WO2023085032A1 - 量子カスケードレーザー素子 - Google Patents
量子カスケードレーザー素子 Download PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
- H01S5/00—Semiconductor lasers
- H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
- H01S5/11—Comprising a photonic bandgap structure
-
- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
- H01S5/00—Semiconductor lasers
- H01S5/30—Structure or shape of the active region; Materials used for the active region
- H01S5/34—Structure or shape of the active region; Materials used for the active region comprising quantum well or superlattice structures, e.g. single quantum well [SQW] lasers, multiple quantum well [MQW] lasers or graded index separate confinement heterostructure [GRINSCH] lasers
Definitions
- the present disclosure relates to quantum cascade laser devices. More particularly, the present disclosure relates to surface-emitting quantum cascade laser devices that emit electromagnetic waves.
- QCL quantum cascade lasers
- THz terahertz
- a QCL element has a semiconductor superlattice structure in which unit structures are repeatedly formed in the thickness direction. There are multiple wells and barriers in the structure. When an external voltage is applied to operate the QCL device, the potentials of the wells and barriers of the semiconductor superlattice structure are uneven and generally graded with thickness position. Electrons, which serve as carriers, repeat intersubband transitions while being transported through subbands, or levels, that are formed in a sloped and uneven potential, causing stimulated emission of electromagnetic waves and laser oscillation.
- the cascade is named after the behavior of electrons transported while losing energy while undergoing intersubband transitions.
- the QCL element it is possible to select a wavelength irrelevant to the energy gap of the material forming the semiconductor superlattice structure and lasing.
- the lasing wavelength can be varied by designing the semiconductor superlattice structure. Therefore, the QCL element is attracting attention as a coherent light source in the mid-infrared region and the terahertz (THz) region, which are wavelength regions (frequency regions) not previously available with solid-state light sources.
- THz terahertz
- a QCL element is of an edge-emitting type that operates in TM-mode optical transition and emits the TM-mode electromagnetic wave from, for example, an edge of the QCL element.
- the electromagnetic wave to which the intersubband transition is coupled is limited to the one whose electric field is oriented in the thickness direction.
- the electromagnetic wave becomes TM mode.
- the TM mode output is emitted from an end face such as a cleaved facet of the QCL element.
- the process (mounting process) of fabricating a practical device of a QCL element that emits light from the edge tends to be complicated, which is disadvantageous for integration.
- a surface-emitting semiconductor laser which emits light with a wave number component in the direction normal to a flat plate, has better resistance to facet damage, wavelength stability, simpler packaging, and lower beam divergence than edge-emitting lasers. , and wafer-level scalability.
- the QCL element can be operated by surface emission, the complexity of the mounting process described above can be alleviated, and furthermore, the QCL element can be expected to have a large area and be integrated by stacking semiconductor and metal layers on the substrate.
- a method using a photonic crystal has been disclosed (for example, Patent Document 1 and Non-Patent Documents 1 to 3).
- the inventors of the present application conceived a concept leading to higher performance of a QCL element (referred to as a "PhC-QCL element" in this application) that employs photonic crystals, and searched for a specific structure.
- a QCL element referred to as a "PhC-QCL element” in this application
- the present disclosure contributes to improving the performance of QCL elements by providing a PhC-QCL element that can easily achieve high output and can be expected to oscillate with low divergence.
- PhC-QCL devices that can operate with surface emission.
- the inventors of the present application made full use of theoretical calculations including the established calculation method FDTD method (finite difference time domain method) and FDM method (filter diagonalization method), and variously studied the preferable structure of the PhC-QCL element.
- FDTD method finite difference time domain method
- FDM method filter diagonalization method
- the practicality of the PhC-QCL device can be greatly improved by devising a photonic crystal, and have completed the invention according to the present application. If the photonic crystal in the PhC-QCL device is suitable, photons generated by intersubband transitions in the semiconductor superlattice structure contribute to lasing in a radiation mode that radiates in the plane normal direction.
- the electrodes should be free from electrically isolated portions.
- a PhC-QCL device employing a footnic crystal having such a photonic band improves the performance of a surface-emitting QCL device.
- a first electrode that is a uniform film extending over a range and a plurality of repeatedly stacked layers disposed on or above the first electrode and a second electrode disposed on or above the semiconductor superlattice structure, the second electrode comprising:
- a photonic crystal including an array of openings passing through itself in a thickness direction is formed to extend over the range, the array of openings being such that the second electrode has no electrical isolation in the range.
- a quantum cascade laser device is provided, wherein the photonic band structure of the photonic crystal has a radiation mode at or near the ⁇ point.
- the suitability of a photonic crystal can be determined by whether the photonic band of the photonic crystal has a radiation mode at or near the ⁇ point at the target laser frequency. Furthermore, whether a mode at or near the ⁇ point is favorable is ⁇ if a parasitic mode, another mode with a large horizontal wavenumber ( k ⁇ ), exists at the same frequency in the photonic band.'' If so, the parasitic mode must have a sufficiently larger radiation constant than the radiation mode at or near the ⁇ point.” More preferably, whether a mode at or near the ⁇ point is preferred depends on whether the radiation mode at or near the ⁇ point has a radiation constant of 10/cm to 40/cm. can also be determined. This is because within this radiation constant range, efficient surface radiation and amplification can be expected, that is, stable high-power light emission can be expected.
- the radiation constant of the radiation mode is smaller than that of another mode having a higher horizontal wavenumber at the same frequency as the radiation mode.
- the radiation constant of the radiation mode is 10/cm or more and 40/cm or less.
- a first electrode that is a uniform film that extends over a range and a plurality of repeatedly stacked electrodes disposed on or above the first electrode and a second electrode disposed on or above the semiconductor superlattice structure, the second electrode itself extending in the thickness direction a second electrode having a triangular lattice array of openings therethrough extending over said range and having no electrical isolation in said range.
- a first electrode that is a uniform film covering a certain area, and a plurality of repeatedly stacked units disposed on or above the first electrode
- a quantum cascade laser device comprising: a semiconductor superlattice structure having an active region composed of a photonic crystal including a triangular lattice array of openings passing through the second electrode itself in the thickness direction is formed so as to spread over the range, and the second electrode is electrically isolated in the range
- Quantum cascade laser devices are also provided that are free of
- electromagnetic waves in the THz region refer to electromagnetic waves in the frequency range of approximately 0.1 THz to 30 THz, ie, the wavelength range of about 10 ⁇ m to 3 mm.
- the device structures and functions are described using technical terms diverted or borrowed from the fields of electronic devices and physics that target visible light and infrared rays. For this reason, even when describing electromagnetic waves in the frequency range or wavelength range of the THz range far from visible light, "light”, “laser”, “light”, “laser”, and " The term “luminescence”, “optical -”, “photo -”, “refraction”, etc. may be used.
- the quantum cascade laser element provided in any one of the embodiments of the present disclosure realizes highly practical surface-emitting laser oscillation operation, contributing to the development of quantum cascade lasers and electronic devices using them.
- FIG. 2 is an explanatory diagram showing an example PhC-QCL element schematic configuration for performance evaluation in an embodiment of the present disclosure
- FIG. 4 is a diagram of photonic bands calculated for a PhC-QCL device of an embodiment of the present disclosure
- FIG. FIG. 2 is an explanatory diagram showing the concept of a two-dimensional reciprocal lattice space in an embodiment of the present disclosure
- FIG. A three-dimensional perspective view of the unit cell considered for the calculation of PhC-QCL devices of embodiments of the present disclosure (FIG. 4A), a cross-sectional view through the center of the y-coordinate of the unit cell (FIG. 4B), and a semiconductor superlattice.
- FIG. 4C is a cross-sectional view at the middle of the thickness of the structure;
- FIG. 4 is a diagram of photonic bands calculated for a PhC-QCL device of an embodiment of the present disclosure;
- FIG. 4 is a graph of surface losses for modes near the ⁇ point calculated using FDM for PhC-QCL elements of embodiments of the present disclosure;
- 8A and 8B are graphs showing the real (FIG. 8A) and imaginary (FIG.
- FIG. 8B parts of ⁇ r (f) and n(f) calculated for PhC-QCL devices of embodiments of the present disclosure.
- FIG. 4 is a mapping diagram showing the strength of electric field components as a function of y and z coordinates at two YZ plane sensor positions calculated for a PhC-QCL device of an embodiment of the present disclosure; FIG.
- FIG. 10 is a graph showing the field and its Fourier transform at a point sensor in a semiconductor superlattice structure, calculated for a PhC-QCL device of embodiments of the present disclosure
- FIG. FIG. 12A is a far-field pattern (FIG. 12A) calculated based on the vector potential method and a radiation pattern (FIG. 12B) calculated for the PhC-QCL device 1000 of an embodiment of the present disclosure.
- FIG. 14A is a perspective view (FIG. 14A), a plan view (FIG. 14B), and a cross-sectional view (FIG. 14C) of a unit cell of a photonic crystal to be calculated in a comparative example of the present disclosure
- FIG. 10 is an explanatory diagram illustrating an irreducible Brillouin zone in a square reciprocal lattice space in a comparative example of the present disclosure
- FIG. 4 is a perspective view of a QCL waveguide structure with unit cells arranged for calculating far-field properties in a comparative example of the present disclosure
- 4 is a diagram of photonic bands calculated for a comparative example of the present disclosure
- FIG. 14A is a perspective view (FIG. 14A), a plan view (FIG. 14B), and a cross-sectional view (FIG. 14C) of a unit cell of a photonic crystal to be calculated in a comparative example of the present disclosure
- FIG. 10 is an explanatory diagram illustrating an irre
- FIG. 4 is an explanatory diagram showing degrees of freedom provided for optimizing the cross-sectional shape of column holes in a unit cell in an embodiment of the present disclosure
- FIG. 4 is a plan view showing cross-sectional shapes of various column holes tried in embodiments of the present disclosure
- FIG. 20A shows a band diagram (FIG. 20A) in the configuration of the PhC-QCL element in which the cross-sectional shape of the optimized column hole is optimized, and a far-field pattern (FIG. 20B) according to the configuration in the embodiment of the present disclosure.
- FIG. 21A shows photonic band modes in a configuration in which column holes having circular (FIG. 21A) and equilateral triangular (FIG. 21B) cross sections are formed.
