Effect of the charge-carrier–phonon interaction on the fundamental 1/f voltage noise

Abstract

It is known that quantum indeterminacy sets a lower bound on the power spectrum of voltage fluctuations in any conducting medium. The low-frequency asymptotic of this bound is $\ensuremath{\sim}1/f$ in the case of freely propagating charge carriers. It is found that on account of the charge-carrier--phonon interaction, the asymptotic becomes $\ensuremath{\sim}1/{f}^{\ensuremath{\gamma}},\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}\ensuremath{\ne}1.$ Its general expression is derived in the case of charge carriers subject to the piezoelectric interaction with acoustic phonons. The sign of $(\ensuremath{\gamma}\ensuremath{-}1)$ depends on the state filling for charge carriers, so that $\ensuremath{\gamma}$ may exceed unity despite the absence of a low-frequency cutoff. It is shown that under stationary physical conditions the voltage variance grows with time as ${t}^{\ensuremath{\gamma}\ensuremath{-}1},$ in agreement with observations. It is proved that despite this growth the power spectrum is well defined and finite for $\ensuremath{\gamma}<2.\phantom{\rule{0.16em}{0ex}}\mathrm{A}$ practical attainability of the quantum bound is discussed. A comparison with the experimental data on $1/f$ noise in InGaAs quantum wells and high-temperature superconductors is made. It is demonstrated that the account of $\ensuremath{\gamma}\ensuremath{\ne}1$ brings the calculated noise levels uniformly within an order of magnitude of the measured. This holds true whether the voltage fluctuations are measured along or across the electric current, though the observed noise levels in the two cases are significantly different.