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Model Effective‐Mass Hamiltonians for Abrupt Degraded Heterojunctions
Author(s) -
Brezini A.,
Sebbani M.,
Marouf S.
Publication year - 1995
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.2221890207
Subject(s) - hermitian matrix , kinetic energy , ground state , heterojunction , physics , effective mass (spring–mass system) , potential energy , matching (statistics) , wave function , statistical physics , quantum mechanics , mathematics , statistics
Abstract A class of hermitian effective‐mass Hamiltonians is considered whose kinetic energy term is 1/4 ( m α pm β pm γ + m γ pm β pm α ) with α + β + γ = −1. These Hamiltonians are applied to abrupt degraded interfaces between crystals and the matching conditions across the interface are searched for the effective‐mass wave function Ψ and its spatial derivative Ψ′. For α ≠ γ it is found that the ground‐state energy is negative, i.e. without physical bearing for the considered potential. Consequently, the only viable cases are for α = γ. In a model calculation, β ≈ −1 is estimated, to be the more relevant candidate although the case β = 0 cannot be excluded for typical interfaces.