Multiband Effective-mass Theory Research Articles

Size-dependent electronic level structure of InAs nanocrystal quantum dots: Test of multiband effective mass theory

The size dependence of the electronic spectrum of InAs nanocrystals ranging in radius from 10–35 Å has been studied by size-selective spectroscopy. An eight-band effective mass theory of the quantum size levels has been developed which describes the observed absorption level structure and transition intensities very well down to smallest crystal size using bulk band parameters. This model generalizes the six-band model which works well in CdSe nanocrystals and should adequately describe most direct semiconductor nanocrystals with band edge at the Γ-point of the Brillouin zone.

Effect of the (101~0) crystal orientation on the optical gain of wurtzite GaN-AlGaN quantum-well lasers

We analyze the valence subband structures of (101~0)oriented wurtzite (WZ) GaN-AlGaN quantum wells (QWs) using the multiband effective-mass theory and calculate the optical gain taking into account the subband structure modification due to the crystal orientation effect and the pseudomorphic strain which is anisotropic in the QW plane. We show that, for the (101~0) GaN/AlGaN QW, the two topmost subbands, Y'1 and X'1, are more widely separated than the HH1 and LH1 subbands in the (0001) GaN-AlGaN QW. The in-plane energy dispersion of the (101~0) QW also becomes anisotropic, giving a reduced band-edge density-of-states in comparison with the (0001) QW. Moreover, states constituting the topmost valence subband at the /spl Gamma/ point and along k-/sub x/, are predominantly |Y'>-like. A combination of the reduced band-edge density-of-states and the existence of the preferred symmetry at the valence band maximum contributes to an improvement of the y'-polarized TE optical gain. A comparison of the QWs of both orientations reveals that the (101~0) QW is capable of achieving lower transparency current densities. Thus, the (101~0) QW could be useful in improving the threshold performance of WZ GaN-based QW lasers.

Uniaxial strain effect on the electronic and optical properties of wurtzite GaN-AlGaN quantum-well lasers

The valence subband structures of uniaxial-strained wurtzite (WZ) GaN-AlGaN quantum wells (QW's) are calculated using multiband effective-mass theory. The optical gain is investigated using a numerical approach in which we account for the subband structure modification and mixing due to the anisotropic strain in the QW plane. We show that the mixing of the HH and LH bases in the uniaxial-strained (0001) GaN-AlGaN QW decouples |X> and |Y> at the /spl Gamma/ point, giving two topmost subbands, Y1 and X1, which can be more widely separated than the HH1 and LH1 subbands in the biaxial-strained (0001) GaN-AlGaN QW. We resolve the states of the subband dispersion in terms of the |X>, |Y>, and |Z> bases, and show the compositional variation as a function of the in-plane wavevector. Under uniaxial strain, it is possible to exploit the existence of the preferred symmetry at the valence band maximum and the reduced band-edge density-of-states due to the anisotropic in-plane energy dispersion to achieve lower transparency carrier and current densities and higher differential gain in comparison with a pseudomorphic biaxial-strained QW. We show that, for a QW laser structure with the optical cavity along the x axis, uniaxial compressive strain in the y direction shows greater improvement than the uniaxial tensile strain in the x direction of the same magnitude. Thus, a suitable uniaxial strain could be used to improve the threshold performance of WZ GaN-based QW lasers.

