Multiband Effective-mass Theory Research Articles

Reduction of efficiency droop in green strain-compensated InGaN/InGaN light-emitting diodes grown on InGaN substrate

The efficiency droop characteristics of green strain-compensated InGaN/InGaN light-emitting diodes (LEDs) grown on an InGaN substrate are investigated by using the multi-band effective mass theory and drift-diffusion model. The radiative recombination coefficient Beff of the strain-compensated quantum well (QW) structure is shown to be much larger than that of the conventional QW structure. Also, we find that the effective active volume of the LEDs increases with the inclusion of strain-compensated layers. This can be explained by the fact that the overlap between electron and hole concentrations increases owing to the decrease in internal field. As a result, the efficiency droop phenomenon for the strain-compensated LEDs is expected to be reduced, compared with that for conventional LEDs.

Light emission characteristics of blue strain-compensated InGaN/InGaN/InGaN light-emitting diodes

The light emission characteristics of blue strain-compensated InGaN/InGaN light emitting diodes (LEDs) grown on InGaN substrates were investigated using the multiband effective mass theory. The radiative recombination rate of the strain-compensated LED structure is shown to be larger than that of the conventional LED structure due to the decrease in the lattice mismatch with the substrate. Also, the light emission distribution in quantum wells (QWs) for the strain-compensated LED structure is found to be much more uniform than that for the conventional LED structure. As a result, the simulation results suggest that the efficiency droop is significantly improved when a conventional GaN barrier and substrate are replaced by an InGaN barrier and substrate. Thus, a possibility exists to employ a strain-compensated QW to improve the optical performance of InGaN-based blue LEDs.

Optical Gain Characteristics in GaAsPN/GaPN Quantum Well Lasers for Silicon Integration

Optical gain characteristics of strain-compensated GaAsPN/GaPN quantum wells (QWs) with the GaPN barrier under 1.0 % tensile strain were investigated using the multiband effective-mass theory and the non-Markovian gain model. The transition energy linearly increases from 1.12 to 1.22 eV when P content ratio changes from 0.1 to 0.4. The theoretical transition energy reasonably agrees with the experiment. The Coulomb enhancement ratio, g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">many</sub> /g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">free</sub> , decreases with increasing compressive strain because the average hole effective mass decreases with increasing strain. As a result, the QW structure with a smaller compressive strain has larger optical gain than that with a larger compressive strain for higher carrier densities. On the other hand, in the case of smaller carrier densities, the QW structure with a larger compressive strain shows larger optical gain than that with a smaller compressive strain because the former has larger optical matrix element producted by Kane's parameter and quasi-Fermi level separation than the latter. The absolute value of the bandgap renormalization increases with increasing carrier density and is about 99 meV at 5×10 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , which is slightly larger than that of GaAs-based or InP-based QW structures.

Effects of depolarization on the electronic and the optical properties of InGaN/MgZnO quantum-well structures

The effects of depolarization on the electronic and the optical properties of InGaN/MgZnO quantum-well (QW) structures are investigated by using the multiband effective-mass theory. The average hole effective mass of the InGaN/MgZnO QW structure with a negligible internal field is shown to be similar to that of the conventional QW structure. On the other hand, the matrix element for the InGaN/MgZnO QW structure is improved greatly compared to that of the conventional InGaN/GaN QW structure because the internal field in the well is reduced. As a result, the light emission and the radiative recombination coefficient of the InGaN/MgZnO QW structure are found to be much larger than those of the conventional InGaN/GaN QW structure.

Polarization characteristics of semipolar (112̄2) InGaN/GaN quantum well structures grown on relaxed InGaN buffer layers and comparison with experiment.

Partial strain relaxation effects on polarization ratio of semipolar (112̄2) InxGa1−xN/GaN quantum well (QW) structures grown on relaxed InGaN buffers were investigated using the multiband effective-mass theory. The absolute value of the polarization ratio gradually decreases with increasing In composition in InGaN buffer layer when the strain relaxation ratio (ε0y′y′−εy′y′)/ε0y′y′ along y′-axis is assumed to be linearly proportional to the difference of lattice constants between the well and the buffer layer. Also, it changes its sign for the QW structure grown on InGaN buffer layer with a relatively larger In composition (x > 0.07). These results are in good agreement with the experiment. This can be explained by the fact that, with increasing In composition in the InGaN subsrate, the spontaneous emission rate for the y′-polarization gradually increases while that for x′-polarization decreases due to the decrease in a matrix element at the band-edge (k‖ = 0).

