**Modelling of strain fields in quantum wires with continuum methods and
molecular statics**

JJ Ramsey and E Pan and PW Chung, JOURNAL OF PHYSICS-CONDENSED MATTER, 20, 485215 (2008).

DOI: 10.1088/0953-8984/20/48/485215

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

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