Theoretical Analysis of Optical Gain in Quantum Well Lasers Including Valence-Band Mixing Effect

The linear optical gain in the. AIGaAs/GaAs quantum well lasers is studied theoretically, taking into account the valence-band mixing effect. Our approach is based on the multiband effective-mass theory (k p method) and the density-matrix formalism. In order to obtain the valence bands' structure we employ the 4 x 4 Luttinger—Kohn Hamiltonian, neglecting the coupling to the split-off band. The spectral dependence of the linear optical gain is calculated using the density-matrix method with interbannd relaxation.. Finally, we analyse the spatial distribution of the optical gain in the quantum well region for the photon energy corresponding to the peak value of the linear gain. PACS numbers: 42.55.Ρx, 73.20.Dx

Interband optical transition spectra in GaAs quantum wires with rectangular cross sections

Interband optical transition spectra of rectangular GaAs quantum wires (QWR's) of various cross-sectional sizes are experimentally and theoretically studied. High-quality GaAs QWR's with lateral sizes below 20 nm are formed in AlAs trench structures with (110) vertical sidewalls by using metal-organic chemical vapor deposition. Polarization-dependent photoluminescence excitation (PLE) spectra in the QWR's clearly exhibit absorption peaks corresponding to optical transitions between quantized one-dimensional conduction and valence subbands. It is found that transition strengths and polarization anisotropies in the lowest- and higher-energy PLE peaks significantly vary, depending on the cross-sectional shape of the rectangular wires. The polarization-dependent interband transition matrix elements and the detailed absorption spectra are calculated by a multiband effective-mass theory considering heavy-hole and light-hole subband mixing. The theoretical results clarify the physical origin of observed PLE peaks and explain the strong dependence of interband transition properties on the cross-sectional ratio of QWR's.

Boundary conditions for heterostructures in the multiband effective mass theory

We consider the Luttinger Hamiltonian for the degenerate Γ8 valence bands. Based on the bulk Hamiltonian we develop a Hermitian Hamiltonian for heterostructures, where the Luttinger parameters are spatially varying. The correct boundary conditions are derived from the minimal mathematical restrictions on the resulting coupled set of second order differential equations. The equations can be generally written to kα Dαβjj' kβFj' + EνFj = εFj' with the effective mass tensor fulfilling the symmetry property (Dαβjj')† = Dβαj'j. This requires Fj' and Dαβjj' kβFj' continuous in the effective mass equation. These boundary conditions automatically imply the conservation of current in the sample. This strict mathematical treatment of the boundary conditions for the multiband effective mass equation for heterostructures can reconcile the controversy on this subject. In an Appendix we comment on the new envelope function method for heterostructures, developed by Burt.

Analysis of valence-subband structures in a quantum wire with an arbitrary cross-section

The subband structures of a GaAs/Al x Ga 1− x As quantum wire with a triangular cross-sectional shape is analyzed by using a finite-element method based on the multiband effective mass theory. In our procedure, the continuity of the probability current densities expressed in terms of the effective mass tensor is rigorously taken into account at the GaAs/AlGaAs interface. A comparison of the subband structures is also made with those of a quantum wire with a square cross-section. As a result, the band structures of the triangular quantum wire are found to show no degeneracy due to lack of inversion symmetry of the confining quantum potential whereas those of the square wire always show degeneracy.

Optical gain of a quantum-well laser with non-Markovian relaxation and many-body effects

In this article, a theoretical description of the optical gain of a quantum-well laser is developed taking into account non-Markovian relaxation and many-body effects. Single-particle energies are calculated using the multiband effective mass theory, and the valence-band mixing including the spin-orbit (SO) split-off band coupling is considered in the formulation. The Coulomb enhancement and the band-gap renormalization are also considered within the Hartree-Fock approximation. The gain spectra calculated with the Lorentzian line shape function show two anomalous phenomena: unnatural absorption region below the band-gap energy and mismatch of the transparency point in the gain spectra with the Fermi-level separation, the latter suggesting that the carriers and the photons are not in thermal (or quasi-) equilibrium. It is shown that the non-Markovian gain model with many-body effects removes the two anomalies associated with the Lorentzian line shape function. It is also found that the optical gain spectra depend strongly on the correlation time of the system which can be determined by the intraband frequency fluctuations.

