Microwave Propagation and Faraday Effect in a Solid State Plasma Waveguide

The conductivity of a solid-state plasma which consists of free electrons and holes in a solid such as a semiconductor becomes a tensor quantity under a dc magnetic field. If we take a coordinate system in such a way that the dc magnetic field B/sub o/ lies along the z-axis, the tensor conductivity may be expressed by /spl =over sigma/= [/spl sigma//sub perp/, -/spl sigma//sub x/, o, /spl sigma//sub x/, /spl sigma//sub perp/, o, o, o, /spl sigma//sub 11/] where if we assume that n/sub e//spl mu//sub e/>>n/sub h//spl mu//sub h/ as in the case of an n-type semiconductor, we have /spl sigma//sub 11/ =qn/sub e//spl mu//sub e/ / (1+j/spl omega//spl tau//sub e/),/spl sigma//sub perp/= /spl sigma//sub 11/ / (1+/spl alpha//sup 2//sub e/) /spl sigma//sub x/ = /spl sigma//sub 11//spl alpha/ sub e/ / (1+ /spl alpha//sup 2//sub e/), and /spl alpha//sub e/ = /spl mu//sub e/B/sub o/ / (1+j /spl omega//spl tau//sub e/). /spl omega/ is the angular frequency, q the electron charge, n the density, /spl mu/ the mobility, and /spl tau/ the relaxation time. The subscripts e and h refer to electrons and holes, respectively. Variations of /spl sigma//sub 11/, /spl sigma//sub perp/, and /spl sigma//sub x/ with B/sub o/ are shown in Fig. 1.