Semiconductor 1/f noise from dynamic coupling of charge carriers and lattice

Abstract

A quantum mechanical model of an intrinsic semiconductor is used to derive the coupled dynamics of the lattice and charge carriers. It is shown that a source of noise current is proportional to vibration displacement of the lattice, and that ground state of this motion has the (1/frequency) power spectrum at frequencies below the lattice vibration frequency and a (1/frequency squared) form above that frequency. The voltage drop across a three-dimensional semiconductor sample is calculated by assuming that the random noise currents in the lattice sites are uncorrelated. The resulting power spectral density of the noise current in a sample has a form similar to the well-known Hooge formula. The scale factor is not a universal constant but instead depends upon the lattice vibration frequency, charge carrier mean-free-path and drift velocity, number of carriers per lattice site, and mass of a lattice atom. Calculated values with reasonable semiconductor parameters are consistent with those obtained from other theories of 1/f noise.