Theoretical analysis of light-emission characteristics in blue saw-like InGaN/GaN light-emitting diodes with several well widths

The light-emission characteristics of saw-like InGaN/GaN quantum-well (QW) light-emitting diodes (LEDs) with several well widths are investigated using the multiband effective mass theory. These results are compared with those of the conventional QW structures. In the case of the conventional QW structures, the spontaneous emission peak rapidly decreases with increasing well width. On the other hand, in the case of the saw-like QW structure, the well width dependence of the spontaneous emission peak is greatly reduced. That is, the spontaneous emission peak of the saw-like QW structure with the well width of 3 nm is shown to be comparable to that of the saw-like QW structure with the well width of 2.5 nm. Also, the saw-like QW structures show much larger spontaneous emission peaks than the conventional QW structures, irrespective of the well width. We expect that saw-like QW structures will be desirable as high-efficiency blue InGaN/GaN LEDs.

Many-body effects on optical gain in GaAsPN/GaPN quantum well lasers for silicon integration

Many-body effects on the optical gain in GaAsPN/GaP QW structures were investigated by using the multiband effective-mass theory and the non-Markovian gain model with many-body effects. The free-carrier model shows that the optical gain peak slightly increases with increasing N composition. In addition, the QW structure with a larger As composition shows a larger optical gain than that with a smaller As composition. On the other hand, in the case of the many-body model, the optical gain peak decreases with increasing N composition. Also, the QW structure with a smaller As composition is observed to have a larger optical gain than that with a larger As composition. This can be explained by the fact that the QW structure with a smaller As or N composition shows a larger Coulomb enhancement effect than that with a larger As or N composition. This means that it is important to consider the many-body effect in obtaining guidelines for device design issues.

Optical gain characteristics of AlGaN/AlN quantum well structures grown on GaN substrate for ultraviolet TM light source

Optical gain characteristics of ultraviolet AlGaN/AlN quantum well (QW) structures grown on GaN substrate were investigated using the multiband effective-mass theory and non-Markovian model with the many-body effect. The TE-polarized optical gain peak of the QW structure on AlN substrate gradually increases with increasing Al composition and begins to decrease rapidly when the Al composition exceeds 0.6. On the other hand, the QW structure on GaN substrate shows that the TE-polarized optical gain peak continuously decreases with increasing Al composition and the TM-polarized optical gain peak begins to increase at much lower Al composition than that of the QW structure on AlN substrate. As a result, the QW structure on GaN substrate shows that the critical Al composition switching from TE to TM polarization is much smaller than that of the QW structure on AlN substrate. Also, the TM-polarized gain peak of the QW structure on GaN substrate is found to be much larger than that of the QW structure on AlN substrate.

Partial strain relaxation effects on polarization anisotropy of semipolar (112¯2) InGaN/GaN quantum well structures

Partial strain relaxation effects on polarization anisotropy of semipolar (112¯2) InGaN/GaN quantum well (QW) structures were investigated using the multiband effective-mass theory. In the case of strain relaxation of ϵx′x′ along x′-axis, the polarization ratio gradually decreases with increasing strain relaxation. Also, with the strain relaxation by the same amount, the variation of the polarization ratio along x′-axis is shown to be much larger than that along y′-axis. However, the polarization switching is not observed even at a high In composition of 0.4 due to a small strain component (ϵx′x′0) with no strain relaxation. On the other hand, in the case of strain relaxation of ϵy′y′ along y′-axis, the polarization switching is observed, and the optical anisotropy is found to change from positive to negative with increasing strain relaxation. Also, the absolute value of the polarization ratio gradually decreases with increasing carrier density. However, the polarization switching due to the carrier density is not observed. Thus, the polarization switching observed at high carrier density may be attributed to inhomogeneous strain distribution in the InGaN layer.

Optical polarization characteristics of m-plane InGaN/GaN quantum well structures and comparison with experiment

The optical polarization characteristics of the light emission in non-polar m-plane InGaN/GaN quantum well (QW) structures were theoretically investigated using the multiband effective-mass theory. The optical anisotropy of m-plane QW structure is ranging from 0.65 at 440 nm to 0.83 at 560 nm at the sheet carrier density of N2D=15×1012 cm−2 and is found to decrease gradually with increasing carrier density, which is in good agreement with the experimental result. The decrease in the optical anisotropy can be explained by the fact that the y′-polarized matrix element decreases with increasing k‖ while the x′-polarized matrix element gradually increases. Also, the decreasing rate of the QW structure with a smaller In composition is shown to be greater than that of the QW structure with a larger In composition.

