extraction efficiency rjhot (in percent or %) as a function of hot-electron excess energy (in electron volts or eV) showing pump energy dependence of the hot-electron extraction efficiencies in about 35 nm-thick 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments.
  • EDT 1,2-ethanedithiol
  • NC nanocrystal
  • Bphen 10-phenanthroline
  • 23G is a plot of extraction efficiency rjhot (in percent or %) as a function of thickness (in nanometres or nm) showing perovskite film thickness dependence of the hot electron extraction efficiencies upon 3.1 eV pump energy excitation for 1,2- ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments and bulk-film/7-diphenyl- l, 10-phenanthroline (Bphen) bilayer.
  • Inset shows the un-normalized TA spectra at 0.8 ps following 3.1 eV photoexcitation with ⁇ No> around 0.1 for about 140 nm-thick EDT-NCs film with/without Bphen.
  • Error bars on the x axis represent the uncertainties in the determination of excess energies in FIG. 23F and sample thickness in FIG. 23G and on the y axis represent uncertainties in the determination of extraction efficiencies.
  • FIG. 24 shows (a) plot of transmittance (in arbitrary units or a.u.) as a function of wavenumber (in per centimeter or cm "1 ) showing the attenuated total reflection- fourier transform infrared (ATR-FTIR) spectra of as-prepared methylammonium lead bromide nanocrystals (MAPbBr 3 NCs), 1,2-ethanedithiol (EDT)-treated nanocrystals (EDT-NCs) and 70 °C annealed 1,2-ethanedithiol nanocrystals (Ann-EDT-NCs) according to various embodiments, and plots of photoemission intensities (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing sulfur (S) 2p X-ray photoelectron spectroscopy (XPS) spectra of (b) non-annealed and (c) 70 °C post-annealed 1,2-
  • Bphen possesses a narrow electron bandwidth, which may allow it to approximate the energy selective contact required in hot-carrier solar cells.
  • EDT treatment may be used to substitute the long and highly insulating oleic acid and oleylamine ligands that is present on the as-prepared NC surfaces with thiolate (see ATR-FTIR and XPS measurements in FIG. 24 and section on FTIR and XPS analysis on ligand exchange) for more effective electronic coupling with Bphen and within NCs films (evident from the closer NCs packing after treatment as shown in TEM images in FIG. 25).
  • FIG. 25 shows (a) atomic form microscopy (AFM) image of un-treated medium methylammonium lead bromide nanocrystals (MAPbBr 3 NCs) film according to various embodiments, and (b) representative transmission electron microscopy (TEM) image of 1,2-ethanedithiol-treated methylammonium lead bromide nanocrystals (EDT-treated MAPbBr 3 NCs) according to various embodiments.
  • AFM atomic form microscopy
  • MAPbBr 3 NCs un-treated medium methylammonium lead bromide nanocrystals
  • TEM transmission electron microscopy
  • TA pseudocolor transient absorption
  • the high energy tails may be reduced for EDT-NCs/Bphen following 3.1 eV photoexcitation.
  • Hot-electron extraction from spin-coated EDT-NCs thin film (see AFM and SEM images in FIGS. 23B-C) by Bphen may be validated by the clear reduction of the high energy tails of TA spectra for the EDT-NCs/Bphen bilayers that occurs instantaneously (see FIG. 23 D, pseudo color TA spectra in FIG. 26 and section on "Effects of photocharged NCs and trions in NCs films on hot-carriers").
  • FIG. 27 shows energy diagrams (y axis: energy in electron- volts or eV) showing flat-band energy level alignment as determined from the ultraviolet photoelectron spectroscopy (UPS) and ultraviolet- visible (UV-VIS) spectroscopy measurements for non-annealed, annealed 1,2-ethanedithiol -nanocrystals (EDT-NCs) films and 7-diphenyl-l,10-phenanthroline (Bphen) according to various embodiments - illustrated for the case of hot-electron extractions.
  • Excess energy of extracted hot-electrons may be determined from the band offset between the conduction band minimum of NCs and the LUMO of Bphen.
  • hot-electrons may be likely to be injected into Bphen through electron diffusion inside the NC and hopping at NC-interfaces.
  • the driving force of hot- electron transfer may be the energy difference between the hot-carrier energy and the LUMO energy with respect to the Fermi energy as shown in FIG. 23A.
  • a large density of states is typical for organic molecules.
  • the highly efficient hot-carrier transfer may thus be attributed to the high density of acceptor states in LUMO levels of Bphen together with the strong electronic coupling between Bphen and NCs.
  • NIR near-infrared
  • PIA photoinduced absorption
  • the efficiency of hot-electron extraction may be estimated based on the percentage reduction of the band-edge photo-bleaching intensities at ⁇ 0.8 ps after adding Bphen (as when the hot-electrons are relaxed to the band-edges, the reduced band-edge bleaching intensity can then be attributed to the extraction of hot-carriers).
  • Calculated hot for -35 nm thick EDT-NCs/Bphen bilayer is -72 % and -58 % at ⁇ N 0 > -0.1 and 2.5 pump intensities, respectively.
  • the reduced multi-hot-electron injection efficiency at higher pump fluence may be due to the increased back-electron transfer from Bphen to the NCs with the estimated back-electron transfer time of -80 ps (FIG. 29 and section under "Estimation of back-electron transfer time").
  • FIG. 29 are plots of normalized transmittance change ⁇ / ⁇ as a function of time (in picoseconds or ps) showing normalized band-edge bleaching dynamics of 1,2- ethanedithiol-treated nanocrystals (EDT-NCs) film according to various embodiments and 1,2-ethanedithiol-treated nanocrystals / 7-diphenyl-l,10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments under (a) low ( ⁇ Vo> ⁇ 0.1) and (b) high ( ⁇ No> -2.5) pump fluence with 3.1 eV photoexcitation.
  • FIG. 30A is a plot of normalized transmittance change ⁇ / ⁇ as a function of energy (electronvolts or eV) showing normalized transient absorption spectra for annealed 1,2-ethanedithiol treated (EDT-treated) medium methylammonium lead bromide nanocrystals (MAPbBr 3 NCs) film with (continuous lines) and without (dashed lines) 7-diphenyl-l,10-phenanthroline (Bphen) extraction layers according to various embodiments at low fluence with ⁇ No> - 0.1.
  • Inset of FIG. 30A shows the un-normalized TA spectra at 0.8 ps. rjhot is determined to be -83 %.
  • FIG. 30B is a plot of carrier temperature (in Kelvins or K) as a function of time (in picoseconds or ps) showing extracted hot-carrier temperature as a function of delay time for two samples according to various embodiments.
  • FIG. 30C is a plot of normalized transmittance change ⁇ / ⁇ as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for methylammonium lead bromide (MAPbBr 3 ) bulk-film (-240 nm thick) with (lines) and without (dashes) 7-diphenyl-l,10-phenanthroline (Bphen) extraction layers at low pump fluence with 2x 10 17 cm "3 .
  • TA transient absorption
  • FIG. 30C shows the un-normalized TA spectra at 0.8 ps. ⁇ hot is determined to be -16 %.
  • FIG. 30D shows a plot of carrier temperature (in Kelvins or K) as a function of time delay (in picoseconds or ps) for two samples according to various embodiments.
  • the photoexcitation energy is 3.1eV.
  • FIG. 31 shows cross-sectional scanning electron microscopy (SEM) images of 1,2-ethanedithiol- treated nanocrystals (EDT-NCs film) with different thickness according to various embodiments. Scale bar in FIG. 31 (a) - (d) is 100 nm.
  • the rjhot of bulk- film/Bphen with thickness of -240 nm is -16 % with changing of T only from -450 to 380 K under similar photoexcitation conditions (FIGS. 30C-D). Even when the bulk- film thickness is reduced to -40 nm, rjhot may be still much smaller than EDT-NCs film.
  • colloidal MAPbBr 3 NCs may exhibit approximately 2 orders slower hot-carrier cooling times and about 4 times larger hot-carrier temperatures as compared to perovskites bulk-films under similar photoexcitation conditions.
  • hot-carrier cooling in NCs may be mediated by the phonon bottleneck effect, which is surprisingly slower in smaller NCs (contrasting with conventional NCs).
  • This finding contravenes the conventional understanding in traditional colloidal semiconductor nanocrystals that intraband Auger effects is more dominant with decreasing dimensionality, resulting in the breach of the phonon bottleneck.
  • Auger heating dominates the hot-carrier cooling rate, which may be slower in larger NCs (previously unobserved in conventional NCs).
  • the augmented slow hot-carrier cooling in these colloidal perovskite nanocrystals may enable efficient hot-carrier extraction. It is demonstrated that the hot electrons with up to -0.6 eV excess energy can be efficiently injected (up to -83%) from surface-treated MAPbBr 3 NCs films into electron extraction layers with an injection time of ⁇ 0.2 ps.
  • Hot-carrier properties in perovskites NCs may enable fresh opportunities for extremely thin absorber (ETA) and concentrator-type hot-carrier solar cells.
  • ETA-solar cells may be conceptually close to dye-sensitized heterojunctions.
  • the molecular dye may be replaced by an extremely thin ( ⁇ tens of nm) semiconductor absorber layer.
  • nano structuring the electrodes e.g., using highly porous T1O2 scaffold, ZnO nanowire arrays etc.
  • the effective area covered by the thin absorber can be increased by several orders of magnitude due to the surface enlargement and multiple scattering.
  • the ETA layer may be extremely beneficial for hot-carrier extractions owing to the shorter transport path length for hot-carriers.
  • the illumination power in the concentrator- type solar-cells can be increased to 1000 suns, much larger than the 1-sun intensity in typical cells, the Auger-heating induced slower hot-carrier cooling in perovskite NCs may also be applicable.
  • LRP ligand-assisted re-precipitation
  • OAm oleylamine
  • OAc oleic acid
  • the precipitation of MAPbBr 3 NCs was re-dissolved in toluene solution for further studies.
  • the precipitate was separated by using centrifuge speed of 12000 rpm, 8000 rpm and 4000 rpm, respectively.
  • the mean diameters are ⁇ 4.9, 8.9 and 11.6 nm for small, medium and large sized NCs, respectively (FIG. 6).
  • a solution containing 0.6 M MAPbBr3 in DMF was spin-coated (5000 rpm, 12 s) on quartz substrates. During spin-coating, few drops of toluene were added to the film at 3 s after the beginning of spinning. The film was then dried in room temperature for 30 minutes and annealed at 70 °C for 5 minutes. All the film deposition and annealing was done in N 2 - filled glove box. The grain size of bulk-film is larger than ⁇ 1 ⁇ and the thickness is around 240 nm (FIG. 7).
  • MAPbBr 3 NCs film and 1,2-ethanedithiol (EDT)-treated NCs were grown by a layer-by-layer spin-coating processing method. All the spin-coating steps were set at 1000 rpm and spin-time was fixed for 30 s.
  • NCs in toluene (10 mg ml "1 ) was spin-coated on glass substrates for two layers.
  • each layer of EDT-treated NCs film consisted of three steps: (1) spin-coating of NCs solution on top of substrate; (2) cover the NCs film with 0.2 M EDT solution in 2- Propanol and wait for 30 s and then spin-coat; (3) dropping of anhydrous toluene on film and followed by spin-coating to clean the remaining long chained ligands. The above process was repeated for 2-10 times to obtain the NCs-film with different thickness. For post-annealed samples, the annealing was performed at 70 °C for 5 mins. All processing was performed in a N 2 -filled glove box.
  • Bphen 4,7-diphenyl-l,10-phenanthroline (bathophenanthroline, or Bphen) was deposited through a thermal evaporation method under a pressure of 10 "6 torr. Bphen was deposited on spin-coated non-annealed or annealed perovskites NCs films at a rate of 0.1-0.2 nm s "1 .
  • CdSe nanocrystals dispersed in toluene were purchased from Sigma-Aldrich Co. LLC.
  • Transient absorption (TA) measurements in the time range of fs-ns were performed using a Helios spectrometer (Ultrafast Systems, LLC).
  • the pump pulse was either generated from an optical parametric amplifier (Coherent OPerA SoloTM or Light Conversion TOPAS- CTM) that was pumped by a 1-kHz regenerative amplifier (i.e., Coherent LibraTM (50 fs, 1 KHz, 800 nm) or Coherent LegendTM (150 fs, 1 KHz, 800 nm)) or by frequency doubling the 800-nm fundamental regenerative amplifier output with a BBO crystal to obtain 400 nm pulses.
  • Coherent OPerA SoloTM or Light Conversion TOPAS- CTM was pumped by a 1-kHz regenerative amplifier (i.e., Coherent LibraTM (50 fs, 1 KHz, 800 nm) or Coherent LegendTM (150 fs, 1 KHz, 800 nm)
  • the white light continuum probe beam (in the range from 400 nm-1500 nm) was generated by focusing a small portion ( ⁇ 10 uJ) of the regenerative amplifier's fundamental 800 nm laser pulses into either a 2-mm sapphire crystal (for visible range) or a 1 cm sapphire crystal (for NIR range).
  • the probe beam was collected using a CMOS sensor for UV-VIS region and InGaAs diode array sensor for NIR region.
  • the samples were kept in a N2-filled chamber at room temperature during measurements.
  • the pump beam excited the samples from the side of Bphen based on the sample structure of Bphen/perovskite/glass substrate.
  • NCs were determined by transmission electron microscopy (TEM, JEOL JEM-2010).
  • TEM transmission electron microscopy
  • AFM Asylum Research MFP-3D
  • SEM scanning electron microscopy
  • Ultraviolet photoelectron spectroscopy was used to investigate the interfacial energy level alignment of the valence occupied states.
  • the spectra collection was performed with the same instrument as that in XPS.
  • Photoelectrons were collected at surface normal using CAE mode with 2.00 eV pass energy with the samples biased at -10 V.
  • X-ray photoelectron spectroscopy (XPS) was performed to analyze the composition of samples. Samples were transferred to an ultra-high vacuum (UHV) analysis chamber from the glove box through an air-tight sample transfer containment. The pressure of the UHV chamber was held under lxlO "9 torr.
  • the crystal structures were analyzed by powder X-ray diffraction (XRD, Bruker D8 Advance).
  • the absorption spectra were recorded using a UV-VIS spectrometer (SHEVIADZU UV-3600 UV-VIS-NIR Spectrophotometer) with an integrating sphere (ISR- 3100).
  • FTIR spectra of the all samples were measured by a Frontier FT-IR/NIR spectrometer (PerkinElmer, Waltham, MA, USA) equipped with a universal attenuated total reflection (ATR) sampling accessory (PerkinElmer, Waltham, MA, USA).
  • Raman spectra were recorded with a WITec Raman microscope (WITec GmbH, Ulm, Germany) using a 633 nm HeNe laser as the excitation source.
  • the pump energy i.e., carriers' excess energy - typically, higher the excess energies lead to longer hot carrier lifetimes
  • the measured hot-carrier lifetime could be limited by the time-resolution of the experimental techniques used, thereby yielding artificially longer lifetimes that are limited by the system temporal response rather than its intrinsic hot-carrier lifetime.
  • measurement of the hot-carrier lifetime by the time-resolved photoluminescence (TRPL) technique using a streak camera or time related single photon counting (TCSPC) system may be constrained by the system resolution of these equipment (i.e., -10 ps for most streak cameras, as high as ⁇ 1 ps for Hamamatsu systems and typically -50 ps for TCSPC systems).
  • the TA or fluorescence upconversion PL techniques have much higher system temporal response of ⁇ 150 fs, which would identify more authentic hot carrier lifetimes of the material. Hence, due care must be taken for a fair comparison of the reported values in the literature.
  • the hot-carrier cooling lifetime in FIG. 14 is defined as the time interval from pulse excitation until the cooling of hot-carriers reach 600 K (for point (iii) above). This temperature is used as the benchmark because previous theoretical calculations have shown that for T > 600 K, there may still be an appreciable hot-carrier conversion efficiency (i.e., > 40%) over a wide range of absorber bandgaps).
  • T lo is the characteristic LO-phonon decay time
  • ⁇ ⁇ is the acoustic phonon temperature
  • hm 0 is the phonon energy (-42 meV)
  • NUJ(T) is the LO-phonon occupation number at temperature T.
  • T D for the MAPbBr 3 NCs (-310 K) and bulk- film (-305 K)
  • TLO is -340 fs, 220 fs and 180 fs for small, medium and large NCs, respectively, in contrast to a fast T lo of - 150 fs for the bulk-film.
  • Auger-heating Model [00161] Auger-heating Model [00162] Auger decay lifetimes of MAPbBr 3 NCs are extracted from the pump fluence dependent band-edge photobleaching dynamics (FIG. 16(f)), which exhibit a sublinear dependence on the NC volume (VNC) as ⁇ 3 ⁇ 4 ⁇ V(VNC ) (FIG. 20(a)). This behavior agrees with recent observations of biexciton Auger recombination in weakly confined CsPbBr 3 NCs, but contrasts with the linear dependence of ⁇ 3 ⁇ 4 on NC size for strongly confined systems. The sublinear dependence can therefore be attributed to the weaker confinement in our perovskites NCs.
  • Equation (4) therefore predicts that the hot-carrier population decays bi-exponentially, with one of its lifetime corresponding to TAug/3.
  • FIG. 20(c) shows the normalized calculated hot-carrier densities as a function of decay time at different pump fluences.
  • the hot-carrier diffusion length in MAPbBr 3 can be estimated as follows. Firstly, the carrier's diffusion coefficient depends on the defect density of the fabricated material.
