Programs in Physics & Physical Chemistry
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|Manuscript Title: TRS: a program to calculate Landau levels and direct dipole transitions in uniaxially stressed semiconductors.|
|Authors: J. Schmitz, H.-R. Trebin, U. Rossler|
|Program title: TRS|
|Catalogue identifier: ACBH_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 66(1991)308|
|Programming language: Fortran.|
|Computer: VAX II/GPX.|
|Operating system: VMS 4.6, TOS, CMSL 4.421.|
|RAM: 434K words|
|Word size: 32|
|Keywords: Narrow gap Semiconductors, Zincblende lattice, Landau levels, Uniaxially stress parallel to magnetic field, Effective hamiltonian, Invariant expansion, Eightfold space of Valence band and lowest Conduction band, Normal and inverted Bands, Energy eigenvalues, Eigenvectors, Direct inter- and Intraband dipole Transitions, Oscillator strengths, Gamma-point,  crystal axis.|
Nature of problem:
An effective Hamiltonian constructed by invariant expansion is used to calculate Landau levels and wave functions in narrow-gap semiconductors with a zincblende lattice under uniaxial stress. It is based on an eightfold space of uppermost valence and lowest conduction bands at the center of the Brillouin zone and its vicinity. The wave functions are futher used to calculate the oscillator strengths of direct inter- and intraband dipole transitions. Thus program TRS is a valuable tool for the experimentalist to analyze quantum resonances measured in semiconductors.
The matrix elements of the Hamiltonian are set up one by one according to the equations derived from the theory. Then the resulting matrix is diagonalized using the QL method. Energy eigenvalues and eigenvectors are further used in the calculation of oscillator strengths.
The dimension of arrays are set to include Landau levels with oscillator quantum number up to na <=39 (na <=19 on computer(2)). Adaptations are easily made. Due to the limitations in the Kane-modell and the underly- ing perturbation theory the program is only suitable for eigenstates in the vicinity of the Gamma-point. Transitions are restricted to direct dipole transitions. All calculations are based on a geometry with magnetic field and uniaxial stress being parallel to the  crystal axis.
TRS contains a subroutine which clears the screen of the terminal before displaying a new page of text. This action is not essential to the operation of the program and may be entirely omitted. In order to preserve the intended screen display it must be adapted to the specific device used.
Execution times depend strongly on the maximum Landau oscillator quantum number and the number of transitions chosen. The test run described in the long write-up requires 25.68 s on the VAX II/GPX, 2.06 s on the Comparex 8/89 and 11 min 17 s on the Atari 1040st.
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