EFFECTIVE-MASS THEORY FOR GAAS/GA1-XALXAS QUANTUM WIRES AND CORRUGATED SUPERLATTICES GROWN ON (311)-ORIENTED SUBSTRATES

The electronic structures of GaAs/Ga1-xAlxAs quantum wires (corrugated superlattices) grown on (311)-oriented substrates are studied in the framework of the effective-mass envelope-function method. The electron and hole subband structure and optical transition matrix elements are calculated. When x=1, the results are compared with experiments, and it is found that the direct transition becomes an indirect transition as the widths of well and barrier become smaller.

EFFECTS OF AN EXTERNAL MAGNETIC-FIELD ON SHALLOW DONOR LEVELS IN SEMICONDUCTORS

An extension of Faulkner's method for the energy levels of the shallow donor in silicon and germanium at zero field is made in order to investigate the effects of a magnetic field upon the excited states. The effective-mass Hamiltonian matrix elements of an electron bound to a donor center and subjected to a magnetic field B, which involves both the linear and quadratic terms of magnetic field, are expressed analytically and matrices are solved numerically. The photothermal ionization spectroscopy of phosphorus in ultrapure silicon for magnetic fields parallel to the [1,0,0] and [1,1,1] directions and up to 10 T is explained successfully.

THEORY OF THE ELECTRONIC-STRUCTURE OF POROUS SI

A theoretical model for the electronic structure of porous Si is presented. Three geometries of porous Si (wire with square cross section, pore with square cross section, and pore with circular cross section) along both the [001] and [110] directions are considered. It is found that the confinement geometry affects decisively the ordering of conduction-band states. Due to the quantum confinement effect, there is a mixing between the bulk X and GAMMA states, resulting in finite optical transition matrix elements, but smaller than the usual direct transition matrix elements by a factor of 10(-3). We found that the strengths of optical transitions are sensitive to the geometry of the structure. For (001) porous Si the structure with circular pores has much stronger optical transitions compared to the other two structures and it may play an important role in the observed luminescence. For this structure the energy difference between the direct and the indirect conduction-band minima is very small. Thus it is possible to observe photoluminescence from the indirect minimum at room temperature. For (110) porous Si of similar size of cross section the energy gap is smaller than that of (001) porous Si. The optical transitions for all three structures of (110) porous Si tend to be much stronger along the axis than perpendicular to the axis.

INTERVALLEY GAMMA-CHI DEFORMATION POTENTIALS IN III-V ZINCBLENDE SEMICONDUCTORS BY ABINITIO PSEUDOPOTENTIAL CALCULATIONS

Intervalley GAMMA-X deformation-potential constants (IVDP's) have been calculated by use of a first-principles pseudopotential method for the III-V zinc-blende semiconductors AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb. When the calculated IVDP's of LA phonons for GaP, InP, and InAs and of LO phonons for AlAs, AlSb, GaAs, GaSb, and InSb are compared with results of a previous calculation that used the empirical pseudopotential method (EPM) and a rigid-ion approximation, good agreement is found. However, our ab initio pseudopotential results on IVDP's of LA phonons for AlAs, AlSb, GaAs, GaSb, and InSb and of LO phonons for GaP, InP, and InAs are about one order of magnitude smaller than those obtained by use of EPM calculations, indicating that the electron redistribution accompanying crystal-lattice deformation has a significant effect on GAMMA-X intervalley scattering for these phonon modes when the anions are being displaced. In our calculations the LA- and LO-phonon modes at the X point have been evaluated in the frozen-phonon approximation. We have also obtained the LAX- and LOX-phonon frequencies for these materials from total-energy calculations, which agree very well with experimental values for these semiconductors. We have also calculated GAMMA-X hole-phonon scattering matrix elements for the top valence bands in these nine semiconductors, from which the GAMMA-X IVDP's of the top valence bands for the longitudinal phonons and transverse phonons are evaluated, respectively.

1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES FOR BAND STRUCTURES OF SI AND GAAS

We have applied the Green function theory in GW approximation to calculate the quasiparticle energies for semiconductors Si and GaAs. Good agreements of the calculated excitation energies and fundamental energy gaps with the experimental band structures were achieved. We obtained the calculated fundamental gaps of Si and GaAs to be 1.22 and 1.42 eV in comparison to the experimental values of 1.17 and 1.52 eV, respectively. Ab initio pseudopotential method has been used to generate basis wavefunctions and charge densities for calculating dielectric matrix elements and electron self-energies.