  • the reported electron diffusion coefficient D may range from ⁇ 1 cmV 1 for polycrystalline perovskite thin films to 5 - 8 cmV 1 for bulk MAPbBr 3 at room temperature (-300 K).
  • the hot-carrier diffusion length may be obtained by Xhot ) ⁇ 16 nm.
  • the high pump fluence at hot-carrier lifetime of -32 ps yields a diffusion length of L ⁇ 90 nm.
  • higher concentration of hot-carriers in perovskites closest to the Bphen may thus be more easily injected into Bphen.
  • NCs-film given that some Bphen molecules could penetrate into the upper layer of the NCs film, and the hot-carriers undergoing rapid hopping, the extracted -70% hot-carrier transfer efficiency for -35 nm thick NCs-film at low pump fluence may therefore be reasonable.
  • the hot-carrier diffusion length may be -10 nm. Therefore, the -15% transfer efficiency for bulk-film may also be reasonable.
  • MAPbBr3 NCs reveals two sets of S 2p doublets, with the 2p 3/2 peak position at binding energies -162.5 eV and -164.2 eV (-162.7 eV and -164.3 eV for post-annealed) arising from bound thiolate and unbounded thiol of EDT to the surface of the NC respectively (FIG. 24).
  • the ratio of bound-to-unbound thiol groups in the NC without post- annealing is -1.04, which increases to -1.47 with post-annealing of the NC at 70 °C.
  • post-annealing treatment further increases the electronic coupling of EDT-NCs with Bphen.
  • FIG. 16(e) shows the comparison of photobleaching dynamics at the band-edges between medium NCs in solution and spin-coated film. From the exponential fitting (solid curves), the lifetime changes from ⁇ 4.5 to ⁇ 3 ns at low pump fluence, the acceleration may be due to the existence of the photocharged NCs. At high pump fluence, another fast decay with lifetime of ⁇ 290 ps except for the Auger recombination may emerge in the spin-coated NCs films, which can be attributed to trions (photocharged excitons). However, they only induced the broadening in the lower energy side of GSB (see the appearance of a bleaching tail at lower energy side for NCs-films in FIG. 26 as compared with FIG.
  • trions 10 for NCs in solution in the pseudo color TA spectra.
  • the reduced energy of trions may be due to the exciton-exciton interactions.
  • the trions in the NCs-film may not affect the dynamics of hot- carriers located at the higher energy side of the GSB.
  • the MAPbBr 3 NCs films demonstrate similar hot-carrier cooling dynamics with/without the EDT-treatment. Without the EDT-treatment, the NCs demonstrate similar hot-carrier cooling dynamics with/without the Bphen extraction layer. Furthermore, we did not find any obvious change in the hot-carrier properties in the NCs films that underwent the exact same processing in the thermal evaporator except no Bphen layer was actually deposited.
  • the NCs are selectively excited with 400 nm light.
  • a weak PIA band similar to pristine Bphen may be observed (FIG. 28(b) and FIG. 28(c)).
  • any further increase of pump power may lead to the degradation of the perovskite.
  • the relaxation of PIA may possess one fast decay lifetime (-70 ps for pristine Bphen, and -25 ps for NCs/Bphen) and one slow decay lifetime (-1 ns for pristine Bphen, and -0.5 ns for NCs/Bphen) (FIG. 28(d)
  • the fast decay may be due to the carrier trapping to defects for pristine Bphen and additional electron back- transfer to the NCs for NCs/Bphen.
  • the slow decay may be due to the recombination of radical anions/excitons in the Bphen and with holes in NCs in the NCs/Bphen hybrids.

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Abstract

Various embodiments may provide a hot-carrier solar cell. The solar cell may include a nanocrystal containing layer containing or including one or more nanocrystals, each of the one or more nanocrystals including a halide perovskite material. The hot-carrier solar cell may also include a first electrode in contact with a first side of the nanocrystal containing layer. The hot-carrier solar cell may further include a second electrode in contact with a second side of the nanocrystal containing layer opposite to the first side. The nanocrystal containing layer may have a thickness of less than 100 nm.

Description

HOT-CARRIER SOLAR CELL, AND METHOD TO FORM THE SAME
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of priority of Singapore Application No. 10201606182S filed on July 27, 2016, the contents of it being hereby incorporated by reference in its entirety for all purposes.
TECHNICAL FIELD
[0002] Various aspects of this disclosure relate to hot-carrier solar cells. Various aspects of this disclosure relate to methods of forming hot-carrier solar cells.
BACKGROUND
[0003] One ubiquitous feature of all current solar cells is that solar photons (spanning from ultraviolet to infra-red wavelengths) possess energies greater than the semiconductor band gap can create free carriers or excitons that have excess energies beyond the band gap; these carriers or excitons with temperature higher than the material lattice temperature are called "hot carriers" or "hot excitons". Such excess carrier energy is kinetic free energy and is lost quickly (in the sub-picosecond time scale) through electron-phonon scattering which converts the excess kinetic energy into heat. In 1961, Shockley and Queisser (SQ) calculated the maximum possible thermodynamic efficiency of converting solar irradiance into electrical free energy in a solar cell assuming radiative recombination was the only other free energy loss mechanism and complete hot carrier cooling. This calculation yields a theoretical maximum thermodynamic efficiency of 31-33% with optimum band gaps between about 1.1 and 1.4 eV.
[0004] Thermodynamic calculations in 1982 first showed that the conversion efficiency can reach 66% if excess energy of hot photo generated carriers is utilized before they cooled to the lattice temperature, thus exceeding the SQ-limit and improving the solar cell efficiency. One approach is to transport the hot carriers to carrier-collecting contacts with appropriate work functions before the carriers are cooled. These cells are termed hot carrier solar cells. As such, the research community is continuously searching for suitable solar cell absorber materials with slow hot-carrier cooling characteristics. [0005] During the early developments of nanotechnology, it was initially believed that quantum confinement in semiconductor nanocrystals (NCs) would slow down the hot-carrier cooling processes through the phonon bottleneck effects. However, further investigations revealed that it was still challenging to achieve slow hot-carrier cooling in quantum confined systems due to the alternative rapid relaxation routes that could outrun the phonon bottleneck. It is therefore highly desirable to develop new types of materials with slow hot-carrier cooling property.
SUMMARY
[0006] Various embodiments may provide a hot-carrier solar cell. The solar cell may include a nanocrystal containing layer containing or including one or more nanocrystals, each of the one or more nanocrystals including a halide perovskite material. The hot-carrier solar cell may also include a first electrode in contact with a first side of the nanocrystal containing layer. The hot-carrier solar cell may further include a second electrode in contact with a second side of the nanocrystal containing layer opposite to the first side. The nanocrystal containing layer may have a thickness of less than 100 nm.
[0007] Various embodiments may provide a method to form a hot-carrier solar cell. The method may include providing or forming the nanocrystal containing layer including one or more nanocrystals (as described herein), each of the one or more nanocrystals including a halide perovskite material. The method may also include forming a first electrode so that the first electrode is in contact with a first side of the nanocrystal containing layer. The method may further include forming a second electrode so that the second electrode is in contact with a second side of the nanocrystal containing layer opposite to the first side. The nanocrystal containing layer may have a thickness of less than 100 nm.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] The invention will be better understood with reference to the detailed description when considered in conjunction with the non-limiting examples and the accompanying drawings, in which:
FIG. 1 shows a general illustration of a nanocrystal according to various embodiments.
FIG. 2 shows a general illustration of a hot-carrier solar cell according to various embodiments. FIG. 3 is a schematic showing a method of forming a nanocrystal according to various embodiments.
FIG. 4 is a schematic showing a method of forming a hot-carrier solar cell according to various embodiments.
FIG. 5 is a schematic showing hot-carrier cooling with (a) intraband Auger-type energy transfer, (b) phonon-bottleneck effect and (c) interband Auger processes in semiconductor nanocrystals.
FIG. 6 shows representative transmission electron microscopy (TEM) images of methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) with relatively (a) small, (c) medium and (e) large sizes according to various embodiments and the respective size histograms (b, d, f) on their right. The size distribution may be modeled with a Gaussian distribution.
FIG. 7 shows (a) top-view and (b) side-view scanning electron microscopy (SEM) images of methylammonium lead bromide (MAPbBr3) bulk-film.
FIG. 8 shows (a) a plot of photoluminescence (PL) intensity (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating photoluminescence (PL) spectra of methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (b) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating ultraviolet-visible (UV-vis) absorption spectra of methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (c) a plot of energy of Is exciton, Els (in electron volts or eV) as a function of average nanocrystal radius, a (in nanometer or nm) showing the energy of Is exciton of methylammonium lead bromide perovskite (MAPbBr3) according to various embodiments as a function of radius, and (d) a plot of X-ray diffraction (XRD) intensity (in arbitrary units or a.u.) as a function of degree, 2Θ (in degrees) showing the XRD patterns of three differently sized methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) according to various embodiments.
FIG. 9A shows pseudo color transient absorption (TA) plot (upper panel, time (in picoseconds or ps) as a function of energy (in electron volts or eV)) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV)) for medium methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) (radii -4-5 nm) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal, <Vo> -0.1 (average carrier density per nanocrystal volume, n0avg~2.6 x 1017 cm ~3) and high pump fluence (right panel) with <Vo> -2.5 (n0avg ~6.5x 1018 cm "3).
FIG. 9B shows pseudo color representation (upper panel, time (in picoseconds or ps) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV)) for MAPbBr3 bulk-film at low pump fluence (left panel) with initially generated carrier density no -2.1 x 1017 cm3 and high pump fluence (right panel) with no -1.5 x 1019 cm3.
FIG. 10 shows plots of time (in picoseconds or ps) as a function of energy (electron volts or eV) showing pseudocolor transient absorption (TA) spectra (time in picoseconds or ps as a function of energy in electron volts or eV) for (a) small and (b) large sized methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal <No> -0.1 and high pump fluence (right panel) with <Vo> -2.5 following 3.1 eV photoexcitation.
FIG. 11 illustrates (a) a plot of normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV) showing normalized TA spectra at different short time delays of medium sized methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments in toluene with average generated electron-hole pair per nanocrystal, <No>~0.1 (following 3.1 eV photoexcitation) and (b) the un-normalized transient absorption (TA) spectra of (a).
FIG. 12 is a plot of carrier temperature (in Kelvins or K) as a function of time (in picoseconds or ps) showing the temporal evolution of the hot-carrier temperature T for the medium nanocrystals (NCs) according to various embodiments and bulk-film at various pump fluence: initial photoexcited hot-carrier density no (bulk-film) and average generated electron- hole pairs per NC <No>, where <No> = Jo, where is the pump fluence and σ is the absorption cross-section.
FIG. 13 illustrates (a) a plot of photoluminescence (PL) intensity (in arbitrary unit or a.u.) as a function of time (in nanoseconds or ns) showing pump fluence dependent time-resolved photoluminescence (PL) of the medium methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments under 3.1 eV photoexcitation, (b) a plot of transient photoluminescence (PL) intensity (in arbitrary units or a.u.) as a function of pump intensity (in micro- Joules per square centimeter or μΐ cm"2) showing normalized PL intensities of three different sized MAPbBr3 NCs according to various embodiments as a function of pump fluence measured at time At = 4 ns, and (c) a plot of occupation probability (in percent or %) as a function of the number of electron-hole (e-h) pairs per NC according to various embodiments.
FIG. 14 shows a table comparing properties of methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments, methylammonium lead bromide perovskite bulk films, and other materials reported in literature.
FIG. 15 show plots of carrier temperatures (in Kelvins or K) as a function of time delay (picoseconds or ps) for three different sized methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments and bulk-film (a) at low pump fluence (corresponding to <No> -0.1 in NCs and no -2.1 x 1017 cm3 in bulk-film) and (b) at high pump fluence (corresponding to <Vo> -2.5 in NCs and no -1.5 x 1019 cm3 in bulk- film) following 3.1 eV photoexcitation.
FIG. 16 illustrates plots of normalized transmittance change ΔΤ/Τ as a function of time (picoseconds or ps) showing normalized photobleaching dynamics probed at the band edges of methylammonium lead bromide (a) bulk-film, (b) small nanocrystals (NCs) according to various embodiments, (c) medium nanocrystals (NCs) according to various embodiments, and (d) large nanocrystals (NCs) according to various embodiments, in solution with high and low pump fluence respectively, as well as (e) comparison of transient absorption (TA) dynamics for medium nanocrystals (NCs) according to various embodiments in solution and spin-coated nanocrystals (NCs) film according to various embodiments, and (f) pump- fluence-dependent bleaching dynamics probed at the band edge of small methylammonium lead bromide nanocrystals (NCs) according to various embodiments in solution.
FIG. 17 shows (a) a plot of energy loss rate (electron volts per picosecond eV ps"1) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate of hot-carriers as a function of carrier temperature T for methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments with <No> -0.1 and methylammonium lead bromide perovskite (MAPbBr3) bulk-film with no -2.1 x 1017 cm"3, (b) a plot of normalized transmittance change ΔΤ/Τ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band-edge for colloidal methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments and bulk-film at low carrier density, and (c) a plot of rise time (in femtoseconds or fs) / confinement energy (in electron volts or eV) showing size dependence of the rise time of band-edge bleachings in methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) (dark solid squares), bulk-film (light solid squares) (the particle size is represented by the film thickness) and cadmium selenide nanocrystals (CdSe NCs) (solid circles), as well as size dependence of quantum confinement energies in MAPbBr3 NCs (hollow square) and CdSe NCs (hollow circle).
FIG. 18 is a plot of Raman intensity (in arbitrary units or a.u.) as a function of wavenumbers (in per centimeter or cm"1) showing room temperature Raman spectrum of as-prepared methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments drop-cast on glass substrate.
FIG. 19 shows (a) a plot of normalized transmittance change ΔΤ/Τ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band edge for colloidal CdSe NCs with different diameters (shown in legend) at low pump fluence, and (b) plots of time (in picoseconds or ps) as a function of energy (in electron volts or eV) illustrating low pump fluence with initially generated <No> -0.1 (left) and high pump fluence with <No> -2.5 (right). The phtotoexcitation energy is 3.1 eV.
FIG. 20 shows (a) a plot of energy loss rate (in electron volts per picosecond or eV ps"1) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate vs carrier temperature Tc for methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments with <Vo> -2.5 and MAPbBr3 bulk-film with no -1.5 x 1019 cm"3, (b) a plot of lifetime (in picoseconds or ps) as a function of nanocrystal volume (in cubic nanometer or nm3) illustrating Auger recombination lifetimes and hot-carrier cooling time vs perovskite nanocrystal (NC) volume according to various embodiments, and (c) a plot of normalized hot carrier concentration ti ot as a function of time (in picoseconds or ps) showing normalized hot-carrier decay at different pump fluences according to various embodiments.
FIG. 21 is a plot of energy loss rate (electron volts per picosecond or eV ps"1) as a function of carrier temperature (in Kelvins or K) showing energy loss rate of hot-carriers as a function of carrier temperature Tc for methylammonium lead bromide (MAPbBr3) bulk-film at low and high carrier densities. FIG. 22 shows plots of photoelectron intensity (counts per second or cts/s) as a function of energy (in electron volts or eV) showing the ultraviolet photoelectron spectroscopy (UPS) spectrum of (a) 1,2-ethanedithiol (EDT)-treated and (b) post-annealed EDT-treated methylammonium lead bromide (MAPbBr3) nanocrystals (NCs) films according to various embodiments, and (c) 7-diphenyl-l, 10-phenanthroline (Bphen) film on indium tin oxide (ITO) substrates.
FIG. 23A is a flat-band energy diagram (vertical axis in electron volts or eV) to illustrate hot- electron extraction from perovskite nanocrystals according to various embodiments to 7- diphenyl- l,10-phenanthroline (Bphen) with competing hot-electron cooling pathways.
FIG. 23B shows an atomic force microscopy (AFM) image of 1,2-ethanedithiol (EDT)- treated nanocrystal (NC) film according to various embodiments.
FIG. 23C is a scanning electron microscopy (SEM) image of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments.
FIG. 23D is a plot of normalized transmittance change (ΔΤ/Τ) as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for about 35 nm thick of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film with (continuous lines) / without (dashed lines) 7-diphenyl- l,10-phenanthroline (Bphen) according to various embodiments following 3.1 eV photoexcitation with <No> around 0.1.
FIG. 23E is a plot of hot-carrier temperature (in Kelvins or K) as a function of delay time (in picoseconds or ps) for 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film and 1,2- ethanedithiol (EDT)-treated nanocrystal (NC) film /7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments at different pump fluences.
