Noise spectra resulting from diffusion processes in a cylindrical geometry

Abstract

A discussion is presented of noise spectra resulting from diffusion in a cylindrical domain D s with volume sources and sinks in the domain, subject to various kinds of boundary conditions at the surface of D s , including the case that D s is part of an infinite domain D. This applies to various physical processes, e.g.: (i) fluctuations caused by diffusion and recombination at the walls in a gaseous plasma; (ii) carrier fluctuations in a solid involving diffusion, surface recombination and volume recombination; (iii) temperature or energy fluctuations in cylindrical bars with spontaneous radiation at the boundaries; (iv) problems involving contact noise. The spectral densities are derived from the relevant Green's functions. For the infinite domain an extension of the Macfarlane-Burgess spectrum is obtained, which yields spectra such as are often observed in insulators with a small photoconductive layer (CdS in band-band absorption). The finite domain case leads to three kinds of spectra (diffusion-limited, surface-limited and volume-limited) analogous to the one dimensional solutions obtained before. The details of these spectra, especially the characteristic break points, are discussed.