Comparative studies of photoluminescence from n and p δ doping wells in GaAs

Luminescence spectra for n and p δ doping wells in GaAs are calculated. The stationary electron and hole states of the wells are obtained self-consistently by means of the multiband effective mass theory. The overlap integrals of the electron and hole envelope functions are crucial for the luminescence intensities. Those for light holes are larger than those for heavy holes, and those for p δ doping wells exceed those for n δ doping wells by almost two orders of magnitude. This explains the experimental findings on luminescence from such wells.

Transverse-Electric and Transverse-Magnetic Mode Switching in Tensile-Strained Quantum-Well Lasers Induced by the Quantum-Confined Stark Effect

Using a multiband effective-mass theory, we have calculated the transverse-electric (TE) and transverse-magnetic (TM) gains of a strained quantum-well laser subject to an external electric field. Our results show that when the well is under a moderate tensile strain, the field can switch the polarization of the room-temperature stimulated emission from the TE to the TM mode.

Orientation dependence of optical properties in long wavelength strained quantum-well lasers

The dependence of optical properties on crystal orientation is analyzed for long wavelength strained quantum-well (QW) GaAsP-InGaAsP lasers. The calculation is based on the multiband effective mass theory which enables us to consider the anisotropy and the nonparabolicity of the valence-band dispersions. It is found that the optical gain increases as the crystal orientation is inclined from [001] toward [110]. This is due to the reduced valence-band density of states. The differential gain is about 1.6 times larger for the [110]-oriented 1.55-/spl mu/m strained QW's than for equivalent [001]-oriented QW's. It is also shown that the threshold current density in 1.3-/spl mu/m strained QW lasers decreases to two-thirds of that in the [001]-oriented laser as the orientation is inclined away from [001] by 40/spl deg/-90.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optical properties in fractional-layer-superlattice quantum wires calculated by multi-band effective mass theory

We present the results of theoretical studies numerically analyzing the optical absorption and gain properties in AlGaAs fractional-layer-superlattice (FLS) quantum wires. With our calculation method we can treat any asymmetrical FLS wire with arbitrary dimensionality from 2D to 1D and to calculate not only absorption spectra but also gain properties. Our theory accurately reproduces the optical absorption anisotropy, experimentally evaluated for an AlGaAs FLS quantum wire. It is numerically shown how optical features evolve as the quantum confinement changes from 2D to 1D by varying the FLS lateral modulation. The small modulation of Al content in the AlGaAs FLS layer is found to change the optical properties markedly and improve the gain characteristics largely.

Dependence of optical gain on crystal orientation in surface-emitting lasers with strained quantum wells

We analyze theoretically optical gains in vertical-cavity surface-emitting lasers (VCSELs) for various crystal orientations. The calculation based on the multiband effective-mass theory takes into account the effects of anisotropy and nonparabolicity on the valence subband dispersion. It is found that in VCSELs employing InGaAs/InP strained quantum wells (QWs) with non-(001) orientations except (111), the polarization in the QW plane can be controlled and high gains are obtained. In particular, the gains in VCSELs with (NN1)-oriented (N≥2) strained QWs are markedly higher than those in the equivalent (001) lasers.

Analysis of differential gain in GaAs/AlGaAs quantum-well lasers

The differential gain of a quantum-well laser is studied theoretically with use of both a parabolic band model and a valence-band-mixing model. In the valence-band-mixing model, the gain profile is derived from the multiband effective mass theory (k⋅p method) as well as the density matrix formalism. The peak gain including the band-mixing effect is significantly reduced to 1.5–2 times when compared to the conventional parabolic band model. There is still a larger differential gain using the parabolic band model than using the band-mixing model. The magnitudes of differential gains for these two models give the order of 10−16–10−15 cm2, which is in agreement with the experimental results. Besides, the quantum-well thickness also influences the differential gain, which is enhanced by a thinner quantum-well structure.

Effect of valence-band anisotropy and nonparabolicity on total scattering rates for holes in nonpolar semiconductors.