FIG. 23F is a plot of extraction efficiency ?/hot (in percent or %) as a function of hot-electron excess energy (in electron volts or eV) showing pump energy dependence of the hot-electron extraction efficiencies in about 35 nm-thick 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl- l,10-phenanthroline (Bphen) bilayer according to various embodiments. FIG. 23G is a plot of extraction efficiency rjhot (in percent or %) as a function of thickness (in nanometres or nm) showing perovskite film thickness dependence of the hot electron extraction efficiencies upon 3.1 eV pump energy excitation for 1,2-ethanedithiol (EDT)- treated nanocrystal (NC)/ 7-diphenyl- l,10-phenanthroline (Bphen) bilayer according to various embodiments and bulk-film/7-diphenyl- l, 10-phenanthroline (Bphen) bilayer. FIG. 24 shows (a) plot of transmittance (in arbitrary units or a.u.) as a function of wavenumber (in per centimeter or cm"1) showing the attenuated total reflection- fourier transform infrared (ATR-FTIR) spectra of as-prepared methylammonium lead bromide nanocrystals (MAPbBr3 NCs), 1,2-ethanedithiol (EDT)-treated nanocrystals (EDT-NCs) and 70 °C annealed 1,2-ethanedithiol nanocrystals (Ann-EDT-NCs) according to various embodiments, and plots of photoemission intensities (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing sulfur (S) 2p X-ray photoelectron spectroscopy (XPS) spectra of (b) non-annealed and (c) 70 °C post-annealed 1,2- ethanedithiol (EDT)-treated nanocrystals (EDT-NCs) film according to various embodiments. FIG. 25 shows (a) atomic form microscopy (AFM) image of un-treated medium methylammonium lead bromide nanocrystals (MAPbBr3 NCs) film according to various embodiments, and (b) representative transmission electron microscopy (TEM) image of 1,2- ethanedithiol -treated methylammonium lead bromide nanocrystals (EDT-treated MAPbBr3 NCs) according to various embodiments.
FIG. 26 shows pseudocolor transient absorption (TA) spectra for (a) medium methylammonium lead bromide nanocrystals (MAPbBr3 NCs) film according to various embodiments, (b) 1,2-ethanedithiol -treated nanocrystals (EDT-treated NCs) film according to various embodiments, and (c) on 1,2-ethanedithiol-treated nanocrystals film/7-diphenyl- 1,10-phenanthroline (EDT-treated NCs film/Bphen) bilayer according to various embodiments at low pump fluence (left panel) with initially generated <No> -0.1 and high pump fluence (right panel) with <Vo> -2.5.
FIG. 27 shows energy diagrams (y axis: energy in electron volts or eV) showing flat-band energy level alignment as determined from the ultraviolet photoelectron spectroscopy (UPS) and ultraviolet-visible (UV-VIS) spectroscopy measurements for non-annealed, annealed 1,2- ethanedithiol -nanocrystals (EDT-NCs) films and 7-diphenyl-l, 10-phenanthroline (Bphen) according to various embodiments - illustrated for the case of hot-electron extractions.
FIG. 28 shows (a) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) showing linear absorption spectra of Bphen film on glass; (b) plot of normalized negative transmittance change -ΔΤ/Τ as a function of wavelength (in nanometer or nm) showing negative transient absorbance spectra of 7-diphenyl- l,10-phenanthroline (Bphen) (300 nm pump with intensity of 20 μΐ cm"2, 400 nm pump with intensity of 40 μΐ cm"2), perovskites nanocrystals (NCs) (400 nm pump with intensity of 15 μΐ cm-2) according to various embodiments and 1,2-ethanedithiol nanocrystals / 7-diphenyl-l ,10-phenanthroline (EDT-NCs/Bphen) (400 nm pump with intensity of 15 μΐ cm-2) according to various embodiments at 2 ps after excitation; (c) plot of time (in picoseconds or ps) as a function of wavelength (in nanometer or nm) showing pseudocolor transient absorption (TA) spectra of 1,2-ethanedithiol-treated nanocrystals / 7-diphenyl-l,10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments excited with 400 nm light at pump intensity of 15 μΐ cm"2; and (d) plot of normalized negative transmittance change -ΔΤ/Τ as a function of time (in picoseconds or ps) showing normalized negative transient absorption spectra of Bphen excited with 300 nm light and 1,2-ethanedithiol-treated nanocrystals / 7-diphenyl- 1, 10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments pumped with 400 nm light and probed at 1300 nm.
FIG. 29 are plots of normalized transmittance change ΔΤ/Τ as a function of time (in picoseconds or ps) showing normalized band-edge bleaching dynamics of 1,2-ethanedithiol- treated nanocrystals (EDT-NCs) film according to various embodiments and 1,2- ethanedithiol-treated nanocrystals / 7-diphenyl- l,10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments under (a) low (<No>~0. l) and (b) high (<No> -2.5) pump fluence with 3.1 eV photoexcitation.
FIG. 30A is a plot of normalized transmittance change ΔΤ/Τ as a function of energy (electron volts or eV) showing normalized transient absorption spectra for annealed 1,2-ethanedithiol treated (EDT-treated) medium methylammonium lead bromide nanocrystals (MAPbBr3 NCs) film with (continuous lines) and without (dashed lines) 7-diphenyl- l, 10-phenanthroline (Bphen) extraction layers according to various embodiments at low fluence with <No> - 0.1. FIG. 30B is a plot of carrier temperature (in Kelvins or K) as a function of time (in picoseconds or ps) showing extracted hot-carrier temperature as a function of delay time for two samples according to various embodiments.
FIG. 30C is a plot of normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for methylammonium lead bromide (MAPbBr3) bulk-film (-240 nm thick) with (lines) and without (dashes) 7-diphenyl- l,10-phenanthroline (Bphen) extraction layers at low pump fluence with 2x 1017cm"3.
FIG. 30D shows a plot of carrier temperature (in Kelvins or K) as a function of time delay (in picoseconds or ps) for two samples according to various embodiments. FIG. 31 shows cross-sectional scanning electron microscopy (SEM) images of 1,2- ethanedithiol-treated nanocrystals (EDT-NCs film) with different thickness according to various embodiments.
DETAILED DESCRIPTION
[0009] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized and structural, and logical changes may be made without departing from the scope of the invention. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.
[0010] Embodiments described in the context of one of the methods or nanocrystals/solar cells/devices is analogously valid for the other methods or nanocrystals/solar cells/devices. Similarly, embodiments described in the context of a method are analogously valid for nanocrystals/solar cell/device, and vice versa.
[0011] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that are described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and/or combinations and/or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.
[0012] The word "over" used with regards to a deposited material formed "over" a side or surface, may be used herein to mean that the deposited material may be formed "directly on", e.g. in direct contact with, the implied side or surface. The word "over" used with regards to a deposited material formed "over" a side or surface, may also be used herein to mean that the deposited material may be formed "indirectly on" the implied side or surface with one or more additional layers being arranged between the implied side or surface and the deposited material. In other words, a first layer "over" a second layer may refer to the first layer directly on the second layer, or that the first layer and the second layer are separated by one or more intervening layers. [0013] In the context of various embodiments, the articles "a", "an" and "the" as used with regard to a feature or element include a reference to one or more of the features or elements.
[0014] In the context of various embodiments, the term "about" or "approximately" as applied to a numeric value encompasses the exact value and a reasonable variance.
[0015] As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
[0016] Organic-inorganic lead halide perovskite semiconductors (e.g., MAPbX3, MA=CH3NH3, X=I, Br or CI) has emerged as one of the most promising family of materials for high-performance and low-cost solar cells since 2013. Solution-processed perovskite polycrystalline thin films have been used as the light absorbing layers in solar cell devices. The present recorded efficiency in the laboratory of perovskites based solar cells with MAPbX3 as absorber may be -20%. Recently, the observations of slow hot-carrier cooling and a hot-phonon bottleneck effect in MAPbI3 thin films suggest that lead halide perovskites may be highly promising materials in constructing the hot-carrier solar cells.
[0017] FIG. 1 shows a general illustration of a nanocrystal 100 according to various embodiments. The nanocrystal 100 may include a halide perovskite material.
[0018] The nanocrystal may have a diameter having a value selected from a range of 1 nm to 100 nm, e.g. of 4 nm to 14 nm or 4 nm to 13 nm.
[0019] A radius of the nanocrystal may be any one value selected from 0.5 nm to 50 nm, e.g. from 2 nm to 7 nm.
[0020] In the current context, the expressions "from X to Y" or "a range of X to Y" may refer to a range including the values of X and Y, in addition to all values between X and Y.
[0021] Various embodiments may slow down the hot-carrier cooling processes through the phonon bottleneck effect or interband Auger process (which is also known as Auger heating). Various embodiments may be employed in solar cells, which may overcome the SQ-limit by harvesting the excess energy from above-bandgap photons, thus improving efficiency.
[0022] There has been previous research carried out on inorganic semiconductor nanocrystals (NCs) as candidates to slowdown hot-carrier cooling processes. However, hot- carrier harvesting in these inorganic semiconductor nanocrystals are compromised by highly competitive relaxation pathways (e.g. , intraband Auger process, defects) that overwhelm their phonon bottlenecks. For instance, Kilina et al. ("Quantum Zero Effect Rationalizes The Phonon Bottleneck In Semiconductor Quantum Dots", Physical Review Letters 110, 180404, p. 1 - 6, 2013) reports that the effect of phonon bottleneck in cadmium selenide (CdSe) quantum dots remains elusive due to Auger processes and structural defects.
[0023] The inventors have found surprisingly that colloidal halide perovskite NCs may transcend these limitations. The halide perovskite NCs may exhibit ~2 orders longer hot- carrier cooling times and ~4 times higher hot-carrier temperatures than their bulk-film counterparts. Under low pump excitation, hot-carrier cooling mediated by a phonon bottleneck, may surprisingly be slower in smaller NCs (in contrast to conventional NCs in which cooling time decreases as size decreases). At high pump fluence, Auger heating may dominate hot-carrier cooling, which is slower in larger NCs (hitherto unobserved in conventional NCs).
[0024] The inventors demonstrate efficient room temperature hot-electrons extraction (up to -83%) by an energy- selective electron extraction layer from surface-treated perovskite NCs thin films within 1 picosecond (ps). These insights may allow fresh approaches for extremely thin absorber and/or concentrator-type hot-carrier solar cells.
[0025] The halide perovskite material may be represented by the general formula AMX3, where A may be a monopositive organic or inorganic cation (e.g. an organic group or organic cation or a metal cation or element), or a mixture of organic and/or inorganic cations, M may be a divalent metal cation or element, and X may be a halogen anion or element. Examples may include CH3NH3PbI3 (MAPbI3), CH3NH3PbBr3 (MAPbBr3), CH3NH3PbBr2I (MAPbBr2I), CsSnI3, CsPbI3, NH2CH=NH2PbI3 (FAPbI3), FAi_yCsyPbI3, or Csx(MAi_ yFAy)i-xPb(Ii-zBrz)3 (where each of x, y or z is a number between 0 and 1). MA may refer to methylammonium (CH3NH3), while FA may refer to formamidinium (NH2CH=NH2).
[0026] In various embodiments, the divalent cation may be Pb2+, Sn2+. In other words, M may be lead (Pb) or tin (Sn).
[0027] In various embodiments, the halide perovskite material may include one or more halide anions selected from a group consisting of Γ, CI" and Br". In other words, X3 may be I3, Cl3, Br3, or a combination thereof (e.g. Cl2Br).
[0028] In various embodiments, the halide perovskite material may include an organic ammonium cation. The organic ammonium cation A may be selected from a group consisting of an ammonium cation, a hydroxylammonium cation, a methylammonium cation (MA+), a hydrazinium cation, an azetidinium cation, a formamidinium cation (FA+), an imidazolium cation, a dimethylammonium cation, an ethylammonium cation, a phenethylammonium cation, a guanidinium cation, and combinations thereof. The organic ammonium cation may be a cation with formula CnEhn+i NH3 + where 2<n<20. In other words, A may be CnEhn+i NH3. In various embodiments, the halide perovskite material may include a metal cation such as cesium ion (Cs+).
[0029] The nanocrystal 100 may exhibit a hot-carrier cooling lifetime of any value of at least 0.5 ps, e.g. from 0.5 ps to 40 ps. The hot-carrier cooling lifetime may be defined as the time interval from pulse excitation till the cooling of hot-carriers to 600K.
[0030] FIG. 2 shows a general illustration of a hot-carrier solar cell 200 according to various embodiments. The solar cell 200 may include a nanocrystal containing layer 202 containing or including one or more nanocrystals (as described herein), each of the one or more nanocrystals including a halide perovskite material. The hot-carrier solar cell 200 may also include a first electrode 204 in contact with a first side of the nanocrystal containing layer 202. The hot-carrier solar cell 200 may further include a second electrode 206 in contact with a second side of the nanocrystal containing layer opposite to the first side. The nanocrystal containing layer 202 may have a thickness of less than 100 nm.
[0031] In other words, the solar cell 200 may include a nanocrystal containing layer 202 which contains one or more nanocrystals. The layer 202 may be sandwiched by electrodes 204, 206.
[0032] The nanocrystal containing layer 202 may also be referred to as the absorbing layer or hot-carrier absorber. In various embodiments, the thickness of the layer 202 may be less than the hot-carrier diffusion length so that hot carriers can be extracted by the electrodes 204, 206 before cooling.
[0033] The hot-carrier solar cell 200 may receive incoming light (from the sun) and may be configured to generate electrical energy based on the solar energy from the incoming light.
[0034] In various embodiments, the hot-carrier solar cell 200 may further include an optical arrangement configured to direct solar energy (from the sun) to the nanocrystal containing layer 202. In various embodiments, the hot-carrier solar cell 200 may be a concentrator hot carrier solar cell. The optical arrangement may include one or more optical elements to direct solar energy to the nanocrystal containing layer 202. The one or more optical elements may be or may include optical lenses and/or mirrors. Hot-carrier cooling may be become slower with increasing photoexcited charge carrier density at higher pump fluence. At pump fluence above 1 electron-hole pair in nanocrystals (corresponding to effective volume carrier density of about 1018 cm"3), the hot-carrier cooling lifetime may exceed 30 ps (compared to 1.5 ps in bulk film), which may be due to Auger-heating effect in the quantum confined system. These features may be favorable for application of concentrator solar cells which are operated at higher power density by focusing light to a spot of the photovoltaic cell. As showed later, compared with other materials, the hot-carrier lifetime in perovskite NCs may be longer at high pump fluence. These features may be favorable for application of concentrator hot carrier solar cells, which may be operated at higher illumination (about or exceeding 1000 suns) using hot-carrier absorbers.
[0035] In various embodiments, the hot-carrier solar cell 200 may be a single-junction solar cell. In various alternate embodiments, the hot-carrier solar cell 200 may be a multi- junction solar cell.
[0036] In various embodiments, the first electrode 204 may be or may include a hot- electron extraction layer.
[0037] In various embodiments, the first electrode 204 may be or may include a n-type layer. The n-type layer or hot-electron extraction layer may include any one material selected from a group consisting of titanium oxide, zinc oxide, phenyl-C61 -butyric acid methyl ester (PCBM), 4,7-diphenyl-l,10-phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4- biphenylyl)-5-phenyl- 1 ,3 ,4-oxadiazole (PBD), 2,2',2"-( 1 ,3 ,5-benzinetriyl)-tris( 1 -phenyl- 1 -H- benzimidazole) (TPBI), poly(9,9-dioctylfluorene) (F8), and bathocuproine (BCP).
[0038] In various embodiments, the first electrode 204 may be an energy selective contact configured to allow electrons having excess energies at or above a predetermined value to pass through, and further configured to reflect electrons having excess energies below the predetermined value back to the nanocrystal containing layer 202. In the current context, excess energies may refer to energy of the electrons beyond the conduction band minimum of the nanocrystal containing layer 202. The predetermined value of excess energy may be any value selected from a range of around 0.1 eV to 2 eV.
[0039] In various embodiments, the second electrode 206 may be or may include a hot- hole extraction layer.
[0040] In various embodiments, the second electrode 206 may be or may include a p-type layer. [0041] In various embodiments, the second electrode 206 may be an energy selective contact configured to allow holes having excess energies at or above a predetermined value to pass through, and further configured to reflect holes having excess energies below the predetermined value back to the nanocrystal containing layer 202. In the current context, excess energies may refer to energy of the holes beyond the valence band maximum of the nanocrystal containing layer 202. The predetermined value of excess energy may be any value selected from a range from around 0.1 eV to 2 eV. In various embodiments, the second electrode 206 may include a molecular semiconductor material. The p-type layer or hot-hole extraction layer may include any one material selected from a group consisting of 2,2' ,7,7'- tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'-spirobifluorene (spiro-OMeTAD), poly(3- hexylthiophene-2,5-diyl) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS), and poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine) (TFB).
[0042] In various embodiments, the one or more nanocrystals exhibit a hot-carrier cooling lifetime of at least 0.5 ps, e.g. above 30 ps. A radius of each of the one or more nanocrystals is any one value selected from 0.5 nm to 50 nm, e.g. 2 nm to 7 nm.
[0043] In various embodiments, the halide perovskite material may be an organic- inorganic halide perovskite material, such as MAPbI3, MAPbBr3, MAPbBr2I, FAPbI3, FAi- yCsyPbI3, or Csx(MAi-yFAy)i-xPb(Ii-zBrz)3 (where each of x, y or z may be any value selected from a range of 0 to 1). Non-limiting specific examples may include CH3NH3PbI3, CH NH PbBr , CH NH PbBr2I, or NH2CH=NH2PbI . In various other embodiments, the halide perovskite material may be an inorganic halide perovskite material such as CsSnI3 or CsPbI3.
[0044] Extraction of hot-carriers may be required to be very fast to limit energy loss; where the competition is between extraction rate and cooling rate rather than recombination rate. In various embodiments, the one or more nanocrystals may be treated with 1,2- ethanedithiol (EDT).
