Analysis of semiconductors with field-dependent mobility

Using the time domain analysis of Lagrangian approach, the small-signal behavior of a semiconductor with field-dependent mobility under various contact conditions is analyzed. A generalized closed form solution for an impulse current response is derived when the carrier velocity characteristic is expressed by a piecewise linear function. This result gives an accurate description of the transient performance of the device and can provide good insight into device operation. Numerical examples are given for a negative differential mobility GaAs crystal, considering the conditions under which negative resistances occur. A generalized small-signal impedance of the semiconductor is given, from which previous results reported for particular devices can be obtained as special cases.