- 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between active layer occupancy and frequency for equilateral triangular column holes and circular column holes.
- 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between active layer occupancy and LEE for equilateral triangular column holes and circular column holes.
- 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between frequency and LEE for an equilateral triangular column hole and a circular column hole.
- 23A and 23B are the electric field distribution (FIG. 23A) and the far field pattern (FIG. 23B) under certain conditions studied in detail in embodiments of the present disclosure.
- 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between active layer occupancy and frequency for equilateral triangular column holes and circular column holes.
- 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between active layer occupancy and LEE for equilateral triangular column holes and circular column holes.
- 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between frequency and LEE for an equilateral triangular column hole and a circular column hole.
- 25A and 25B are beam profiles under one condition and another condition (FIG.
- 4 is a graph showing calculation results under certain conditions studied in detail in an embodiment of the present disclosure, showing the relationship between FF and frequency; 4 is a graph showing calculation results under certain conditions studied in detail in an embodiment of the present disclosure, showing the FF-LEE relationship; 4 is a graph showing calculation results under certain conditions studied in detail in an embodiment of the present disclosure, showing a frequency-LEE relationship; 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between active layer occupancy and frequency for two modes in an equilateral triangular column hole.
- FIG. 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the relationship between active layer occupancy and LEE for two modes in equilateral triangular column holes. 4 is a graph showing calculation results under certain conditions studied in detail in the embodiment of the present disclosure, showing the frequency-LEE relationship for two modes in an equilateral triangular column hole. Photonic band structure (FIG. 28A) and far-field pattern (FIG. 28B) under certain conditions studied in detail in embodiments of the present disclosure.
- An embodiment of the present disclosure provides a configuration of a QCL device (PhC-QCL device) that employs a photonic crystal to operate the QCL device, which normally emits light in the TM mode, in surface emission.
- the PhC-QCL device of the present embodiment particularly has a schematic structure of a first electrode layer/active layer/second electrode layer, and one electrode layer (second electrode) side is the emitting surface.
- the surface emitting operation is performed as follows. Both the first electrode and the second electrode are typically metal. At least the second electrode layer has a periodic structure forming a photonic crystal formed by etching or the like.
- the active layer is a layer for light emission operation by a semiconductor, and has a semiconductor superlattice structure composed of a plurality of unit structures repeatedly laminated.
- the semiconductor superlattice structure may also have a periodic structure formed by etching or the like to form a part of the photonic crystal.
- the electrode (second electrode) serving as the emission surface of surface emission and the semiconductor superlattice structure constitute a photonic crystal
- the electrode (second electrode ) constitutes the photonic crystal alone
- FIG. 1 is an explanatory diagram showing a schematic configuration of an exemplary PhC-QCL element 1000 for performance evaluation in this embodiment.
- PhC-QCL device 1000 generally consists of a pair of electrodes 101 and 102 and a semiconductor superlattice structure 110 sandwiched therebetween.
- the electrode (first electrode) 101 and the electrode (second electrode) 102 receive externally a voltage for forming an electric field and a current for emitting electromagnetic waves or emitting light with respect to the semiconductor superlattice structure 110.
- a semiconductor superlattice structure 110 has an active region 112 consisting of a plurality of unit structures repeatedly stacked.
- Semiconductor superlattice structure 110 may include other layers necessary for operation.
- Electrodes 101 and 102 are typically made of metal, and electrode 101 is a uniform film with a certain area.
- a typical thickness of the electrode 101 is arbitrarily set to a value that does not require consideration of permeability to electromagnetic waves at the operating frequency.
- Electrode 101 may be supported by some substrate 90 .
- the electrode 102 is provided with a pattern of holes (apertures 22 ) such that no electrically isolated portion occurs within the unit cell 10 .
- the typical thickness of the electrode 102 is also determined to be a thickness that does not require consideration of the permeability to electromagnetic waves, similarly to the electrode 101 .
- the half space above the electrode 102 (in the direction of the z-axis in the figure) is typically filled with vacuum or air, with no medium having a significant effect on electromagnetic waves of the operating frequency.
- the electrode 102 a substance whose dielectric constant and refractive index are small when viewed from the semiconductor superlattice structure 110 or the like can be placed (not shown).
- the electrodes 101 and 102 physical constants for perfect conductors that do not need to consider transparency are adopted in the calculations described later. Even if the electrodes 101 and 102 are made of a metal film that does not have a sufficient thickness or a material that should be made transparent, the electromagnetic properties of the substrate 90 and the semiconductor superlattice structure 110 are reduced. A person skilled in the art can easily make calculations that reflect material parameters of actual conductors by considering the response and design changes accordingly.
- the semiconductor superlattice structure 110 has an active region 112 .
- the active region 112 a large number (for example, 100) of unit structures are stacked repeatedly.
- the semiconductor superlattice structure 110 is provided with layers for electrical operation, for example layers, such as highly doped n-type layers (not shown). As such, semiconductor superlattice structure 110 may include layers not explicitly shown.
- the units of the periodic structure of the photonic crystal 120 in the PhC-QCL device 1000 are unit cells 10 indicated by rectangular parallelepipeds in FIG.
- the unit cell 10 includes at least an electrode 101, a semiconductor superlattice structure 110, and an electrode 102 in order of thickness. In numerical calculations to be described later, the unit cell 10 may include the vacuum and air portions described above.
- the unit cell 10 typically includes at least one column hole 20 and is defined in a shape such that a large number of photonic crystals 120 of the same shape can be arranged two-dimensionally and filled up. That is, the photonic crystal 120 is constructed by tiling the unit cells 10 along the xy plane of FIG.
- the range and shape of the unit cell 10 can be arbitrarily determined as long as it can serve as a unit of the periodic structure of the photonic crystal 120 .
- the unit cell 10 can also be determined according to the convenience of various calculations to be described later.
- column holes 20 have openings 22 in electrodes 102 .
- the column holes 20 In the semiconductor superlattice structure of the present embodiment in which a periodic structure is also incorporated, typically, the column holes 20 have the same cross-sectional shape as the openings 22, and the unit structure of the semiconductor superlattice structure 110 is laminated. extending in the direction of Such column holes 20 can be made by any method such as etching.
- the electrode 101 is a uniform film over the extent of the photonic crystal 120 containing multiple column holes 20 .
- the arrangement of the unit cells 10 is preferably such that a large number of column holes 20 are arranged to form a triangular lattice.
- the electrodes 102 on both sides of at least one boundary separating adjacent unit cells 10 are electrically connected to each other so that no electrically isolated portion is generated in the range of any unit cell 10, and a large number of electrodes 102 are connected to each other. Electrical continuity is ensured across the electrodes 102 that span the unit cell 10 .
- the configuration of the photonic crystal 120 that is, the shape and range of the unit cell 10, and the specific shape of the column holes 20 in the unit cell 10 are determined according to the final performance. In other words, these specific designs can be tuned to have good performance at frequencies of interest.
- the column holes 20 there are no particular conditions required for the column holes 20 to be able to become the unit cells 10 and the photonic crystals 120 in this embodiment before the specific design. , is determined according to criteria described later for the photonic crystal 120 after design.
- the depth of the column holes 20 may be determined to pass through both the electrode 102 and the semiconductor superlattice structure 110 or may be determined to pass through the electrode 102 only and not through the semiconductor superlattice structure 110 at all.
- the cross-sectional shape of the column hole 20 is also the same.
- the photonic band formed by the photonic crystal is carefully investigated and its suitability is judged.
- FIG. 2 is a diagram of an example photonic band calculated for the PhC-QCL device of this embodiment.
- FIG. 3 is an explanatory diagram showing the concept of a two-dimensional reciprocal lattice space, showing a two-dimensional reciprocal lattice space of a triangular lattice.
- the photonic crystal 120 forms a photonic band due to its periodicity.
- the photonic band is described in the planarly spreading reciprocal space of the PhC-QCL device 1000 along the XY plane in FIG. 1, that is, in the two-dimensional reciprocal space of the k x and ky components in FIG. In Fig.
- the photonic band is summarized in a region surrounded by a small number of feature points, based on the concept of the irreducible Brillouin zone based on the symmetry of the photonic crystal, in order to follow the conventional representation of the photonic band.
- FIG. 2 the components of the wave vector in the plane direction in the reciprocal lattice space on the XY plane of FIG.
- the k-index of 0 to 60 shown on the horizontal axis of FIG. correspond to positions in the reciprocal lattice space passing through point K (k-index 20), point M (k-index 40), and returning to point ⁇ .
- the ⁇ point, K point, and M point are feature points in the triangular lattice.
- FIG. 2 is of a photonic crystal that is infinitely wide and has no defects.
- the ⁇ point which is the position of the left and right ends of the graph paper surface in FIG. Only the k z component has a non-zero value. That is, the ⁇ point corresponds to an electromagnetic wave traveling in the surface normal direction (the z-axis direction in FIG. 1) for a generally planar (slab)-shaped element of the PhC-QCL element 1000 .
- the vicinity of the ⁇ point corresponds to a direction with a slight inclination from the surface normal direction, and the positions where at least one of the k x component and the k y component are non-zero correspond to electromagnetic waves traveling in a direction inclined from the surface normal. .
- the PhC-QCL element 1000 has a schematic structure of a PhC slab with a laminated structure of metal/photonic crystal (PhC)/metal.
- a light line LL can be assumed in the PhC-QCL device.
- This light line LL defines the boundaries of propagation and emission. That is, the mode below it (lower frequency side) is the mode propagating inside the plate-like PhC-QCL element 1000, that is, the guided mode that cannot escape from the surface of the slab, and the mode above the light line LL
- the light line LL defines a boundary that makes the (high frequency side) mode a mode in which electromagnetic waves can propagate to the outside, that is, a radiation mode.
- the procedure for designing the photonic crystal 120 in the PhC-QCL device 1000 in this embodiment is to first specify the shape and size of each part that determines the photonic crystal 120, and then the second electrode 102 is formed.
- a photonic band is calculated for the photonic crystal 120 .
- the photonic band can determine which frequencies are suitable or promising for lasing operation and emission to the outside. That is, in the calculated photonic band, if it is possible to obtain a frequency at which the value of the radiation constant necessary for laser oscillation operation and the desired radiation profile are realized, the photonic band having the photonic band can be obtained. It can be said that the nick crystal 120 is well designed for that frequency.