[0045] Efficient hot-carrier extraction from 1,2-ethanedithiol (EDT)-treated MAPbBr3 NCs (EDT-NCs) to 4,7-diphenyl-l,10-phenanthroline (Bphen) is demonstrated herein. Bphen may be selected as the hot-electron extraction material because this molecular semiconductor has a high electron mobility and a higher lowest unoccupied molecular orbital (LUMO) than the conduction band minimum (CBM) of the EDT-treated NC's. EDT treatment may be used to substitute the long and highly insulating oleic acid ligands that is present on the as- prepared NC surfaces with thiolate for more effective electronic coupling with Bphen and within NCs films.
[0046] FIG. 3 is a schematic 300 showing a method of forming a nanocrystal according to various embodiments. The method may include, in 302, using a solution-based process to form the nanocrystal including a halide perovskite material.
[0047] The nanocrystal may have a diameter having a value selected from a range of 1 nm to 100 nm, e.g. of 4 nm to 14 nm.
[0048] The solution-based process may include mixing a plurality of precursors with a solvent to form a precursor solution. The plurality of precursors may include an organic ammonium halide. The solution-based process may further include adding one or more ligands and/or one or more surfactants to the precursor solution. For instance, methylammonium bromide (MABr, with MA representing methyammonium) may be mixed with lead bromide (PbBr2) in a solvent of dimethyformamide (DMF) to form an initial precursor solution. Oleyamine (OAm) and oleic acid (OAc) may be added to the DMF solvent to form a final precursor solution for forming methylammonium lead bromide perovskite nanocrystals.
[0049] The solution-based process may further include heating a further solvent. The further solvent may be heated to a predetermined temperature, e.g. 60 °C. The solution based process may additionally include mixing the precursor solution with the heated further solvent under stirring to form the nanocrystal. The further solvent may be toluene.
[0050] FIG. 4 is a schematic 400 showing a method of forming a hot-carrier solar cell according to various embodiments. The method may include, in 402, providing or forming the nanocrystal containing layer including one or more nanocrystals (as described herein), each of the one or more nanocrystals including a halide perovskite material. The method may also include, in 404, forming a first electrode so that the first electrode is in contact with a first side of the nanocrystal containing layer. The method may further include, in 406, forming a second electrode so that the second electrode is in contact with a second side of the nanocrystal containing layer opposite to the first side. The nanocrystal containing layer may have a thickness of less than 100 nm.
[0051] In other words, a method of forming a solar cell as described herein may be provided. The solar cell may include a nanocrystal containing layer containing one or more nanocrystals as described herein and electrodes. [0052] For avoidance of doubt, the method steps shown in FIG. 4 may not necessarily be in sequence. For instance, in various embodiments, the first electrode may be formed, before forming the nanocrystal containing layer.
[0053] In various embodiments, the method may further include forming an optical arrangement configured to direct solar energy to the nanocrystal containing layer. The optical arrangement may include one or more optical elements configured to direct solar energy to the nanocrystal containing layer. The one or more optical elements may be or may include optical lenses and/or mirrors.
[0054] In various embodiments, the first electrode 204 may be or may include a hot- electron extraction layer.
[0055] In various embodiments, the first electrode 204 may be or may include a n-type layer. The n-type layer or hot-electron extraction layer may include any one material selected from a group consisting of titanium oxide, zinc oxide, phenyl-C61 -butyric acid methyl ester (PCBM), 4,7-diphenyl-l,10-phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4- biphenylyl)-5-phenyl-l,3,4-oxadiazole (PBD), 2, 2',2"-(l,3,5-benzinetriyl)-tris(l-phenyl-l-H- benzimidazole) (TPBI), poly(9,9-dioctylfluorene) (F8), and bathocuproine (BCP).
[0056] In various embodiments, the first electrode 204 may be an energy selective contact configured to allow electrons having excess energies at or above a predetermined value to pass through, and further configured to reflect electrons having excess energies below the predetermined value back to the nanocrystal containing layer 202. In the current context, excess energies may refer to energy of the electrons beyond the conduction band minimum of the nanocrystal containing layer 202. The predetermined value of excess energy may be any value selected from a range of around 0.1 to 2 eV.
[0057] In various embodiments, the second electrode 206 may be or may include a hot- hole extraction layer.
[0058] In various embodiments, the second electrode 206 may be or may include a p-type layer.
[0059] In various embodiments, the second electrode 206 may be an energy selective contact configured to allow holes having excess energies at or above a predetermined value to pass through, and further configured to reflect holes having excess energies below the predetermined value back to the nanocrystal containing layer 202. In the current context, excess energies may refer to energy of the holes beyond the valence band maximum of the nanocrystal containing layer 202. The predetermined value of excess energy may be any value selected from a range of around 0.1 to 2 eV. In various embodiments, the second electrode 206 may include a molecular semiconductor material. The p-type layer or hot-hole extraction layer may include any one material selected from a group consisting of 2,2',7,7'- tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'-spirobifluorene (spiro-OMeTAD), poly(3- hexylthiophene-2,5-diyl) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS), and poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine) (TFB).
[0060] In various embodiments, the one or more nanocrystals exhibit a hot-carrier cooling lifetime of at least 0.5 ps, e.g. above 30 ps. A radius of each of the one or more nanocrystals is any one value selected from 0.5 nm to 50 nm, e.g. 2 nm to 7 nm.
[0061] In various embodiments, the halide perovskite material may be an organic- inorganic halide perovskite material, such as MAPbI3, MAPbBr3, MAPbBr2I, FAPbI3, FAi- yCsyPbI3, or Csx(MAi-yFAy)i-xPb(Ii-zBrz)3 (where each of x, y or z may be any value selected from a range from 0 to 1). Non-limiting specific examples may include CH3NH3PbI3, CH NH PbBr , CH NH PbBr2I, or NH2CH=NH2PbI . In various other embodiments, the halide perovskite material may be an inorganic halide perovskite material such as CsSnI3 or CsPbI3.
[0062] Various embodiments may provide solution-processed colloidal MAPbBr3 (methylammonium lead bromide) perovskite nanocrystals (NCs) which can be a very promising absorber material for the hot-carrier solar-cell. The hot-carrier cooling may be dramatically slower than the perovskite bulk-films. The hot-carrier cooling time may be increased to 30 ps (or above) in MAPbBr3 NCs which is ~2 orders slower than their bulk-film counterparts under comparable photoexcitation conditions. Further, the hot-carrier temperature of the MAPbBr3 NCs is 4 times larger than their bulk-film counterparts under comparable photoexcitation conditions.
[0063] Controlling hot-carrier cooling dynamics may be challenging but critical for improving the performance of many semiconductor photonic and electronic devices. In the NCs, the hot-carrier cooling time/rate may depend both on the volume and carrier densities. These findings can thus be applied to control the hot-carrier cooling by tuning the NCs size and carrier injection densities.
[0064] The hot-carrier cooling in the NCs according to various embodiments may be modulated by varying the size of NCs. The hot-carrier cooling rate may be lower in smaller sized NCs due to confinement induced phonon bottleneck effect. Besides MAPbBr3 perovskites NCs, other perovskites NCs with substitution of organic component and/or the metal element such as MAPbI3, MAPbBrxIi-x (x is the ratio of Br/(Br + I), which is determined by the contents of Br and I in the precursors during synthesis), CsSnI3, CsPbI3, FAPbI3. NCs may allow a wide choice of hot-carrier absorbers with different bandgaps. Moreover, after the surface chemical treatment, the hot electrons from NCs thin film may be efficiently injected (up to -83%) into electron extraction layers within ~ 1 ps. These insights may enable fresh approaches for hot-carrier and concentrator-type perovskite NC photovoltaic s.
[0065] Various embodiments may relate to the fabrication of the low temperature solution processed organic-inorganic perovskite nanocrystals, the observation of slow hot-carrier cooling, and/or the potential application of these nanocrystals for hot-carrier solar cells and concentrator hot-carrier solar cells. Contrary to conventional hot-carrier solar cell systems, concentrator hot-carrier solar cell may use focusing lenses or curved mirrors to focus the sunlight by a factor of between 300 to 1000 times onto a small cell area. A concentrator cell may therefore operate at much higher light-generated current densities than the normal hot- carrier solar cell. The higher injection densities may induce the higher hot-carrier temperature and longer hot-carrier lifetimes, which may further increase the efficiencies of hot-carrier solar cells.
[0066] The nanocrystals may be fabricated using a low temperature solution processed approach in atmosphere. In contrast, traditional Si-based solar cells are usually produced at elevated temperatures and using high vacuum growth techniques that require significant infrastructural investments.
[0067] Thermodynamic calculations reveal that single junction solar cell conversion efficiencies can reach -66% under 1-sun illumination if the excess energy of hot photogenerated carriers is utilized before they cool to the lattice temperature. The key for effective extraction of hot-carrier energies is to retard the hot-carrier cooling. It was commonly believed that energy and momentum conservation together with improbability of multi-phonon processes would cause the phonon bottleneck that slows down hot-carrier cooling in semiconductor nanoscale systems. However, further investigations revealed that the cooling rate becomes faster as dimensionality decreases for nanoscale inorganic semiconductors. [0068] Hot-carrier cooling may be critical in many photonic and electronic devices. A solution processable material may have much greater versatility than traditional material for integration with existing silicon based technologies. It can be applied to a much wider range of device designs and substrates by simply spin-coating, dip-coating or drop-casting.
[0069] Solution processed organic-inorganic perovskite nanocrystals may provide simple and inexpensive alternatives of material for potential photovoltaic applications as compared to traditionally silicon thin film produced with expensive gas-phase methods. The low temperature of processing may also enable integration of these materials into flexible substrates. The perovskites NCs may have much slower hot-carrier cooling as compared with that of current perovskites thin films used as absorbers in solar-cells which permit the efficient hot-carrier extraction. These features may be beneficial for the achievement of hot- carrier solar cell. Furthermore, as first observed in the perovskites NCs, the hot-carrier cooling time/rate may also be tuned by modifying NC size.
[0070] Various embodiments may find wide use in the application area of photovoltaics as absorption materials, such as NCs- sensitized nanocrystalline T1O2 solar cells, concentrator solar cells, NCs-conducting polymer blend solar cells, p-i-n array solar cells and/or concentrator solar cells.
[0071] FIG. 5 is a schematic 500 showing hot-carrier cooling with Auger processes in semiconductor nanocrystals. In (a), hot-carrier cooling is made possible via intraband Auger- type energy transfer. A hot electron (dot) may be cooled by Auger-type energy transfer to densely spaced hole states (e.g. , CdSe NCs), then the hot holes (circle) can relax rapidly via a cascade of single phonon emissions (arrows); (b) shows phonon bottleneck effect induced slow hot-carrier cooling in symmetric conduction and valence bands with discrete energy levels, while (c) shows, hot-carrier re-excitation by interband Auger-recombination of carriers at band edges, also called Auger-heating.
[0072] Alternative rapid relaxation pathways (e.g., intraband Auger-type energy transfer ((a) in FIG. 5), atomic fluctuations and surface effects) were found to be highly effective in negating this perceived phonon bottleneck at low carrier densities.
[0073] The reduced dimensionality also brings about competing effects at higher carrier densities: interband Auger recombination. This latter Auger re-excitation process (also known as Auger heating, shown in (c) in FIG. 5) would decelerate the hot-carrier cooling processes. Consequently, hot-carrier cooling in nanoscale inorganic semiconductors is convolved with a complex interplay of disparate mechanisms. To date, it remains extremely challenging to achieve slow hot-carrier cooling even with strongly quantum-confined inorganic semiconducting nanocrystals. Despite the advances in theory and materials synthesis, practical hot-carrier colloidal nanocrystal (NC) photovoltaics remain elusive. Although slow intraband hot-electron cooling was found in the lowest excited levels (lPe- lSe) in strongly confined PbSe quantum dots, the confined hot-electrons had to be separated from holes with exceptionally well-engineered epitaxial grown multi- shells in order to reduce the abovementioned competing relaxation pathways. Nevertheless, the multi-shells would complicate subsequent charge extraction. It may therefore be necessary to design NCs that can simultaneously fulfill both criteria of slow hot carrier cooling and efficient charge extraction.
[0074] Organic-inorganic lead halide perovskite semiconductors (e.g., MAPbX3, MA=CH3NH3, X=I, Br or CI) have recently emerged as a leading contender in low-cost high- performance solar cells. Recent observations of a hot-phonon bottleneck effect in MAPbI3 thin films at high carrier densities suggest that lead halide perovskites are also promising candidates for developing hot-carrier solar cells. Emulating semiconductor nanoscience, an interesting question would be if the hot-carrier cooling rate in halide perovskites could be further modulated through confinement effects. Here, the hot-carrier cooling dynamics and mechanisms in colloidal MAPbBr3 NCs of different sizes (with mean radius -2.5 - 5.6 nm) (FIG. 6) and their bulk-film counterpart (FIG. 7) were compared using room-temperature transient absorption (TA) spectroscopy.
[0075] FIG. 6 shows representative transmission electron microscopy (TEM) images of methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) with relatively (a) small, (c) medium and (e) large sizes according to various embodiments and the respective size histograms (b, d, f) on their right. The size distribution may be modeled with a Gaussian distribution. FIG. 7 shows (a) top-view and (b) side-view scanning electron microscopy (SEM) images of methylammonium lead bromide (MAPbBr3) bulk-film.
[0076] FIG. 8 shows (a) a plot of photoluminescence (PL) intensity (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating photoluminescence (PL) spectra of methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (b) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) illustrating ultraviolet-visible (UV-vis) absorption spectra of methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) according to various embodiments dispersed in toluene and bulk film counterpart, (c) a plot of energy of Is exciton, Els (in electron volts or eV) as a function of average nanocrystal radius, a (in nanometer or nm) showing the energy of Is exciton of methylammonium lead bromide perovskite (MAPbBr3) according to various embodiments as a function of radius, and (d) a plot of X-ray diffraction (XRD) intensity (in arbitrary units or a.u.) as a function of degree, 2Θ (in degrees) showing the XRD patterns of three differently sized methylammonium lead bromide perovskite (MAPbBr3) nanocrystals (NCs) according to various embodiments.
[0077] The exciton Bohr radius i¾ of MAPbBr3 was reported to be -2 nm. Given that the radius of the NCs (from -2.5 to 5.6 nm, see size distribution histogram in FIG. 6) is larger than ciB, the NCs are thus in the weak confinement regime. Hence, the small blue shift of emission (from 525 to 517 nm, FIG. 8(a)) of NCs with reducing NC size may be due to the weak confinement effect. In the weak confinement, the first exciton resonance of NCs as a function of NCs radius a can be written as
Figure imgf000023_0001
(1) where Ego is the bandgap energy without quantum confinement while the second term represents the confinement energy, μ is the electron-hole reduced mass, M=me * + mh * , Eb is the exciton binding energy. Using equation (1) above and the reported values of the effective masses me * ~0.29, m¾~0.31, the absorption edges of NCs may be reasonably well-fitted (see line in FIG. 8(c)) to yield a bandgap of Ego -2.38 eV and binding energy of Eb -50 meV, which are close to the reported values for MAPbBr3 NCs. These fitting results further validate the weak confinement in the perovskites NCs according to various embodiments.
[0078] Results reveal that the weakly confined MAPbBr3 NCs (FIG. 8) are very promising hot-carrier absorber materials as they possess much higher hot-carrier temperatures and longer cooling times (as compared to typical perovskite bulk-films under comparable photoexcitation conditions). This may be attributed to their intrinsic phonon bottleneck and Auger-heating effects at low and high carrier densities, respectively. Importantly, the hot- carriers may be efficiently extracted from MAPbBr3 NC thin films at room temperature by using a molecular semiconductor as an energy selective contact. [0079] FIG. 9A shows pseudo color transient absorption (TA) plot (upper panel, time (in picoseconds or ps) as a function of energy (in electron volts or eV)) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV)) for medium methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) (radii -4-5 nm) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal, <Vo> -0.1 (average carrier density per nanocrystal volume, n0avg~2.6 x 1017 cm ~3) and high pump fluence (right panel) with <No> -2.5 (n0avg ~6.5x 1018 cm ~3). FIG. 9B shows pseudo color representation (upper panel, time (in picoseconds or ps) and normalized transient absorption (TA) spectra (lower panel, normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV)) for MAPbBr3 bulk-film at low pump fluence (left panel) with initially generated carrier density no -2.1 x 1017 cm3 and high pump fluence (right panel) with no -1.5 x 1019 cm3.
[0080] FIGS. 9A-B show a comparison of the pseudo color TA plots and TA spectra of the medium MAPbBr3 NCs (radius -4.5 nm) against MAPbBr3 bulk-film at low and high pump fluence, respectively. For both types of samples, the plots/spectra display a prominent photo-bleaching (PB) peak with a high energy tail near the bandgap because of the state- filling effects. Similar results were also observed in the small and large NCs.
[0081] FIG. 10 shows plots of time (in picoseconds or ps) as a function of energy (electron volts or eV) showing pseudocolor transient absorption (TA) spectra (time in picoseconds or ps as a function of energy in electron volts or eV) for (a) small and (b) large sized methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments in solution at low pump fluence (left panel) with initially average generated electron-hole pair per nanocrystal <No> -0.1 and high pump fluence (right panel) with <Vo> -2.5 following 3.1 eV photoexcitation.
