WO2018142321A1

WO2018142321A1 - Nanostructured subcells with high transparency in multi-junction pv applications

Info

Publication number: WO2018142321A1
Application number: PCT/IB2018/050634
Authority: WO
Inventors: Nicklas Anttu; Jonas Ohlsson; Ingvar Aberg
Original assignee: Sol Voltaics Ab
Priority date: 2017-02-02
Filing date: 2018-02-01
Publication date: 2018-08-09
Also published as: TW201840013A

Abstract

A method of making a stacked tandem photovoltaic device including determining nanostructure and index of refraction parameters of subcells of the stacked tandem photovoltaic device to reduce in-plane waveguiding of light incident on the stacked tandem photovoltaic device, providing a first photovoltaic subcell, the first photovoltaic subcell comprising nanostructures based on the step of determining and providing a second photovoltaic subcell based on the step of determining. The first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap. Light incident on the stacked tandem photovoltaic device passes through the first photovoltaic subcell before entering the second photovoltaic subcell.

Description

NANOSTRUCTURED SUBCELLS WITH HIGH TRANSPARENCY IN MULTI- JUNCTION PV APPLICATIONS

FIELD

[0001] The present invention is directed generally to photovoltaic cells and specifically to tandem photovoltaic cells.

BACKGROUND

[0002] III-V semiconductor nanowires are a platform for next-generation photovoltaic s. A nanowire array embedded in a transparent polymer, can either act as a stand-alone flexible solar cell, or be stacked on top of a conventional Si bottom cell to create a tandem structure. To optimize the tandem cell performance, high energy photons should be absorbed in the nanowires whereas low energy photons should be transmitted, and absorbed in the Si cell.

[0003] III-V nanowire arrays have shown promise for photovoltaics with a demonstrated efficiency of 13.8 % for InP nanowires and 15.3 % for GaAs nanowires. Theoretical modeling has shown that the absorption of light in such arrays can be nearly as efficient as in a

corresponding bulk cell.

SUMMARY

[0004] An embodiment is drawn to a method of making a stacked tandem photovoltaic device including determining nanostructure and index of refraction parameters of subcells of the stacked tandem photovoltaic device to reduce in-plane waveguiding of light incident on the stacked tandem photovoltaic device, providing a first photovoltaic subcell, the first photovoltaic subcell comprising nanostructures based on the step of determining and providing a second photovoltaic subcell based on the step of determining. The first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap. Light incident on the stacked tandem photovoltaic device passes through the first photovoltaic subcell before entering the second photovoltaic subcell.

[0005] Another embodiment is drain to photovoltaic device comprising a first photovoltaic subcell comprising nanostructures, wherein at least one feature in the first photovoltaic subcell reduces or eliminates reflection loss due to in-plane waveguiding of incident light when the first photovoltaic cell is located over a second photovoltaic cell in a stacked tandem photovoltaic device, and wherein the first photovoltaic cell is configured to permit light incident on the stacked tandem photovoltaic device to passes through the first photovoltaic subcell before entering the second photovoltaic subcell. Another embodiment is drawn to a stacked tandem photovoltaic device including the first photovoltaic subcell comprising nanostructures, and a second photovoltaic subcell. The first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap. At least one feature in the stacked tandem photovoltaic device reduces or eliminates reflection loss due to in-plane waveguiding of incident light on the stacked tandem photovoltaic device. Light incident on the stacked tandem photovoltaic device passes through the first photovoltaic subcell before entering the second photovoltaic subcell.

[0006] Another embodiment is drawn to a method of operating a stacked tandem photovoltaic device comprising receiving incident light on a first photovoltaic subcell comprising

nanostructures such that at least a portion of the incident light passes through the first photovoltaic subcell and enters a second photovoltaic subcell, and generating a current or voltage from the first and the second photovoltaic subcells. In an embodiment, the current or voltage in the first photovoltaic subcell and the second photovoltaic subcell may be generated and output separately, i.e., independently, from each other using separate subcell electrodes. The first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap, and at least one feature in the stacked tandem photovoltaic device reduces or eliminates reflection loss due to in-plane waveguiding of the incident light.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIG. 1 is a schematic illustration of a stacked tandem photovoltaic cell according to an embodiment.

[0008] FIGs. 2A and 2B are schematic illustrations of conventional stacked tandem photovoltaic cells. FIG. 2C is a schematic illustration of a stacked tandem photovoltaic cell according to an embodiment.

[0009] FIGs. 3A-3D are schematic illustrations of embodiments of a stacked tandem

photovoltaic cell.

[0010] FIG. 4 is a schematic illustration of nanowire subcell showing (1) incident light, (2) reflected light, (3) transmitted light, and (4) waveguiding in the plane of the nanowire array.

[0011] FIG. 5A is a schematic illustration of a GaAs nanowire array on top of a Si substrate according to an embodiment.

[0012] FIG. 5B is a schematic illustration of a GaAs nanowire array within a membrane having an index of refraction n = 1.5.

[0013] FIGs. 6A-6C are plots of the current density as a function of nanowire diameter and pitch of a GaAs nanowire array directly on Si substrate with a membrane having an n = 1.5 between and on top of nanowires. In an embodiment, the GaAs nanowires of the nanowire array comprise GaAs p-n or p-i-n junction solar cells. FIG. 6A illustrates the current density of the nanowires J^'NW_S- FIG. 6B illustrates the current density of the silicon substrate: FIG. 6C illustrates the current density of the reflection loss

[0014] FIGs. 7A-7F are plots of the current density as a function of nanowire diameter and pitch of a GaAs nanowire array with a membrane having an

between and on top of nanowires. FIG. 7A illustrates the current density of the nanowires

FIG. 7B illustrates the current density of the silicon substrate: j i- FIG. 7C illustrates the current density of the reflection loss Jsi,R-ioss- FIG. 7D illustrates the current density of the reflection loss jsi,R ioss for nanowires having a length of 500nm. FIG. 7E illustrates the current density of the reflection loss jsi,R ioss for nanowires having a length of 3000nm. FIG. 7F illustrates the current density of the reflection loss jsi,R-ioss for nanowires having a length of 6000nm.

[0015] FIGs. 8A-8E are plots of the current density as a function of nanowire diameter and pitch of a GaAs nanowire array on substrates of varying refractive index. The nanowires have n = 1.5 material between and on top of them.

[0016] FIG. 9A is a schematic diagram illustrating reflection loss in a nanowire array on a silicon substrate.

[0017] FIG. 9B is a schematic diagram illustrating reflection loss in a nanowire array with a spacer layer on a silicon substrate.

[0018] FIG. 9C is a plot of the current density as a function of nanowire diameter and pitch of a GaAs nanowire array on a silicon substrate.

[0019] FIG. 9D is a plot of the loss of current density due to reflection as a function of the size of the gap between the nanowires and the substrate for an array having nanowires with a diameter of 300nm, a pitch of 500 nm and a length of 3000nm.

