Free-Carrier Magneto-Microwave Kerr Effect in Semiconductors

Abstract

The free-carrier magneto-Kerr effect is analyzed in terms of $R$, the amplitude ratio of the two orthogonal linearly polarized components of the reflected wave, and $\ensuremath{\delta}$, the phase difference between these two components. Equations relating $R$ and $\ensuremath{\delta}$ to the elements of the magnetoconductivity tensor are presented for the plane-wave case and the T${\mathrm{E}}_{11}$ mode in a circular waveguide. Simple approximate expressions for $R$ and $\ensuremath{\delta}$ are given for the high-loss case where $\frac{{\ensuremath{\sigma}}_{s}}{\ensuremath{\omega}{\ensuremath{\epsilon}}_{s}}\ensuremath{\gg}1$, ${\ensuremath{\mu}}_{\mathrm{H}}B\ensuremath{\ll}1$, and $\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\ll}1$ (${\ensuremath{\sigma}}_{s}=\mathrm{z}\mathrm{e}\mathrm{r}\mathrm{o}\ensuremath{-}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}\phantom{\rule{0ex}{0ex}}\mathrm{d}\mathrm{c}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}$; ${\ensuremath{\epsilon}}_{s}=\mathrm{static}\mathrm{dielectric}\mathrm{constant}$; ${\ensuremath{\mu}}_{\mathrm{H}}=\mathrm{Hall}\mathrm{mobility}$; $\ensuremath{\tau}=\mathrm{scattering}\mathrm{time}$). These approximate expressions are compared with curves computed from the more complex expressions. The effect of multiple reflections within the semiconductor is considered. Experimental data for $R$ and $\ensuremath{\delta}$ as functions of magnetic flux density and resistivity are presented for $n$-type germanium, $n$- and $p$-type silicon, and $n$-type indium antimonide at room temperature for the T${\mathrm{E}}_{11}$ mode in a circular waveguide. It is found experimentally that the T${\mathrm{E}}_{11}$-mode analysis of the magneto-Kerr effect applies equally well to samples placed inside the circular waveguide and to those abutting on the end of the waveguide. Data on one $n$-type germanium and one $n$-type indium antimonide crystal are presented for temperatures between about 100 and 300\ifmmode^\circ\else\textdegree\fi{}K. The effect of surface treatment on the measurements is also discussed.