Microcycle spectral estimates of 1/f noise in semiconductors

Abstract

Many physical occurrences are characterized by extremely low spectral variations, the measurement and estimation of which has been invariably difficult. An estimate of the density of the power spectrum of very-low-frequency semiconductor 1/f noise is experimentally obtained from 10−6.3 to 1.0 cps with a greater accuracy than that achieved in previous similar attempts; it is concluded that the spectrum is 1/fα with α approximately 1.3 over most of the frequency range, but appearing to have a value of about 1.0 in the lowest decade. A peculiar form of stationarity seems to distinguish 1/f noise from other noise in semiconductors. Ten independent noise sources were time multiplexed and their spectral estimates were subsequently averaged. If the sources have similar spectra, this reduces the necessary data-taking time by a factor of 10 for a given accuracy. An estimator is derived for optimal spectral estimation based on a number of statistically independent noise sources. Other related topics considered are nonequidistant sampling, and a plausible mathematical model of such flicker noise. Finally, the variance of the spectral estimate obtained through the Blackman/Tukey algorithm is analyzed in great detail; the variance is shown to diverge for α≥1.0 in an assumed power spectrum of k/|f|α, unless the assumed spectrum is ``truncated''.