Quantum approach to1fnoise

Abstract

On the basis of the known experimental properties of $\frac{1}{f}$ noise, some previous models are analyzed. The presence of $\frac{1}{f}$ noise in the simplest systems such as beams of charged particles in vacuum, the existence of $\frac{1}{f}$ noise in currents limited by the surface recombination rate, bulk recombination rate, or by the finite mobility determined by interaction with the phonons in solids, suggests a fundamental fluctuation of the corresponding elementary cross sections. This leads to fluctuations of the kinetic transport coefficients such as mobility $\ensuremath{\mu}$ or recombination speed, observable both in equilibrium and nonequilibrium. In the first case the available Johnson noise power $\mathrm{kT}$, determined by the Nyquist theorem, is free of this type of $\frac{1}{f}$ fluctuation. An elementary calculation is presented which shows that any cross section, or process rate, involving charged particles, exhibits $\frac{1}{f}$ noise as an infrared phenomenon. For single-particle processes, the experimental value of Hooge's constant is obtained as an upper limit, corresponding to very large velocity changes of the current carriers, close to the speed of light. The obtained ${sin}^{2}(\frac{\ensuremath{\theta}}{2})$ dependence on the mean scattering angle predicts much lower $\frac{1}{f}$ noise for (low-angle) impurity scattering, showing a strong ($\ensuremath{\sim}\frac{{\ensuremath{\mu}}^{2}}{{\ensuremath{\mu}}_{\mathrm{latt}}^{2}}$) noise increase with temperature at the transition to lattice scattering. This is in qualitative agreement with measurements on thin films and on heavily doped semiconductors, or on manganin. The theory is based on the infrared quasidivergence present in all cross sections (and in some autocorrelation functions) due to interaction of the current carriers with massless infraquanta: photons, electron-hole pair excitations at metallic Fermi surfaces, generalized spin waves, transverse phonons, hydrodynamic excitations of other quanta, very low-energy excitations of quasidegenerate states observed, e.g., in disordered materials, at surfaces, or at lattice imperfections, etc. The observed $\frac{1}{f}$ noise is the sum of these contributions, and can be used to detect and study new infraquanta.