[0082] For the bulk sample, the high energy tails of the PB peak originate from the rapid distribution of initial non-equilibrium carriers into a Fermi-Dirac distribution via elastic scatterings (including electron-hole scattering at low pump fluence and carrier-carrier scattering at high pump fluence) that can be characterized by a carrier temperature T . T can thus be extracted by fitting the high-energy tail of the TA spectra with a simple Maxwell- Boltzmann function of exp(Ef - E/KB 7 ), where KB is the Boltzmann's constant and Ef is the quasi-Fermi energy. [0083] For NCs, the discrete energy levels can be approximately treated as a continuum in the case where thermal energy k^T » energy level spacing AE. In contrast to conventional semiconductor NCs with strong confinement, the perovskites NCs may be in the weak confinement regime with energy levels that are more closely spaced. Thus, in the microscopic picture of a single dot, we expect that the efficient electron-hole scattering (due to the enhanced Coulomb interaction under confined conditions) at low pump fluence (i.e. , with one or below electron-hole pair per NC) as well as carrier-carrier scattering at high pump fluence can cause the rapid nonthermal energy distribution to evolve into a Fermi-Dirac-like distribution within 150 fs. In the macroscopic picture, the TA spectra may be collected from an ensemble of NCs whose size distribution may cause inhomogeneous broadening, (i.e., overlapping TA spectrum from single NC). All these properties rightly lead to a continuous TA spectrum from the NCs ensemble to resemble that of the bulk materials. Hence, the high- energy tail of the NCs' TA spectra may also be described by a Maxwell-Boltzmann distribution. The representative fits of the high-energy tails and non-normalized TA spectra are presented in FIG. 11. FIG. 11 illustrates (a) a plot of normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV) showing normalized TA spectra at different short time delays of medium sized methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments in toluene with average generated electron-hole pair per nanocrystal, <Vo>~0.1 (following 3.1 eV photoexcitation) and (b) the un-normalized transient absorption (TA) spectra of (a). The solid black lines in (a) fit to the high-energy tails using the Maxwell-Boltzmann distribution function.
[0084] It is evident from both the pseudo color TA plots and spectra that the high energy tails (starting at the kink in the spectrum where the exponential decay region begins, see FIG. 11 of the PB peak persists much longer for NCs than that of the bulk-film, suggesting higher carrier temperatures and slower hot-carrier cooling.
[0085] The analysis and interpretation of the TA spectra of halide perovskites are well- documented in the literature. The TA spectra of MAPbBr3 perovskites (bulk and nanocrystals) are similar with that of previous studies. The positive TA peak (at -2.3 eV as shown in FIG. 11) arose from ground states bleaching (GSB) due to the state-filling of the carriers at the band edge. At the high energy side of the GSB peak, the first slope (i.e. , the steeper one closer to the GSB peak) is dependent on the ground state transitions which affect its width and shape; while the second gentler slope of the high energy tail (e.g. , start at -2.5 eV in FIG. 11) is resulted from the hot-carrier distribution. The negative part (photoinduced absorption) of this high energy side is caused by the photoinduced change of the imaginary part of the refractive index; while the negative part of the low energy side of the GSB is attributed to bandgap renormalization.
[0086] Hot-carrier temperature T is extracted by fitting the high-energy tail of the TA spectra with a Maxwell-Boltzmann function. When the difference between the carrier's energy and the Fermi level is large as compared to κΒΤ (i.e. , E—Ej > κΒΤ), the Fermi-Dirac distribution function can be approximately described with an exponential - i.e. , a Maxwell- Boltzmann distribution:
1 Ef-E
—f - exp ^— (2) l+exp - - ΚΒ '
ΚβΤ
[0087] Approximating the Fermi-Dirac distribution by a Maxwell-Boltzmann distribution for hot-carrier energies »E is a valid and generally accepted practice to extract the hot- carrier temperature T . For intrinsic (untreated) perovskites NCs and bulk-film, the Fermi level may be located between the valence and conduction band edge (-0.4 eV below the conduction band minimum from the ultraviolet photoelectron spectroscopy (UPS) data (see below)). Thus, the generated hot-carriers may be far from the Fermi energy (~ 1 eV above). Although the Fermi level may shift slightly towards the band edge (~0.1 eV) under intense photoexcitation, the energy difference may still very large (i.e. , E—Ej » κΒΤ (-25 meV at room temperature)). Thus, the high energy tail of the TA spectrum can be fitted using a Maxwell-Boltzmann distribution to extract T .
[0088] FIG. 12 is a plot of carrier temperature (in Kelvins or K) as a function of time (in picoseconds or ps) showing the temporal evolution of the hot-carrier temperature T for the medium nanocrystals (NCs) according to various embodiments and bulk-film at various pump fluence: initial photoexcited hot-carrier density no (bulk-film) and average generated electron-hole pairs per NC <No>, where <No> = Jo, where is the pump fluence and σ is the absorption cross-section.
[0089] FIG. 13 illustrates (a) a plot of photoluminescence (PL) intensity (in arbitrary unit or a.u.) as a function of time (in nanoseconds or ns) showing pump fluence dependent time- resolved photoluminescence (PL) of the medium methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments under 3.1 eV photoexcitation, (b) a plot of transient photoluminescence (PL) intensity (in arbitrary units or a.u.) as a function of pump intensity (in micro- Joules per square centimeter or μΐ cm"2) showing normalized PL intensities of three different sized MAPbBr3 NCs according to various embodiments as a function of pump fluence measured at time At = 4 ns, and (c) a plot of occupation probability (in percent or %) as a function of the number of electron-hole (e-h) pairs per NC according to various embodiments.
[0090] Based on the Poisson distribution of initial photon occupancies in NCs, the probability of a NC to contain i e-h pairs is given by =— ^— e~<No>, where <No>=Jo is the initially generated average number of e-h pairs per NC ( is the pump fluence, σ is the absorption cross-section of NC). When the delay time after photoexcitation is much longer than multicarrier recombination (e.g., Auger recombination), the NCs may mainly recombine with single exciton emission, hence the late-time PL intensity may be proportional to occupation probabilities of photoexcited NCs as /PL oc (1— P0) = (1— e~Ja) . FIG. 13(b) shows the pump fluence dependent time-resolved photoluminescence (TRPL) of the pump fluence dependent TRPL was normalized at time t = 4 ns when multicarrier recombination is completed and PL intensity represents the emitting NCs with only one electron-hole pair, σ of NCs can be obtained by fitting the data with equation of 1— e~Ja (solid lines). The fitted σ are 8.5+0.5xl0"15, 3.2+0.2xl0"14 and 6.8+0.3xl0"14 cm2 from small to large NCs, respectively.
[0091] For comparison with bulk- films, the average carrier density per NC volume in NCs which is defined as n0avg = N0/VNC, where VNC is the NC volume, may also be determined. For NCs, the maximum T at the excitation onset with <No> -0.1 may be around 1700 K, which is about four times higher than that for the bulk-film sample with comparable carrier densities. The smaller T in the latter may be attributed to arise from the ultrafast cooling of hot-carriers, which had occurred on a timescale much shorter than the temporal resolution of the TA measurements.
[0092] It is important to note the complex interplay of the hot-carrier cooling times due to several factors: (i) the pump energy (i.e., carriers' excess energy - typically, higher excess energies lead to longer hot carrier lifetimes); (ii) the initial hot-carrier densities (i.e., higher carrier densities usually lead to longer hot carrier lifetimes); and/or (iii) the energy loss rate at a specific hot-carrier temperature (i.e., generally, lower hot carrier temperatures yield smaller energy loss rates). Hence, due care must be taken for a fair comparison of the reported values in the literature. More discussion on hot-carrier lifetime comparison between different materials may be found below under "hot carrier lifetimes" section.
[0093] Furthermore, for clearer and easier comparison of hot-carrier cooling lifetimes reported for different materials in the literature, the hot-carrier cooling lifetime as described herein may be defined as the time interval from pulse excitation till the cooling of hot-carriers to 600 K. This temperature is used as the benchmark because previous theoretical calculations have shown that for T > 600 K, there may still be an appreciable hot-carrier conversion efficiency (i.e., > 40%) over a wide range of absorber bandgaps.
[0094] With these considerations in mind, for the control MAPbBr3 bulk-film, hot-carrier cooling lifetimes ranging from < 0.1 ps to 0.8 ps were obtained for no - 2.1- 15 x 1018 cm"3. These lifetimes are of the same magnitude as those reported for MAPbI3 thin-films excited at similar no and excess energies of 0.7 eV; but is shorter than those for highly excited hot- carriers with twice the excess energies (-1.44 eV). Notably, the MAPbBr3 NCs may exhibit hot-carrier cooling lifetimes 1-2 orders longer than those of the perovskite bulk-film control sample under similar noavg (shown in FIG. 14). FIG. 14 shows a table 1400 comparing properties of methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments, methylammonium lead bromide perovskite bulk films, and other materials reported in literature. As highlighted previously, the hot-carrier cooling lifetime may be defined as the time interval from pulse excitation till the cooling of hot- carriers to 600K. 600K may be used as the benchmark because previous theoretical calculations have shown that for T > 600 K, there may still be an appreciable hot-carrier conversion efficiency (i.e., > 40%) over a wide range of absorber bandgaps. TA refers to "Transient Absorption" and TRPL refers to "time-resolved photoluminescence".
[0095] FIG. 15 show plots of carrier temperatures (in Kelvins or K) as a function of time delay (picoseconds or ps) for three different sized methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments and bulk-film (a) at low pump fluence (corresponding to <No> -0.1 in NCs and no -2.1 x 1017 cm3 in bulk-film) and (b) at high pump fluence (corresponding to <Vo> -2.5 in NCs and no -1.5 x 1019 cm3 in bulk- film) following 3.1 eV photoexcitation. The lifetime of large NCs may be around 40x longer than that for the bulk-film sample, where the bulk film was excited at almost one order higher carrier density of 1.5 x 1019 cm"3. For instance, the hot-carrier cooling lifetimes can be as long as -32 ps (FIG. 15) for large NCs with <N0> - 2.5 (or n0avg of - 3.5 x 1018 cm"3). In fact, the hot-carrier cooling lifetimes of the MAPbBr3 NCs may be much longer than those reported for other semiconductor bulk and nano materials. With reference to FIG. 14, for GaAs thin film, the reported cooling lifetime is -2 ps with carrier densities of -6.0 x 1018 cm" 3 and excess energies of 1.7 eV; and for CdSe nanorods, the reported cooling lifetime is -0.8 ps with carrier densities of -5.5 x 1018 cm"3 and excess energies of 1.1 eV. The MAPbBr3 NCs may compare very favorably with much longer lifetimes of 18 ps, excited with much lower excess energies of -0.7 eV at comparable carrier densities of 6.5 x 1018 cm"3.
[0096] To discern the slower hot-carrier cooling mechanisms in MAPbBr3 NCs, the relaxation dynamics under low pump excitation is examined. For <No> - 0.1, up to 10% of NCs are excited with one e-h pair based on the Poisson distribution (FIG. 13). At such low carrier densities, multi-particle recombination may be negligible, which is evident from the absence of any fast decay of band-edge carriers in NCs (FIG. 16).
[0097] FIG. 16 illustrates plots of normalized transmittance change ΔΤ/Τ as a function of time (picoseconds or ps) showing normalized photobleaching dynamics probed at the band edges of methylammonium lead bromide (a) bulk-film, (b) small nanocrystals (NCs) according to various embodiments, (c) medium nanocrystals (NCs) according to various embodiments, and (d) large nanocrystals (NCs) according to various embodiments, in solution with high and low pump fluence respectively, as well as (e) comparison of transient absorption (TA) dynamics for medium nanocrystals (NCs) according to various embodiments in solution and spin-coated nanocrystals (NCs) film according to various embodiments, and (f) pump-fluence-dependent bleaching dynamics probed at the band edge of small methylammonium lead bromide nanocrystals (NCs) according to various embodiments in solution. The inset of (f) in FIG. 16 shows the extracted Auger recombination component after subtracting the single-exciton decay at longer time. The photoexcitation energy is about 3.1 eV.
[0098] Hence, the hot-carrier relaxation mechanism at low pump excitation may therefore be representative of the material's intrinsic properties and may not be influenced by extrinsic effects such as the multi-particle Auger-recombination.
[0099] At low pump fluence, T may decay faster with increasing NC size (FIG. 15). FIG. 17 shows (a) a plot of energy loss rate (electron volts per picosecond eV ps"1) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate of hot-carriers as a function of carrier temperature T for methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments with <No> -0.1 and methylammonium lead bromide perovskite (MAPbBr3) bulk-film with no -2.1 x 1017 cm"3, (b) a plot of normalized transmittance change ΔΤ/Τ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band-edge for colloidal methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments and bulk-film at low carrier density, and (c) a plot of rise time (in femtoseconds or fs) / confinement energy (in electron volts or eV) showing size dependence of the rise time of band-edge bleachings in methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) (dark solid squares), bulk-film (light solid squares) (the particle size is represented by the film thickness) and cadmium selenide nanocrystals (CdSe NCs) (solid circles), as well as size dependence of quantum confinement energies in MAPbBr3 NCs (hollow square) and CdSe NCs (hollow circle). Error bars represent standard errors. Photoexcitation energy for FIG. 17 (a) - (c) is 3.1 eV. FIG. 18 is a plot of Raman intensity (in arbitrary units or a.u.) as a function of wavenumbers (in per centimeter or cm"1) showing room temperature Raman spectrum of as-prepared methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments drop-cast on glass substrate. The peaks originate from LO phonons. From the Raman measurement shown in FIG. 18, the available phonon modes for hot-carrier cooling in MAPbBr3 NCs are located at around -150 cm"1 (assigned to the stretching of the Pb-Br bonds) and 300 cm"1 (which could be from the second-order of 150 cm"1 and/or the torsional mode of MA cations), respectively.
[00100] Solid lines in FIG. 17(a) represent the numerical fits with LO-phonon model. The arrow indicates the maximum T obtained for the bulk-film. The inset in FIG. 17(a) shows the representative TEM images of small (S), medium (M) and large (L) perovskites NCs. Solid lines in FIG. 17(b) are the single exponential fits. Inset in FIG. 17(b) shows a schematic of the phonon bottleneck induced slow hot-carrier cooling in symmetric conduction and valence bands with discrete energy levels.
[00101] For all three NCs, the energy loss rates per carrier Jt (-1.5KB dTVdt) may slowly decrease within the range of 0.6-0.3 eV ps"1 until Tc reaches -700 K (FIG. 17(a)), below which Jr plunges by several orders of magnitude until the T approaches the lattice temperature. Such cooling trend is similar to that for the bulk-film sample as well as in other bulk inorganic semiconductors and nanostructures. Here, the initial rapid cooling (i.e., higher cooling rate) may be attributed to the carrier coupling to longitudinal optical (LO)-phonons which establishes a thermal equilibrium between the LO-phonon population and the hot- carriers. Comparing the different NCs, the initial Jt for small NCs is smaller than the large NCs by a factor -2 (indicating a weaker carrier-phonon interaction in the former). The subsequent slower cooling of the hot-carriers closing to the band-edges (i.e., -300 - 500 K in FIG. 17(a)) is determined by the thermal equilibration between longitudinal optical phonons (LO phonons) and acoustic phonons.
[00102] The energy loss rate was fitted by using a LO-phonon interaction model (see below under LO-phonon model), the fitted TLO (characteristic LO-phonon decay time) increases with reducing NCs dimensionality (see FIG. 17(a)), which may provide direct evidence of the reduction in the optical phonon relaxation by the quantum confinement. This is a characteristic of the phonon bottleneck effect, which thus retards the hot-carriers cooling. Although the NCs are in the weak confinement regime with confinement energy around -15- 60 meV, several early theoretical papers had shown that even in this weak confinement regime where the level spacing is only a few meV, the carrier relaxation mediated by phonon interactions can still be dramatically hindered. This is because of restrictions imposed by energy and momentum conservations and the weak energy dispersion of the longitudinal optical (LO) phonons, which together cause the phonon bottleneck. Moreover, the comparable acoustic phonon temperature (Ta) of -310 K for all three NC samples, which is also close to the lattice temperature at room temperature, strongly suggests that the deceleration of hot-carrier cooling may be unlikely to be induced by the acoustic phonon bottleneck.
[00103] The band-edge bleach buildup approach was also used to elucidate the hot-carrier cooling properties. Apart from the approach of fitting the high energy tail of PB peak to elucidate the hot-carrier cooling properties, an alternative method is to probe the intraband relaxation of the photoexcited carriers high above the band-edge. This can be achieved through monitoring the buildup of the band-edge bleach as the recombination of the band- edge carriers (~ns) is much slower than its intraband relaxation process (from several to tens of ps). This latter approach is commonly used for investigating the hot-carrier dynamics in strongly confined quantum colloidal semiconductor NCs given the overlapping PB bands from the discrete energy levels make resolving their hot-carrier distribution extremely challenging. The latter approach may be applied for a fair comparison of the hot-carrier cooling of perovskites NCs with that of conventional inorganic semiconductor NCs (e.g., CdSe NCs).
[00104] FIG. 17(b) shows the normalized TA spectra of the perovskite samples probed at their band-edge PB peaks following photoexcitation with similar excess energies at low carrier densities. Each buildup process is fitted with a single-exponential growth function to yield a rise time (Trise). The rise of the band-edge bleach occurs at sub-ps timescale that becomes slower with decreasing NC size, consistent with the smaller Jr and slower hot-carrier temperature decay (FIG. 15) for smaller perovskites NCs. Surprisingly, the trend exhibited by the perovskite NCs is completely opposite to that for CdSe NCs (spanning the strong to weak quantum confinement regimes - FIG. 17(c) and FIG. 19).
