Robinson–Martin: Relating the 4¯3m and 6mm nonlinear piezoelectric tensors

Abstract

Binary semiconductors are central to all modern electronic, optoelectronic, and electromechanical systems. Given such practical importance, there is value in finding routes to simplify the determination of physical properties, particularly with respect to nonlinearities. Fortunately, nearly all binary semiconductors crystallize into one of two structures: cubic zinc blende or hexagonal wurtzite. Correspondences between the linear rank 3 piezoelectric and rank 4 elastic tensors of zinc blende and wurtzite polytypes have been addressed. Nonlinear rank 6 elastic tensors have similarly been discussed. Provided herein are the analogous relations for the nonlinear rank 5 tensors that have not previously been treated and which complete this missing transformation gap and enable some nonlinear atomic-level phenomena to be investigated.