We investigate theoretically the effect of the warped and nonparabolic valence-band structure on the total scattering rates for holes in cubic semiconductors with diamond lattices using the multiband effective-mass theory. All numerical calculations are done for silicon and include ionized-impurity scattering, optical-, and acoustical-phonon scattering. We find that the anisotropy and nonparabolicity of the valence bands result in a considerable dependence of the total scattering rates on the incident direction of the hole wave vector.

Band-edge optical absorption spectra of GaAs quantum wires calculated by multiband effective mass theory

Optical absorption spectra of quasi-1D GaAs quantum well wires are theoretically investigated within the framework of multiband effective mass theory. In the calculation, the mixing of heavy-hole and light-hole bands resulting from both 1D quantum confinement and electron-hole Coulomb interaction is considered. Detailed excitonic structures in the absorption spectrum near the band edge are clarified by taking into account Coulombic bound states and unbound continuum states. Polarization dependence of the optical absorption spectra is discussed in terms of the band mixing effects.

Effects of nonuniform well width on compressively strained multiple quantum well lasers

We theoretically investigate the effects of nonuniform well widths on compressively strained In0.2Ga0.8As/GaAs multiple quantum well lasers using multiband effective mass theory and density matrix formalism. We find that the well width fluctuations do not degrade the transparency current, differential gain, and linewidth broadening factor. Besides, lasers with intentionally designed chirped well width have much broader gain profiles compared to uniform well lasers. This feature is attractive for applications requiring large gain bandwidth such as tunable lasers, mode-locked lasers, and wavelength division multiplexed laser arrays.

Gain Switching in Coupled Quantum Wells

Optical gain switching in coupled quantum wells is studied theoretically. Our analysis is based on the multiband effective mass theory and the density matrix formalism with the intraband relaxation taken into account. Significant enhancement of the Stark effect on the gain of the coupled quantum wells is predicted. Comparison with the single quantum well shows that the gain is substantially more reduced for the coupled quantum wells at the same electric field because of enhanced charge separation in this structure. These results may allow low-voltage operation of the recently proposed field-effect quantum-well laser.

Electron states in a quantum dot in an effective-bond-orbital model.

The electronic-level structure in semiconductor quantum dots is investigated in a tight-binding framework. The energy levels and wave functions of GaAs and CdS crystallites containing up to \ensuremath{\sim}4000 atoms are calculated using an effective-bond-orbital model. The results obtained for GaAs crystallites by using parameters that accurately reproduce the band structure near the \ensuremath{\Gamma} point are compared with those obtained by calculations based on a multiband effective-mass theory. The effective-mass approximation (EMA) is found to correctly describe the qualitative features of the level structure, such as the bunching of levels and the spatial dependence of the wave functions. However, for very small particles the EMA grossly overestimates the confinement energies mainly because of the deviation of the bulk band structure from parabolic dispersion at high energies. For CdS crystallites we use a parametrization scheme that reproduces the main features of the bulk band structure throughout the Brillouin zone, and compare the results with those obtained by the multiband EMA, as well as with experimental data on interband transitions.

Interband optical transitions in doping superlattices

The absorption coefficient associated with interband transitions in doping superlattices is studied theoretically. Our calculations are based on a multiband effective-mass theory which simultaneously determines the electron and hole subband states self-consistency. Valence band mixing effects are calculated using a Luttinger-Kohn Hamiltonian. The absorption coefficients of both hetero- and homo-doping superlattices are evaluated from the complex dielectric function. The calculated absorption coefficients show that there are remarkable differences between our model and the conventional, uncoupled parabolic band model. Our results show that the valence band mixing can essentially eliminate the strong step-like structure in the absorption spectrum predicted by the conventional model. This suggests that the lack of an experimental observation of the step-like structure in the absorption spectrum may be due to valence band mixing and need not be attributed to potential fluctuations, spatial variations in the design parameters, or inhomogeneous excitation.