- the shape, extent and size of the parameters of the photonic crystal 120 can be readjusted so that the photonic band becomes lasing at that frequency. and emission to the outside are reviewed by the criteria described above. Such readjustment and review are repeated to achieve the required radiation constant value and the desired radiation profile.
- the semiconductor superlattice structure 110 of the PhC-QCL device 1000 is then designed for lasing operation for the likely frequencies.
- the frequency range in which the semiconductor superlattice structure 110 can oscillate in, for example, a normal double metal wall waveguide structure is determined.
- the frequency range in which the laser oscillation operation can be realized is reflected in advance. This is because it is meaningless even if the photonic crystal 120 is well designed at a frequency at which the semiconductor superlattice structure 110 cannot be expected to oscillate.
- the design of the photonic crystal 120 is then adjusted to search for a suitable frequency for lasing operation of the semiconductor superlattice structure 110 . It is also possible to use the internal structure of the unit structure of the active region 112 in order to adjust the characteristics of the photonic crystal 120 .
- the frequency at which the photonic crystal 120 has a photonic band suitable for oscillation can be changed by adjusting the size reflecting the geometric aspect. This property makes it possible to adjust the frequency suitable for the photonic crystal 120 when the oscillation frequency and its range are specified from the viewpoint of the application.
- each candidate frequency for the photonic band of FIG. 2 is as follows: (Frequency 1) Although frequency 1 satisfies the criteria as a candidate frequency in terms of radiation constant, there remains concern about a parasitic mode. This is because if a parasitic mode occurs on the write line LL at frequency 1, the parasitic mode may cause unexpected results. This concern can be removed by trial calculations with reasonable boundary conditions. There is also concern about the presence of multiple modes near the ⁇ point of the candidate frequency.
- the beam quality may be lower than that of pure ⁇ -point emission.
- Frequency 2 has too small a radiation constant. Therefore, frequency 2 does not meet the criteria as a candidate frequency.
- Frequency 3 Although frequency 3 satisfies the criteria as a candidate frequency in terms of radiation constant, there remains concern about a parasitic mode. This is because a parasitic mode is seen on the light line LL at frequency 3, which can lead to unexpected results. It should be noted that the number of modes near the ⁇ point is smaller at frequency 3 than at frequency 1, so it is expected that better beam quality than at frequency 1 will be obtained if no problematic mode occurs on the light line LL. be done.
- Frequency 4 At frequency 4, the radiation constant of the mode near the ⁇ point is too small. Therefore, frequency 4 does not meet the criteria as a candidate frequency.
- Frequency 5 At frequency 5, the radiation constant of the mode near the ⁇ point is too small. Therefore, frequency 5 does not meet the criteria as a candidate frequency.
- Frequency 6 Frequency 6 satisfies the criteria as a candidate frequency in terms of radiation constant. This frequency 6 has no parasitic modes on the write line LL. The only possible problem is the interaction between the ⁇ -point mode and the boundary conditions.
- frequencies 1, 3, and 6 among frequencies 1 to 6 can be promising frequency candidates from the viewpoint of radiation constant and parasitic mode. Specifically, frequencies 1 and 3 are promising, although they require investigation of parasitic modes. Frequency 6 does not require investigation of parasitic modes and is particularly promising.
- the photonic band has a radiation mode of the relevant frequency (referred to as "target radiation mode” in this section) at or near the ⁇ point.
- the target radiation mode should have a radiation constant within a predetermined range (eg, 10/cm to 40/cm). As a result, efficient surface radiation and amplification can be expected.
- C3 If there is no other mode with a larger horizontal wavenumber (k
- the radiation constant referred to in the above judgment is the radiation output loss per unit distance, which is calculated in each mode after determining the complex frequency component by the FDM method. That is, the radiation constant is an index of the propagation mode loss of the electromagnetic wave, and is a quantity proportional to the reciprocal of the resonance Q value.
- a mode with a small radiation constant has a stronger resonance and a narrower spectral width than a mode with a large emission constant.
- a target radiation mode and a parasitic mode coexist.
- the parasitic mode exhibits a smaller radiation constant than the radiation constant of the target radiation mode, the electromagnetic waves due to the stimulated emission are consumed in the electromagnetic wave amplification of the parasitic mode. Therefore, that frequency is not suitable as the oscillation frequency, and the mode at or near the ⁇ point of that frequency is also not suitable as the target radiation mode.
- the target radiation mode loses the mode competition if there is a parasitic mode with a similar frequency and the parasitic mode exhibits a smaller radiation constant.
- the target radiation mode is relatively hard to excite. It is irrelevant whether or not a parasitic mode that has a small radiation constant and can become an obstacle is a waveguide mode. A parasitic mode that becomes a waveguide mode does not emit light to the outside and becomes an obstacle.
- parasitic modes involving kz rather than waveguide modes, allow beams of surface emitting beams to have oblique angles due to the total wavevector, because the beams are difficult to use. .
- the preferred scenario for realizing light emission in the direction normal to the surface with small beam divergence is that “at the target laser oscillation frequency, the mode (radiation mode) at or near the ⁇ point exists, and if other modes exist. have a relatively smaller radiation constant even if the
- the mode of the target frequency in the photonic band can be preferable if it gives either the lower limit or the upper limit of the bandgap at or near the ⁇ point.
- a mode that gives the lower limit or upper limit of the bandgap at or near the ⁇ point does not have a mode other than at or near the ⁇ point, so C is satisfied.
- the details of the specific structure shown in FIG. 1 can be omitted as appropriate to the extent that they do not affect the results.
- the laminate of the first electrode 101, the semiconductor superlattice structure 110, and the second electrode 102 is simplified to a perfect conductor (PEC)/semiconductor layer/PEC structure. This replacement is made in order to describe the first electrode 101 and the second electrode 102 as lossless perfect conductors.
- unit cell analysis is performed.
- photonic band structures and radiation constants are calculated using several variables under periodic boundary conditions.
- variables here are active layer occupancy, photonic crystal geometry, frequency, and horizontal wavenumber.
- the calculation method of unit cell analysis is a combination of the finite difference time domain (FDTD) method, the discrete Fourier transform (DFT) method, and the filter diagonalization method (FDM).
- FDTD finite difference time domain
- DFT discrete Fourier transform
- FDM filter diagonalization method
- This candidate mode is likely to exist only near the ⁇ point and has a sufficient radiation constant.
- Section 2.1 describes the band structure, radiation constant, and far field calculation method based on the method adopted in this embodiment. Results derived based on unit cells and finite chip area are described in Section 2.2.
- FIG. 4A shows a three-dimensional perspective view of the unit cell considered in this embodiment.
- spheres S1-S3 and spheres D1-D4 represented in unit cell 10 are point sensors and dipole radiation sources, respectively.
- FIG. 4B shows a typical unit cell in cross section through its center, with column holes 20 extending from openings 22 through semiconductor superlattice structure 110 in the direction of stacking. Column holes 20 consist of air and Convolutional Perfect Matched Layers (CPML) in areas where openings 22 are not shown in FIG. 4B.
- CPML Convolutional Perfect Matched Layers
- FIG. 4C shows a cross-section of unit cell 10 at the middle of the thickness of semiconductor superlattice structure 110 .
- the mesh of the elements set by the discretized Maxwell's equations is clearly shown at the lower left, thereby clearly showing fine irregularities occurring in the model reproducing part of the side surface of the column hole 20 .
- explanations and illustrations using a GaAs-based compound semiconductor as a typical material for the semiconductor superlattice structure 110 may be given, but the material of the semiconductor superlattice structure 110 is not limited. .
- the boundaries of the +z and -z coordinate axes of the simulation region were set as CPML. All other boundaries were set to periodic boundaries.
- the practical average refractive index n of a QCL structure depends on barrier thickness, doping density, operating frequency, and optical It fluctuates according to the change of the gain. Therefore, using an experimentally measured refractive index n before starting the unit cell design would be a better approach for more accurate waveguide design.
- the metal layer is replaced by a lossless perfect electrical conductor (PEC).
- the calculation results in this embodiment give good predictions in a parameter range where substituting the material of the electrodes 101 and 102 with PEC does not cause any substantial problems.
- the performance in the wavelength range of 16 ⁇ m or more, that is, the frequency range of 18.7 THz or less, in which consideration of loss may not be necessary when an existing metal material is formed into appropriate conditions and shapes, is appropriately predicted from the calculation results of this embodiment. be.
- the DFT in FDTD can take an unreasonably long simulation time to extract the radiation constant and split the close modes together around a certain frequency.
- FDM FDM
- n and c are the refractive index of the QCL material of the semiconductor superlattice structure 110 and the speed of light in vacuum.
- Radiation constant is defined as the radiation power loss ratio per unit length of a mode and is synonymous with surface radiation loss.
- the beam pattern, divergence angle, and emitted/absorbed power in surface-emitting operation in the PhC-QCL device 1000 are converted from near-field to far-field (NF-FF conversion). can be estimated using Poynting's theorem.
- NF-FF conversion near-field to far-field
- 15 columns and a half (for 7 unit cells) are arranged in the x direction, and 15 rows of unit cells are arranged in the y direction. Due to the symmetry of both ends in the x direction, the present disclosure describes 15 (16) x 15 unit cells in order to express that seven more unit cells are added.
- FIG. 5A is a three-dimensional perspective view of the waveguide structure employed for the calculation of the PhC-QCL device 1000.
- FIG. 5B shows a cross-sectional view along the yz plane cutting through the center of the semiconductor superlattice structure 110 .
- the ⁇ x-axis edge boundaries of the box sensor are located near the ⁇ x-axis CPML. The placement of this box sensor is indicated by the dotted white line.
- the Lorentz model was adopted assuming that the active region 112 of the semiconductor superlattice structure 110 is a linear gain material.
- three-dimensional Maxwell-Bloch equations are modeled taking into account detailed epitaxial structures and doping profiles within the unit structure of active region 112. must be resolved.
- the Lorentzian model assuming a linear gain material is sufficient.
- the Lorenz model is represented by the following equation (2).
- ⁇ r , ⁇ r,base , ⁇ LORENTZ , ⁇ o , ⁇ o are, in order, the total dielectric constant, the dielectric constant of the substrate, the Lorentz permittivity, the Lorentz resonance, and the Lorentz linewidth.
