Nonlinear conductivity tensor in graded mixed semiconductors

A mixed semiconductor crystal with graded composition (i.e., a heterojunction) is characterized by a position-dependent effective mass, which leads to an additional force acting on free carriers. Taking this force into account, as well as the carrier-concentration gradient, the Boltzmann equation is solved in the presence of two oscillating electric fields of arbitrary frequencies, and a general expression for the second-order conductivity tensor is obtained. This tensor is linear in the effective-mass gradient and in the carrier-concentration gradient, and independent of carrier statistics. Limiting cases ωτ1 and ωτ1 are discussed in detail. For ωτ1, the expected second-harmonic generation associated with the mass gradient is at least comparable with that observed in homogeneous semiconductors. For ωτ1, nonlinear effects are much stronger than in a homogeneous material in this frequency range. Measurement of the nonlinear current offers a method of directly determining the effective-mass gradient.