Impurity Band Conduction in a High Temperature Ferromagnetic Semiconductor

The band structure of a prototypical dilute magnetic semiconductor (DMS), ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$, is studied across the phase diagram via infrared and optical spectroscopy. We prove that the Fermi energy ($E_F$) resides in a Mn-induced impurity band (IB). Specifically the changes in the frequency dependent optical conductivity [${\sigma }_1(\omega )$] with carrier density are only consistent with $E_F$ lying in an IB. Furthermore, the large effective mass ($m^{*}$) of the carriers inferred from our analysis of ${\sigma }_1(\omega )$ supports this conclusion. Our findings demonstrate that the metal to insulator transition in this DMS is qualitatively different from other III-V semiconductors doped with nonmagnetic impurities. We also provide insights into the anomalous transport properties of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$.

Figure 1

The real part of the conductivity for all samples in this study as well as the results of previous studies (black and gray lines) [8]. A clear increase in ${\sigma }_1(\omega )$ is seen as the result of larger $x$ and/or annealing. Right side: The results of fitting the 52A data with the two-component model [Eq. (1)].

Figure 2

Two scenarios for the electronic structure of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ that have different implications for the resonant frequency of the MIR interband absorption. (a) $E_F$ lies in the light and heavy hole (LH and HH, respectively) bands at low $x$, producing a transition between the two. (b) As $p$ is increased, $E_F$ moves farther into the LH and HH bands, causing the transition to blueshift. (c) If $E_F$ lies in the IB, then at low $x$ a transition occurs from the VB to the IB. (d) At higher $p$, $E_F$ moves deeper in the IB, causing the feature to redshift.

Figure 3

Left panel: The peak position of the MIR feature determined by two alternative methods: setting $\frac{d{\sigma }_1(\omega ,x)}{d\omega }=0$ and from the two-component analysis. This is plotted versus the spectral weight below $6,450{\mathrm{cm}}^{-1}$, which is proportional to the number of holes [$N_{\mathrm{eff}}(6450{\mathrm{cm}}^{-1})\propto p$]. This figure demonstrates that, regardless of the growth method, the MIR feature redshifts with increasing doping or $p$. Right panel: The results from the predicted behavior of the GaAs VB versus $p$ for $x=0.05$ [2], determined by the $\frac{d{\sigma }_1(\omega ,x)}{d\omega }$ analysis [22].