Strain-induced variations of electronic energy band edges of embedded semiconductor quantum dots in half-space substrates

Abstract

The strain-induced local electronic band edge states in semiconductor quantum dots (QDs) are studied using a k⋅p description of the electronic eigenstates coupled with the induced lattice strain as calculated using the continuum mechanics (CM) description. In the CM method, the misfit-lattice induced strain can be reduced to an analytical expression that is straightforward to evaluate numerically. Different from most previous analyses for QDs in infinite spaces, we address cubic and pyramidal QDs located in half-space substrates with different lattice orientations, which more realistically describe experimental situations in most instances. The band edges within the cubic and pyramidal InAs QDs embedded in GaAs substrates are predicted within the six-band k⋅p basis via both a published approximation and the presented exact approach. Comparison of the strain-induced local band edge shows that the approximate method adopted previously in literature could result in a substantial error near the interface region of the QD. The strain-induced band edges along the bottom center line of the QD can differ by a factor of 2 between the two approaches. Furthermore, the effect of the free surface on the strain-induced band edges is studied by varying the depth of the buried QD. When the QD is moved away from the surface, the band edges converge in a consistent way to the infinite-space solution. Comparison with available experimental results validates our exact model within the half-space substrate and shows the importance of treating the surface in a theoretically rigorous way.