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 $x=3.2\times {10}^{-4}$ 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 depletion layers of the active material via infrared (IR) spectroscopy at room temperature. 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 suppression of these features in the depletion polarity. These latter 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 electrodynamics of FM Ga${}_{1-x}$Mn${}_x$As. We add that 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.

Figure 1

Panels (a) and (b) highlight the operating principle of the EDL field-effect devices used in our IR experiments, as described in the text. Panel (a) shows a device in the absence of any applied voltage, while panel (b) shows the device under applied $V_{\text{gs}}$. Panels (c) and (d) show the transmission spectra, under applied $V_{\text{gs}}$, through the $x=0.015$ Ga${}_{1-x}$Mn${}_x$As and $x=3.2\times {10}^{-4}$ Ga${}_{1-x}$Be${}_x$As based devices, normalized to their respective transmission spectrum at $V_{\text{gs}}=0$. The data are cut near 300 cm${}^{-1}$ due to a GaAs phonon that eliminates transmission over the cut frequency range. The data are also cut where sharp features from strong vibrational modes in the ion gel obscure the spectra (near 1200 and 3200 cm${}^{-1}$). Only select spectra are shown for clarity. The light gray lines in panels (c) and (d) are the model fits to the transmission spectra described in the text.

Figure 2

Panels (a) and (b) show the $V_{\mathrm{eff}}=0$ IR conductivity spectrum of the $x=0.015$ Ga${}_{1-x}$Mn${}_x$As film and the $x=3.2\times {10}^{-4}$ Ga${}_{1-x}$Be${}_x$As film used in our devices, respectively. The two-dimensional differential conductivity $\Delta$${\sigma }^{2\text{D}}$($V_{\mathrm{eff}}$,$\omega$) spectra at all $V_{\mathrm{eff}}$ are shown for the (Ga,Mn)As-based device in panel (c), and for the (Ga,Be)As-based device in panel (d). The data are cut near 300 cm${}^{-1}$ due to GaAs opacity over the cut frequency range.

Figure 3

Schematic illustrating the density of states in (Ga,Be)As (left panel) and (Ga,Mn)As (right panel) according to our experimental interpretation. The red arrow in the right panel represents transitions giving rise to the mid-IR resonance in the (Ga,Mn)As data. For these interband transitions, $m_{\mathrm{opt}}$ is approximately equal to the VB mass, as discussed in the text.

Figure 4

Panel (a) shows the $\Delta {\sigma }_1^{2\text{D}}(V_{\mathrm{eff}},\omega )$ for the (Ga,Mn)As-based device and the (Ga,Be)As-based device at $V_{\mathrm{eff}}=0.55$ and 0.58 V, respectively. The orange and gray shaded regions indicate the area included for equivalent intragap spectral weight in application of Eq. (3) for the (Ga,Mn)As and (Ga,Be)As accumulation layers, respectively. Panel (b) shows the change in spectral weight according to Eq. (3) at all $V_{\mathrm{eff}}$ for the (Ga,Be)As-, (Ga,Mn)As-, and second (Ga,Mn)As- (device B) based devices. The choice in integration cutoff ${\omega }_c$ is described in the text. Using the calibration procedure described in the text, the right axis is converted into the two-dimensional change in hole concentration, $\Delta p^{2\text{D}}$.