[0020] FIG. 9E is a plot of the loss of current density due to reflection as a function of the size of the gap between the nanowires and the substrate for an array having nanowires with a diameter of 180nm, a pitch of 350 nm and a length of 3000nm.

[0021] FIG. 10A is a schematic illustration of a nanowire subcell with an encapsulation layer having an index of refraction of n=1.5 on a substrate having an index of refraction of n=3.0.

[0022] FIG. 10B is a plot of the current density as a function of nanowire diameter and pitch illustrating the reflective loss of the device of FIG. 10A.

[0023] FIG. IOC is a schematic illustration of a nanowire subcell with an encapsulation layer having an index of refraction of n=3.0 on a substrate having an index of refraction of n=3.0.

[0024] FIG. 10D is a plot of the current density as a function of nanowire diameter and pitch illustrating the reflective loss of the device of FIG. IOC.

[0025] FIG. 11 A is a schematic illustration of a nanowire subcell with a membrane layer having an index of refraction of n=1.5-3.5 and window layers having an index of refraction of 1.5 above and below the nano wires.

[0026] FIGs. 1 IB- 1 IF are plots of the current density as a function of nanowire diameter and pitch of the subcell illustrated in FIG. 11 A illustrating the reflection loss for varying refractive indices of the membrane layer.

[0027] FIG. 12A is a schematic illustration of a nanowire subcell with a membrane layer, indium tin oxide (ΓΓΌ) layers above and below the nanowires and window layers having an index of refraction of 1.5 above and below the ITO layers.

[0028] FIGs. 12B-12F are plots of the current density as a function of nanowire diameter and pitch of the subcell illustrated in FIG. 12A illustrating the reflection and absorption loss in the presence of the ITO layers.

[0029] FIG. 13 A is a schematic illustration of a nanowire subcell with a membrane layer, indium tin oxide (ΓΓΌ) layers above and below the nanowires and window layers having an index of refraction of 1.5 above and below the ITO layers and a silicon substrate.

[0030] FIGs. 13B and 13C are plots of the current density as a function of nanowire diameter and pitch of the subcell illustrated in FIG. 13A illustrating the reflection and absorption loss in the presence of the ITO layers and a silicon substrate.

[0031] FIGs. 14A-14C are plots of the current density as a function of nanowire diameter and pitch of GaAs nanowire arrays in a membrane having an index of refraction of n= 1.5 on a silicon substrate. FIG. 14A illustrates the current density of the nanowires. FIG. 14B illustrates the current density of the silicon substrate in the silicon bottom cell. FIG. 14C illustrates the current density due to the reflection loss.

[0032] FIGs. 14D-14F are plots of the current density as a function of nanowire diameter and pitch of a 1.7 eV bandgap GaAsP nanowire arrays in a membrane having an index of refraction of n=1.5 on a silicon substrate. FIG. 14D illustrates the current density of the nanowires. FIG. 14E illustrates the current density of the silicon substrate in the silicon bottom cell. FIG. 14 illustrates the current density due to the reflection loss.

[0033] FIGs. 15A-15C are plots of the current density as a function of nanowire diameter and pitch of a square GaAs nanowire array in a membrane having an index of refraction of n= 1.5 on a silicon substrate.

DETAILED DESCRIPTION

[0034] To optimize the absorption of sun light in a direct bandgap III-V semiconductor nanowire solar cell (i.e., photovoltaic cell) array, the guided modes in the individual nanowires may play a role. As used herein, "solar cell" has the same meaning as "photovoltaic cell". Absorption peaks due to resonant absorption of such single-nanowire modes red-shift with increasing diameter. By placing one of these absorption peaks close to the band gap of the nanowire material, the absorption in the nanowires can be enhanced in this close-to-bandgap wavelength region where the absorption coefficient of the III-V material is low.

[0035] In this way, there is a set of diameters for which the absorption of sunlight in the nanowires may be optimized. At each such diameter, one of the single-nanowire modes is placed close to the bandgap wavelength. For the chosen diameter, the length of the nanowires and the pitch of the nanowire array may be optimized. Typically, the optimum pitch increases with increasing nanowire length. This behavior is ascribed to the following physics: (1) with increasing pitch, the reflection at the top interface of the nanowire array decreases, (2) with increasing pitch, there is a smaller amount of absorbing material in the nanowire array, so the absorption drops and (3) by increasing the length of the nanowires, that drop in absorption can be compensated for. Therefore, it is preferable to increase the pitch to decrease the in-coupling reflection losses for light entering the nanowire array. However, the pitch cannot be increased without limit. This is because at some point the absorption will drop more than the reflection. The pitch at which the absorption drop and the reflection drop balance each other increases with increasing nanowire length.

[0036] Conventionally, the absorption in a nanowire array is optimized without emphasis on transmission of below-bandgap photons. However, in a tandem solar cell with a nanowire- array subcell on top of a lower bandgap subcell, such transmission is of high importance. As used herein, the nanowires of the nanowire array comprise GaAs p-n or p-i-n junction solar cells (or subcells of a tandem solar cell). The junctions may be axial and/or radial with respect to the elongation direction of the nanowire.

[0037] A tandem cell may be formed by epitaxially growing III-V nanowires directly on top of a Si cell. A nanowire is a structure with a diameter (or width in the case of hexagonal shaped nanowires) less than 1 micron, such as 10-500 nm. The length may be greater than 1 micron. The length to diameter/width ratio may be 10: 1 or greater. Alternatively, the III-V nanowires may be grown separately and then placed on top of a Si cell by embedding the nanowires in a transparent polymer and/or inorganic dielectric (e.g., by embedding the nanowire solar cells containing a p-n or p-i-n junction in a dielectric membrane). This latter approach is compatible with aerotaxy, the high-throughput, low-cost, substrate-free nanowire fabrication technique, as well as with traditional VLS-based nanowire growth combined with subsequent removal of the nanowires from the growth substrate in a peel-able polymer membrane. Preferably, for a nanowire-cell-on-planar silicon-cell tandem approach, the nanowire array should absorb high energy photons efficiently and show high transmission of low energy photons into the silicon bottom cell.

[0038] In the first configuration described above, when the nanowires are located directly on top of a Si substrate, the Si substrate constituting the lower bandgap bottom subcell, the optimum dimensions of the nanowire array will mainly depend on absorption in the nanowire subcell.

[0039] However, in the embodiments of the second configuration described above, in a nanowire- array subcell that is "free-standing" (e.g., where the nanowires are embedded in a freestanding dielectric membrane), the nanowires don't stand in direct contact with an underlying substrate subcell (which can be, for example, a silicon solar subcell containing a p-n or p-i-n junction in silicon). Rather, in these embodiments disclosed herein include a dielectric material and/or thin conductive layer is located between the nanowire array (e.g., the nanowire solar subcell) and the substrate solar subcell.

