Valence Subband Mixing Research Articles

Effect of interdiffusion on the subbands in an AlxGa1-xAs/GaAs single-quantum-well structure.

The subband energies and wave functions in an interdiffusion-induced ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs single-quantum-well structure are calculated. The confinement profile of this interdiffused quantum well is nonlinear and is modeled here by an error function. The spatially dependent electron effective mass is taken into consideration using a nonparabolic band model derived from a fourth-order expansion in k with the coefficients determined using a 14-band calculation. The valence subband mixing between the heavy and light holes is also considered using an effective Hamiltonian approach. The results show that subband properties of the nonsquare quantum well differ from the conventional square quantum well. The subband-edge energy initially increases and then decreases with interdiffusion; this effect is explained by the evolution of the nonsquare quantum-well shape in terms of a crossover point, which is defined as the confinement profile intersection at the well barrier interface of the as-grown and interdiffused quantum wells. A depth-dependent quantum-well width is discussed and a cutoff scheme is introduced to quantify the division between bound and unbound states. An enhancement of interband transition is predicted for the off-diagonal selection rule at the initial stages of interdiffusion, and a reduced confinement of the wave functions is also observed. The effect of valence-band mixing remains strong, in general, with increasing interdiffusion and an almost parabolic band is restored at the latter stages of interdiffusion. An enhancement of the lowest energy light-hole negative mass is also obtained with interdiffusion. The nonmonotonic behavior of the subband-edge energies suggests that when only the lowest interband energy is used to characterize the interdiffusion process, errors are likely to occur.

Orientation dependence of subband structure and optical properties in GaAsAlGaAs quantum wells: [001], [111], [110] and [310] growth directions

We calculate the valence subband dispersion in GaAsAl xGa 1−xAs quantum wells, with growth axes along the [001], [111], [110] and [310] directions, by solving the multiband effective mass equations for the four-component envelope function. Boundary conditions for conservation of probability current are given for each growth direction. The conduction band dispersion is obtained from an accurate expression for the bulk dispersion which includes the effects of anisotropy and nonparabolicity. We use the calculated dispersion to examine the dependence of optical interband transitions on both polarization and valence-subband mixing.

Self-consistent subband calculations of hetero n-i-p-i superlattices and the effect of valence subband mixing

Hetero n-i-p-i superlattices combine the interesting and useful tunability of conventional doping superlattices (“n-i-p-i crystals”) with the high mobility and the weakly broadened subband structure of modulation-doped heterostructure superlattices. The recombination rate for injected electrons and holes can be very low in these systems due to the spatial separation of electrons and holes. Consequently, large non-equilibrium charge carrier concentrations can be maintained. These charge carrier distributions affect significantly the superlattice potential. We present calculations of the electron and hole subbands taking into account the self-consistent potentials of both electron and hole distributions. Type-I and type-II hetero n-i-p-i structures are investigated. The in-plane dispersion relations and the effects of valence subband mixing on subband structures are also discussed.

Mixing of valence subbands in GaAs/AlxGa1-xAs multiple quantum wells by uniaxial stress.

The effects of uniaxial stress on the energies of exciton transitions in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As multiple quantum wells are investigated both theoretically and experimentally. The valence subbands and the corresponding wave functions are analyzed at the Brillouin-zone center by solving a 4\ifmmode\times\else\texttimes\fi{}4 Luttinger-Kohn Hamiltonian in conjunction with a 4\ifmmode\times\else\texttimes\fi{}4 strain Hamiltonian in the spin J=(3/2 basis. Appropriate boundary conditions are obtained by integrating the total Hamiltonian across the interfaces of the wells. Good agreement is obtained between numerical calculations on a 22-nm-wide quantum well subjected to a uniaxial stress in the plane of the well and experimental results obtained using photoluminescence excitation spectroscopy at liquid-helium temperatures. Evidence of valence-subband mixing between the light-hole exciton and higher levels of heavy-hole excitons is clearly observed.

Electronic properties and optical-absorption spectra of graded-gap GaAs-AlxGa

A study of the electronic and optical properties of GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As graded-gap quantum wells is presented using a formalism which takes into account the valence-subband mixing effects. The system considered in this investigation consists of two semi-infinite slabs of ${\mathrm{Al}}_{\mathrm{y}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{y}}$As barrier material having aluminum concentration y surrounding a graded-gap region of ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As whose aluminum concentration x is a linear function of z (the direction of growth) such that x=(${x}_{0}$/w)(z +w/2). Here w is the width of the graded region. At z=-w/2, x=0 and at z=+w/2, x=${x}_{0}$, where ${x}_{0}$ varies between 0 and y. Conduction- and valence-subband structure, exciton binding energies, exciton oscillator strengths, and the total absorption spectra are calculated as a function of well size and aluminum concentration ${x}_{0}$. Optical transitions associated with several conduction and valence subbands are considered. Computed electronic and optical properties are found to be the result of an interplay between the effects of the overlap of electron and hole envelope functions and the valence-subband mixing. Valence-subband mixing leads to the removal of Kramers degeneracy in the quantum-well system when ${x}_{0}$ is different from zero, as in this case the system does not possess inversion symmetry.

Electronic properties and optical-absorption spectra of GaAs-AlxGa1-xAs quantum wells in externally applied electric fields.

A study of the electronic and optical properties of GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum wells in external electric fields is presented using a theory which incorporates valence-subband-mixing effects. Electric-field-induced changes in the conduction- and valence-subband structure, exciton binding energies, exciton oscillator strengths of both allowed (\ensuremath{\Delta}n=0) and forbidden (\ensuremath{\Delta}\ensuremath{\ne}0) transitions, and the total absorption spectrum are calculated. Optical transitions associated with several conduction and valence subbands are considered. Computed electronic and optical properties are found to be the result of an interplay between the effects of the overlap of electron and hole envelope wave functions and the valence-subband mixing. Valence-subband mixing results in a large splitting of the Kramer's degeneracy in a quantum-well system in the presence of an electric field. The electric-field-induced changes in the computed exciton binding energies and oscillator strengths are caused mainly by the variation of the degree of overlap between the electron and hole wave functions. The foregoing results are compared with those obtained assuming no valence-band-mixing effects and are shown to be both qualitatively and quantitatively different. A brief comparison of our results with available experimental data is presented.