- ⁇ r , ⁇ r,base , ⁇ LORENTZ , ⁇ o , ⁇ o are, in order, the total dielectric constant, the dielectric constant of the substrate, the Lorentz permittivity, the Lorentz resonance, and the Lorentz linewidth.
- the same simulation parameters used for the unit cell calculations were used for the large-area PhC ⁇ Applies to QCL waveguide calculations.
- a TM-polarized dipole radiation source and point sensors were placed at random locations on a semiconductor superlattice structure 110 simulated in GaAs.
- Two planar sensors are placed on the semiconductor superlattice structure 110, on the right PEC, and near the CPML at the +x boundary, respectively. All sensors collect field strength as a function of time for post-processing. After completing the time evolution process, NF-FF conversion, DFT, and optical power calculation are performed.
- Example 1 Structure that employs equilateral triangular lattices
- the present embodiment will be described with specific calculation results by using the found preferable configuration as an example and the configuration to be compared as a comparative example.
- FIG. 6 is a diagram of photonic bands actually extracted.
- the unit time step was fixed at ⁇ t ⁇ 2.86 ⁇ 10 ⁇ 16 s for the photonic band calculation.
- FIG. 6A shows the relative field strength after Fourier transformation as a function of frequency and k-index representing the irreducible Brillouin zone.
- the 0, 20, 40, and 60 indices of k are the ⁇ -point, K-point, M-point, and ⁇ -point, respectively (Fig. 3).
- a frequency whose field strength is stronger than that of its immediate neighbors implies that a resonant mode or mode exists at that frequency for a fixed wave vector.
- FIG. 6B is a diagram of photonic bands extracted by post-processing by enlarging the vicinity of the frequency domain of the bandgap.
- FIG. 6B clearly shows frequencies with resonant modes only at the ⁇ point just below the bandgap.
- FIG. 7 is a graph of surface losses for modes near the ⁇ point calculated using FDM for a PhC-QCL device.
- FDM analysis was performed over the regions 0 ⁇ k index ⁇ 5 and 55 ⁇ k index ⁇ 59 in FIGS. 6A, 6B.
- the unit cell structure was recalculated after adopting a narrow-bandwidth modulated Gaussian waveform to reduce the error rate of the FDM analysis. 1.5 ⁇ 10 6 time evolution iterations were performed on the narrow bandwidth waveform.
- the time constant of the narrowband modulated Gaussian waveform was determined by 8.58/ ⁇ /(bandwidth).
- the mode located at 2.7638 THz on the far right in FIG. 5 is the FDM-extracted ⁇ point mode.
- the square marks and circle marks in FIG. 5 denote positive and negative frequencies, respectively, and each numerical value attached to the top indicates the k index in FIG. It is judged that a near-degenerate mode is a mode in which the circular circle and the square mark at the top are fused at almost the same frequency.
- the wavevectors k x and k y in the modes with k index 1 close to k index 0 are 2834 m ⁇ 1 and 0 m ⁇ 1 respectively.
- the beam divergence can increase for modes near the ⁇ -point when the coupling between modes becomes stronger.
- Such beam divergence can also be suppressed by designing the semiconductor superlattice structure 110 such that the energy that gives the maximum gain is slightly above the ⁇ -point mode. It is also possible to refine the shape of the unit cell to have a better surface loss map than FIG. 7 for PhC-QCL, ie to search for a better unit cell structure (described later as Example 2).
- FIG. 9A-C show
- 2 is a map showing magnitudes of electric field components of
- the field distribution results appear to be overwhelmingly dominated by the surface-normal radiation compared to the oblique direction.
- the electric field distribution at the end of the time evolution was also very similar to the distribution in FIG. Since the CPML is set as the boundary, the field distribution near the edge gradually disappears and no periodic field pattern is observed near the boundary.
- Figures 9A-C show the expected results from unit cell calculations even for a countable small number of unit cells, 15 (16) x 15 unit areas (EA).
- Figures 10A-F show the strength of the electric field components as a function of the y and z coordinates at the positions of the two YZ planar sensors.
- a first YZ-plane sensor is located in the middle thickness of the semiconductor superlattice structure 110 .
- the second YZ planar sensor is positioned to keep the distance between the PhC-QCL element 1000 and the sensor at 100 ⁇ m, ie 100 ⁇ m away from the PhC-QCL element 1000 in the x-direction in FIG. 5A.
- FIGS. 10A-C and 10D-F show
- FIG. 11 is a graph showing the field and its Fourier transform at a point sensor in semiconductor superlattice structure 110 .
- An exponential amplification is evident in the oscillating curve recorded by this point sensor.
- a Fourier transform of it shows a sharp peak.
- An FDM analysis was also performed based on the field data of FIG.
- the peak frequency and loss of E x (f) in FIG. 11 were derived by FDM to be 2.77357 THz and ⁇ 20.27 cm ⁇ 1 , respectively.
- the calculated loss of semiconductor superlattice structure 110 at 2.77357 THz based on the Lorentz model of FIG. 8B was approximately ⁇ 27.867 cm ⁇ 1 . Negative losses are associated with positive gains. Therefore, the sum of surface loss and interfacial loss is about 7.597 cm ⁇ 1 .
- the discrepancy between 7.597 cm ⁇ 1 and FIG. 7 is due to whether or not the Lorentz model is applied.
- FIG. 12A is a far-field pattern calculated based on the vector potential method calculated for the PhC-QCL element 1000, and FIG. 12B is its radiation pattern.
- An additional YZ planar sensor was set up to fill inside the dashed line in FIG. 5B for NF-FF conversion.
- the distance in x-coordinate between the planar sensor and the PhC-QCL element 1000 is 110 ⁇ m near the CPML boundary.
- NF-FF conversion was performed at 2.78 THz.
- FIG. 12A shows a heatmap representation of the far field as a function of ⁇ and ⁇ for the spherical coordinates illustrated in the inset of FIG. 12B.
- the distance of observation point r from the QCL was fixed at 1000 m.
- a typical beam divergence is calculated based on the full width at half maximum (FWHM) of the far-field pattern.
- the maximum intensity in the far field is concentrated in the surface normal direction. Beam divergence is reduced by increasing the chip area and the number of unit cells.
- the slab of the semiconductor superlattice structure 110 of the PhC-QCL device 1000 should be advanced in the in-plane direction toward the boundary and the light output absorbed at the interface should be minimized. is.
- the ratio of the power radiated through the surface to the power absorbed through the interfaces of the slabs of semiconductor superlattice structure 110 (referred to in this disclosure as the "power ratio") is 1.958:1 for that of FIG.
- Example 2 (optimization from Example 1)
- r 32 ⁇ m.
- the oscillation frequency is accordingly set to 2.76 THz.
- the photonic band structure showed almost no graphical difference from that of FIG. 6B, but good characteristics were realized in a direction slightly inclined from the ⁇ point (direction near k index 58 in FIG. 6B).
- the optimization results in a power ratio of 20.6:1 between the power radiated through the surface and the power absorbed through the interfaces of the slabs of semiconductor superlattice structure 110 . The reason for this is that by changing the size of each part in the photonic crystal shown in FIGS. This is thought to be due to the fact that the electromagnetic waves reaching the interface of the slab decreased.
- Comparative Example 1 (triangular lattice of circular air holes)
- the surface-emitting PhC-QCL waveguide established in this disclosure is compared against another structure (Comparative Example 1) with cylindrical air holes in the metal layer and active region.
- the unit cell structure of Comparative Example 1 has cylindrical air holes.
- each candidate frequency of the photonic band in the case of having the cylindrical air hole of FIG. 13 is determined as follows.
- Frequency 1 has too small a radiation constant for the mode near the ⁇ point. This makes it impossible to meet established standards.
- Frequency 2 is 2.02 THz and may satisfy the criteria in terms of radiation constant as a candidate frequency, but parasitic modes on the light line at the target frequency may cause unpredictable results. Therefore, trial calculations under reasonable boundary conditions are required.
- a mode that cannot be said to be pure ⁇ -point emission may degrade the beam quality.
- Comparative Example 2 (Square lattice of isosceles right triangle air holes) As Comparative Example 2, a photonic crystal with a square lattice in which the cross-sectional shape of the column hole disclosed in Patent Document 1 and FIG. So we investigated.
- 14A to 14C are a perspective view (FIG. 14A), a plan view (FIG. 14B), and a cross-sectional view (FIG. 14C) at a position passing through the center of the square of the unit cell of the photonic crystal to be calculated in Comparative Example 2.
- FIG. 15 is an explanatory diagram for explaining the irreducible Brillouin zone in the reciprocal lattice space of the square lattice.
- FIG. 16 is a perspective view of the QCL waveguide structure of Comparative Example 2 in which unit cells are arranged for calculating properties in the far field.
- 17A to 17C show the photonic bands calculated in Comparative Example 2, where the conditions of Candidate 1 are shown.
- the frequencies evaluated were 1.21, 3.02, or 3.07 THz for candidate 1 and 1.43, 1.54, 2.04, 3.11, or 3.22 THz for candidate 2.
- ⁇ r,base was set to 12 and ⁇ LORENTZ was set to ⁇ 0.002.
- the number of cells is 15 ⁇ 15 EA, and the CMPL is 2 EA, for a total of 17 ⁇ 17 EA.
- Example 3 As Example 3 for the embodiment of the present disclosure, a case will be shown in which the cross-sectional shape of the column holes in the unit cell is optimized by extending it to other than triangular while maintaining the arrangement of the triangular lattice.
- various cross-sectional shapes with three-fold symmetry were tried, in response to the fact that the equilateral triangular cross-sectional shape gave good results in Examples 1 and 2. This is because, for a triangular lattice with three-fold symmetry, if the column holes serving as lattice points have a cross-sectional shape that does not have three-fold symmetry, the mode configuration of the photonic band becomes complicated. This is to get away from the concept of the present disclosure.
- FIG. 18A and 18B are explanatory diagrams showing the degree of freedom provided for optimizing the cross-sectional shape of the column hole in the unit cell in Example 2.
- FIG. A unit cell arranged in a triangular lattice is provided with representative coordinates (a, b), and an equilateral triangle for arrangement centered thereon is considered.
- the size of this array equilateral triangle can be described by the distance r1 from the coordinates (a, b).