[0040] FIG. 1 is a schematic illustration of a stacked tandem photovoltaic cell 100 according to an embodiment. This embodiment includes a first photovoltaic subcell 102, a second

photovoltaic subcell 104 and may include any number of additional photovoltaic subcells 106. As illustrated in Figure 1, the first photovoltaic subcell 102 is located on top of the stack, that is, the full solar spectrum of light I(E_Ph) is incident on the top surface of the first photovoltaic subcell 102. The second photovoltaic subcell 104 is located under the first photovoltaic subcell 102 and the additional photovoltaic subcells 106 are located under the second photovoltaic subcell 104. The first photovoltaic subcell 102 has a bandgap Ei. Preferably, the first photovoltaic subcell 102 absorbs at least the majority of photons (e.g., at least 70%, such as at least 90%, for example essentially all photons) having an energy Further, the first

photovoltaic subcell 102 should be transparent to light having energy less than the energy of

the first bandgap Ei.

[0041] The stacked tandem photovoltaic cell 100 is configured such that the second photovoltaic subcell 104 has second bandgap E₂ that is smaller than the first bandgap Preferably, the

second photovoltaic subcell 104 absorbs at least the majority of photons (e.g., at least 70%, such as at least 90%, for example essentially all photons) having an energy Further, the

second photovoltaic subcell 104 should be transparent to light having energy

less than the energy of the second bandgap E₂. The same pattern is true for all succeeding additional subcells 106. However, the final subcell in the stacked tandem photovoltaic cell 100 does not need to be transparent.

[0042] FIGs. 2A and 2B are schematic illustrations of conventional stacked tandem photovoltaic cells 200a, 200b. In the conventional stacked tandem photovoltaic cells 200a, the photovoltaic subcells 102, 104, 106 are planar/bulk photovoltaic devices. Some of the light incident on the first photovoltaic subcell 102 is absorbed in the first photovoltaic subcell 102, some of the light passes through to the second photovoltaic subcell 104 and some of the light is reflected back from the interface between the first photovoltaic subcell 102 and the second photovoltaic subcell 104. Some of the light incident on the second photovoltaic subcell 104 is absorbed in the second photovoltaic subcell 104, some of the light passes through to the third photovoltaic subcell 106 and some of the light is reflected back from the interface between the second photovoltaic subcell 104 and the third photovoltaic subcell 106. Light that is neither absorbed nor reflected 108 by the third photovoltaic subcell 106 may pass through the third photovoltaic subcell 106. Optionally, a mirror or reflective coating may be applied to the bottom of the third photovoltaic subcell 106 to reflect the light 108 back into the stacked tandem photovoltaic cell 200a.

[0043] The stacked tandem photovoltaic cell 200b illustrated in Figure 2B is similar to the device illustrate in Figure 2A. However, the stacked tandem photovoltaic cell 200b includes spacer layers 103 and 105 between the first photovoltaic subcell 102 and the second photovoltaic subcell 104 and between the second photovoltaic subcell 104 and the third photovoltaic subcell 106, respectively.

[0044] FIG. 2C is a schematic illustration of a stacked tandem photovoltaic cell 200c according to an embodiment. In this embodiment, the planar/bulk photovoltaic devices of the conventional stacked tandem photovoltaic cells 200a, 200b are replaced with subcells 202, 204, 206 which comprise nanostructures. In an embodiment, the nanostructures are nanowires. Unlike the conventional planar subcells 102, 104, 106, the nano structured subcells 202, 204, 206 may suffer loss via mechanisms not present in conventional, planar/bulk photovoltaic subcells 102, 104, 106. Specifically, the waveguiding nature of the nanowires may generate in-plane waveguide modes 210 and/or diffraction orders 212. Although not illustrated, in-plane waveguide modes 210 and diffraction orders 212 may exist at the same time in the same photovoltaic subcells 202, 204, 206. The in-plane waveguide modes 210 and diffraction orders 212 are discussed in more detail below.

[0045] FIGs. 3A-3D are schematic illustration of embodiments of a stacked tandem photovoltaic cell 300a-300d. In the stacked tandem photovoltaic cell 300a illustrated in Figure 3A, the first photovoltaic subcell 202 is adjacent a second photovoltaic subcell 204. In this embodiment, the second photovoltaic subcell 204 comprises a membrane made of a material having a high index of refraction while the first photovoltaic subcell 202 comprises a membrane made of a material having a low index of refraction. A low index of refraction is defined as 1 < n < 2. A high index of refraction is defined as n >2, such as 2 < n < 7, including 2 < n < 4.

[0046] The stacked tandem photovoltaic cell 300b illustrated in Figure 3B is similar to the embodiment illustrated in Figure 3A. However in the embodiment illustrated in Figure 3B, a transparent conductive oxide (TCO) layer 203 is provided between the first photovoltaic subcell 202 and the second photovoltaic subcell 204. In this embodiment, the thickness of the TCO layer 203 is less than half the wavelength (λ) of the light to be absorbed in the second

photovoltaic subcell 204. As used herein, at least the majority of photons (e.g., at least 70%, such as at least 90%, for example essentially all photons) of a given wavelength or wavelength range are understood to be absorbed or transmitted for a given condition in a real world (i.e., non-theoretical device).

[0047] In the stacked tandem photovoltaic cell 300c illustrated in Figure 3C, a second TCO layer 205 is optionally provided in addition to a window layer 207. In this embodiment, the window layer 207 is made of a material with a high index of refraction. The second TCO layer, if present, preferably has a thickness less than half the wavelength of the light to be absorbed in the second photovoltaic subcell 204. Preferably, the window layer 205 is located between the first TCO layer 203 and the second TCO layer 205 between the first photovoltaic subcell 202 and the second photovoltaic subcell 204.

[0048] The stacked tandem photovoltaic cell 300d illustrated in Figure 3D is similar to the embodiment illustrated in Figure 3C. However, in this embodiment, the window layer 207 is made from a material with a low index of refraction and has a thickness greater than λ 2. The window layer 207 has a lower index of refraction than the second photovoltaic subcell 204 and the same or greater or smaller index of refraction than the first photovoltaic subcell 202.

[0049] An embodiment is drawn to a method of making a stacked tandem photovoltaic device 300a-300d. The method includes determining nanostructure and index of refraction parameters of subcells 202, 204 of the stacked tandem photovoltaic device 300a-300d to reduce in-plane waveguiding of light incident on the stacked tandem photovoltaic device 300a-300d. The method also includes providing a first photovoltaic subcell 202, the first photovoltaic subcell 202 comprising nanostructures based on the step of determining the nanostructure and index of refraction parameters of subcell 202 (and optionally based on the step of determining index of refraction parameters of the underlying second subcell 204), such as determining reduction of in- plane waveguiding, which can be reduced at the expense of a slight reduction in the amount of transmitted solar radiation through the first photovoltaic subcell 202. The method also includes providing the second photovoltaic subcell 204 based on the step of determining nanostructure and index of refraction parameters of at least the first subcell 202. The first photovoltaic subcell 202 has a first bandgap, the second photovoltaic subcell 204 has a second bandgap and the first bandgap is larger than the second bandgap. Light incident on the stacked tandem photovoltaic device 300a-300d passes through the first photovoltaic subcell 202 before entering the second photovoltaic subcell 204.

