TABLE OF CONTENTS In this section, we will analyze the steady-state transport in short diodes under small concentrations of injected electrons. This case is interesting because extremely nonequilibrium electron distributions can be achieved, which makes new applications possible.
For small electron concentrations, the space-charge does not affect the transport and the electric field is almost constant across the device. Confining ourselves to the case of small/intermediate electric fields, we can neglect both the nonpar abolicity and upper-valley effects. In contrast to the previous analysis, where two parameters ? dr and ? characterized the electron distribution, we now need to solve Eq. (1) and find the distribution function c( p). Assuming only the optical phonon scattering, we rewrite Eq. (1) in the following form:
| (16) |  |
where we introduce new dimensionless coordinate ?= ?z. The equation contains a single controlling parameter the dimensionless field ?. Injection from the collector electrode and reflection of the electrons from this electrode are supposed to be absent and the distribution function of the injected electrons is assumed to be:
| (17) |  |
i.e., the electrons are injected with the concentration n 0 and initial momentum p z =p i . The resulting function f c( p ?, p z p ?, i, p i) is, in fact , the Green function of the problem. To find the distribution function in the sample for any injected electron distribution, one should use...