- Seven reference points are assumed, which are the midpoints of the three sides of an equilateral triangle (Point1 to Point3) and the vertices (Point4 to Point6) of the upper, lower left, and lower right equilateral triangles viewed from the center. .
- a cross-sectional shape can be expressed by arranging small figures (sub-patterns) centered at respective reference points and overlapping them as necessary. This sub-pattern is arranged or not, and its size and shape are changed. As for the shape of the sub-pattern, in the optimization of Example 2, an equilateral triangle, a regular hexagon, or a disc is tried. Using the length that determines the size of each sub-pattern in addition to the above-described distance r1, the cross-sectional shape of the column hole provided in the unit cell can be changed in an extremely diverse manner. In the present disclosure, a shape specified by an overlapping range of sub-patterns is called a combined shape.
- the depth h of the column hole is also adopted as a parameter used for calculation.
- the calculation target is the case where the same depth is applied to the sub-patterns provided at all the reference points. Further, the sub-patterns also employ shapes exhibiting at least three-fold symmetry.
- FIG. 19 is a plan view showing cross-sectional shapes of various column holes tested in Example 3 of the present embodiment.
- the cross-sectional shape is diverse, with discs, regular hexagons, and equilateral triangles being adopted as sub-patterns.
- good properties were obtained with the nine cross-sectional shapes enclosed by solid lines. All of them have a combined shape in which a sub-pattern disc and three equilateral triangles are overlapped.
- Equilateral triangles are identical in size and orientation to each other.
- three equilateral triangles of good quality combination shapes are arranged with their centers in different directions of 120° at equal distances from the center of the disk serving as the subpattern.
- the sizes are such that each does not overlap the entire circumference of the disc on at least one side. Note that the cross-sectional shape shown in the first row, second column in FIG. 19 is not preferable because an electrically isolated minute piece of the electrode remains in the center of the three circles.
- a sub-pattern is a circular plate having the center aligned with the center of the equilateral triangle for arrangement. No subpattern is placed at the midpoint of the array equilateral triangle.
- the radius Rc of the disk and the size of the equilateral triangle of the subpattern are required to indicate the size of the disk.
- the parameters are the distance R2 given in the same manner as the equilateral triangle for arrangement, and the depth h of the column hole.
- FIG. 20B is the far-field pattern for that configuration.
- the power ratio is between 1.958:1 in Example 1 and 20.6:1 in Example 2, which is extremely good.
- QCL elements can be designed that exhibit similar far-field patterns.
- the Y-axis and Z-axis are also set so as to cover the region of the PhC-QCL device 1000 .
- the box sensor is placed near the CPML in the simulation domain and contains a perfect conductor (PEC), a semiconductor superlattice structure 110, and air. Therefore, of the six components in the denominator of the above equation, only P +x is output from the PhC-QCL element 1000 to the space on the side of the second electrode 102 and contributes to radiation, but the remaining five components are The PhC-QCL device 1000 does not contribute to radiation due to being absorbed.
- PEC perfect conductor
- the FDM method was used to determine the complex frequency component for each component of the electromagnetic waves, and further determine the radiation output loss per unit distance for each mode.
- a frequency having a mode only in the vicinity of the ⁇ point is taken as a candidate.
- Predicted photonic band structures corresponding to the candidate frequencies are once collected.
- the target frequency mode preferably has a radiation constant of 10/cm or more in the THz region.
- the reason for this is that when the active layer occupancy is small, the electronic band structure becomes complicated, the area for photon generation decreases, and current diffusion in the metal layer of the second electrode 102 becomes difficult.
- the radiation constant is set to 10/cm or more and 40/cm or less.
- b. There are no modes except in the immediate vicinity of the ⁇ point at the target frequency.
- c. In FDTD, FT (Fourier transform), and FDM, it is sometimes difficult to detect the mode on the light line. Also, the Fourier transform or FDM may fail to extract possible modes. Therefore, it is important for searching the target frequency and mode in FDTD to estimate the beam quality and LEE by far-field analysis after arranging several unit cells.
- a unit cell of a triangular lattice is defined as a rectangular area with (3) 1/2 /2a and a as sides in a plane.
- a is a parameter that gives the lattice constant of the triangular lattice and is fixed in the calculation.
- r On a cylinder, we change the diameter of the circle, and on an equilateral triangle, we change r (FIG. 4C). This changes the size of the modified column hole, whether it is a circle or an equilateral triangle.
- h is the thickness of the semiconductor superlattice structure 110;
- 21A and 21B show photonic band modes in configurations in which column holes with circular and equilateral triangular cross sections are formed through the second electrode 102 and the semiconductor superlattice structure 110, respectively.
- This is the above calculation result when h is set to 85 ⁇ m and a is set to 64 ⁇ m.
- the lower limit of the active layer occupancy is determined within a numerical range in which the second electrode 102 does not have an electrically isolated portion.
- Empty triangle symbols represent the frequency of the electric field intensity peak when the gradient dI/df of the electric field intensity switches from positive to negative in the frequency domain after DFT.
- I means the sum of the intensities of the electrical and magnetic components after DFT from all distributed point sensors.
- the filled round symbols in FIG. 3 represent the modes extracted by the FDM analysis.
- the modes extracted by FDM for each electric field component are painted in order from the one with the largest error to the one with the smallest error, and the PBS with the radiation constant is observed. Of the modes extracted by FDM, only those with an error rate of 10-4 or less are considered meaningful.
- the color of the filled circle means the value of the radiation constant.
- the scale of FIG. 21A is common to all figures describing radiation constants in this embodiment. From the plotted results based on both DFT and FDM, it is possible to trace the frequency shift trend of each mode as a function of active layer occupancy.
- the three modes near active layer occupancy ⁇ 1 are located at frequencies near 1.5 THz, 2.5 THz, and 3 THz, respectively. These modes are distributed as a function of active layer occupancy. During the trace of each mode, some irregular modes are observed that deviate from the trace. Such modes can be caused by numerical noise, imperfections in the shape description due to coarse spatial discretization by Yee's algorithm, and some peculiar scattering phenomena. In this embodiment, we focus on modes that can be systematically traced as a function of the active layer occupancy. In this design, since stable high-power light emission is targeted, we focus on a mode with a radiation constant of 10/cm or more and 40/cm or less.
- the planar shape of the circle or equilateral triangle is smaller than a certain size, no electrically isolated portion is generated in the second electrode 102. However, if the planar shape exceeds that size, a circular shape or an equilateral triangle appears at the boundary of the unit cell. An electrically isolated portion is generated in the second electrode 102 by overlapping with those of the adjacent unit cells. For this reason, the lower limit of the active layer occupancy, which reflects the upper limit of dimensions that do not cause electrical isolation, is also geometrically determined. becomes. As for the conditions adopted in the numerical calculation, the above lower limit is set to a value slightly larger than the geometrical value in order to meet the requirement of not having an electrically isolated portion.
- FIGS. 21A and 21B show that one and three modes with a radiation constant of 10/cm or more are found for photonic crystals of a cylinder (C1) and uniform triangular prisms (T1 to T3), respectively. Such modes are indicated by black arrows in FIGS. 21A,B as a function of active layer occupancy. Although some 3 THz-derived trajectories in Fig. 21A,B meet the established simple selection criteria, the 3 THz-derived ⁇ -point mode frequencies exhibit a complex band structure as a function of horizontal wavenumbers. This means that severe mode competition will occur. Therefore, we will not analyze such modes.
- FIGS. 22A-C are graphs showing the change in performance when the active layer occupancy is changed along the C1 line and the T1-T3 line (FIGS. 21A, B) by changing the shape parameter;
- the relationships of active layer occupancy-frequency (FIG. 22A), active layer occupancy-LEE (FIG. 22B), and frequency-LEE (FIG. 22C) are shown.
- the LEE is plotted in accordance with the change series, and a schematic plan view is attached to show those with circular column holes and those with equilateral triangular column holes. .
- a schematic diagram of a cross-sectional view for distinguishing from other structures described later is attached outside the graph.
- the shape of the black region is indicated by the shape of the column hole, and in the cross-sectional view, the active layer is removed at the position passing through the column hole.
- the arrows from the plan view point to the positions of the active layer occupancies that give rise to the shape of the plan view.
- FIGS. 22A and 22B show arrows pointing to the position and data of the active layer occupancy at which the highest LEE was obtained in the designs of circular column holes and equilateral triangular column holes. It is assumed that the ratio is drawn accurately under these conditions.
- Parameter a and parameter d employed to realize the active layer occupancy are also shown as appropriate.
- the parameter a is a parameter (FIG. 4C) that defines the planar shape of the unit cell 10 as a rectangular area with (3) 1/2 /2a and a as the sides.
- Electric field distribution in operation Fig. 23A
- far-field pattern Fig. 23B
- the emission profile is also concentrated near the surface normal, predicting high quality surface emitting operation.
- the frequency at which a good LEE and beam profile are obtained can be adjusted by changing the dimensions that determine the shape (for example, a that gives the lattice constant of the triangular lattice).
- a that gives the lattice constant of the triangular lattice For example, a that gives the lattice constant of the triangular lattice.
- FIGS. 24A to 24C show calculation results when (a, h) are (32 ⁇ m, 10 ⁇ m) for equilateral triangular column holes. At that time, the results for circular column holes in FIGS. 22A to 22C are displayed as they are for comparison. Schematic diagrams of a cross-sectional view and a plan view are attached outside the graph, and the definitions of the parameters there are the same as those described above with respect to FIGS. 22A and 22B. FIGS.
- 25A and 25B are for (a, h, r, active layer occupancy, frequency) when (32 ⁇ m, 10 ⁇ m, 15.5 ⁇ m, 0.648, 3.77 THz) and (32 ⁇ m, 10 ⁇ m, 16 .5 ⁇ m, 0.601, 3.95 THz). Since the respective LEEs are 0.904 and 0.981, it was confirmed that good operation in the region of 3 to 4 THz can also be realized by necessary design changes in this embodiment.
- the electrode 102 of the semiconductor superlattice structure 110 has the opening pattern of the second electrode 102, but the semiconductor superlattice structure 110 is a uniform structure that is not patterned.
- Nicked crystals are also useful.
- the design was attempted by applying the selection policy described above.
- FIGS. 26A to 26C against FF (electrode coverage or filling factor in a planar pattern), FF vs. frequency (FIG. 26A), FF vs. LEE (FIG. 26B), frequency vs. LEE (FIG. 26C).