[0050] In an embodiment, the bandgap Ei of the first photovoltaic subcell 202 is less than a bandgap of a first photovoltaic subcell optimized for optical transparency without considering in- plane waveguiding. In an embodiment, the method further includes forming a first layer 203 having a higher index of refraction than the effective index of refraction of the photovoltaic subcell 202 between the first photovoltaic subcell 202 and the second photovoltaic subcell 204. In an embodiment, the first layer 203 having the higher index of refraction has a thickness less than λ 2, wherein λ is the wavelength of the light to be absorbed in the second photovoltaic subcell 204. An effective index of refraction of a subcell, such as a nanostructured subcell is a function of geometry and materials of the subcell.

[0051] In an embodiment, the first layer 203 having the higher index of refraction comprises a transparent conducting oxide. Another embodiment includes forming a window layer 207 between the first photovoltaic subcell 202 and the second photovoltaic subcell 204, the window layer 207 having higher index of refraction than the effective index of refraction of the first photovoltaic subcell 202 and a thickness less than λ 2. Another embodiment includes forming a second layer 205 comprising a transparent conducting oxide between the first photovoltaic subcell 202 and at least one of the window layer 205 or the second photovoltaic subcell 204, the second layer 205 of transparent conducting oxide having a thickness less than λ 2.

[0052] Another embodiment includes forming a window layer 207 between the first photovoltaic subcell 202 and the second photovoltaic subcell 204, the window layer 207 having a lower index of refraction than the effective index of refraction of the second photovoltaic subcell 204 and a thickness greater than λ 2. In other embodiments, the window layer 207 has a lower index of refraction than the effective index of refraction of the second photovoltaic subcell 204 and a thickness less than λ 2. Another embodiment includes forming a second layer 205 comprising a transparent conducting oxide between the first photovoltaic subcell 202 and at least one of the window layer 207 or the second photovoltaic subcell 204, the second layer 205 of transparent conducting oxide having a thickness less than λ 2. The second layer 205 of transparent conducting oxide may be located closer or more proximal to the first photovoltaic subcell 202 than the window layer 207.

[0053] In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher refractive index, that is the real portion of the index of refraction at the wavelength of the transmitted light, than the dielectric, and the nanowires have a smaller diameter than a diameter of nanowires of the same composition optimized for optical transparency or absorption without considering in-plane waveguiding. In another embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and the dielectric has a lower index of refraction than a dielectric of the same composition optimized for optical transparency or absorption without considering in-plane waveguiding.

[0054] In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and the nanowires comprise a semiconductor material with a lower effective index of refraction than an index of refraction of nanowires optimized for optical transparency without considering in- plane waveguiding. In another embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and a nanowire density for a fixed nanowire diameter is less than the nanowire density of the same composition optimized for optical transparency without considering in-plane waveguiding.

[0055] In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and a nanowire diameter for a fixed nanowire density is less than the nanowire diameter of the same composition optimized for optical transparency without considering in-plane waveguiding. In another embodiment, the nanostructures are configured in a periodic array in which a pitch between nanostructures is selected such that no in-plane waveguide modes exist for in-plane k- vectors in a relevant wavelength range (e.g. 400 to 750 nm) for transparency (i.e., the wavelength range for light transmitted through the first photovoltaic subcell containing the nanostructures).

[0056] An embodiment includes tuning a transparency wavelength window with bandgaps of subcells; or placing a subcell that shows reflection issues close enough to an adjacent subcell such that in-plane waveguide modes cannot be excited due to "leakage" into the adjacent subcell; or choosing a small enough contrast between higher and lower index of refraction material(s) in each subcell that shows resonant reflection; or choosing a small enough inclusion of higher index of refraction material to reduce scattering of light into an in-plane direction; or using a periodic system with a small enough period to prohibit excitation of in-plane waveguiding. In an embodiment, the first photovoltaic subcell absorbs, for example, a majority, such as greater than 80% of light having an energy greater than the first bandgap and less than 50%, such as less than 20% of light having an energy less than the first bandgap. Example stacked tandem photovoltaic devices which can achieve these results are illustrated in Figures 3A-5B and described in more detail above and in the "solar cell design considerations" section below.

[0057] An embodiment includes tailoring a dispersion of in-plane waveguide modes such that they cannot be excited by k-vector allowed processes in a relevant wavelength range for transparency or allowing for excitation of in-plane waveguide modes through k-vector selection, but diminishing the actual excitation strength of the modes through tailoring of the scattering geometry of the array. Another embodiment includes selecting to a nanowire diameter to prevent resonant reflection when the nanostructures comprise nanowires.

[0058] An embodiment is drawn to a stacked tandem photovoltaic device 300a-300d. The device comprises a first photovoltaic subcell 202, the first photovoltaic subcell 202 comprising nanostructures. The device comprise a second photovoltaic subcell 204. The first photovoltaic subcell 202 has a first bandgap Ei, the second photovoltaic subcell 204 has a second bandgap E₂ and the first bandgap Ei is larger than the second bandgap E₂. The first photovoltaic subcell 202 and the second photovoltaic subcell 204 are configured based on determining nanostructure and index of refraction parameters of the first and second subcells 202, 204 of the stacked tandem photovoltaic device 300a-300d to reduce in-plane waveguiding of light incident on the stacked tandem photovoltaic device 300a-300d. Light incident on the stacked tandem photovoltaic device 300a-300d passes through the first photovoltaic subcell 202 before entering the second photovoltaic subcell 204, as will be described in more detail above and in the "solar cell design considerations" section below.

[0059] In an embodiment, the bandgap Ei of the first photovoltaic subcell 202 is less than a bandgap of a first photovoltaic subcell optimized for optical transparency without considering in- plane waveguiding. An embodiment further comprises a first layer 203 having a higher index of refraction located between the first photovoltaic subcell 202 and the second photovoltaic subcell 204. In an embodiment, the first layer 203 having the higher index of refraction has a thickness less than λ 2, wherein λ is the wavelength of the light to be absorbed in the second photovoltaic subcell 204.

[0060] In an embodiment, the first layer 203 having the higher index of refraction comprises a transparent conducting oxide. An embodiment further comprises a window layer 207 located between the first photovoltaic subcell 202 and the second photovoltaic subcell 204, the window layer 207 having a higher index of refraction then the first photovoltaic subcell 202 and a thickness less than λ 2. Another embodiment comprises a second layer 205 comprising a transparent conducting oxide located between the first photovoltaic subcell 202 and the second photovoltaic subcell 204, the second layer 205 of transparent conducting oxide having a thickness less than λ 2.

