The expression for Hooge's $\alpha$ for $\frac{1}{f}$ noise has been derived on the basis of scattering of charged carriers by acoustic phonons in thermal equilibrium; $\alpha =\frac{{\left(\frac{m{s}^2}{\mathrm{kT}}\right)}^{\frac{2}{3}}\exp \left(\frac{2\overline{\beta }}{3}\right)}{\ln \left(\frac{f_H}{f_L}\right)}$, where $m$ is the carrier mass, $s$ the sound velocity; $k$ the Boltzmann constant, $T$ the lattice temperature, $\overline{\beta }$ the mean phonon energy divided by $\mathrm{kT}$, and $\frac{f_H}{f_L}$ a ratio of upper to lower frequency limits of $\frac{1}{f}$ noise.

• Received 18 January 1982

DOI:https://doi.org/10.1103/PhysRevB.26.1042