Free-Carrier Magneto-Microwave Kerr Effect in Semiconductors

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 δ, the phase difference between these two components. Equations relating R and δ to the elements of the magnetoconductivity tensor are presented for the plane-wave case and the TE₁₁ mode in a circular waveguide. Simple approximate expressions for R and δ are given for the high-loss case where σₛωεₛ1, μHB1, and ωτ1 (${{σ}}ₛ=zero{-}field{{0ex}{0ex}}dc{{0ex}{0ex}}conductivity$; ${{ε}}ₛ=staticdielectricconstant$; ${{μ}}H=Hallmobility$; ${τ}=scatteringtime$). 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 ${δ}$ 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${E}₁₁$ mode in a circular waveguide. It is found experimentally that the T${E}₁₁$-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^∘{}K. The effect of surface treatment on the measurements is also discussed.