Temperature characteristics of spontaneous emission and optical gain in blue InGaN/GaN quantum well structures

Temperature characteristics of the light emission in blue InGaN/GaN quantum well (QW) structures were investigated using the multiband effective mass theory. The light emission intensity decreases gradually with increasing temperature because of the reduction in the optical matrix element due to the decrease in the potential well depth. On the other hand, the spillover is shown to be negligible in the investigated range of temperature and the T0 value of about 255 K is obtained. The radiative recombination coefficient Beff decreases from 0.3 × to 0.2×10−4 cm6/s at the sheet carrier density of 5×1012 cm−2 when changing from 300 to 400 K. As a result, the internal efficiency is reduced with increasing temperature because of the reduction in the radiative recombination rate.

Carrier density dependence of polarization switching characteristics of light emission in deep-ultraviolet AlGaN/AlN quantum well structures

The carrier density dependence of the polarization switching characteristics of the light emission in deep-ultraviolet AlGaN/AlN quantum well structures was investigated using the multiband effective-mass theory and non-Markovian model. The critical Al composition from transverse electric (TE) to transverse-magnetic (TM) polarization decreases gradually with increasing carrier density. This can be explained by the fact that matrix elements for TM-polarization above the band-edge (k||=0) is much larger than those for TE-polarization. That is, the light emission for TM-polarization becomes larger than that for TE-polarization at higher carrier density because carriers will occupy higher states above k||=0 in the conduction and valence bands. As a result, the critical Al composition is reduced with increasing carrier density. Also, the critical Al composition is observed to decrease with increasing well width.

High optical polarization ratio of semipolar (202¯1¯)-oriented InGaN/GaN quantum wells and comparison with experiment

Optical anisotropy properties of (202¯1¯)-plane wurtzite (WZ) InGaN/GaN quantum well (QW) structures were investigated using the multiband effective-mass theory and the non-Markovian model with many-body effects. The results were compared with those of non-polar (112¯0) a-plane InGaN/GaN QW structures. The In content dependence of the transition wavelength of the (202¯1¯)-plane QW structure is found to be very similar to that of (112¯0)-plane QW structure. The (202¯1¯)-plane shows slightly smaller y′-polarized spontaneous emission coefficient than that with the (112¯0)-plane. On the other hand, in the case of x′-polarization, the (202¯1¯)-plane QW structure has a larger spontaneous emission coefficient than the (112¯0)-plane QW structure. The in-plane optical anisotropies of both QW structures are shown to increase gradually with increasing transition wavelength or In content. The optical anisotropy of (202¯1¯)-oriented QW structure is ranging from 0.50 at 400 nm to 0.75 at 530 nm, which is in good agreement with the experimental result.

High-efficiency InGaN/GaN light-emitting diodes with electron injector

The efficiency in non-polar m-plane InGaN/GaN light-emitting diodes (LEDs) with an electron injector (EI) layer was investigated using multiband effective mass theory. The electron overflow is shown to decrease with the inclusion of an electron-blocking layer. In particular, with the inclusion of the EI layer, the electron overflow is significantly reduced even for a large bias voltage. In the case of the single EI layer, the layer thicker than 13 nm would be needed to reduce electron overflows substantially. However, it will be difficult to grow epitaxially high-quality thick single EI layer. Instead, we show that the quantum-well structure with the superlattice-like EI layer is more effective in reducing the ballistic and quasiballistic electron transport across the active region, compared with a thick single EI layer.

Comparison of light emission in InGaN/GaN light-emitting diodes with graded, triangular, and parabolic quantum-well structures

The light emission properties of InGaN/GaN quantum well (QW) light-emitting diodes with non-square layers with graded, triangular, and parabolic shapes are investigated using multiband effective mass theory. These results are compared with those of conventional InGaN/GaN QW structures. The spontaneous emission peak of non-square QW structures is shown to be improved compared to a conventional QW structure. In particular, the parabolic QW structures shows a slightly larger emission peak than the graded or triangular QW structure. This can be explained by the fact that a smaller In composition in the well is needed to give a transition wavelength of 440 nm.

