Voltage Fluctuations in a Diode

A thermodynamically consistent microscopic model is used to derive a Fokker-Planck equation governing voltage fluctuations across a diode in the limit of small electron charge. In going to this limit, strong nonlinearities in the diode current characteristic are allowed to persist for voltages in the range of the thermal fluctuations. This requires greater freedom in the choice of the microscopic transition probabilities than exists in other diode models that have been studied. It is pointed out that this added freedom is essential for the achievement of a regime in which the thermal fluctuations are strongly nonlinear while at the same time the charge may legitimately be treated as a continuous variable. The transition probabilities appearing in the master equation are required to be consistent with the thermodynamically correct equilibrium voltage distribution and to satisfy the condition of time reversibility. It is shown that the resulting Fokker-Planck equation is compatible with an equivalent circuit that includes a fluctuating current source having the form of white noise multiplied by a function of the diode voltage. This equivalent noise source has the form of a mathematical representation developed by Hurwitz and Kac for a related stochastic problem.