ANALYSIS OF THE LINEARIZED ENERGY AND MOMENTUM BALANCE-EQUATIONS OF THE SINGLE-ELECTRON GAS-TRANSPORT MODEL

The linearized energy and momentum balance equations of the single ele ctron gas transport model are considered. A general analytic solution is obtained for transient velocity responses to arbitrary time depende nt field perturbations. A criterion for the occurrence of velocity ove rshoot following a field step is determined. Various characteristics o f such overshoot are established, and a new ''differential overshoot m obility'' is defined. Compact analytic expressions are obtained for Th ornber's augmented drift-diffusion overshoot coefficient B, and the sm all-signal complex mobility. Calculated results are presented for elec tron transport in silicon at 77, 300, and 450 K, for material that is undoped and for material that is doped n type at a level of 10(18) cm- 3.