Generation-recombination noise in semiconductors-The equivalent circuit approach

Generation-recombination noise in semiconductors in thermal equilibrium is treated from the standpoint of thermal fluctuations in equivalent electrical circuits. For the general volume recombination model, a method based on network reduction is presented which allows one to calculate the spectral density of the electron and hole fluctuations without solving for the spectra of the fluctuations in occupancy of the recombination centers and traps. The method is extended to a surface recombination model, thereby avoiding the ambiguities found in previous formal treatments. It is shown that the concept of ambipolar diffusion, the location and spectral density of the random sources, and the spatial correlation of Fourier coefficients of carrier density fluctuations all have simple significance in electrical terms. Using transmission line techniques, the generation-recombination (GR) spectrum is calculated for a two-level semiconductor where recombination occurs at opposite plane surfaces. This new result is examined in detail for the limiting cases approached when the recombination process is 1) volume-limited, 2) surface-limited, and 3) diffusion-limited. It is shown that in the first two cases, the spectrum is identical with that obtained from a zero-dimensional analysis provided the time constant is properly defined. For the diffusion-limited case, however, the spectrum varies as 1/ω 3/2 at high frequencies, and at low frequencies the noise is 5/6 that predicted by the simple theory. The new result is shown to compare favorably with measurements reported previously by Hill and van Vliet.