ELECTRONIC-STRUCTURES OF QUANTUM WIRES FORMED BY LATERAL STRAIN

The electronic structures of quantum wires formed by lateral strain are studied in the framework of the effective-mass envelope-function method. The hole energy levels, wave functions, and optical transition matrix elements are calculated for the real quantum-wire structure, and the results are compared with experiment. It is found that one-dimensional confinement effects exist for both electronic and hole states related to the n (001) = 1 state. The lateral strained confinement causes luminescence-peak redshifts and polarization anisotropy, and the anisotropy is more noticeable than that in the unstrained case. The variation of hole energy levels with well widths in the [110] and [001] directions and wave vector along the [110BAR] direction are also obtained.

EFFECTIVE-MASS THEORY FOR SUPERLATTICES GROWN ON (11N)-ORIENTED SUBSTRATES

An effective-mass formulation for superlattices grown on (11N)-oriented substrates is given. It is found that, for GaAs/AlxGa1-xAs superlattices, the hole subband structure and related properties are sensitive to the orientation because of the large anisotropy of the valence band. The energy-level positions for the heavy hole and the optical transition matrix elements for the light hole apparently change with orientation. The heavy- and light-hole energy levels at k parallel-to = 0 can be calculated separately by taking the classical effective mass in the growth direction. Under a uniaxial stress along the growth direction, the energy levels of the heavy and light holes shift down and up, respectively; at a critical stress, the first heavy- and light-hole energy levels cross over. The energy shifts caused by the uniaxial stress are largest for the (111) case and smallest for the (001) case. The optical transition matrix elements change substantially after the crossover of the first heavy- and light-hole energy has occurred.

1ST-PRINCIPLES CALCULATIONS FOR QUASI-PARTICLE ENERGIES OF GAP AND GAAS

We have applied the Green-function method in the GW approximation to calculate quasiparticle energies for the semiconductors GaP and GaAs. Good agreement between the calculated excitation energies and the experimental results was achieved. We obtained calculated direct band gaps of GaP and GaAs of 2.93 and 1.42 eV, respectively, in comparison with the experimental values of 2.90 and 1.52 eV, respectively. An ab initio pseudopotential method has been used to generate basis wave functions and charge densities for calculating the dielectric matrix elements and self-enegies. To evaluate the dynamical effects of the screened interaction, the generalized-plasma-pole model has been utilized to extend the dielectric matrix elements from static results to finite frequencies. We presen the calculated quasiparticle energies at various high-symmetry points of the Brillouin zone and compare them with the experimental results and other calculations.

1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES FOR BAND STRUCTURES OF SEMICONDUCTORS

We successfully applied the Green function theory in GW approximation to calculate the quasiparticle energies for semiconductors Si and GaAs. Ab initio pseudopotential method was adopted to generate basis wavefunctions and charge densities for calculating dielectric matrix elements and electron self-energies. To evaluate dynamical effects of screened interaction, GPP model was utilized to extend dieletric matrix elements from static results to finite frequencies. We give a full account of the theoretical background and the technical details for the first principle pseudopotential calculations of quasiparticle energies in semiconductors and insulators. Careful analyses are given for the effective and accurate evaluations of dielectric matrix elements and quasiparticle self-energies by using the symmetry properties of basis wavefunctions and eigenenergies. Good agreements between the calculated excitation energies and fundamental energy gaps and the experimental band structures were achieved.

Effective-mass theory for InAs/GaAs strained superlattices

By using the recently developed exact effective-mass envelope-function theory, the electronic structures of InAs/GaAs strained superlattices grown on GaAs (100) oriented substrates are studied. The electron and hole subband structures, distribution of electrons and holes along the growth direction, optical transition matrix elements, exciton states, and absorption spectra are calculated. In our calculations, the effects due to the different effective masses of electrons and holes in different materials and the strain are included. Our theoretical results are in agreement with the available experimental data.

