Taylor series and δ‐perturbation expansions for a nonlinear semiconductor transport equation

A one‐dimensional, nonlinear equation for steady‐state carrier transport in semiconductors is solved by two approaches: a Taylor series–first integral method and the δ‐perturbation method. The square of the carrier speed is found as a function of the distance where collisions are treated by an energy‐independent mean‐free time. The coefficients of the Taylor series at the first maximum are exact expressions in the function determined from the first integral. In the perturbation expansion the function is evaluated to first order in δ. For both methods expressions for the distance from the first maximum to the emitting electrode are found and the distance is evaluated numerically for the Taylor series–first integral method.