[0061] Another embodiment comprises a window layer 207 located between the first

photovoltaic subcell 202 and the second photovoltaic subcell 204, the window layer 207 having a lower index of refraction then the first photovoltaic cell 202 and a thickness greater than λ 2. Another embodiment comprises a second layer 205 comprising a transparent conducting oxide located between the first photovoltaic subcell 202 and the second photovoltaic subcell 204, the second layer of transparent conducting oxide having a thickness less than λ 2.

[0062] In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and the nanowires have a smaller diameter than a diameter of nanowires of the same composition optimized for optical transparency without considering in-plane waveguiding. In an

embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and the dielectric has a lower index of refraction than a dielectric optimized for optical transparency without considering in-plane waveguiding.

[0063] In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and the nanowires comprise a semiconductor material with a lower index of refraction than an index of refraction of nanowires optimized for optical transparency without considering in-plane waveguiding. In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and a nanowire density for a fixed nanowire diameter is less than the nanowire density of the same composition optimized for optical transparency without considering in-plane waveguiding.

[0064] In an embodiment, the nanostructures comprise nanowires, a dielectric is provided between the nanowires, the nanowires have a higher index of refraction than the dielectric, and a nanowire diameter for a fixed nanowire density is less than the nanowire diameter of the same composition optimized for optical transparency without considering in-plane waveguiding. In an embodiment, the nanostructures are configured in a periodic array in which a pitch between nanostructures is selected such that no in-plane waveguide modes exist for in-plane k-vectors in a relevant wavelength range for transparency.

[0065] As described above, in an embodiment, the first photovoltaic subcell absorbs, for example, a majority, such as greater than 80% of light having an energy greater than the first bandgap and less than 50%, such as less than 20% of light having an energy less than the first bandgap.

[0066] The optimization of the absorption in the nanowire- array subcell is not sufficient for optimizing the combined absorption of above bandgap photons in the nanowire array and the transmission of below bandgap photons through the nanowire array.

[0067] First, considering a nanowire array completely embedded in a dielectric membrane, the nanowire array has, as calculated from volume averaging, a higher effective index of refraction than the dielectric on the top and the bottom side. In this case, optical waves can be excited in the plane of the nanowire array. That is, excitation of in-plane waveguide modes may be observed. When such waves couple out from the membrane, they can lead to enhanced reflection as compared to a situation where such in-plane waveguide modes are not excited.

[0068] Resonant excitation of such in-plane waveguide modes can lead to a substantial reflection loss of the below-bandgap photons. However, the in-plane modes don't typically lead to considerable reflection losses for above bandgap photons since these are absorbed strongly in the nanowires. If the nanowire dimensions reported for nanowires placed directly on a Si substrate are the sole guide for device design, then the resonant reflection losses of below bandgap photons result in a less efficient device.

[0069] The inventors have discovered that the resonant excitation of the in-plane waveguide modes depends on the nanowire diameter, the array pitch, and the materials surrounding the nanowires, as well as the material between the nanowires. In principle, the physics underlying resonant reflection from in-plane waveguide modes can be complicated. The dispersion of the in-plane waveguide modes, as well as the excitation strength of the nanowires, changes when the diameter and period of the nanowires are changed. To prevent the resonant excitation of in-plane waveguide modes, there are two pathways: (1) tailoring the dispersion of the in-plane waveguide modes such that they cannot be excited by k-vector allowed processes in the relevant wavelength range for transparency, or (2) allowing for excitation of in-plane waveguide modes through k- vector selection, but diminish the actual excitation strength of the modes through tailoring of the scattering geometry of the array.

SOLAR CELL DESIGN CONSIDERATIONS [0070] The following points apply for the above described methods and devices:

1) Preliminary background for k-vector matching: The excitation of the waveguide mode depends on matching one of the allowed k-vectors in the array to the in-plane k-vector of the in-plane waveguide mode. In a periodic array of pitch P, the smallest allowed in- plane k-vector is 2π/Ρ for the normally incident light that we consider. Typically, the in- plane k-vector of an in-plane waveguide mode decreases with increasing wavelength. Therefore, there is for a given pitch and diameter, a maximum wavelength above which the waveguide modes cannot be excited, since the in-plane k-vector 2π/Ρ is larger than that of any in-plane waveguide mode.

2) Typically, the largest in-plane k-vector of any of the in-plane waveguide modes increases with increasing diameter D of the high index of refraction material nanowires (for a fixed pitch) since this increases the volume-averaged index of refraction of the array where the waveguide mode propagates. Further, the longest wavelength for which the in-plane waveguide mode can be excited, for a given pitch, red-shifts with increasing D into the transparency region of the nanowires, and resonant reflection can show up. Or in other words, the resonant excitation decreases with decreasing diameter D. Such behavior can be seen in Figure 15C, where the resonant excitation diminishes when D decreases below 200 nm.

3) The excitation of the in-plane waveguide mode relies on diffraction of light to a perpendicular direction from that of the normally incident light. Such diffraction is enabled by the index of refraction contrast between the nanowires and the medium between the nanowires. Furthermore, such scattering is expected to increase with increasing amount of high-refractive index inclusion in the array (starting from small diameter), since this increases the volume of the scattering region. Traces of such behavior can be seem in Figure 15C, where the resonant excitation diminishes with decreasing D for a fixed pitch.

) For a given nanowire array, both effects described above in points (2) and (3) are seen. With increasing period, by the k-vector selection rules, excitation of the waveguide mode is allowed for smaller diameter. However, with decreasing diameter, the actual excitation strength of the in-plane waveguide mode decreases. Thus, in the D<200 nm region in Figures 15A-15C, right panel, there is actually two different mechanisms that prevent the resonant reflection. For small values of P, the k-selection rule prohibits the excitation (2π/Ρ is larger than the largest k-vector of any in-plane mode). For larger values of P, the resonant excitation is diminished instead by the decreasing diameter-to-period ratio (which is expected to decrease the excitation strength of the in-plane mode). Indeed, starting from very small P, the diameter at which resonant excitation shows up decreases with increasing P, in line with point (2). However, with increasing P for P > 600 nm, the diameter for which resonant excitation shows up increases instead, in line with point (3) above.

) As discussed above, the excitation of the array mode relies on diffraction of light to a perpendicular direction from that of the normally incident light. Such diffraction is enabled by the index of refraction contrast between the nanowires and the medium between the nanowires. Therefore, the excitation of the in-plane waveguide modes decreases as the index of refraction n of the medium between the nanowires is increased, from the initial value of n = 1.5, to better match the n ~ 3.5 of the semiconductor nanowires (Figures 11A-11F).