Quantum confinement effect in thin quantum wires

The electronic states and optical transition properties of three semiconductor wires Si? GaAs, and ZnSe are studied by the empirical pseudopotential homojunction model. The energy levels, wave functions, optical transition matrix elements, and lifetimes are obtained for wires of square cross section with width from 2 to 5 (root 2a/2), where a is the lattice constant. It is found that these three kinds of wires have different quantum confinement properties. For Si wires, the energy gap is pseudodirect, and the wave function of the electronic ground state consists mainly of four bulk Delta states. The optical transition matrix elements are much smaller than that of a direct transition, and increase with decreasing wire width. Where the width of wire is 7.7 Angstrom, the Si wire changes from an indirect energy gap to a direct energy gap due to mixing of the bulk Gamma(15) state. For GaAs wires. the energy gap is also pseudodirect in the width range considered, but the optical transition matrix elements are larger than those of Si wires by two orders of magnitude for the same width. However, there is no transfer to a direct energy gap as the wire width decreases. For ZnSe wires, the energy gap is always direct, and the optical transition matrix elements are comparable to those of the direct energy gap bulk semiconductors. They decrease with decreasing wire width due to mixing of the bulk Gamma(1) state with other states. All quantum confinement properties are discussed and explained by our theoretical model and the semiconductor energy band structures derived. The calculated lifetimes of the Si wire, and the positions of photoluminescence peaks, are in good agreement with experimental results.

Effective-mass theory for InAs/GaAs strained coupled quantum dots

In the framework of effective-mass envelope-function theory, the optical transitions of InAs/GaAs strained coupled quantum dots grown on GaAs (100) oriented substrates are studied. At the Gamma point, the electron and hole energy levels, the distribution of electron and hole wave functions along the growth and parallel directions, the optical transition-matrix elements, the exciton states, and absorption spectra are calculated. In calculations, the effects due to the different effective masses of electrons and holes in different materials are included. Our theoretical results are in good agreement with the available experimental data.

Optical properties of delta-doped GaAs and GaAs/Al0.1Ga0.9As superlattices

Radiative transition in delta-doped GaAs superlattices with and without Al0.1Ga0.9As barriers is investigated by using photoluminescence at low temperatures. The experimental results show that the transition mechanism of delta-doped superlattices is very different from that of ordinary superlattices. Emission intensity of the transition from the electron first excited state to hole states is obviously stronger than that from the electron ground state to hole states due to larger overlap integral between wavefunctions of electrons in the first excited state and hole states. Based on the effective mass theory we have calculated the self-consistent potentials, optical transition matrix elements and photoluminescence spectra for two different samples. By using this model we can explain the main optical characteristics measured. Moreover, after taking into account the bandgap renormalization energy, good agreement between experiment and theory is obtained.

Electronic structures of the zinc-blende GaN/Ga1-xAlxN compressively strained superlattices and quantum wells

The electronic structures of the zinc-blende GaN/Ga0.85Al0.15N compressively strained superlattices and quantum wells are investigated using a 6 x 6 Hamiltonian model (including the heavy hole, light hole and spin-orbit splitting band). The energy bands, wavefunctions and optical transition matrix elements are calculated. It is found that the light hole couples with the spin-orbit splitting state even at the k=0 point, resulting in the hybrid states. The heavy hole remains a pure heavy hole state at k=0. The optical transitions from the hybrid valence states to the conduction states are determined by the transitions of the light hole and spin-orbit splitting states to the conduction states. The transitions from the heavy hole, light hole and spin-orbit splitting states to the conduction states obey the selection rule Delta n=0. The band structures obtained in this work will be valuable in designing GaN/GaAlN based optoelectronic devices. (C) 1996 Academic Press Limited

Strain effects on optical polarisation properties in (11(2)over-bar2) plane GaN films

We present the theoretical results of the electronic band structure of wurtzite GaN films under biaxial strains in the (11 (2) over bar2)-plane The calculations are performed by the kappa p perturbation theory approach through using the effective-mass Hamiltonian for an arbitrary direction The results show that the transition energies decrease with the biaxial strains changing from -0 5% to 0 5% For films of (11 (2) over bar2)-plane, the strains are expected to be anisotropic in the growth plane Such anisotropic strains give rise to valence band mixing which results in dramatic change in optical polarisation property The strain can also result in optical polarisation switching phenomena Finally, we discuss the applications of these properties to the (11 (2) over bar2) plane GaN based light emitting diode and lase diode