Modelling of strain fields in quantum wires with continuum methods and molecularstatics

Abstract

The maximum and minimum principal strains of an InAs quantum wire (QWR) buried in aGaAs matrix are computed using the boundary element method (BEM), the inclusionmethod, and molecular statics, and the results from each method are comparedwith each other. The first two methods are based on continuum mechanics andlinear elasticity, while the third is atomistic. The maximum principal strains arelargely in agreement among the different methods, especially outside the QWR,though in the centre of the QWR, the discrepancy between the continuum andatomistic methods can be as large as 11.9%. The gradients of the strain tensor are inagreement among the methods. The inclusion method is faster than the BEM,and both continuum methods are an order of magnitude faster than molecularstatics. Although the inclusion method, unlike the BEM, ignores the difference inmaterial properties between the QWR and its surrounding matrix, its results are inbetter agreement with the molecular statics results than the results from theBEM. The rough quantitative and qualitative agreements indicate the utility ofclassical continuum methods for estimating strain profiles in nanoscale structures.