Theory of lateral bandgap variation achievable by strain engineering in patterned substrate strain epitaxy

Abstract

Energy minimization considerations are used to estimate the strain tensor for pseudomorphic structures grown on a patterned substrate. We show that if a material B is deposited below critical thickness in a hole of width W in a substrate A the strain is biaxial unless W ≤ 50 Å, when the strain becomes hydrostatic. For W > 50 Å if the material A is deposited on top of the layer B, as the thickness of A is increased, the lattice matched overlayer A gradually readjusts the strain causing the strain in region B to change from biaxial to hydrostatic. For reasonable film thickness we find that hydrostatic strain can be produced for patterns with widths up to 0.3μm. Since the bandgap changes considerably when the strain changes from biaxial to hydrostatic, this concept can be used to produce lateral variation in the bandgap of heterostructures in single step epitaxy.