- FF electrode coverage or filling factor in a planar pattern
- FIGS. 26A to 26C schematic diagrams of cross-sectional views and plan views are attached, and the definitions of parameters therein are the same as those described for FIGS. 22A and 22B.
- the cross-sectional view shows the placement of the semiconductor superlattice structure whether or not it is directly below the electrode opening pattern.
- FIG. 27B frequency-LEE
- T1-a a promising mode distinguished from T1-a and T1-b, which give different frequencies. are doing.
- the LEE was 0.8 at 3.01 THz operation under the condition that FF was 0.320. It was also confirmed that at 3.01 THz of this operation, a very good beam profile is achieved.
- Figures 28A-B are the photonic band structure (Figure 28A) and the far-field pattern ( Figure 28B) for this condition.
- the bandgap has a frequency of about 3 to 3.4 THz, and the position of about 3 THz, which gives the lower limit of the bandgap, has a mode (T1) only near the ⁇ point.
- the radiation constant of that mode satisfies 10-40/cm. Since this design has a mode only near the ⁇ point, it is expected that the radiation will be concentrated near the normal to the two-dimensional spread that forms the metal photonic crystal, and a good radiation profile will be obtained at a frequency of 3.01 THz. predicted (Fig. 28B). Even at a slightly lower 2.99 THz, which is the T1-a mode near the ⁇ point, the LEE drops to about 0.763 (FIG. 27B), but good operation is maintained (not shown).
- the PhC-QCL element of the present disclosure can be used in any device that uses it.
- PhC-QCL element 10 unit cell 20 column hole 90 substrate 101 electrode (first electrode) 102 electrode (second electrode) 110 semiconductor superlattice structure 112 active region LL light line
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Abstract
Description
本開示の実施形態では、通常はTMモードで発光動作するQCL素子を面発光で動作させるためにフォトニック結晶を採用するQCL素子(PhC-QCL素子)の構成が提供される。本実施形態のPhC-QCL素子は、特に、第1の電極層/活性層/第2の電極層との概略構造をもつものであり、一方の電極層(第2の電極)側を放射面とするような面発光動作をする。第1の電極、第2の電極は、典型的にはともに金属である。少なくとも第2の電極層には、フォトニック結晶をなす周期構造がエッチングなどにより作り込まれている。活性層は、半導体による発光動作のための層であり、繰り返して積層されている複数の単位構造からなる半導体超格子構造を取っている。具体的設計によっては、第2の電極に加え、半導体超格子構造においても周期構造がエッチングなどにより作り込まれて上記フォトニック結晶の一部となっている場合もある。本開示の実施形態では、主に、面発光の放射面となる電極(第2の電極)と半導体超格子構造との両方がフォトニック結晶を構成する実施形態と、その電極(第2の電極)だけがフォトニック結晶を構成する実施形態とが、この順に説明される。
図1は、本実施形態において性能を評価する例示のPhC-QCL素子1000の概略構成を示す説明図である。PhC-QCL素子1000は、概して、一対の電極101および102と、その間に挟まれるようになっている半導体超格子構造110とにより構成されている。電極(第1の電極)101および電極(第2の電極)102は、半導体超格子構造110に対し電界を形成するための電圧と電磁波の放出または発光のための電流とを外部から受けるために利用される。半導体超格子構造110は、繰り返して積層されている複数の単位構造からなる活性領域112を有している。それ以外にも半導体超格子構造110は動作に必要な層を含む場合がある。
つぎに、具体的なフォトニック結晶の設計手順を、その良否の判定基準とともに例示により説明する。図2は、本実施形態のPhC-QCL素子に対して算出した一例のフォトニックバンドのダイヤグラムである。図3は、2次元逆格子空間の概念を示す説明図であり、三角格子の2次元逆格子空間を示している。フォトニック結晶120は、その周期性によりフォトニックバンドを形成する。そのフォトニックバンドは、図1のXY平面に沿ったPhC-QCL素子1000の平面的な広がりの逆格子空間つまり図3のkx成分とky成分の2次元逆格子空間で説明される。図2では、フォトニックバンドの慣用的な表現に従うよう、フォトニック結晶の対称性に基づく既約(irreducible)ブリルアンゾーンの概念に基づいて、フォトニックバンドが少数の特徴点で囲んだ領域に集約して説明されている。具体的には、図2は、図1のXY平面の逆格子空間において波数ベクトルの平面方向の成分を横軸にとり、縦軸fを周波数として表現している。図2の横軸に示す0~60のk-indexは図3の代表的な経路上の各位置に対応させた波数ベクトルの平面方向の成分であり、図3のΓ点(k-index0)から順に、K点(k-index20)、M点(k-index40)を通過し、再びΓ点に戻る逆格子空間における位置に対応している。Γ点、K点、M点は三角格子における特徴点である。また、説明のため、図2は無限に広く欠陥のないフォトニック結晶のものとしている。図2におけるグラフ紙面の左右両端の位置であるΓ点は、現実の電磁波の3次元成分をもつ全波数ベクトルのうち、kx成分とky成分とが共にゼロの位置であるため、残りのkz成分だけがゼロでない値をもつ。つまりΓ点はPhC-QCL素子1000の平面的な広がりをもつ概して平板(スラブ)状の素子にとっての面法線方向(図1、z軸方向)に進む電磁波に対応する。Γ点近傍は面法線方向からわずかな傾斜をもつ方向に対応し、kx成分かky成分の少なくともいずれかが非ゼロの位置は、面法線から傾斜した方向に進む電磁波に対応する。
候補となる発振周波数では、半導体超格子構造110中にTM偏光の光子(電磁波)が生成されたときに放射定数が好ましいようなモードがΓ点近傍に見いだされる必要がある。その周波数において、水平方向波数が大きくΓ点近傍といえない他のモードは、たとえ存在したとしても、Γ点近傍のモードよりも放射定数が大きいことに起因してモード競合に敗れてしまう。図2は、後述する計算手法(DFTとFDM)により正三角形のPhC(ただし、a=64μm、r=30μm、活性領域占有率=0.67、図4C参照)を対象に算出したフォトニックバンドである。この計算例に基づいて、発振周波数候補の選択指針を説明し、つづけてより一般化した場合の選択指針を具体的に説明する。なお、図2では、Γ点であるk-indexが60の位置において、6個の周波数を円で囲って符号1~6を付している。本図に関する説明において、周波数1等はこの周波数を指す。
(周波数1) 周波数1は、放射定数の点では候補周波数として基準を満たすものの、寄生モードによる懸念が残る。周波数1でライトラインLL上に寄生モードが生じていると、その寄生モードが予測外の結果を引き起こす可能性があるためである。この懸念は、妥当な境界条件で試算すれば取り除かれうる。なお、候補周波数のΓ点付近に複数のモードが存在する点も懸念される。すわなち、純粋なΓ点発光よりもビーム品質が低下する可能性がある。
(周波数2) 周波数2は、放射定数が小さすぎる。したがって、周波数2は候補周波数としての基準を満たさない。
(周波数3) 周波数3は、放射定数の点で候補周波数として基準を満たすものの、寄生モードによる懸念が残る。周波数3でライトラインLL上に寄生モードが見られ、これが予測外の結果を引き起こす可能性があるためである。なお、周波数1と比較して周波数3ではΓ点近傍のモード数が少なく、そのため、ライトラインLL上に問題となるモードが発生しなければ、周波数1よりも良好なビーム品質が得られると予測される。
(周波数4) 周波数4はΓ点近傍のモードの放射定数が小さすぎる。したがって、周波数4は候補周波数としての基準を満たさない。
(周波数5) 周波数5はΓ点付近のモードの放射定数が小さすぎる。したがって、周波数5は候補周波数としての基準を満たさない。
(周波数6) 周波数6は、放射定数の点で候補周波数としての基準を満たしている。この周波数6はライトラインLLに寄生モードを持たない。唯一考えられる問題は、Γ点モードと境界条件との相互作用である。
C1.フォトニックバンドがΓ点またはその近傍において当該周波数の放射モード(本節において「目標放射モード」と呼ぶ)をもっていること。
C2.目標放射モードが、所定範囲(例えば10/cm~40/cm)の放射定数をもつものであること。これにより、効率的な表面放射と増幅が期待できる。
C3.もし当該放射モードの周波数に、より大きな水平方向波数(k∥)をもつ別のモードが存在しないか、または存在するのであれば、その別のモードよりも目標放射モードが相対的により小さな放射定数をもっていること。この別のモードの例としては、ライトラインの寄生モードを挙げることができる。
本開示の実施形態では、表面発光フォトニック結晶量子カスケードレーザーのための構造例を調査するために、複数の手法を組合わされる。その調査では、数値的な理論計算による評価(estimation)のためのモデル化を含みうる。
2.1.1 単位セルの解析
