3 - Fluctuations in nonequilibrium gases

Summary

One of the most important parts of the physics of fluctuations in solids is the physics of fluctuations in solid-state plasma, i.e., in a gas of charge carriers, electrons and/or holes. The spectral density of electric fluctuations in an equilibrium conductor (zero bias voltage and current) is given by the Nyquist fluctuation–dissipation relation (Sec. 2.2) in terms of the dissipative part of the complex impedance Z(f). It means that the problem of calculation and measurement of noise in an equilibrium state is reduced to the problem of, respectively, calculation and measurement of the complex resistance. This problem is usually considered to be simpler. In an equilibrium system, the spectral density of noise does not contain any information other than that contained in Z(f). However, the fluctuation–dissipation relation holds only in the equilibrium state. For conductors that are in nonequilibrium states, for instance, for conductors with hot electrons in strong electric fields, there is no general relation between the spectral density of noise, on one hand, and any characteristics of the response, frequency dependent or static, of the current or voltage, on the other hand. Thus, the calculation of current noise can not be reduced to the calculation of mean current (e.g., its dependence on voltage) and is an individual problem.

This chapter is devoted mainly to fluctuations in a gas of hot charge carriers (for brevity we call them ‘hot electrons’). As is well known, electrons become hot in strongly biased conductors.