Theory of non-polar and semi-polar nitride semiconductor quantum-well structures

We investigate the electronic and optical properties of non-polar a- and m-planes and semi-polar InGaN–GaN quantum-well structures using the multiband effective-mass theory taking into account the many-body effects. These results are compared with those of (0 0 0 1) oriented c-plane wurtzite InGaN–GaN quantum wells. We derive explicitly the valence-band Hamiltonian and interband optical matrix elements with polarization dependence for an arbitrary crystal polar angle θ and an azimuthal angle φ. The average hole effective masses of the topmost valence band along the wave vector perpendicular to the crystal orientation for the non-polar and semi-polar cases are substantially lower than that of the c-plane case. It is found that the azimuthal angle φ does not change the shape of the band structure but shifts the sub-band position. Thus the transition energy will be dependent on both the polar angle θ and the azimuthal angle φ. It is expected that the optical matrix elements are strongly anisotropic and optical gain would be larger for the non-polar and semi-polar cases because of the vanishing of the internal electric fields.

Optical gain characteristics of non-polar Al-rich AlGaN/AlN quantum well structures

Optical properties of non-polar Al-rich AlGaN/AlN quantum well (QW) structures were investigated using the multiband effective-mass theory and non-Markovian optical model with the many-body effect. These results are compared with those of the c-plane, i.e., the (0001)-oriented QW structures. The theoretical PL transition wavelength is found to agree well with the experimental result. The optical gain for the x′-polarization is much larger than that for the y′-polarization because the optical matrix element for the x′-polarization is larger than for the y′-polarization. The x′-direction in the non-poalr plane corresponds to c-axis direction. Also, the optical gain for the x′-polarization is shown to decrease with increasing Al composition. This is mainly attribute to the fact that the optical matrix element is decreased due to the reduction in the electron-hole overlap for QW structures with higher Al contents.

Optical Properties of Staggered InGaN/InGaN/GaN Quantum-Well Structures with Ga- and N-Faces

Optical properties of staggered InGaN/InGaN/GaN quantum-well (QW) light-emitting diodes with Ga- and N-faces were investigated using the multiband effective mass theory. The staggered QW structure shows that the carrier density dependence of the transition wavelength is largely reduced compared to the conventional QW structure. On the other hand, the heavy-hole effective mass around the topmost valence band is almost unaffected by the polarity. The N-face staggered InGaN/InGaN/GaN QW structure has a greater spontaneous emission peak than the Ga-face staggered InGaN/InGaN/GaN QW structure because the former has a larger matrix element than the latter. We expect the N-face staggered InGaN/InGaN/GaN QW structure to have improved characteristics compared with the Ga-face staggered InGaN/InGaN/GaN QW structure.

광통신용 GaAs 기반 1.3 μm GaAsSb/InGaAs와 GaAsSb/InGaNAs 양자우물 레이저의 광학적특성 시뮬레이션

Optical gain characteristics of type-II GaAsSb/InGaNAs/GaAs trilayer quantum well structures were studied using multi-band effective mass theory. The results were compared with those of GaAsSb/InGaNAs/GaAs trilayer quantum well structures. In the case of GaAsSb/InGaNAs/GaAs trilayer quantum well structure, the energy difference between the first two subbands in the valence band is smaller than that of GaAsSb/InGaNAs/GaAs trilayer quantum well structure. Also, GaAsSb/InGaNAs/GaAs trilayer quantum well structure shows larger optical gain than GaAsSb/InGaNAs/GaAs trilayer quantum well structure. This means that GaAsSb/InGaNAs/GaAs system is promising as long-wavelength optoelectronic devices for optical communication.

Higher-order nonlinear electromechanical effects in wurtzite GaN/AlN quantumdots

As we demonstrated earlier, conventional mathematical models based on linearapproximations may be inadequate in the analysis of properties of low-dimensionalnanostructures and band structure calculations. In this work, a general three-dimensionalaxisymmetric coupled electromechanical model accounting for lattice mismatch,spontaneous polarization and higher-order nonlinear electrostriction effects has beenapplied to analyze properties of GaN/AlN quantum dots coupled with wetting layer. Thegeneralized model that accounts for five independent electrostriction coefficients has beensolved numerically via a finite-element implementation. The results, exemplified fortruncated conical GaN/AlN quantum dots, demonstrate that the effect of nonlinearelectrostriction in GaN/AlN nanoheterostructure quantum dots could be significant. Inparticular, the influence of nonlinear electromechanical effects on optoelectronic propertiesis highlighted by the results on band structure calculations based on a multiband effectivemass theory.