Specific features of the temperature dependence of the conduction electron concentration in the narrow-gap and zero-gap states of Cd$_x$Hg$_{1-x}$Te

Results of studies of the conductivity $\sigma$ and the Hall coefficient $R$ in the Cd$_x$Hg$_{1-x}$Te crystals with $x$ = 0.1, 0.12, 0.14, and 0.15 are analyzed in the temperature range $T$ = 4.2–300 K and the magnetic field range $B$ = 0.005–2.22 T. Using data on the $R(B)$ in low and high magnetic fields and the data on $\sigma(T)$, electron and hole concentrations and mobilities are determined. It is shown that the electron concentration $n$ in the studied samples is almost independent of $T$ in the range 4.2–15 K, while as $T$ increases, it increases according to the law $n\propto T^r$ ($r>$ 3/2), where $r = f(n, T, x)$. It is found that $r$ varies from 1.7 at $x$ = 0.1 to 3.1 at compositions with $x$ = 0.14 and 0.15. The results for $n(T)$ are compared with theory, taking into account nonparabolicity of the variance law for $(T)$, and with the theory of impurity states in narrow-gap and zero-gap semiconductors. It is shown that the constancy of $n(T)$ up to $\sim$15 K and the strong dependence $n(T)$ ($r >$ 3/2) at higher temperatures are caused by the intense ionization of electrons localized at acceptor states.