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Effective‐mass Hamiltonian for strained superlattices
Author(s) -
Brezini A.,
Sebbani M.,
Depollier C.
Publication year - 1996
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221940211
Subject(s) - effective mass (spring–mass system) , hamiltonian (control theory) , physics , condensed matter physics , homogeneous , semiconductor , heterojunction , conduction band , schrödinger equation , superlattice , mathematical physics , band gap , electronic band structure , quantum mechanics , mathematics , statistical physics , electron , mathematical optimization
For an abrupt heterojunction between two otherwise homogeneous semiconductors in one dimension, the effective‐mass Hamiltonian\documentclass{article}\pagestyle{empty}\begin{document}$$ H = - \frac{{\hbar ^2 }}{2}m(z)^\alpha \,a(z)^v \,\frac{{\rm d}}{{{\rm d}z}}m(z)^\beta \,a(z)^{ - 2v} \frac{{\rm d}}{{{\rm d}z}}m(z)^\alpha \,a(z)^v + E_c (z) $$\end{document} is examined with 2α + β = −1, where m ( z ), a ( z ), and E c ( z ), are the position dependent effective mass, the local lattice parameter, and the local conduction band edge, respectively. The exact Schrödinger equation is compared with that for the effective‐mass equation in the case of an analytically solvable model. In the asymptotic limit of the energy close to the band edge, the conclusions obtained are shown to be dependent on the parity of the bands.