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

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 $\lambda =336.8, 118.6, 78.4, 55.1, \mathrm{and} 47.5$ μm. Measurements of the 4.2 °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 × ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$, one obtains a zero-field 4.2 °K effective-mass ratio of 0.0139 ± 0.0002. At laser frequencies below the optical-phonon frequencies, an anomalous narrowing of the lines was observed whose width implies a collision time $\tau$ near ${10}^{-11\mathrm{}}$ 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 $\stackrel{}{\epsilon }(\overrightarrow{\mathrm{q}},\omega )$ complete with a collisional energy term of the form $\Delta +i\Gamma$ 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 $\tau (\overrightarrow{\mathrm{B}},k_z)$, 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 $\hslash {\omega }_c>k_{B}T$. Another experiment, done in the Voigt configuration at 77 °K using $\lambda =336.8\mathrm{}$ μm, yielded at 4.5-kG mass ratio of 0.0132 ± 0.0002 and a scattering time of 2.75 × ${10}^{-12\mathrm{}}$ sec, which is within a factor of 2 of the zero-field mobility time.