General R-matrix approach for integrating the multiband k⋅pk⋅p equation in layered semiconductor structures

A Fortran 90 code is provided for calculating the electron reflection and transmission coefficients in semiconductor heterostructures within the 14-band k⋅pk⋅p approximation. The code may easily be adapted for use with any k⋅pk⋅p model, including magnetic field and/or strain effects, for example. Numerical instability, which is problematic in type-II systems due to the simultaneous presence of propagating and evanescent states, is reduced by developing a novel log-derivative R-matrix approach based on the Jost solution to the k⋅pk⋅p equation.Program summaryProgram title: multiband-kpCatalogue identifier: AEKG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKG_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7088No. of bytes in distributed program, including test data, etc.: 90 237Distribution format: tar.gzProgramming language: Fortran 90Computer: HP 128-node cluster (8 Intel 3.0 GHz Xeon processors per node)Operating system: RedHat Enterprise Linux 5.1RAM: 11 MBClassification: 7.3, 7.9External routines: LAPACK [1], ODE [2]Nature of problem: Calculating the electron transmission (or reflection) coefficient for single, double or multiple semiconductor quantum wells.Solution method:   Makes use of a log-derivative reflection matrix approach which is based on obtaining the Jost solution to the multiband envelope function k⋅pk⋅p equation.Restrictions:   Accuracy depends on the limitations of the k⋅pk⋅p model. In this implementation a “bare” 14-band model is used.Unusual features: By default Intelʼs math-kernel-library (MKL) [3] runs in serial mode. MKL also has built in parallel matrix algorithms which can be invoked without explicit parallelization in the source code. In this case all of the 8 CPUs in one node are used by the LAPACK subroutines.Running time: The given sample output, for the transmission coefficient at 750 different energies, required 376.51 CPU seconds (less than 7 minutes on a single CPU).References:[1]E. Anderson, et al., LAPACK Usersʼ Guide, 3rd edition, Society for Industrial and Applied Mathematics, Philadelphia, 1999.[2]L.F. Shampine, M.K. Gordan, Computer Solution to Ordinary Differential Equations: The Initial Value Problem, W.H. Freeman and Company, San Francisco, 1975.[3]http://software.intel.com/en-us/articles/intel-math-kernel-library-documentation/.