) The in-plane waveguide modes can leak into a high-index of refraction region adjacent to the nanowire array (Figures 8A-8E). Therefore, resonant reflection has not been seen in prior-art modeling of absorption and transmission of nanowire arrays on Si substrate. Thus, the nanowire solar cell membrane is designed to dampen the in-plane excitation in one embodiment. Further, by increasing the index of refraction of the materials surrounding (e.g. between, over and under) the nanowire array, resonant excitation of the waveguide modes can be prohibited.

) It can be shown that if the nanowire array is lifted a distance more than approximately λ/3 (λ the wavelength of light in vacuum) above the high refractive index substrate, the waveguide modes will not leak efficiently into the high index of refraction substrate. In other words, a true near-field coupling to the high-refractive-index region is needed in order to prevent strong excitation of the waveguide mode. Therefore, the high index refraction layer should be close, e.g. less than λ/3 from the nanowires.

) Since the wavelength region that defines the below bandgap photons depends on the bandgap of the nanowires, there exists a connection between the bandgap of the nanowires; and the nanowire diameter and array pitch for avoiding resonant excitation of the in-plane waveguide modes. Typically, with increasing bandgap energy of the nanowires, the diameter and pitch need to be scaled down simultaneously, in a similar manner as the bandgap wavelength was scaled down, to avoid the resonant reflection, since the shortest wavelength that the nanowires don't absorb decreases.

) If transparent conductive oxides are used at the top and at the bottom of the nanowire array, the resonant excitation of the in-plane modes can lead to a large absorption loss in these layers, e.g., due to leakage.

] Other design considerations include: ) For a given pitch, the nanowire diameter cannot be chosen too small since then the absorption in the nanowires is too weak.

) The diameter cannot be chosen too large since then the resonant reflection decreases the transparency of below bandgap photons.

) Based on (1) and (2), there is a limit on the diameter for optimum absorption, which is stricter than when optimizing just the absorption in the nanowires.

) For nanowire-array-subcell on Si substrate, the optimum diameter is the smallest diameter that still provides an optimum for the absorption in the nanowires.

) To enable larger diameters by decreasing the resonant reflection loss, one can: i) place the nanowires directly on top of a high index of refraction substrate or above a solar subcell (e.g., silicon subcell) in which absorption of the transmitted wavelengths of light is desired and/or optimized. In this case, the waveguide modes "leak" into the substrate and/or the underlying subcell, preventing resonant excitation of them; or ii) Use an embedding material with higher refractive index, preferentially matched to that of the nanowires. To excite in-plane waveguide modes, the device should have a index of refraction difference in the plane of the nanowire array. By diminishing this difference, the excitation of the in-plane modes may be diminished.

6) Further, the use of indium tin oxide (ITO) at the top and bottom of the nanowires can lead to strong absorption in the ITO if the in-plane waveguide modes are excited strongly.

[0072] For the absorption in the nanowires, according to prior art, the smallest diameter that optimizes the absorption in the nanowire array is typically also the global optimum for absorption in nanowire-array-subcell-directly-on-silicon-subcell tandem cell. Therefore, one would choose this diameter to optimize the dimensions of nanowires in the membrane, for tandem applications. However, the problem of possible resonant reflection from in-plane waveguide modes would manifest, especially at larger diameters.

[0073] Results and simulations disclosed herein were generated on periodic systems (hexagonal and square array). However, also randomized arrays show excitation of the in-plane modes (since the k-vector matching is relaxed). Thus, the embodiments disclosed above may include subcells with randomly oriented nanowires.

[0074] The optical response of the stacked tandem photovoltaic cells 300a-300d can be modeled with the Maxwell equations. The optical response of the underlying materials through their wavelength (λ) dependent refractive indexes (or equivalently through their dielectric functions) may be included. For the incident light, a normally incident plane wave toward the nanowire array is selected.

[0075] In this calculation, the reflectance R ) and transmittance Τ(λ) of the system can be determined. The total absorptance of the system is given by Α(λ) = 1 - R( ) - Τ(λ). Here, the reflectance, transmittance, and absorptance are defined as the fraction of incident light of a given wavelength that is reflected, transmitted, or absorbed.

[0076] Also, the power flow F(z, ) in varying z planes (z is along the axis of the vertically standing nanowires) can be obtained. For example, a case where a top ITO layer occupies the space defined by z

, nanowires the space defined by z

and a bottom ITO layer the space defined by Then, the absorptance in the ITO layers and the NWs is defined

by Α

and

where is the incident power flow [which has units of

W/(m²nm)].

[0077] A stacked cell, without constraint of current matching between the nanowire subcell and the Si subcell is selected. Preferably, the current-generation performance of both cells is maximized. However, absorption in the nanowire-array cell will cause a drop in the short-circuit current in the Si cell. In principle, a Shockley-Queisser detailed balance efficiency calculation for the combined tandem cell can be performed. However, such a detailed balance calculation is not practical when varying a large number of parameters. Instead, the analysis may be limited to varying processes that limit the absorption in the Si cell.

[0078] For calculating the incident intensity, the AM1.5D direct and circumsolar 1 sun spectrum ΐΑΜΐ.5( ) is used, scaled to 1000 W/m incident intensity.

[0079] For translating a spectrum Χ(λ) into corresponding short-circuit current (density), the equation is used:

[0080]

[0081] Here, q is the elementary charge, h is the Planck constant, and c is the speed of light in vacuum.

[0082] To calculate the estimated upper bound for the short-circuit current j in the nanowire-

array, use in Eq.

below which the AMI .5 direct and circumsolar spectrum shows negligible intensity, and Here, is the

bandgap wavelength of the nanowires with

the bandgap energy of the nanowires. [0083] To calculate the estimated upper bound for the short-circuit current jsi for the Si cell, assume that all the transmitted light can couple into the underlying Si cell. In this case, use in Eq. and with

[0084] Considering the cases where That is, considering the cases where

In this case, the light with is intended for absorption in the Si cell.

For the specific purpose of this study, we consider the losses of such light. Therefore, the reflection loss jsi,R-loss of photons dedicated for the Si cell is given using in

[0085] Also, if ΓΓΌ layers are present in the modeled system, we consider the absorption

in the ITO of photons dedicated for absorption in the Si cell, by using in

[0086] For GaAs nanowires with

under the assumption of perfect absorption, that is, with

, the upper limit of

Similarly, assuming for GaAs nanowires that

and that Τ

[0087] Note that when selecting nanowires with

with the above perfect absorption and transmission, and

[0088] Comparing the response of a GaAs nanowire array on top of a Si substrate, or completely within a n = 1.5 index of refraction membrane (see Figures 5 A, 5B for schematic). The nanowires are placed in a hexagonal array and the results averaged for x and y polarized light. [0089] Figures 6A-6C, show the calculation of the optical response of a GaAs nanowire array on top of a Si substrate. The nanowires are of 3000 nm in length, but the results are similar for varying nanowire length (with the main difference that shorter/longer nanowires lead to lower/higher jNWs)- The short-circuit current in the nanowire array is optimized for diameter of D ~ 170 nm or D ~ 400 nm.

