Study of the Shape of Cyclotron-Resonance Lines in Indium Antimonide Using a Far-Infrared Laser

Abstract

An experimental and theoretical study of the shape of cyclotron-resonance lines in highpurity $n$-type InSb has been conducted at cryogenic temperatures, using a repetitively pulsed far-infrared gas laser at $\ensuremath{\lambda}=336.8, 118.6, 78.4, 55.1, \mathrm{and} 47.5$ \ensuremath{\mu}m. Measurements of the 4.2 \ifmmode^\circ\else\textdegree\fi{}K effective mass and scattering times have been obtained as a function of frequency via transmission through a thin sample arranged in the Faraday configuration. For carriers at a concentration of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, one obtains a zero-field 4.2 \ifmmode^\circ\else\textdegree\fi{}K effective-mass ratio of 0.0139 \ifmmode\pm\else\textpm\fi{} 0.0002. At laser frequencies below the optical-phonon frequencies, an anomalous narrowing of the lines was observed whose width implies a collision time $\ensuremath{\tau}$ near ${10}^{\ensuremath{-}11}$ sec, which is about 160 times longer than the value derived from dc magnetoconductivity at 20 kG. The theoretical analysis uses the quantum plasma dielectric tensor $\stackrel{}{\ensuremath{\epsilon}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ complete with a collisional energy term of the form $\ensuremath{\Delta}+i\ensuremath{\Gamma}$ and a nonparabolic energy expression for conductionband electrons. The dispersion equations for photon propagation in the Faraday and Voigt geometries are then solved to obtain the cyclotron-resonance line shape, using both constant-and energy-dependent collision times. It is shown that the observed line shapes and widths may be predicted without adjustable parameters to within the experimental error by a scattering time $\ensuremath{\tau}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}},{k}_{z})$, which describes adiabatic and nonadiabatic Coulomb scattering. Thus the narrowed lines are attributed to the reduced scattering rate from long-range ionized impurities that occurs in the quantum limit $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}g{k}_{B}T$. Another experiment, done in the Voigt configuration at 77 \ifmmode^\circ\else\textdegree\fi{}K using $\ensuremath{\lambda}=336.8$ \ensuremath{\mu}m, yielded at 4.5-kG mass ratio of 0.0132 \ifmmode\pm\else\textpm\fi{} 0.0002 and a scattering time of 2.75 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ sec, which is within a factor of 2 of the zero-field mobility time.