Calculating relaxation time distribution function from power spectrum based on inverse integral transformation method

Abstract

A novel method is presented for obtaining the distribution function of relaxation times G(τ) from power spectrum 1/fα(1≤2). It is derived using McWhorter model and its inverse Stieltjes transform. Unlike the pre-assumed conventional g(τ) distribution, the extracted G(τ) has a peak whose width increases as the slope of the power spectrum α decreases. The peak position determines the dominant time constant of the system. Our method is unique because the distribution function is directly extracted from the measured power spectrum. We then demonstrate the validity of this method in the analysis of noise in transistor.