[00105] FIG. 19 shows (a) a plot of normalized transmittance change ΔΤ/Τ as a function of time (in picoseconds or ps) illustrating normalized bleaching dynamics probed at the band edge for colloidal CdSe NCs with different diameters (shown in legend) at low pump fluence, and (b) plots of time (in picoseconds or ps) as a function of energy (in electron volts or eV) illustrating low pump fluence with initially generated <No> -0.1 (left) and high pump fluence with <No> -2.5 (right). The phtotoexcitation energy is 3.1 eV. Solid lines in FIG. 19 (a) are the single exponential growth fitting curves. The inset in FIG. 19(a) schematically shows the hot-carrier cooling process via Auger-type energy transfer.
[00106] Furthermore, the perovskite NCs rise times may also be much longer. The faster hot-carrier cooling with decreasing CdSe NCs is consistent with previous reports, which is attributed to an Auger-type energy transfer from the hot electrons to the dense hole states. Results clearly show that such Auger-transfer mechanism present in conventional inorganic semiconductor NCs may be naturally suppressed in perovskites NCs. Concerning the schematic energy level diagram of CdSe NCs (FIG. 5), one possible reason could be the symmetric energy dispersion and small effective mass for both electrons and holes of perovskite NCs illustrated in inset of FIG. 17(b). Other factors such as surface reconstruction, surface defects, atom fluctuations, etc., may also result in faster hot-carrier cooling with decreasing inorganic semiconductor size (e.g., in quantum confined IV- VI semiconductor PbSe with identical and small electron and hole effective masses). The low defect density of the perovskite NCs (consistent with the high PL quantum yield of MAPbBr3 NCs (-80%)) may thus be another reason for this unique behavior (i.e., intrinsic phonon bottleneck effect). These new insights into the slow hot-carrier cooling in perovskite colloidal NCs (under low pump excitation) may challenge the conventional wisdom established for traditional semiconductor NCs.
[00107] These perovskite NCs also exhibit unique hot-carrier cooling properties under high pump excitation. FIG. 20 shows (a) a plot of energy loss rate (in electron volts per picosecond or eV ps-1) as a function of carrier temperature (in Kelvins or K) illustrating energy loss rate vs carrier temperature T for methylammonium lead bromide perovskite nanocrystals (MAPbBr3 NCs) according to various embodiments with <No> -2.5 and MAPbBr3 bulk-film with no -1.5 x 1019 cm"3, (b) a plot of lifetime (in picoseconds or ps) as a function of nanocrystal volume (in cubic nanometer or nm3) illustrating Auger recombination lifetimes and hot-carrier cooling time vs perovskite nanocrystal (NC) volume according to various embodiments, and (c) a plot of normalized hot carrier concentration Hhot as a function of time (in picoseconds or ps) showing normalized hot-carrier decay at different pump fluences according to various embodiments. The solid line in FIG. 20(a) represents the LO-phonon model at low carrier densities. The dashed lines in FIG. 20(b) are guides to the eye showing the scaling of the lifetimes with the square root of nanocrystal (NC) volume, while the inset illustrates the hot-carrier re-excitation by Auger-recombination of carriers at band-edge (also known as Auger-heating), and the error bars represent standard errors. Solid lines in FIG. 20(c) are bi-exponential decay fits. Photoexcitation energy for FIG. 20 (a) - (c) is 3.1 eV. The bulk film is about 240 nm thick.
[00108] FIG. 20(a) shows contrasting trends of energy loss rates vs carrier temperature between the three-different sized NCs (at <No> -2.5) and the bulk-film sample (at no - 1.5xl019 cm"3). For both NCs and bulk-film, the initial hot-carrier cooling governed by the carrier- LO-phonon interactions may be nearly independent of carrier densities. This can be concluded from: (i) the almost identical initial fast decay of T at different carrier densities (FIG. 12), and (ii) the similar initial energy loss rate at high carrier temperatures for both low and high carrier densities (FIG. 17(a) and FIG. 20(a)). For the bulk-film, the elongation of hot-carrier lifetime (FIG. 12) and the slight deviation of Jr from the LO-phonon model (line in FIG. 20(a)) below 600 K may be due to the 'hot phonon bottleneck effect' (commonly observed in bulk inorganic semiconductors and more recently reported for MAPbI3 thin films). This may be attributed to the reduced decay of LO phonons caused by partial heating of acoustic modes. This assumption may be supported by the higher acoustic phonon temperature Ta of 350 K at the high pump fluence. [00109] FIG. 21 is a plot of energy loss rate (electron volts per picosecond or eV ps"1) as a function of carrier temperature (in Kelvins or K) showing energy loss rate of hot-carriers as a function of carrier temperature T for methylammonium lead bromide (MAPbBr3) bulk-film at low and high carrier densities. Solid lines represent the fits numerically fitted with Equation (3) (shown below under section on "LO-phonon model"). The fitted LO-phonon lifetime TLO and acoustic temperature Td are 150 + 20, 280 + 20 fs, and 305 + 10 and 350 + 10 K with low and high carrier densities, respectively.
[00110] However, for NCs, from FIG. 20(a), although the Λ of the NCs (at <N0> -2.5) initially follows the LO-phonon model at high carrier temperatures, they deviate greatly from the LO-phonon model as the hot-carrier population cools below 1500 K. For temperature range <1000 K, Jr reduces drastically by several orders of magnitude when the carrier density is increased from <N0> -0.1 (FIG. 17(a)) to <N0> -2.5 (FIG. 20(a)). For example, at <N0> -0.1, Jr at 700 K is around 0.3 eV ps-1 whereas it is -0.008 eV ps-1 at <No> -2.5. Furthermore, reduces with increasing NC size at carrier temperatures <1200 K at <No> -2.5. All these signatures suggest the existence of another slow hot-carrier cooling mechanism that only becomes dominant at high carrier densities, which we posit is the Auger heating mechanism, as it is well-known that Auger recombination is strongly enhanced in confined semiconductor NCs at higher carrier densities due to the increased carrier-carrier interactions. Thus, there may be a finite probability for the relaxed hot-carrier (at the band- edges) to be re-excited to higher energy states through the Auger recombination of carriers at the band-edge (inset of FIG. 20(b)).
[00111] FIG. 20(c) shows that the calculated concentration («hot (t)) of hot-carriers for different sized NCs relaxes bi-exponentially with a fast decay occurring within 1 ps and a slower decay of several tens of ps - similar to the behavior of the hot-carrier temperatures (FIG. 12 and FIG. 15). The fast decay may be attributed to the carrier-LO-phonon interactions. In addition, the fitted slow decay lifetimes of nhot (t) are well-matched with the 1/3 relation of their Auger lifetime TAug (i.e., Thot~TAug/3 - FIG. 20(b), see also below under "Auger-heating model" section). For example, the slower decay lifetime for the small NCs is fitted to be -12 ps, which is very close to 1/3 of its ΤΑ¾ of 38 ps. The excellent agreement between the experimental data and our simple model that includes Auger effects may strongly substantiate the dominant Auger heating contribution in further retarding the hot- carrier cooling at high carrier densities. Given that TAug~ (VNC ) and the slow hot-carrier lifetimes Thot~TAug/3, Auger induced hot-carrier cooling lifetime may be sublinearly dependent on the NC volume (FIG. 20(b)). Although Auger heating causes a slowdown of the hot- carrier cooling rate favorable for hot-carrier extraction, it should also be noted that Auger effects may conversely reduce the carrier densities. It may therefore be necessary to balance the hot-carrier lifetime and carrier losses in the application of concentrator-type hot-carrier solar cells at high pump fluence.
[00112] Apart from slow hot-carrier cooling, the feasibility of efficient hot-carrier extraction may be another challenging issue for hot-carrier solar-cells. Such extraction may be required to be very fast to limit energy loss; where the competition is between extraction rate and cooling rate rather than recombination rate. Considering the estimated hot-carrier diffusion length of -16 - 90 nm (depending on hot-carrier lifetime and diffusion coefficient) in MAPbBr3 film (see below under "Estimation of Hot-Carrier Diffusion Length"), it may therefore be technically feasible to extract hot-carriers. Here, efficient hot-electron extraction from 1,2-ethanedithiol (EDT)-treated MAPbBr NCs (EDT-NCs) to 4,7-diphenyl-l,10- phenanthroline (Bphen) is demonstrated.
[00113] FIG. 22 shows plots of photoelectron intensity (counts per second or cts/s) as a function of energy (in electron volts or eV) showing the ultraviolet photoelectron spectroscopy (UPS) spectrum of (a) 1,2-ethanedithiol (EDT)-treated and (b) post-annealed EDT-treated methylammonium lead bromide (MAPbBr3) nanocrystals (NCs) films according to various embodiments, and (c) 7-diphenyl-l,10-phenanthroline (Bphen) film on indium tin oxide (ITO) substrates. The valence band maximum (VBM) may be determined by linear extrapolation of the leading edge of the valence band to the background intensity, which is 1.9 + 0.1, 2.3 + 0.1 and 2.9 + 0.1 eV for FIG. 22 (a) -(c), respectively.
[00114] Bphen may be selected as the hot-electron extraction material because this molecular semiconductor has a high electron mobility and possess a higher lowest unoccupied molecular orbital (LUMO) than the conduction band minimum (CBM) of our EDT-treated NCs (see FIG. 22 for UPS measurements), implying only hot-carriers with sufficient excess energies above band-edge can be injected into Bphen (see FIG. 23A).
[00115] FIG. 23 A is a flat-band energy diagram (vertical axis in electron volts or eV) to illustrate hot-electron extraction from perovskite nanocrystals according to various embodiments to 7-diphenyl-l,10-phenanthroline (Bphen) with competing hot-electron cooling pathways. Conduction band minimum (CBM) (or LUMO levels) and valence band minimum (VBM) (or highest occupied molecular orbital (HOMO) levels) of NCs (or Bphen) may be determined from UPS and ultraviolet-visible measurements. FIG. 23B shows an atomic force microscopy (AFM) image of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film according to various embodiments. FIG. 23C is a scanning electron microscopy (SEM) image of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl- l, 10-phenanthroline (Bphen) bilayer according to various embodiments. The scale bar is 100 nm.
[00116] FIG. 23D is a plot of normalized transmittance change (ΔΤ/Τ) as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for about 35 nm thick of 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film with (continuous lines) / without (dashed lines) 7-diphenyl- l,10-phenanthroline (Bphen) according to various embodiments following 3.1 eV photoexcitation with <No> around 0.1. Inset of FIG. 23D shows the un-normalized transient absorption (TA) spectra at 0.8 ps. FIG. 23E is a plot of hot-carrier temperature (in Kelvins or K) as a function of delay time (in picoseconds or ps) for 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film and 1,2-ethanedithiol (EDT)- treated nanocrystal (NC) film /7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments at different pump fluences. Dotted arrows show the decrease of the initial hot-carrier temperatures after adding the Bphen layer, indicating effective hot-electron extraction.
[00117] FIG. 23F is a plot of extraction efficiency rjhot (in percent or %) as a function of hot-electron excess energy (in electron volts or eV) showing pump energy dependence of the hot-electron extraction efficiencies in about 35 nm-thick 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments. Inset of FIG. 23F shows the un-normalized TA spectra at 0.8 ps following 2.5eV photoexcitation with <No> around 0.1 for about 35nm thick EDT-NCs film with/without Bphen. FIG. 23G is a plot of extraction efficiency rjhot (in percent or %) as a function of thickness (in nanometres or nm) showing perovskite film thickness dependence of the hot electron extraction efficiencies upon 3.1 eV pump energy excitation for 1,2- ethanedithiol (EDT)-treated nanocrystal (NC)/ 7-diphenyl-l, 10-phenanthroline (Bphen) bilayer according to various embodiments and bulk-film/7-diphenyl- l, 10-phenanthroline (Bphen) bilayer. Inset shows the un-normalized TA spectra at 0.8 ps following 3.1 eV photoexcitation with <No> around 0.1 for about 140 nm-thick EDT-NCs film with/without Bphen. Error bars on the x axis represent the uncertainties in the determination of excess energies in FIG. 23F and sample thickness in FIG. 23G and on the y axis represent uncertainties in the determination of extraction efficiencies.
[00118] FIG. 24 shows (a) plot of transmittance (in arbitrary units or a.u.) as a function of wavenumber (in per centimeter or cm"1) showing the attenuated total reflection- fourier transform infrared (ATR-FTIR) spectra of as-prepared methylammonium lead bromide nanocrystals (MAPbBr3 NCs), 1,2-ethanedithiol (EDT)-treated nanocrystals (EDT-NCs) and 70 °C annealed 1,2-ethanedithiol nanocrystals (Ann-EDT-NCs) according to various embodiments, and plots of photoemission intensities (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing sulfur (S) 2p X-ray photoelectron spectroscopy (XPS) spectra of (b) non-annealed and (c) 70 °C post-annealed 1,2- ethanedithiol (EDT)-treated nanocrystals (EDT-NCs) film according to various embodiments. S 2p can be deconvolved into unbound thiol and bound thiolate on the NC surface (see section on FTIR and XPS analysis on ligand exchange for discussions).
[00119] Bphen possesses a narrow electron bandwidth, which may allow it to approximate the energy selective contact required in hot-carrier solar cells. EDT treatment may be used to substitute the long and highly insulating oleic acid and oleylamine ligands that is present on the as-prepared NC surfaces with thiolate (see ATR-FTIR and XPS measurements in FIG. 24 and section on FTIR and XPS analysis on ligand exchange) for more effective electronic coupling with Bphen and within NCs films (evident from the closer NCs packing after treatment as shown in TEM images in FIG. 25). FIG. 25 shows (a) atomic form microscopy (AFM) image of un-treated medium methylammonium lead bromide nanocrystals (MAPbBr3 NCs) film according to various embodiments, and (b) representative transmission electron microscopy (TEM) image of 1,2-ethanedithiol-treated methylammonium lead bromide nanocrystals (EDT-treated MAPbBr3 NCs) according to various embodiments. FIG. 26 shows pseudocolor transient absorption (TA) spectra for (a) medium methylammonium lead bromide nanocrystals (MAPbBr3 NCs) film according to various embodiments, (b) 1,2- ethanedithiol-treated nanocrystals (EDT-treated NCs) film according to various embodiments, and (c) on 1,2-ethanedithiol-treated nanocrystals film/7-diphenyl- l,10- phenanthroline (EDT-treated NCs film/Bphen) bilayer according to various embodiments at low pump fluence (left panel) with initially generated <No> -0.1 and high pump fluence (right panel) with <No> -2.5. The high energy tails may be reduced for EDT-NCs/Bphen following 3.1 eV photoexcitation. [00120] Hot-electron extraction from spin-coated EDT-NCs thin film (see AFM and SEM images in FIGS. 23B-C) by Bphen may be validated by the clear reduction of the high energy tails of TA spectra for the EDT-NCs/Bphen bilayers that occurs instantaneously (see FIG. 23 D, pseudo color TA spectra in FIG. 26 and section on "Effects of photocharged NCs and trions in NCs films on hot-carriers").
[00121] For -35 nm thick EDT-NCs film, after adding Bphen layer, the initial T cooled from -1300 to 450 K at low pump intensity, and from -1800 to 800 K at high pump intensity within -200 fs after photoexcitation (FIG. 23E), indicating that the carriers with higher energies and temperature may be injected into Bphen. From the conduction band minimum and LUMO offset between EDT-NCs and Bphen, hot-carriers with excess energy > 0.2 + 0.1 eV may be extracted (FIG. 27). FIG. 27 shows energy diagrams (y axis: energy in electron- volts or eV) showing flat-band energy level alignment as determined from the ultraviolet photoelectron spectroscopy (UPS) and ultraviolet- visible (UV-VIS) spectroscopy measurements for non-annealed, annealed 1,2-ethanedithiol -nanocrystals (EDT-NCs) films and 7-diphenyl-l,10-phenanthroline (Bphen) according to various embodiments - illustrated for the case of hot-electron extractions. Excess energy of extracted hot-electrons (Ehot-excess) may be determined from the band offset between the conduction band minimum of NCs and the LUMO of Bphen.
[00122] Considering the increased diffusion coefficient for hot-carriers (see section on Estimation of hot-carrier diffusion length) and ultrafast hot-carrier hopping between NCs (within several tens of fs), hot-electrons may be likely to be injected into Bphen through electron diffusion inside the NC and hopping at NC-interfaces. The driving force of hot- electron transfer may be the energy difference between the hot-carrier energy and the LUMO energy with respect to the Fermi energy as shown in FIG. 23A. A large density of states is typical for organic molecules. The highly efficient hot-carrier transfer may thus be attributed to the high density of acceptor states in LUMO levels of Bphen together with the strong electronic coupling between Bphen and NCs. Additional control experiments to prove that Bphen may be the only pathway for extraction of hot-carriers from NCs in EDT-NCs/Bphen and the presence of the transferred charge carriers in Bphen may be found in sections under "Controls experiments to validate hot-carrier transfer" and "PIA signal of transferred charge carrier in Bphen". [00123] FIG. 28 shows (a) a plot of absorbance (in arbitrary units or a.u.) as a function of wavelength (in nanometers or nm) showing linear absorption spectra of Bphen film on glass; (b) plot of normalized negative transmittance change -ΔΤ/Τ as a function of wavelength (in nanometer or nm) showing negative transient absorbance spectra of 7-diphenyl-l,10- phenanthroline (Bphen) (300 nm pump with intensity of 20 μΐ cm"2, 400 nm pump with intensity of 40 μΐ cm"2), perovskites nanocrystals (NCs) (400 nm pump with intensity of 15 μΐ cm"2) according to various embodiments and 1,2-ethanedithiol nanocrystals / 7-diphenyl- 1,10-phenanthroline (EDT-NCs/Bphen) bilayer (400 nm pump with intensity of 15 μΐ cm"2) according to various embodiments at 2 ps after excitation; (c) plot of time (in picoseconds or ps) as a function of wavelength (in nanometer or nm) showing pseudocolor transient absorption (TA) spectra of 1,2-ethanedithiol-treated nanocrystals / 7-diphenyl-l,10- phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments excited with 400 nm light at pump intensity of 15 μΐ cm"2; and (d) plot of normalized negative transmittance change -ΔΤ/Τ as a function of time (in picoseconds or ps) showing normalized negative transient absorption spectra of Bphen excited with 300 nm light and 1,2- ethanedithiol-treated nanocrystals / 7-diphenyl-l,10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments pumped with 400 nm light and probed at 1300 nm. Solid lines are fitting curves with bi-exponential decay functions.