本実施形態では多層PhCスラブの周期構造を計算するためにFDTD法を用いる。図4Aは本実施形態で考慮される単位セルの3次元の透視図を示す。図4Aにて、単位セル10中に表している球S1~S3と球D1~D4は、それぞれ点センサーと双極子放射源である。図4Bは、典型的な単位セルをその中央を切る断面にて示しており、カラム穴20は、開口22から半導体超格子構造110を積層の方向に通って延びている。カラム穴20は、開口22が図4Bに示されていない領域では、エアーと畳み込み完全マッチング層(Convolutional Perfect Matched Layer、CPML)とからなる。図4Cは、半導体超格子構造110の厚みの中央での単位セル10の断面を示している。ここでは、離散化マックスウェル方程式にて設定される要素のメッシュを左下に明示し、それにより、カラム穴20の側面の一部を再現するモデルに生じる微細な凹凸を明示している。なお、本開示において半導体超格子構造110のために典型的な材質としてGaAs系化合物半導体を用いた説明や図示を行なうことがあるが、半導体超格子構造110はその材質が限定されるものではない。シミュレーション領域の+zと-z座標軸の境界はCPMLと設定された。他の境界は、すべて周期的境界に設定された。シミュレーション領域において三角格子を記述するために、その周期境界には、同時ひずみシフト(coincident skewed shift)が採用された。サブバンド間遷移がTM偏光の電磁波を支配的に放射するため、いくつかのTMモードの双極子放射源(source)を、半導体超格子構造110におけるランダムな位置に設定した。本実施形態の計算では、代表的なQCL層の構成に従って半導体超格子構造110を平均屈折率n=12をもつ厚いGaAs層と記述したが、本実施形態は別の材質によるPhC-QCL素子にも適用可能である。QCL構造の実際的な平均屈折率nは、GaAs/AlGaAs層の積層構成のTHz-QCLといったものであっても、複雑な量子カスケード構造に起因してバリア厚、ドープ密度、動作周波数、および光学ゲインの変化に応じ変動してしまう。そのため、単位セルの設計を始める前に実験的に測定された屈折率nを用いることが、一層正確な導波路設計のためのよりよいアプローチとなるだろう。表面損失の計算のためには、金属層が、ロスのない完全電気導体(PEC)によって置き換えられる。
PhC-QCL素子1000における導波路内に生成されたモードの放射定数(品質因子)の計算は、FDM(filter diagonalization method)を利用し時間ベースのフィールドをスペクトル解析して行う。FDMでは、時間発展されたフィールドデータを以下の式にフィットさせる:
PhC-QCL素子1000における面発光動作でのビームパターン、拡がり角、および放出/吸収されたパワーは、近接場から遠方場への変換(NF-FF変換)とポインティングの定理を用いて推定することができる。これらを観測するために、特定の境界条件と限られたチップ面積を持つ15(16)×15個のユニットセルを配置した。本実施形態では、図5A、5Bのように、x方向に15列と半分(7単位セル分)、y方向に15行の単位セルを配置する。x方向の両端の対称性から、さらに7単位セル分を付加していることを表現するため、本開示では15(16)×15単位セル、と記述する。PhC-QCLのフィールド分布を観測するためには、2つの平面センサー、いくつかの点センサー、および箱センサーを設置し、電界分布、光出力、ビームパターンを観測する。図5Aは、PhC-QCL素子1000の算出のために採用する導波路構造の3次元透視図である。なお、計算の都合により、xyz軸の取り方を変更し、厚み方向をx軸に取っている。図5Bは半導体超格子構造110の中央を切断するyz平面での断面図を示している。箱センサーの±x軸の端の境界は、±x軸のCPMLの近くに位置している。この箱センサーの配置が、白点線により示されている。この計算の目的ではすべての境界がCPMLに設定されている。現実的なケースでは、境界による反射を抑制するため、効率の良い吸収体が図5Aの+y、-y、+z、-zの境界に取り付けられていなくてはならず、高次モードを生じかねない。我々は必要となる実質的計算リソースを削減するためその現実的で効率の良い吸収体をCPMLによって表現した。なお、吸収体の境界が存在しない場合、高次のモードが発生しやすく、意図した動作を妨げる可能性がある。ここでは、現実的に効率の良い吸収体をCPMLで表現することで、必要な計算資源を大幅に削減している。
本実施形態は、見いだした好ましい構成を実施例として、また対比されるべき構成を比較例として、具体的な計算結果により説明される。
図1の構想に基づく図4A~図4Cの単位セル構造において、h=8.5μm,r=28μm,a=64μmを適用して数値計算を実行することによりフォトニックバンドを抽出した。図6は実際に抽出されたフォトニックバンドのダイヤグラムである。本実施形態では、シミュレーション領域の空間的離散化を、Δx=1.28μm、Δy~1.11μm、Δz=0.5μmと固定した。フォトニックバンドの計算のために単位時間ステップをΔt~2.86×10-16sと固定した。Yeeの方法論に基づく離散化マックスウェル方程式をそのΔtで3×105回のイタレーションで解いた。調査目的は半導体超格子構造110でTM偏光フォトンが生成される場合に図2の構想を満たすモードを抽出することにあるため、TM偏光双極子放射源が半導体超格子構造110のQCL領域内のみに置かれた。図6Aは、周波数と既約ブリルアンゾーンを表しているkインデックスの関数としてフーリエ変換後の相対的フィールド強度を示している。ここで、kの0、20、40、および60インデックスは、それぞれ、Γ点、K点、M点、およびΓ点である(図3)。ごく近傍の強度よりも強いフィールド強度の周波数は、固定した波数ベクトルについてその周波数に共鳴モードまたはモードが存在していることを意味している。ライトラインより下の共鳴モードには我々は興味がないためライトラインより下の領域を省略した。本開示全般に、バンドダイヤグラムにライトラインを記載する場合、ライトラインより低周波数領域を塗りつぶして記載することがある。2.8~2.9THzの間の領域近くで完全バンドギャップが観察された。図6Bは、バンドギャップの周波数領域の近傍を拡大して後処理をすることにより抽出したフォトニックバンドのダイヤグラムである。図6Bは、バンドギャップ真下のΓ点の所だけに共鳴モードをもつ周波数を明瞭に示している。
2.1にて説明した設計において、15(16)×15個の単位セルを一様に配置して構築された構造について、遠方場パターンおよび視野分布が計算された。その計算において、Δt~1.289×10-15sを採用し、マックスウェル方程式を解く時間進展のイタレーションを2×105回繰り返し。全体の幾何学的構成は図5A、図5Bと同一である。時間依存性の場の強度を集めて後処理を実行するために、点、箱、および平面センサーが設定される。半導体超格子構造110における活性領域112つまり利得媒体中で増幅されたモードが支配的になった後、PhC-QCL素子1000内外の電磁波のスペクトル解析のために6万回のイタレーションに次いですべてのフーリエ変換が実行される。ゲイン媒体のためのローレンツモデルのパラメーターがεr,base=12,εLORENTZ=-0.002,ωo=2.780THzおよびδo=3GHzと与えられた。図8A、図8Bは、ローレンツモデルと上述したパラメーターによって算出されたεr(f)およびn(f)の実部(図8A)および虚部(図8B)を示している。
さらに、上述した構成の精密な最適化を実施した。具体的には、図4A~Cの単位セル構造において、a=64μm、h=8.5μm、r=28μmとして発振周波数を2.775THzとしていたところを、a=64μmを維持したままh=6μm、r=32μmとする。発振周波数はこれに伴い2.76THzとする。結果、フォトニックバンドの構造は図6Bのものから図形的にほとんど違いが見られないものの、Γ点かわずかに傾斜した方向(図6Bにおけるkインデックス58付近の方向)で良好な特性が実現した。最適化したものでは、表面を通る放射パワー対半導体超格子構造110のスラブの界面を通じて吸収されるパワーとの間のパワーレシオが20.6:1となる。この理由は、図4A~Cに示したフォトニック結晶における各部のサイズをh=6μm、r=32μmへと変化させたことにより、フォトニック結晶中を面内に伝播する電磁波の反射率が高まってスラブの界面にまで到達する電磁波が減少したためと考えている。
本開示にて確立した面発光PhC-QCL導波路を、金属層および活性領域に円筒形のエアーホールを持つような別の構造のもの(比較例1)と対比させて比較する。比較例1の単位セル構造は円筒のエアホールをもつものである。図13は、図4C同様の単位セルにおいてa=64μm、円の半径r=22μmとして活性層占有率を0.571とし、h=8.5μmとした円筒のエアホールをもつ比較例1の構成でのフォトニックバンドのダイアグラムである。上述した図2と同様に候補周波数を円で囲んで示している。図2の説明と同様にして、図13の円筒形のエアーホールを持つ場合のフォトニックバンドの各候補周波数についての適否を判断すると次のようになる。
a.周波数1は、Γ点付近のモードの放射定数が小さすぎる。これにより、確立された基準を満たすことができない。
b.周波数2は2.02THzであり、候補周波数として放射定数の点で基準を満たしうるものの、ターゲット周波数のライトライン上の寄生モードが予測できない結果を引き起こす可能性がある。したがって、妥当な境界条件での試算を必要とする。なお、この候補周波数2のΓ点付近にはモードが多数存在する点も懸念される。純粋なΓ点発光といえないモードではビーム品質が低下する可能性がある。さらに、DFT(離散フーリエ変換)で検出されたライトライン下のモードも、高いLEEの妨げとなって顕著な問題となる。
c.周波数3は、Γ点近傍の放射定数が低すぎるモードを示している。
d.周波数4は、Γ点近傍の放射定数が低すぎるモードを示している。
このように、円筒エアホールのフォトニック結晶によって得られるフォトニックバンドは、正三角形エアホールのものとの比較において、発振動作のためには不利となる。
比較例2として、特許文献1、図9(第3の実施形態)に開示されるカラム穴の断面形状が直角二等辺三角形であるような正方格子のフォトニック結晶の構成を本開示の手法にしたがって調査した。図14A~Cは、比較例2で計算対象とするフォトニック結晶の単位セルの透視図(図14A)、平面図(図14B)および正方形の中央を通る位置での断面図(図14C)である。図15は、正方格子の逆格子空間において既約ブリルアンゾーンを説明する説明図である。図16は、遠方場での特性を計算するために、単位セルを配置した比較例2のQCL導波路構造の透視図である。
候補1 (a、w、h)=(60,50,10)
候補2 (a、w、h)=(60,55, 6)
