Simplified Theory of One-Carrier Currents with Field-Dependent Mobilities

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Abstract
A general method is presented for the calculation of steady‐state, one‐carrier currents in nonmetallic solids where the mobility is field dependent. The analysis includes the effects of space charge and trapping. The essential mathematical step is the representation of the electric‐field intensity as a polynomial in the drift velocity. Detailed applications are made to semiconductor and insulator problems. A new mobility function of convenient mathematical form is proposed for the case that the carrier has a constant mean free path. Some very general properties of the current flow are established by geometric analysis.