[0090] Considering the case of GaAs nanowires completely within the n = 1.5 membrane

(Figures 7A-7F), for large diameter (D > 200 nm), noticeable values for jsi,R-loss are found. That is, there can be considerable reflection that decreases the transmittance T.

[0091] When increasing the nanowire length from 500 nm and 6000 nm (Figures 7D-7F), it is found that the resonant reflection shows an increasing number of fringes, as expected from a larger number of in-plane waveguide modes with thicker waveguide region.

[0092] Such reflection can be assigned to in-plane waveguide resonances in the x-y plane of the nanowire array.

[0093] Above, the resonant reflection was found when the nanowires were completely embedded in the n = 1.5 membrane (Figure 7C). However, such resonant reflection was not observed when the nanowires were on the Si substrate, which is of n ~ 3.5 (right panel of Figure 6C). From the behavior of in-plane waveguide modes, it is known that they can leak into a high-index of refraction substrate. Such "leakage" may prevent resonant excitation of the modes, which explains the lack of resonant reflection when the nanowires are on the Si substrate.

[0094] In Figures 8A-8E, results are shown for varying index of refraction of the substrate. As expected, with increasing refractive index, the resonant reflection decreases. It is also shown that the region of resonant reflection decreases, toward smaller pitch of the array.

[0095] Since it appears that the in-plane waveguide modes can leak into the substrate, if the index of refraction of the substrate is high enough, the inventors investigated also how such "leakage" can occur through a lower index of refraction space. It appears that for spacer thickness s > λ/3, the in-plane waveguide modes don't couple effectively into the substrate and can instead lead to resonant reflection (Figures 9A-9E). Additionally, the inventors investigated whether the resonant reflection doesn't come back if a high-index of refraction superstate is included (Figures 10A-10D).

[0096] In a planar system, it is not possible to excite the in-plane waveguide modes. To couple light into a perpendicular direction, there must exist a refractive-index change in the in-plane direction. Therefore, when trying to match the index of refraction of the material between the nanowires to that of the nanowires, the excitation, and resonant reflection due to resonant excitation, of the in-plane waveguide modes diminishes. When increasing the index of refraction from the n=1.5 to the n=3.5, which is approximately that of GaAs at λ ~ 1000 nm, the resonant reflection diminishes (Figures 11A-11F).

[0097] When ITO layers are present in the system, the in-plane waveguide modes can lead to resonant absorption within the ITO (Figure 1 IE). Such ΓΓΌ absorption loss can be decreased if the ITO-nanowire-ITO stack is placed directly on top of a Si substrate (assuming a 100 nm thick ITO layer, for which the in-plane waveguide mode is expected to leak into the substrate, preventing resonant excitation, as seen in Figures 12A-12F).

[0098] In Figures 11A-11F, the optical response of GaAs (Ebg,NWs = 1.43 eV) and GaAsP (with composition chosen to give Ebg,NWs = 1.7 eV) nanowire arrays are compared. As discussed above, the higher bandgap with the GaAsP nanowires leads to lower jNWs and also to higher jSi (for nanowire geometry where the nanowires absorb strongly). The resonant reflection is also found for GaAsP nanowires, with higher values than for GaAs (since jSi can be higher for GaAsP in this region, which leads to potentially higher losses also). Also, it is found that the diameter below which resonant reflection is not found decreases for GaAsP.

[0099] To demonstrate that the resonant reflection through resonant excitation by the in-plane waveguide modes is not exclusive to the hexagonal array, a square array was considered (Figures 12A-12C). Here, a resonant reflection is found similarly as for the hexagonal array. Also, the range of investigated pitch was extended to higher values. Also for this increased pitch range, it was found that D < 200 nm appears as a "good" region where resonant reflection is not pronounced (except for a small region around 550 nm in pitch where even smaller D is needed to "prevent" resonant reflection).

[00100] By the above criteria, a free-standing nanowire photovoltaic membrane (e.g., film) may be prepared and provided for a stacked tandem photovoltaic device. The membrane may be placed over a bulk photovoltaic subcell, such as a bulk silicon subcell, to form the tandem photovoltaic device. In another embodiment, a pre-existing photovoltaic panel may be upgraded by placing the first photovoltaic subcell (e.g., the membrane containing the

nanostructures) over the photovoltaic panel.

[00101] Although the foregoing refers to particular preferred embodiments, it will be understood that the invention is not so limited. It will occur to those of ordinary skill in the art that various modifications may be made to the disclosed embodiments and that such

modifications are intended to be within the scope of the invention. All of the publications, patent applications and patents cited herein are incorporated herein by reference in their entirety.

Claims

WHAT IS CLAIMED IS:

1. A method of making a stacked tandem photovoltaic device comprising:

determining nanostructure and index of refraction parameters of subcells of the stacked tandem photovoltaic device to reduce in-plane waveguiding of light incident on the stacked tandem photovoltaic device;

providing a first photovoltaic subcell, the first photovoltaic subcell comprising nanostructures based on the step of determining; and

providing a second photovoltaic subcell based on the step of determining, wherein the first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap,

wherein light incident on the stacked tandem photovoltaic device passes through the first photovoltaic subcell before entering the second photovoltaic subcell.

2. The method of claim 1, wherein the bandgap of the first photovoltaic subcell is less than a bandgap of a first photovoltaic subcell optimized for optical transparency without considering in-plane waveguiding.

3. The method of claim 1, further comprising forming a first layer having a higher effective index of refraction than the first photovoltaic subcell between the first photovoltaic subcell and the second photovoltaic subcell.

4. The method of claim 3, wherein the first layer having the higher effective index of refraction has a thickness less than λ/2, wherein λ is the wavelength of the light to be absorbed in the second photovoltaic subcell.

5. The method of claim 4, wherein the first layer having the higher index of refraction comprises a transparent conducting oxide.

6. The method of claim 5, further comprising forming a window layer between the first photovoltaic subcell and the second photovoltaic subcell, the window layer having higher effective index of refraction than the first photovoltaic subcell and a thickness less than λ/2.

7. The method of claim 6, further comprising forming a second layer comprising a transparent conducting oxide between at least one of the first photovoltaic subcell and the window layer or the second photovoltaic subcell, the second layer of transparent conducting oxide having a thickness less than λ/2.

8. The method of claim 5, further comprising forming a window layer between the first photovoltaic subcell and the second photovoltaic subcell, the window layer having a lower index of refraction than the second photovoltaic subcell and a thickness greater than λ/2.

9. The method of claim 8, further comprising forming a second layer comprising a transparent conducting oxide between at least one of the first photovoltaic subcell and window layer or the second photovoltaic subcell, the second layer of transparent conducting oxide having a thickness less than λ/2.

10. The method of claim 1, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

the nanowires have a smaller diameter than a diameter of nanowires optimized for optical transparency without considering in-plane waveguiding.

