Study of plasmon—LO-phonon coupling in Te-doped ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$

Plasmon-LO-phonon coupling in $n$-type ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ has been investigated by measuring the infrared reflectivity spectra of differently doped $n$-type samples having $x\simeq 0.14$, $x\simeq 0.30$, and $x\simeq 0.46$. Two expressions for the dielectric function, one an additive form and the other a factorized form, have given satisfactory fits to the reflectivity data. The mode frequencies and damping rates in the plasmon-LO-phonon coupled mode systems are calculated and compared with the observed ones for the samples having $x\simeq 0.14$ and $x\simeq 0.46$. The $\Gamma$-point conduction-band effective mass for $x\simeq 0.14$ is found to be $m_{\Gamma }^{*}=(0.13\mathrm{}\pm 0.01)m_e$ and the resistivity obtained from the infrared spectra is approximately 30% higher than the value from dc measurements. The reflectivity minima are broadened by the large plasma damping in the samples having $x\simeq 0.46$.