Non-linear thermal fluctuations in a diode

Abstract

As an example of non-linear noise the fluctuations in a circuit consisting of a diode and a condenser C are studied. From the master equation for this system the following results are derived.

1. (i) The equilibrium distribution of the voltage is rigorously Gaussian, the average voltage being equal to the contact potential of the two electrodes.

2. (ii) The ordinary I-V characteristic of the diode is found in the limit C → ∞.

3. (iii) An expansion in e2/kTC is used to find the spectral density of the fluctuations to first order. It is shown that to this order the Fokker-Planck equation gives the same result.

4. (iv) Another approximation method leads to an expansion of the fluctuation spectrum in inverse powers of the frequency. It is rigorously shown that the first term in this expansion is not affected by the presence of the non-linearity.

5. (v) The so-called fluctuation-dissipation theorem is not valid beyond the linear approximation.

6. (vi) The expansion of the fluctuation spectrum in e2/kTC can be calculated to all orders. However, the complete spectrum contains additional terms, which do not show up in this expansion, as they are of infinite order in e2/kTC.