11. The method of claim 1, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

the dielectric has a lower index of refraction than a dielectric optimized for optical transparency without considering in-plane waveguiding.

12. The method of claim 1, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

the nanowires comprise a semiconductor material with a lower index of refraction than an index of refraction of nanowires optimized for optical transparency without considering in-plane waveguiding.

13. The method of claim 1, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and a nanowire density for a fixed nanowire diameter is less than une nanowire density of the same composition optimized for optical transparency without considering in-plane waveguiding.

14. The method of claim 1, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

a nanowire diameter for a fixed nanowire density is less than the nanowire diameter of the same composition optimized for optical transparency without considering in-plane waveguiding.

15. The method of claim 1, wherein the nanostructures are configured in a periodic array in which a pitch between nanostructures is selected such that no in-plane waveguide modes exist for in-plane k-vectors in a relevant wavelength range for transparency.

16. The method of claim 1, further comprising:

tuning a transparency wavelength window with bandgaps of subcells; or

placing a subcell that shows reflection issues close enough to an adjacent subcell such that in-plane waveguide modes cannot be excited due to leakage into the adjacent subcell; or choosing a small enough contrast between higher and lower index of refraction materials in each subcell that shows resonant reflection; or

choosing a small enough inclusion of higher index of refraction material to reduce scattering of light into an in-plane direction; or

using a periodic system to prohibit excitation of in-plane waveguiding with a small enough period.

17. The method of claim 1, further comprising:

tailoring a dispersion of in-plane waveguide modes such that they cannot be excited by k-vector allowed processes in a relevant wavelength range for transparency; or allowing for excitation of in-plane waveguide modes through k-vector selection, but diminishing the actual excitation strength of the modes through tailoring of the scattering geometry of the array.

18. The method of claim 1, further comprising selecting a nanowire drameter to prevent resonant reflection, wherein the nanostructures comprise nanowires.

19. A photovoltaic device, comprising a first photovoltaic subcell comprising

nanostructures, wherein at least one feature in the first photovoltaic subcell reduces or eliminates reflection loss due to in-plane waveguiding of incident light when the first photovoltaic cell is located over a second photovoltaic cell in a stacked tandem photovoltaic device, and wherein the first photovoltaic cell is configured to permit light incident on the stacked tandem photovoltaic device to passes through the first photovoltaic subcell before entering the second photovoltaic subcell.

20. The photovoltaic device of claim 19, wherein the first photovoltaic subcell comprises a free-standing membrane containing the nanostructures embedded in a dielectric matrix.

21. The photovoltaic device of claim 20, wherein the dielectric matrix comprises a polymer matrix and the nanostructures comprise III- V semiconductor nanowires containing a p-n or p-i-n junction.

22. The photovoltaic device of claim 21, wherein the III-V semiconductor nanowires GaAs or GaAsP nanowires, and wherein the first photovoltaic subcell is configured to be located over the second photovoltaic subcell which comprises a bulk silicon subcell.

23. A stacked tandem photovoltaic device comprising:

the first photovoltaic subcell of claim 19; and

the second photovoltaic subcell, wherein the first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap,

wherein at least one feature in the stacked tandem photovoltaic device reduces or eliminates reflection loss due to in-plane waveguiding of incident light on the stacked tandem photovoltaic device, and

24. The stacked tandem photovoltaic device of claim 23, wherein the banggap of the first photovoltaic subcell is less than a bandgap of a first photovoltaic subcell optimized for optical transparency without considering in-plane waveguiding.

25. The stacked tandem photovoltaic device of claim 23, further comprising a first layer having a higher index of refraction located between the first photovoltaic subcell and the second photovoltaic subcell.

26. The stacked tandem photovoltaic device of claim 25, wherein the first layer having the higher index of refraction has a thickness less than λ/2, wherein λ is the wavelength of the light to be absorbed in the second photovoltaic subcell.

27. The stacked tandem photovoltaic device of claim 26, wherein the first layer having the higher index of refraction comprises a transparent conducting oxide.

28. The stacked tandem photovoltaic device of claim 27, further comprising a window layer located between the first photovoltaic subcell and the second photovoltaic subcell, the window layer having a higher index of refraction then the first photovoltaic subcell and a thickness less than λ/2.

29. The stacked tandem photovoltaic device of claim 28, further comprising a second layer comprising a transparent conducting oxide located between the first photovoltaic subcell and the second photovoltaic subcell, the second layer of transparent conducting oxide having a thickness less than λ/2.

30. The stacked tandem photovoltaic device of claim 27, further comprising a window layer located between the first photovoltaic subcell and the second photovoltaic subcell, the window layer having a lower index of refraction than the first photovoltaic subcell and a thickness greater than λ/2.

31. The stacked tandem photovoltaic device of claim 30, further comprising a second layer comprising a transparent conducting oxide located between the first photovoltaic subcell and the second photovoltaic subcell, the second layer of transparent conducting oxide having a thickness less than λ/2.

32. The stacked tandem photovoltaic device of claim 23, wherein:

the nanostructures comprise nanowires, a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

the nanowires have a smaller diameter than a diameter of nanowires of the same composition optimized for optical transparency without considering in-plane waveguiding.

33. The stacked tandem photovoltaic device of claim 23, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

34. The stacked tandem photovoltaic device of claim 23, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

35. The stacked tandem photovoltaic device of claim 23, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

a nanowire density for a fixed nanowire diameter is less than the nanowire density of the same composition optimized for optical transparency without considering in-plane waveguiding.

36. The stacked tandem photovoltaic device of claim 23, wherein:

the nanostructures comprise nanowires,

a dielectric is provided between the nanowires,

the nanowires have a higher index of refraction than the dielectric, and

37. The stacked tandem photovoltaic device of claim 23, wherein une nanostructures are configured in a periodic array in which a pitch between nanostructures is selected such that no in-plane waveguide modes exist for in-plane k- vectors in a relevant wavelength range for transparency.

38. The stacked tandem photovoltaic device of claim 23, wherein the first photovoltaic subcell absorbs greater than 80% of light having an energy greater than the first bandgap and less than 20% of light having an energy less than the first bandgap.

39. A method of upgrading a photovoltaic panel comprising placing the first photovoltaic subcell of claim 19 over the photovoltaic panel.

40. A method of operating a stacked tandem photovoltaic device comprising:

receiving incident light on a first photovoltaic subcell comprising nanostructures such that at least a portion of the incident light passes through the first photovoltaic subcell and enters a second photovoltaic subcell; and

generating a current or voltage from the first and the second photovoltaic subcells; wherein:

the first photovoltaic subcell has a first bandgap, the second photovoltaic subcell has a second bandgap and the first bandgap is larger than the second bandgap, and

at least one feature in the stacked tandem photovoltaic device reduces or eliminates reflection loss due to in-plane waveguiding of the incident light.