本開示の実施形態のための実施例3として、三角格子の配列を保ちつつ、単位セルにおけるカラム穴の断面形状を三角形以外にも拡張して最適化する事例を示す。なお、最適化においては、実施例1、2において正三角形の断面形状が良好な結果を与えたことに対応して、三回対称である種々の断面形状を試行対象にする。これは、三回対称である三角格子について、格子点となるカラム穴を三回対称の対称性をもたないような断面形状にした場合には、フォトニックバンドのモード構成が複雑となって本開示のコンセプトから遠ざかるためである。図18は、実施例2において単位セルにおけるカラム穴の断面形状を最適化するために与える自由度を示す説明図である。三角格子に配置される単位セル内に、代表する座標(a,b)を設け、そこを中心とする配列用正三角形を考える。図18に示すように、この配列用正三角形のサイズは、座標(a,b)からの距離r1によって記述できる。正三角形をなす3つの辺の中点(Point1~Point3)と中心からみて紙面上方、左下、右下の正三角形の各頂点(Point4~Point6)とを中心に加えた7つの基準点を想定する。各7基準点の座標を図18に示ししている。断面形状は、各基準点に中心をもつような小さな図形(サブパターン)を配置し、必要に応じて互いに重ねることで表現することができる。このサブパターンは、配置するかしないか、サイズ、形状を変更する。サプパターンの形状は、実施例2の最適化では正三角形、正六角形、または円板を試行する。上述した距離r1に加え、それぞれのサブパターンのサイズを決定する長さを用いれば、単位セルに設けるカラム穴の断面形状を極めて多様に変化させることができる。本開示において、サブパターンの重なる範囲により特定される形状を組み合わせ形状と呼ぶ。断面形状に加え、計算に用いるパラメーターにカラム穴の深さhも採用する。現実のQCL素子の作製工程におけるプロセスを考慮し、すべての基準点に設けるサブパターンに同じ深さを適用する場合を計算対象としている。また、サブパターンについても、少なくとも三回対称を示す形状を採用する。
実施例1、比較例2を含む上述した調査により確認された対称性に関する知識を前提に、光取出し効率(LEE)に着目してさらに詳細な調査を実施した。この調査は、特に有用な3回対称性の場合に、パターン検討(8.1)と、電極のみの開口とするかカラム穴とするかの違いの検討(8.2)とを行なった。
円パターンと正三角形パターンで高い光取出し効率(LEE)が実現する条件を明確化した。この際、図4A~図4Cに示した条件を採用し、さらに次の仮定を置いた。
・構成材料による吸収はゼロとする。
・すべての方向に進む放射出力のうち、x軸に垂直な2つの平面のうち、x座標が大きい位置でX軸を切断する平面を通過する成分が占める割合、つまり、
P+x/(P+x+P-x+P+y+P-y+P+z+P-z)
をLEEとする。
ここで、図5Bにてパターンが設けられる領域を取り囲み、XYZ軸の各軸に垂直な平行な2つの平面対で切り取られる箱センサーを図5Aのように設定する。そのセンサーのX軸に垂直な2つの面のうちX座標が大きい位置でX軸を切断する平面を通過する放射出力(パワー)をP+xとする。P-xは、それに平行でX座標が小さい位置でX軸を切断する平面である。Y、Zについても同様である。図5Aの箱形状のX軸に垂直な2つの平面は、CPML(畳み込み完全マッチング層)を含まないがその近傍に配置されている。Y軸、Z軸についてもPhC-QCL素子1000の領域をカバーするように設定する。上記箱センサーはシミュレーション領域においてCPMLの近傍に配置されており、完全導体(PEC)、半導体超格子構造110、および空気を含んでいる。このため、上式の分母の6つの成分のうち、P+xのみがPhC-QCL素子1000から第2の電極102側の空間に出力されて放射に寄与するが、残りの5つの成分は、現実のPhC-QCL素子1000では吸収されるなどにより放射に寄与しない。
・Γ点の近傍のみにモードをもつ周波数を、候補とする。その候補周波数に対応させて、予測されるフォトニックバンド構造を一旦集める。
・目標周波数のモードは、THz領域で10/cm以上の放射定数を備えていると好ましい。
・十分な数の単位セルを配置した後に遠方場パターンと近接場光学出力を計算することより、ビーム品質とLEEを見積もる。
・その後、高いビーム品質(つまり可能な限りガウシアン形状のシングルローブ形状で垂直放射)を示し、高いLEEとなるような構造と周波数を選択する。
・活性層占有率(=1-FF、ここで、FFは開口またはカラム穴の断面パターンの充填率)が)小さいものは、好ましくないとする。この理由は、活性層占有率が小さいと、電子バンド構造が複雑となり、光子生成の面積が減少し、第2の電極102の金属層における電流拡散が困難となるためである。
a.放射定数を10/cm以上40/cm以下にする。
b.目的周波数においてΓ点のごく近傍を除きモードが存在しない。
c.しかし、FDTD、FT(フーリエ変換)、FDMではライトライン上のモードの検出が時に困難となる。またフーリエ変換またはFDMは可能なモードの抽出に失敗することがある。そこで、ユニットセルをいくつか配置したのち、遠方場解析によってビーム品質とLEEを見積ることが、FDTDにおける目的周波数とモードの探索にとって重要である。
本実施形態では、図4Bに示すような第2の電極102と半導体超格子構造110との両方を通るようなカラム穴によるフォトニック結晶は必ずしも要さず、第2の電極102、半導体超格子構造110のうち第2の電極102の開口パターンをもつものの、半導体超格子構造110はパターン化されない一様な構造であるフォトニック結晶を採用する構造(以下、メタルフォトニック結晶と呼ぶ)を採用することも有用である。メタルフォトニック結晶を採用した場合の具体的設計について、上述した選択方針を適用して設計を試みた。
以上の通り、第2の電極102の開口と半導体超格子構造110のカラム穴の両方、または第2の電極102の開口のみに三角格子のメタルフォトニック結晶を採用する場合において、各平面形状が円形状と正三角形の場合について、良好に動作可能なPhC-QCL素子1000を設計しうることを確認した。
本開示において、我々は、フォトニックバンドの工夫(photonic band engineering)に基づいて、高いEQEと低いビーム発散の面発光PhC-QCLのための適切なモードについて再考察した。具体的には、我々は、図2Bおよび図6A、6Bの手法に従うような例示の単位セル構造を示した。しかし、図2Bに例示されるフォトニックバンドを持てば、任意の導波路構造であっても、ビーム発散が小さい面発光PhC-QCLを設計できる。その際、電気的孤立部をもたず導通に支障のない電極をもてば、フォトニック結晶がQCL素子の動作には悪影響はせず、製造プロセスも簡略化しうる。したがって、解析した例示構造それ自体も意味があるものである。われわれの結果は、PhC-QCLにおける大きなEQE改善の契機となりうる。
10 単位セル
20 カラム穴
90 基板
101 電極(第1の電極)
102 電極(第2の電極)
110 半導体超格子構造
112 活性領域
LL ライトライン
Claims (18)
- ある範囲を超えて広がる一様な膜である第1の電極と、
該第1の電極の上または上方に配置されており、繰り返して積層されている複数の単位構造からなる活性領域を有している半導体超格子構造と、
該半導体超格子構造の上または上方に配置されている第2の電極と
を備えており、
該第2の電極には、それ自体を厚み方向に通り抜ける開口の配列を含むフォトニック結晶が前記範囲に広がるように形成されていて、該開口の配列は、前記範囲において前記第2の電極が電気的孤立部をもたないようになっており、
該フォトニック結晶のフォトニックバンド構造は、Γ点またはその近傍に放射モードを持つものである、
量子カスケードレーザー素子。 - 前記放射モードの放射定数が、該放射モードと同一の周波数において水平方向波数がより大きい別のモードの放射定数よりも小さい
請求項1に記載の量子カスケードレーザー素子。 - 前記放射モードの放射定数が、10/cm以上40/cm以下である
請求項1または請求項2に記載の量子カスケードレーザー素子。 - 前記開口の配列が三角格子である
請求項1に記載の量子カスケードレーザー素子。 - ある範囲を超えて広がる一様な膜である第1の電極と、
該第1の電極の上または上方に配置されており、繰り返して積層されている複数の単位構造からなる活性領域を有している半導体超格子構造と、
該半導体超格子構造の上または上方に配置されている第2の電極であって、該第2の電極自体を厚み方向に通り抜ける開口の三角格子の配列が前記範囲に広がるように設けられており、前記範囲において電気的孤立部をもたない第2の電極と
を備える量子カスケードレーザー素子。 - 前記半導体超格子構造は、前記三角格子と同一配列のカラム穴の配列が設けられており、
各カラム穴は、前記第2の電極の各開口の形状と同一の断面形状をもち前記活性領域を積層の方向に通って延びるものである、
請求項4または請求項5に記載の量子カスケードレーザー素子。 - 前記開口の形状が正三角形である、
請求項4または請求項5に記載の量子カスケードレーザー素子。 - 前記範囲において前記開口の設けられていない部分の面積比である活性層占有率が0.53以上0.73以下である、
請求項7に記載の量子カスケードレーザー素子。 - 前記開口の形状が、互いにサイズと向きが同一の3つの正三角形と円板とが重なる組み合わせ形状にされており、
該組み合わせ形状は、前記3つの正三角形が、前記円板の中心から等しい距離の120°異なる方向に中心をもつように配置され、前記3つの正三角形の前記サイズが、それぞれが少なくとも一つの辺の全体を前記円板の円周と重ならないものである、
請求項1または請求項5に記載の量子カスケードレーザー素子。 - ある範囲を覆う一様な膜である第1の電極と、
該第1の電極の上または上方に配置されており、繰り返して積層されている複数の単位構造からなる活性領域を有している半導体超格子構造と、
該半導体超格子構造の上または上方に配置されている第2の電極と
を備える量子カスケードレーザー素子であって、
前記第2の電極には、該第2の電極自体を厚み方向に通り抜ける開口の三角格子の配列を含むフォトニック結晶が前記範囲に広がるように形成されており、
前記第2の電極が前記範囲において電気的孤立部をもたないものである、
量子カスケードレーザー素子。 - 前記フォトニック結晶は、前記半導体超格子構造に設けられた前記三角格子と同一配列のカラム穴の配列を含んでおり、
各カラム穴は、前記第2の電極の各開口の形状と同一の断面形状をもち前記活性領域を積層の方向に通って延びるものである、
請求項10に記載の量子カスケードレーザー素子。 - 前記フォトニック結晶は、前記活性領域が動作時に誘導放出しうる電磁波の周波数において、Γ点またはその近傍にのみ放射モードを有するフォトニックバンド構造をもつものである、
請求項5、請求項10、請求項11のいずれか1項に記載の量子カスケードレーザー素子。 - 前記フォトニックバンドの前記放射モードが、前記Γ点またはその近傍において、バンドギャップの下限または上限のいずれかを与えるものである、
請求項12に記載の量子カスケードレーザー素子。 - 前記活性領域がTHz領域の電磁波を放出するものである
請求項1、請求項5、請求項10のいずれか1項に記載の量子カスケードレーザー素子。 - 前記周波数が18.7THz以下のいずれかの値である、
請求項14に記載の量子カスケードレーザー素子。 - 前記第1の電極および前記第2の電極が金属材料からなる、
請求項14に記載の量子カスケードレーザー素子。 - 前記第2の電極が放射面である、
請求項14に記載の量子カスケードレーザー素子。 - 請求項1、請求項5、請求項10のいずれか1項に記載の量子カスケードレーザー素子を備える機器。
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