Influence of a strong longitudinal static electric field on free carrier faraday effect in an n-type InSb at room temperature at submillimeter wave frequencies

Abstract

The expression for free carrier Faraday rotation θ and for ellipticity Δ, as the function of the applied parallel static electric field $$\mathop {E_0 }\limits_ \to $$ and static magnetic field $$\mathop {B_0 }\limits_ \to $$ for a given value of wave angular frequency and electron concentration N0, are obtained and theoretically analyzed with the aid of one-dimensional linearized wave theory and Kane's non-parabolic isotropic dispersion law. It is shown that the maximum Faraday rotation occurs near the cyclotron resonance condition, which can be expressed as $$\chi \omega = \omega _{ce} $$ , where $$\chi = 1{1 \mathord{\left/ {\vphantom {1 {\sqrt {1 - ({{v_0 } \mathord{\left/ {\vphantom {{v_0 } {v_c }}} \right. \kern-\nulldelimiterspace} {v_c }})^2 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - ({{v_0 } \mathord{\left/ {\vphantom {{v_0 } {v_c }}} \right. \kern-\nulldelimiterspace} {v_c }})^2 } }}$$ , $$v_c = \sqrt {{{\varepsilon _g } \mathord{\left/ {\vphantom {{\varepsilon _g } {2m}}} \right. \kern-\nulldelimiterspace} {2m}}} *$$ , and $$\omega _{ce} = ({{eB_0 } \mathord{\left/ {\vphantom {{eB_0 } {m*}}} \right. \kern-\nulldelimiterspace} {m*}})$$ . Here m* and e denote the effective mass and charge of electron, respectively. ɛg is the forbidden bandgap of semiconductor. v0 is the carrier drift velocity, which is a non-linear function of E0 in high field condition. A possibility of a simple way of determining the non-linear “v0 vs E0” characteristics of semiconductors by the measurement of Faraday rotation is also discussed.