EVALUATION OF VARIOUS APPROXIMATIONS USED IN THE ENVELOPE-FUNCTION METHOD

被引:107
作者
MENEY, AT [1 ]
GONUL, B [1 ]
OREILLY, EP [1 ]
机构
[1] FRAUHOFER INST ANGEW FESTKORPERPHYS, D-79108 FREIBURG, GERMANY
关键词
D O I
10.1103/PhysRevB.50.10893
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We investigate a number of issues related to the application of the envelope-function method to calculate confined-state energies and subband structure in quantum-well structures. We first consider zone-center confined-state energies and show how the explicit elimination of spurious solutions from the envelope-function band structure leads to a slightly modified form of the standard result through which the conduction-band confined-state energies are calculated using a one-band model and an energy-dependent effective mass. We show that the effects of nonparabolicity can be predicted directly from the bulk band structure in an infinitely deep quantum well, and demonstrate how the bulk band structure can also be used to predict the errors in calculated confinement energies in wells of finite depth. The correct choice of boundary conditions still remains controversial for the calculation of valence-subband structure using the Luttinger-Kohn Hamiltonian. We compare the valence-band structure calculated with the lowest conduction band included either explicitly or treated as a remote band, using perturbation theory. We demonstrate that the boundary conditions recently derived by Burt and Foreman are correct. Finally, we compare the valence-band structure calculated using the 4X4 and 6X6 Luttinger-Kohn Hamiltonians. We show how the warping of the highest valence band is markedly different at both intermediate and large wave vectors when the spin-split-off band is included. The use of the axial model to calculate valence-band density of states is therefore questionable with the 6X6 Hamiltonian. The calculated warping is very sensitive to the values of the Luttinger gamma parameters used, indicating the importance of investing more effort to determine these parameters accurately.
引用
收藏
页码:10893 / 10904
页数:12
相关论文
共 48 条
[1]   ELECTRONIC-STRUCTURE AND SEMICONDUCTOR-SEMIMETAL TRANSITION IN INAS-GASB SUPER-LATTICES [J].
ALTARELLI, M .
PHYSICAL REVIEW B, 1983, 28 (02) :842-845
[2]   CALCULATIONS OF HOLE SUBBANDS IN SEMICONDUCTOR QUANTUM WELLS AND SUPERLATTICES [J].
ALTARELLI, M ;
EKENBERG, U ;
FASOLINO, A .
PHYSICAL REVIEW B, 1985, 32 (08) :5138-5143
[3]  
ALTARELLI M, 1986, HETEROJUNCTIONS SEMI, P12
[4]   HOLE SUBBANDS IN STRAINED GAAS-GA1-XALX AS QUANTUM-WELLS - EXACT SOLUTION OF THE EFFECTIVE-MASS EQUATION [J].
ANDREANI, LC ;
PASQUARELLO, A ;
BASSANI, F .
PHYSICAL REVIEW B, 1987, 36 (11) :5887-5894
[5]  
[Anonymous], 1982, LANDOLTBORENSTEIN NU
[6]  
BASTARD G, 1991, SOLID STATE PHYS, V44, P229
[7]   SUPER-LATTICE BAND-STRUCTURE IN THE ENVELOPE-FUNCTION APPROXIMATION [J].
BASTARD, G .
PHYSICAL REVIEW B, 1981, 24 (10) :5693-5697
[8]   THEORETICAL INVESTIGATIONS OF SUPER-LATTICE BAND-STRUCTURE IN THE ENVELOPE-FUNCTION APPROXIMATION [J].
BASTARD, G .
PHYSICAL REVIEW B, 1982, 25 (12) :7584-7597
[9]  
BASTARD G, 1988, WAVE MECHANICS APPLI
[10]   VALENCE SUBBAND STRUCTURE AND OPTICAL GAIN OF GAAS-ALGAAS (111) QUANTUM WELLS [J].
BATTY, W ;
EKENBERG, U ;
GHITI, A ;
OREILLY, EP .
SEMICONDUCTOR SCIENCE AND TECHNOLOGY, 1989, 4 (11) :904-909