[00124] Notably, we also observed similar near-infrared (NIR) photoinduced absorption (PIA) signals for EDT-NCs/Bphen bilayer (in which only NCs were selectively excited) and the Bphen (above-bandgap excitation) (see FIG 28 and section on "PIA signal of transferred charge carriers in Bphen"), which could arise from the photogenerated radical anions in Bphen. Thus, the photoinduced absorption (PIA) signal in EDT-NCs/Bphen bilayer may be attributed to the population of transferred hot-carriers from NCs to Bphen (FIG. 28(b)). Nonetheless, there is also the possibility of an alternative explanation of excited singlet absorption induced by hot-state energy transfer from NCs to Bphen.
[00125] The efficiency of hot-electron extraction (τ/hot) may be estimated based on the percentage reduction of the band-edge photo-bleaching intensities at ~ 0.8 ps after adding Bphen (as when the hot-electrons are relaxed to the band-edges, the reduced band-edge bleaching intensity can then be attributed to the extraction of hot-carriers). Calculated hot for -35 nm thick EDT-NCs/Bphen bilayer is -72 % and -58 % at <N0> -0.1 and 2.5 pump intensities, respectively. The reduced multi-hot-electron injection efficiency at higher pump fluence may be due to the increased back-electron transfer from Bphen to the NCs with the estimated back-electron transfer time of -80 ps (FIG. 29 and section under "Estimation of back-electron transfer time").
[00126] FIG. 29 are plots of normalized transmittance change ΔΤ/Τ as a function of time (in picoseconds or ps) showing normalized band-edge bleaching dynamics of 1,2- ethanedithiol-treated nanocrystals (EDT-NCs) film according to various embodiments and 1,2-ethanedithiol-treated nanocrystals / 7-diphenyl-l,10-phenanthroline (EDT-NCs/Bphen) bilayer according to various embodiments under (a) low (<Vo>~0.1) and (b) high (<No> -2.5) pump fluence with 3.1 eV photoexcitation. FIG. 30A is a plot of normalized transmittance change ΔΤ/Τ as a function of energy (electronvolts or eV) showing normalized transient absorption spectra for annealed 1,2-ethanedithiol treated (EDT-treated) medium methylammonium lead bromide nanocrystals (MAPbBr3 NCs) film with (continuous lines) and without (dashed lines) 7-diphenyl-l,10-phenanthroline (Bphen) extraction layers according to various embodiments at low fluence with <No> - 0.1. Inset of FIG. 30A shows the un-normalized TA spectra at 0.8 ps. rjhot is determined to be -83 %. FIG. 30B is a plot of carrier temperature (in Kelvins or K) as a function of time (in picoseconds or ps) showing extracted hot-carrier temperature as a function of delay time for two samples according to various embodiments. FIG. 30C is a plot of normalized transmittance change ΔΤ/Τ as a function of energy (in electron volts or eV) showing normalized transient absorption (TA) spectra for methylammonium lead bromide (MAPbBr3) bulk-film (-240 nm thick) with (lines) and without (dashes) 7-diphenyl-l,10-phenanthroline (Bphen) extraction layers at low pump fluence with 2x 1017cm"3. Inset of FIG. 30C shows the un-normalized TA spectra at 0.8 ps. ^hot is determined to be -16 %. FIG. 30D shows a plot of carrier temperature (in Kelvins or K) as a function of time delay (in picoseconds or ps) for two samples according to various embodiments. The photoexcitation energy is 3.1eV.
[00127] Considering the voids in the NCs film (FIG. 23B AFM image), some Bphen molecules may penetrate the upper layer of NCs film, which could further enhance the hot- carrier extraction efficiency by increasing the NC/Bphen interfaces in the thinner NCs film/Bphen bilayers. Furthermore, moderate post-heating (e.g., at 70 °C for 5 mins) of EDT- NCs may not only further enhance the electronic coupling (see XPS spectra in FIG. 24 and under section on "FTIR and XPS analysis on ligand exchange") and rjhot to -83% (FIG. 30A), but also increased the Fermi-level of NCs relative to its valence band minimum (VBM) (FIG. 27) (possibly due to the sulfur doping during annealing). This may enable the extraction of hot-carriers with even higher excess energies above the band-edges (up to 0.5 + 0.1 eV) with Tc cooling from -1300 to 400 K (FIG. 30B).
[00128] Further proof of hot-electrons injection into Bphen may be revealed by the pump- energy dependent rjhot- As shown in FIG. 23F rjhot decreases from -72% to 15% with a reduction of the excess hot-carrier energies from -0.7 eV to 0.1 eV (using above bandedge excitation with pump energy from 3.1 eV to 2.5 eV). These results may validate that only hot carriers with sufficient excess energies can be injected into Bphen (consistent with the energy level diagram in Fig. 4a). They also demonstrate the high selectivity of using Bphen with narrow LUMO to extract the hot-electrons. Importantly, when the thickness of NCs film increases from -35 nm to -140 nm (FIG. 31), τ/hot drops dramatically from -72% to 20% following 3.1 eV photoexcitation (FIG. 23G). The reduced hot-electron extraction may be caused by the limited hot-electron diffusion/hopping range inside the NCs-films. FIG. 31 shows cross-sectional scanning electron microscopy (SEM) images of 1,2-ethanedithiol- treated nanocrystals (EDT-NCs film) with different thickness according to various embodiments. Scale bar in FIG. 31 (a) - (d) is 100 nm.
[00129] Comparatively, due to the initial rapid hot-carrier cooling, the rjhot of bulk- film/Bphen with thickness of -240 nm is -16 % with changing of T only from -450 to 380 K under similar photoexcitation conditions (FIGS. 30C-D). Even when the bulk- film thickness is reduced to -40 nm, rjhot may be still much smaller than EDT-NCs film.
[00130] In summary, it is found that colloidal MAPbBr3 NCs may exhibit approximately 2 orders slower hot-carrier cooling times and about 4 times larger hot-carrier temperatures as compared to perovskites bulk-films under similar photoexcitation conditions. Under low pump fluence, hot-carrier cooling in NCs may be mediated by the phonon bottleneck effect, which is surprisingly slower in smaller NCs (contrasting with conventional NCs). This finding contravenes the conventional understanding in traditional colloidal semiconductor nanocrystals that intraband Auger effects is more dominant with decreasing dimensionality, resulting in the breach of the phonon bottleneck. At high pump fluence, Auger heating dominates the hot-carrier cooling rate, which may be slower in larger NCs (previously unobserved in conventional NCs). Importantly, the augmented slow hot-carrier cooling in these colloidal perovskite nanocrystals may enable efficient hot-carrier extraction. It is demonstrated that the hot electrons with up to -0.6 eV excess energy can be efficiently injected (up to -83%) from surface-treated MAPbBr3 NCs films into electron extraction layers with an injection time of ~ 0.2 ps.
[00131] Hot-carrier properties in perovskites NCs may enable fresh opportunities for extremely thin absorber (ETA) and concentrator-type hot-carrier solar cells. For the former, ETA-solar cells may be conceptually close to dye-sensitized heterojunctions. The molecular dye may be replaced by an extremely thin (~ tens of nm) semiconductor absorber layer. By nano structuring the electrodes (e.g., using highly porous T1O2 scaffold, ZnO nanowire arrays etc.), the effective area covered by the thin absorber can be increased by several orders of magnitude due to the surface enlargement and multiple scattering. Most importantly, the ETA layer may be extremely beneficial for hot-carrier extractions owing to the shorter transport path length for hot-carriers. For the later, the illumination power in the concentrator- type solar-cells can be increased to 1000 suns, much larger than the 1-sun intensity in typical cells, the Auger-heating induced slower hot-carrier cooling in perovskite NCs may also be applicable.
[00132] Size-varied perovskites nanocrystals synthesis
[00133] Methylammonium lead bromide (MAPbBr3) nanocrystals (NCs) were synthesized by the ligand-assisted re-precipitation (LARP) method as reported by Zhang et. al. ("Brightly luminescent and colour tunable colloidal CH3NH3PBX3 (X=Br, I, CI) quantum dots: potential alternatives for display technology, ACS Nano 9, 4533-4542 (2015). At first in a glass vial, 0.16 mmol of methylammonium bromide (MABr), 0.2 mmol of lead bromide (PbBr2) were mixed in 5 mL dimethylformamide (DMF) solution. Later 50
Figure imgf000042_0001
of oleylamine (OAm) and 0.5 mL oleic acid (OAc) were also mixed in the DMF solution to form the final precursor solution. Another round bottom flask containing 5 mL of toluene was preheated to 60°C in an oil bath. Then 250
Figure imgf000042_0002
of as-prepared precursor solution was swiftly injected into hot toluene solution under vigorous stirring condition. The solution immediately turned green, confirming the formation of MAPbBr3 NCs. The reaction was continued for another 5 min and stopped by cooling in a water bath. The reaction solution was transferred into a centrifuge tube and centrifuged at the desired speed for different sized spherical shaped MAPbBr3 NCs. The precipitation of MAPbBr3 NCs was re-dissolved in toluene solution for further studies. For small, medium and large sized NCs, the precipitate was separated by using centrifuge speed of 12000 rpm, 8000 rpm and 4000 rpm, respectively. The mean diameters are ~ 4.9, 8.9 and 11.6 nm for small, medium and large sized NCs, respectively (FIG. 6).
[00134] MAPbBr bulk-film fabrication
[00135] A solution containing 0.6 M MAPbBr3 in DMF was spin-coated (5000 rpm, 12 s) on quartz substrates. During spin-coating, few drops of toluene were added to the film at 3 s after the beginning of spinning. The film was then dried in room temperature for 30 minutes and annealed at 70 °C for 5 minutes. All the film deposition and annealing was done in N2- filled glove box. The grain size of bulk-film is larger than ~1 μιη and the thickness is around 240 nm (FIG. 7).
[00136] MAPbBr NCs and EDT-treated MAPbBr NCs films fabrications
[00137] MAPbBr3 NCs film and 1,2-ethanedithiol (EDT)-treated NCs were grown by a layer-by-layer spin-coating processing method. All the spin-coating steps were set at 1000 rpm and spin-time was fixed for 30 s. To prepare the NCs film, NCs in toluene (10 mg ml"1) was spin-coated on glass substrates for two layers. For the EDT-treatment of NCs film, the growth of each layer of EDT-treated NCs film consisted of three steps: (1) spin-coating of NCs solution on top of substrate; (2) cover the NCs film with 0.2 M EDT solution in 2- Propanol and wait for 30 s and then spin-coat; (3) dropping of anhydrous toluene on film and followed by spin-coating to clean the remaining long chained ligands. The above process was repeated for 2-10 times to obtain the NCs-film with different thickness. For post-annealed samples, the annealing was performed at 70 °C for 5 mins. All processing was performed in a N2-filled glove box.
[00138] Bphen thin film fabrication
[00139] 4,7-diphenyl-l,10-phenanthroline (bathophenanthroline, or Bphen) was deposited through a thermal evaporation method under a pressure of 10"6 torr. Bphen was deposited on spin-coated non-annealed or annealed perovskites NCs films at a rate of 0.1-0.2 nm s"1.
[00140] CdSe nanocrystals
[00141] CdSe nanocrystals dispersed in toluene were purchased from Sigma-Aldrich Co. LLC.
[00142] TA measurements
[00143] Transient absorption (TA) measurements in the time range of fs-ns were performed using a Helios spectrometer (Ultrafast Systems, LLC). The pump pulse was either generated from an optical parametric amplifier (Coherent OPerA Solo™ or Light Conversion TOPAS- C™) that was pumped by a 1-kHz regenerative amplifier (i.e., Coherent Libra™ (50 fs, 1 KHz, 800 nm) or Coherent Legend™ (150 fs, 1 KHz, 800 nm)) or by frequency doubling the 800-nm fundamental regenerative amplifier output with a BBO crystal to obtain 400 nm pulses. Both systems were seeded by mode-locked Ti-sapphire oscillators (Coherent Vitesse™, 80 MHz). The white light continuum probe beam (in the range from 400 nm-1500 nm) was generated by focusing a small portion (~ 10 uJ) of the regenerative amplifier's fundamental 800 nm laser pulses into either a 2-mm sapphire crystal (for visible range) or a 1 cm sapphire crystal (for NIR range). The probe beam was collected using a CMOS sensor for UV-VIS region and InGaAs diode array sensor for NIR region. The samples were kept in a N2-filled chamber at room temperature during measurements. For the hot-carrier extraction measurements, the pump beam excited the samples from the side of Bphen based on the sample structure of Bphen/perovskite/glass substrate.
[00144] PL and time-resolved PL measurements
[00145] Steady-state PL spectra were collected in a conventional backscattering geometry and detected by a charge-coupled device array (Princeton Instruments, Pixis™) coupled to a monochromator (Acton, Spectra Pro™). The temporal evolution of PL was resolved by an Optronis Optoscope™ streak camera system. The excitation source is the same regenerative amplifier (Coherent Libra™) and optical parametric amplifier (Coherent OPerA Solo™) described above. All the above measurements were performed at room temperature.
[00146] TEM, AFM and SEM measurements
[00147] The shape and size of the NCs were determined by transmission electron microscopy (TEM, JEOL JEM-2010). The surface morphology of the perovskite NCs-films was recorded by atomic force microscopy (AFM, Asylum Research MFP-3D) with a silicon cantilever operating in tapping force mode. The morphology and thickness of samples were characterized by scanning electron microscopy (SEM, JEOL, JSM-7600F)
[00148] UPS and XPS measurements
[00149] Ultraviolet photoelectron spectroscopy (UPS) was used to investigate the interfacial energy level alignment of the valence occupied states. The spectra collection was performed with the same instrument as that in XPS. The excitation source is He-I (h = 21.2 eV) with lamp power at 50 W. Photoelectrons were collected at surface normal using CAE mode with 2.00 eV pass energy with the samples biased at -10 V. X-ray photoelectron spectroscopy (XPS) was performed to analyze the composition of samples. Samples were transferred to an ultra-high vacuum (UHV) analysis chamber from the glove box through an air-tight sample transfer containment. The pressure of the UHV chamber was held under lxlO"9 torr. Al Ka (hv = 1486.6 eV) photon source at 200 W were used to excited the sample, while spectra collection was performed through a hemispherical electron energy analyzer (Omicron EA- 125). The measurements were performed at room temperature, with photoelectrons collected along surface normal direction.
[00150] XRD, UV-VIS, AR-FTIR and Raman measurement
[00151] The crystal structures were analyzed by powder X-ray diffraction (XRD, Bruker D8 Advance). The absorption spectra were recorded using a UV-VIS spectrometer (SHEVIADZU UV-3600 UV-VIS-NIR Spectrophotometer) with an integrating sphere (ISR- 3100). FTIR spectra of the all samples were measured by a Frontier FT-IR/NIR spectrometer (PerkinElmer, Waltham, MA, USA) equipped with a universal attenuated total reflection (ATR) sampling accessory (PerkinElmer, Waltham, MA, USA). Raman spectra were recorded with a WITec Raman microscope (WITec GmbH, Ulm, Germany) using a 633 nm HeNe laser as the excitation source.
[00152] Hot carrier lifetimes
[00153] It is important to note the complex interplay of the hot-carrier cooling times due to several factors:
[00154] (i) the pump energy (i.e., carriers' excess energy - typically, higher the excess energies lead to longer hot carrier lifetimes);
[00155] (ii) the initial hot-carrier densities (i.e., typically higher carrier densities lead to longer hot carrier lifetimes); and
[00156] (iii) the energy loss rate at a specific hot-carrier temperature (as shown in FIG. 17a where the energy loss rate changes over several orders of magnitude for hot-carrier temperatures spanning from 1600 to 300K) - typically, lower hot carrier temperatures yield smaller energy loss rates. (It should be noted that the listed lifetimes are the time intervals from pulse excitation until the cooling of hot-carriers reach 600 K.)
[00157] Without specifying the above parameters/conditions, it is difficult to generalize and very unfair to compare the hot-carrier lifetimes among different materials. Furthermore, the measured hot-carrier lifetime could be limited by the time-resolution of the experimental techniques used, thereby yielding artificially longer lifetimes that are limited by the system temporal response rather than its intrinsic hot-carrier lifetime. For example, measurement of the hot-carrier lifetime by the time-resolved photoluminescence (TRPL) technique using a streak camera or time related single photon counting (TCSPC) system may be constrained by the system resolution of these equipment (i.e., -10 ps for most streak cameras, as high as ~1 ps for Hamamatsu systems and typically -50 ps for TCSPC systems). On the other hand, the TA or fluorescence upconversion PL techniques have much higher system temporal response of < 150 fs, which would identify more authentic hot carrier lifetimes of the material. Hence, due care must be taken for a fair comparison of the reported values in the literature.
