Impurity Band Conduction in a High Temperature Ferromagnetic Semiconductor

The band structure of a prototypical dilute ferromagnetic semiconductor, Ga${}_{1-x}$Mn${}_x$As, is studied across the phase diagram via optical spectroscopy. We prove that the Fermi energy ($E_F$) resides in a Mn induced impurity band (IB). This conclusion is based upon careful analysis of the frequency and temperature dependence of the optical conductivity (${\sigma }_1(\omega ,T)$). From our analysis of ${\sigma }_1(\omega ,T)$ we infer a large effective mass ($m^{\ast }$) of the carriers, supporting the view that conduction occurs in an IB. Our results also provide useful insights into the transport properties of Mn-doped GaAs.