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Numerical solution to the general one‐dimensional diffusion equation in semiconductor heterostructures
Author(s) -
Harrison P.
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.2221970113
Subject(s) - superlattice , heterojunction , diffusion , photoluminescence , diffusion equation , quantum well , materials science , semiconductor , annealing (glass) , condensed matter physics , effective diffusion coefficient , computational physics , thermodynamics , physics , optoelectronics , quantum mechanics , medicine , laser , economy , radiology , magnetic resonance imaging , economics , composite material , service (business)
A method of solving numerically the one‐dimensional diffusion equation for arbitrary profiles and arbitrary functional dependencies of the diffusion coefficient on the position, diffusant concentration and the time, is described. The technique is applied to a variety of diffusion problems in semiconductor quantum wells to illustrate its power and versatility. In particular solutions are shown for diffusion of graded interfaces, a concentration dependent diffusion coefficient, and the effect of a depth and time dependent diffusion coefficient on a superlattice, as occurs in ion implantation and the subsequent annealing out of the resulting radiation damage. The depth dependence of the intermixing due to ion implantation and subsequent rapid thermal anneal, of a GaAs/Ga 1− x Al x As multiple‐quantum‐well structure, is deduced from the broadening of the low temperature photoluminescence emission.