[00158] To ensure a fair comparison of the hot-carrier temperature and cooling dynamics, an extensive compilation of the materials complete with the consideration of the abovementioned parameters (i.e., carrier densities, carrier temperatures, pump energies and techniques) is presented in FIG. 14. Furthermore, it should be noted that the hot-carrier cooling lifetime in FIG. 14 is defined as the time interval from pulse excitation until the cooling of hot-carriers reach 600 K (for point (iii) above). This temperature is used as the benchmark because previous theoretical calculations have shown that for T > 600 K, there may still be an appreciable hot-carrier conversion efficiency (i.e., > 40%) over a wide range of absorber bandgaps). As the hot carrier distribution approaches thermal equilibrium with the lattice (300 K), the energy-loss rate may become much slower (see FIG. 17(a)). Although these pseudo "hot-carriers" give rise to a long lifetime, they may in fact have little contribution to the operation of a hot-carrier solar-cell. Therefore, this should not be compared here.
[00159] LQ-phonon model
00160 The ener loss rates er carrier J was determined b extracted Tc with - —
Figure imgf000046_0001
where Tlo is the characteristic LO-phonon decay time, ΤΆ is the acoustic phonon temperature, hm0 is the phonon energy (-42 meV) and NUJ(T) is the LO-phonon occupation number at temperature T. The fitting from Fig. 2a yielded a comparable TD for the MAPbBr3 NCs (-310 K) and bulk- film (-305 K), while TLO is -340 fs, 220 fs and 180 fs for small, medium and large NCs, respectively, in contrast to a fast Tlo of - 150 fs for the bulk-film.
[00161] Auger-heating Model [00162] Auger decay lifetimes of MAPbBr3 NCs are extracted from the pump fluence dependent band-edge photobleaching dynamics (FIG. 16(f)), which exhibit a sublinear dependence on the NC volume (VNC) as ΤΑ¾ ~ V(VNC ) (FIG. 20(a)). This behavior agrees with recent observations of biexciton Auger recombination in weakly confined CsPbBr3 NCs, but contrasts with the linear dependence of ΤΑ¾ on NC size for strongly confined systems. The sublinear dependence can therefore be attributed to the weaker confinement in our perovskites NCs.
[00163] Given that Auger recombination is a three-particle process, the Auger-heating rate in NCs is therefore proportional to ~n3, where n is the effective carrier density at the band- edge. Hence, the evolution of the hot-carrier population can be described by the following equation:
^ = -Anhot + Cn3 (4) where the first term represents the relaxation of the hot-carriers unrelated to Auger heating, and the second term corresponds to the Auger heating contribution; C refers to the Auger recombination coefficient of the carriers at the band-edge. Within the lifetimes of the hot- carriers, one can neglect single exciton recombination given its long lifetime (of several ns). As a first approximation, the band-edge carriers recombine through the dominant Auger process given by: n(t)~e _t/TAu§. Direct integration of this equation yields the time evolution of: nhot(t) = nhot0(l - O)e~At + De~3t^ (5) where nhoto is the initial population of the generated hot-carriers and D equals to c/(A-3/TAug). Equation (4) therefore predicts that the hot-carrier population decays bi-exponentially, with one of its lifetime corresponding to TAug/3.
[00164] Considering the Fermi-Dirac distribution of hot-carriers, the effective hot-carrier
[00165] FIG. 20(c) shows the normalized calculated hot-carrier densities as a function of decay time at different pump fluences.
[00166] Estimation of Hot-Carrier Diffusion Length
[00167] The hot-carrier diffusion length in MAPbBr3 can be estimated as follows. Firstly, the carrier's diffusion coefficient depends on the defect density of the fabricated material. The reported electron diffusion coefficient D may range from ~1 cmV1 for polycrystalline perovskite thin films to 5 - 8 cmV1 for bulk MAPbBr3 at room temperature (-300 K). Secondly, D may also depend on the carrier temperatures (T ) in the relation D= μκΒ TJe. For NCs-film, taking 800 K as the average hot-carrier temperature, the lower D value of 1 cmV1, and hot-carrier lifetime of 1 ps at low pump fluence, the hot-carrier diffusion length may be obtained by
Figure imgf000048_0001
Xhot )~16 nm. The high pump fluence at hot-carrier lifetime of -32 ps yields a diffusion length of L~90 nm. Considering that the perovskites/Bphen sample was excited at the Bphen side, and the initial exponential carrier distribution in semiconductors after fs laser pulse excitation, higher concentration of hot-carriers in perovskites closest to the Bphen may thus be more easily injected into Bphen. For NCs-film, given that some Bphen molecules could penetrate into the upper layer of the NCs film, and the hot-carriers undergoing rapid hopping, the extracted -70% hot-carrier transfer efficiency for -35 nm thick NCs-film at low pump fluence may therefore be reasonable. For bulk-film, taking 400 K as the average hot-carrier temperature, the higher D values of 5 cmV1, and hot-carrier lifetime of 0.15 ps at low pump fluence, the hot-carrier diffusion length may be -10 nm. Therefore, the -15% transfer efficiency for bulk-film may also be reasonable.
[00168] FTIR and XPS analysis on ligand exchange
[00169] FTIR spectroscopy of EDT-treated MAPbBr3 NPs revealed highly efficient removal of the original oleic acid and oleylamine ligands (FIG. 24). The removal of these ligands is clearly observed from the reduction of the CH2 stretching at 2921 and 2841 cm"1. The complete removal of C=0 stretch at 1710 cm-1 along with the disappearance of wagging vibration of N-H at 800 cm-1 and C-O-H bond at 1384 cm-1 further supports the EDT ligand exchange of oleic acid and oleylamine ligands.
[00170] XPS analysis of Sulphur in non-annealed and post-annealed EDT-treated
MAPbBr3 NCs reveals two sets of S 2p doublets, with the 2p3/2 peak position at binding energies -162.5 eV and -164.2 eV (-162.7 eV and -164.3 eV for post-annealed) arising from bound thiolate and unbounded thiol of EDT to the surface of the NC respectively (FIG. 24).
The ratio of bound-to-unbound thiol groups in the NC without post- annealing is -1.04, which increases to -1.47 with post-annealing of the NC at 70 °C. Thus, post-annealing treatment further increases the electronic coupling of EDT-NCs with Bphen.
[00171] Effects of photocharged NCs and trions in NCs films on hot-carriers
[00172] FIG. 16(e) shows the comparison of photobleaching dynamics at the band-edges between medium NCs in solution and spin-coated film. From the exponential fitting (solid curves), the lifetime changes from ~ 4.5 to ~3 ns at low pump fluence, the acceleration may be due to the existence of the photocharged NCs. At high pump fluence, another fast decay with lifetime of ~ 290 ps except for the Auger recombination may emerge in the spin-coated NCs films, which can be attributed to trions (photocharged excitons). However, they only induced the broadening in the lower energy side of GSB (see the appearance of a bleaching tail at lower energy side for NCs-films in FIG. 26 as compared with FIG. 10 for NCs in solution in the pseudo color TA spectra). The reduced energy of trions may be due to the exciton-exciton interactions. The trions in the NCs-film may not affect the dynamics of hot- carriers located at the higher energy side of the GSB.
[00173] Control experiments to validate the hot-carrier transfer
[00174] The MAPbBr3 NCs films demonstrate similar hot-carrier cooling dynamics with/without the EDT-treatment. Without the EDT-treatment, the NCs demonstrate similar hot-carrier cooling dynamics with/without the Bphen extraction layer. Furthermore, we did not find any obvious change in the hot-carrier properties in the NCs films that underwent the exact same processing in the thermal evaporator except no Bphen layer was actually deposited.
[00175] PIA signal of transferred charge carriers in Bphen
[00176] For the pristine Bphen film, upon excitation above band-gap with 300 nm light (refer to the absorption spectrum in FIG. 28(a), there is a very broad photoinduced absorption (PIA) in NIR range (FIG. 28(b)), typical of organic semiconductors (e.g., P3HT, PCBM). Its intensity increases gradually with increasing probe wavelength. The PIA bands may be tentatively assigned primarily to the absorption by the photogenerated radical anions in Bphen. Control experiments with 400 nm excitation (below bandgap) of Bphen (at both low and high pump fluence) yielded a null (PIA) signature (FIG. 28(b)), indicating the absence of photogenerated radical anions in Bphen.
[00177] For the EDT-NCs/Bphen sample (with NCs-film thickness ~ 50 nm), the NCs are selectively excited with 400 nm light. At low pump fluence, there may be no measureable TA signal. This could be due to the even weaker TA signal (of the indirectly generated radical anions) that is below the detection limit of the TA setup (at 10"4 ΔΤ/Τ). At higher pump fluence (i.e., at -15 μΐ cm"2' corresponding to <V>~2.5), a weak PIA band similar to pristine Bphen may be observed (FIG. 28(b) and FIG. 28(c)). However, any further increase of pump power may lead to the degradation of the perovskite. [00178] The control experiments also show that there is no TA signal from the EDT- NCs/Bphen sample under 500 nm excitation (i.e., with negligible excess energies for photoexcited carriers in NCs) and NCs film alone under 400 nm excitation (FIG. 28(b)) up to high pump fluence. These experiments therefore indicate that the observation of PIA in EDT- NCs/Bphen hybrids may be caused solely by the hot-charge carrier injection into Bphen from the NCs.
[00179] Furthermore, the relaxation of PIA may possess one fast decay lifetime (-70 ps for pristine Bphen, and -25 ps for NCs/Bphen) and one slow decay lifetime (-1 ns for pristine Bphen, and -0.5 ns for NCs/Bphen) (FIG. 28(d) The fast decay may be due to the carrier trapping to defects for pristine Bphen and additional electron back- transfer to the NCs for NCs/Bphen. The slow decay may be due to the recombination of radical anions/excitons in the Bphen and with holes in NCs in the NCs/Bphen hybrids. Lastly, considering the smaller energy difference between hot-electrons and hot-holes (-3.1 eV at most extreme case) in NCs as compared to the bandgap of Bphen (3.5 eV), the generation of carriers in Bphen via energy transfer from hot-carrier recombination may be highly unlikely.
[00180] Estimation of back-electron transfer time
[00181] The back transfer of injected electrons from Bphen to NCs may induce an increase of the relaxation time of electrons in NCs in the TA signal. A back-electron transfer rate (1/xbk) may be estimated from the change of the relaxation rate of NCs' bandedge bleaching between EDT-NCs film (1/XNC ) and EDT-NC/Bphen bilayers (1/XNC/BP) ) by 1/xbk =1/XNC -
[00182] At low pump fluence ( <No>~0.1), the invariance in the relaxation dynamics for the EDT-NCs film and the EDT-NC/Bphen bilayers (FIG. 29 (a)) indicates a very small back- electron transfer rate and a long back transfer time beyond our measurement time window, which may be due to the rapid trapping and localization that hinder the carriers from drifting back to the NCs film. The long Xbk therefore is beneficial for the hot-electron injection. At high pump fluence (<No> -2.5), there is an obvious lengthening of XNC/BP (FIG. 29). Using the above relation, the estimated back-electron time Xbk is -80 ps. The reduced back-electron transfer time (i.e., increased back-electron transfer rate) is consistent with the reduced hot- electron injection efficiency from 72% at <No>~0.1 to 58% at <No> -2.5.
[00183] While the invention has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

A hot-carrier solar cell comprising:
a nanocrystal containing layer comprising one or more nanocrystals, each of the one or more nanocrystals comprising a halide perovskite material;
a first electrode in contact with a first side of the nanocrystal containing layer; and
a second electrode in contact with a second side of the nanocrystal containing layer opposite to the first side;
wherein the nanocrystal containing layer has a thickness of less than 100 nm.
The hot-carrier solar cell according to claim 1, further comprising:
an optical arrangement that is configured to direct solar energy to the nanocrystal containing layer.
The hot-carrier solar cell according to claim 2,
wherein the optical arrangement comprises one or more optical elements configured to direct solar energy to the nanocrystal containing layer.
The hot-carrier solar cell according to claim 3,
wherein the one or more optical elements are optical lenses.
The hot-carrier solar cell according to any one of claims 1 to 4,
wherein the first electrode is a hot-electron extraction layer comprising any one material selected from a group consisting of titanium oxide, zinc oxide, phenyl-C61 -butyric acid methyl ester (PCBM), 4,7-diphenyl-l,10- phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK),
2-(4-biphenylyl)-5- phenyl-l,
3,
4-oxadiazole (PBD), 2,2',2"-(l,3,
5-benzinetriyl)-tris(l-phenyl-l-H benzimidazole) (TPBI), poly(9,9-dioctylfluorene) (F8), and bathocuproine (BCP).
6. The hot-carrier solar cell according to any one of claims 1 to 5, wherein the second electrode is a hot-hole extraction layer comprising any one material selected from a group consisting of 2,2',7,7'-tetrakis[N,N-di(4- methoxyphenyl)amino]-9,9'-spirobifluorene (spiro-OMeTAD), poly(3- hexylthiophene-2,5-diyl) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS), and poly(9,9-dioctyl-fluorene-co-N-(4- butylphenyl)diphenylamine) (TFB ) .
The hot-carrier solar cell according to any one of claims 1 to 6,
wherein the first electrode is an energy selective contact which is configured to allow electrons having excess energies at or above a predetermined value to pass through, and further configured to reflect electrons having excess energies below the predetermined value back to the nanocrystal containing layer.
The hot-carrier solar cell according to any one of claims 1 to 7,
wherein the second electrode is an energy selective contact which is configured to allow holes having excess energies at or above a predetermined value to pass through, and further configured to reflect holes having excess energies below the predetermined value back to the nanocrystal containing layer.
The hot-carrier solar cell according to any one of claims 1 to 8,
wherein the one or more nanocrystals exhibit a hot-carrier cooling lifetime of above 30 ps.
The hot-carrier solar cell according to any one of claims 1 to 9,
wherein a radius of each of the one or more nanocrystals is any one value selected from 2 nm to 7 nm.
The hot-carrier solar cell according to any one of claims 1 to 10,
wherein the halide perovskite material is an organic-inorganic halide perovskite material.
12. The hot-carrier solar cell according to any one of claims 1 to 10,
wherein the halide perovskite material is an inorganic halide perovskite material.
13. A method to form a hot-carrier solar cell, the method comprising:
providing a nanocrystal containing layer comprising one or more nanocrystals, each of the one or more nanocrystals comprising a halide perovskite material; forming a first electrode so that the first electrode is in contact with a first side of the nanocrystal containing layer; and
forming a second electrode layer so that the second electrode is in contact with a second side of the nanocrystal containing layer opposite to the first side; wherein the nanocrystal containing layer has a thickness of less than 100 nm.
14. The method according to claim 13, the method further comprising:
forming an optical arrangement configured to direct solar energy to the nanocrystal containing layer.
15. The method according to claim 14,
wherein the optical arrangement comprises one or more optical elements configured to direct solar energy to the nanocrystal containing layer.
16. The method according to claim 15,
wherein the one or more optical elements are optical lenses.
17. The method according to any one of claims 13 to 16,
wherein the first electrode is a hot-electron extraction layer comprising any one material selected from a group consisting of titanium oxide, zinc oxide, phenyl-C61 -butyric acid methyl ester (PCBM), 4,7-diphenyl-l,10- phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4-biphenylyl)-5- phenyl-l,3,4-oxadiazole (PBD), 2,2',2"-(l,3,5-benzinetriyl)-tris(l-phenyl-l-H- benzimidazole) (TPBI), poly(9,9-dioctylfluorene) (F8), and bathocuproine (BCP).
The method according to any one of claims 13 to 17,
wherein the second electrode is a hot-hole extraction layer comprising any one material selected from a group consisting of 2,2',7,7'-tetrakis[N,N-di(4- methoxyphenyl)amino]-9,9'-spirobifluorene (spiro-OMeTAD), poly(3- hexylthiophene-2,5-diyl) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS), and poly(9,9-dioctyl-fluorene-co-N-(4- butylphenyl)diphenylamine) (TFB ) .
The method according to any one of claims 13 to 18,
wherein the second electrode is an energy selective contact which is configured to allow holes that have excess energies at or above a
predetermined value to pass through, and further configured to reflect holes that have excess energies below the predetermined value back to the nanocrystal containing layer.
The method according to any one of claims 13 to 19,
wherein the first electrode is an energy selective contact which is configured to allow electrons having excess energies at or above a predetermined value to pass through, and further configured to reflect electrons that have excess energies below the predetermined value back to the nanocrystal containing layer.
The method according to any one of claims 13 to 20,
wherein the one or more nanocrystals exhibit a hot-carrier cooling lifetime of above 30 ps.
The method according to any one of claims 13 to 21,
wherein a radius of each of the one or more nanocrystals is any one value selected from 2 nm to 7 nm. The method according to any one of claims 13 to 22,
wherein the halide perovskite material is an organic-inorganic halide perovskite material.
The hot-carrier solar cell according to any one of claims 13 to 22,
wherein the halide perovskite material is an inorganic halide perovskite material.
PCT/SG2017/050365 2016-07-27 2017-07-20 Hot-carrier solar cell, and method to form the same WO2018021966A2 (en)

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