Quantum 1/<i>f</i>noise associated with ionized impurity scattering and electron-phonon scattering in condensed matter

Abstract

Abstract Scattering of charged particles is accompanied by the emission of soft photons. Handel's theory of 1/f noise, based on the infrared quasi-divergent coupling of the system to the electromagnetic field, indicates that the current associated with a beam of scattered particles will exhibit 1/f noise. His derivation is valid in a vacuum. Here we extend his results and obtain the fluctuation spectrum for the fluctuations in cross-section and for the scattering rates w kk′ in k-space, using the Born approximation. Next we consider mobility fluctuations due to these scattering rates, employing the relaxation time solutions of the Boltzmann transport equation, valid in non-degenerate semiconductors. Explicit results are obtained for the mobility-fluctuation noise caused by ionized impurity scattering, acoustic phonon scattering, optical phonon scattering, polar optical phonon scattering, and intervalley scattering. We derive Hooge's law, and the Hooge parameters for the above-mentioned processes are obtained in detail. This is then applied to n-type silicon and n-type gallium arsenide; the overall Hooge parameter, which is a weighted average of the partial α-parameters, is computed as a function of temperature and compared with experiment. For silicon, good agreement is obtained with available data. As a byproduct we also find the mobilities as function of temperature for these materials. Excellent agreement with the well-known experimental data is observed. We still note that this is the first theoretical derivation of Hooge's law and that the magnitude of the noise is obtained in detail without adjustable parameters. We believe that quantum 1/f noise gives the limiting value of 1/f noise that can be observed.