Band Structure Engineering of Non-Linear Response in Semiconductor Superlattices

Abstract

Mobile electrons in a nonparabolic band have a non-linear velocity-momentum relation. If an external electromagnetic field is applied, the electron momentum follows the frequency of the applied field. The nonlinear velocity component causes the induced current to contain mixed frequency components. The magnitude of this nonlinearity is measured by the third order nonlinear susceptibility which is proportional to the fourth derivative of the band energy versus wave vector. The bulk conduction band non-parabolicity in, say GaAs is quite small. However, we have argued that momentum mixing associated with the breakdown of the particle-in-a-box model of confinement affects the position of the confined levels and the composition of the momentum wave function. Consequently, it alters the optical matrix elements between confined states. In particular, it also alters the matrix elements involving higher lying states associated with the primary and secondary conduction band minima above the semiclassical confining barrier.