Extensions of Handel's 1/f-noise equations and their semiclassical theory.

Abstract

By replacing the change in velocity \ensuremath{\Delta}v by the low-frequency Fourier transform ${\mathrm{F}}_{a}$(0) of the electron acceleration a(t), Handel's equations for the Hooge parameter ${\ensuremath{\alpha}}_{H}$ are put in equivalent forms that are not only applicable to collision 1/f noise in semiconductors but also to acceleration 1/f noise in long semiconductor resistors. To prove these expressions semiclassically, one evaluates first the bremsstrahlung energy dE of a single radiation pulse in a frequency interval df, and then defines dn=dE/hf as the number of photons of a single radiation pulse in a frequency interval df and finally dr=dn/${\ensuremath{\tau}}_{a}$=dE/hf${\ensuremath{\tau}}_{a}$ as the rate of photon emission in a single pulse in a frequency interval df. It is then found that the expression for dr already contains the Hooge parameter ${\ensuremath{\alpha}}_{H}$. It thus seems that the Hooge parameter depends only on the bremsstrahlung emission process but not on the details of the electron-photon interaction. This may explain why Handel's expressions for ${\ensuremath{\alpha}}_{H}$ so often agree with experiment. One must now bear in mind that the elementary current event is described by a current pulse i(t) of duration ${\ensuremath{\tau}}_{a}$ having a Fourier transform ${\mathrm{F}}_{i}$(0). If one next defines ${S}_{r}^{\mathcal{'}\mathcal{'}}$(f)=dr/df, then the current noise spectrum is obtained by multiplying ${S}_{r}^{\mathcal{'}\mathcal{'}}$(f) first by ${2\mathrm{F}}_{i}^{2}$(0), to obtain the effect of a single elementary event per second, and then multiply by \ensuremath{\lambda}, the number of elementary events per second. This leads immediately to the Hooge equation and to the Hooge parameter ${\ensuremath{\alpha}}_{H}$. .AE