Infrared conductivity of hole accumulation and depletion layers in (Ga,Mn)As- and (Ga,Be)As-based electric field-effect devices

We have fabricated electric double-layer field-effect devices to electrostatically dope our active materials, either $x$=0.015 Ga$_{1-x}$Mn$_x$As or $x$=3.2$\times10^{-4}$ Ga$_{1-x}$Be$_x$As. The devices are tailored for interrogation of electric field induced changes to the frequency dependent conductivity in the accumulation or depletions layers of the active material via infrared (IR) spectroscopy. The spectra of the (Ga,Be)As-based device reveal electric field induced changes to the IR conductivity consistent with an enhancement or reduction of the Drude response in the accumulation and depletion polarities, respectively. The spectroscopic features of this device are all indicative of metallic conduction within the GaAs host valence band (VB). For the (Ga,Mn)As-based device, the spectra show enhancement of the far-IR itinerant carrier response and broad mid-IR resonance upon hole accumulation, with a decrease of these features in the depletion polarity. These later spectral features demonstrate that conduction in ferromagnetic (FM) Ga$_{1-x}$Mn$_x$As is distinct from genuine metallic behavior due to extended states in the host VB. Furthermore, these data support the notion that a Mn-induced impurity band plays a vital role in the electron dynamics of FM Ga$_{1-x}$Mn$_x$As. We add, a sum-rule analysis of the spectra of our devices suggests that the Mn or Be doping does not lead to a substantial renormalization of the GaAs host VB.