In a nondegenerate n-type semiconductor, the electron conduction at low temperatures is due to the Efros-Shklovskii variable-range hopping in a narrow donor energy band separated from the conduction band by the donor ionization energy. As the donor density reaches the critical density for the Mott transition ($n_{\text{c}}$), the donor ionization energy turns to zero and the electrons released from the donors form a degenerate gas in the conduction band. Usually, the Fermi energy of the degenerate gas exceeds the Anderson mobility edge and the Mott transition is therefore accompanied by a change of the hopping conductance to the metallic conductance. Here we study the highly Si-doped $\beta –\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ semiconducting films by measuring the conductivity, Hall effect, Seebeck coefficient, and optical absorption spectrum, as well as by structural and chemical characterization. We vary the density of the electrically active Si donors ($n$) from low values up to $n=n_{\text{c}}$ (we show that $n_{\text{c}}=5.7\times {10}^{18}{\text{cm}}^{-3}$) and slightly above. We observe the donor-density-driven Mott transition from the nondegenerate disordered semiconductor to a degenerate disordered metal with Fermi energy well below the mobility edge. At low temperatures on the semiconducting side of the Mott transition ($n<n_{\text{c}}$), we observe the Efros-Shklovskii hopping with characteristic energy $\propto {\left(1-n/n_{\text{c}}\right)}^2$, as predicted by theory. Similarly, the donor ionization energy tends to diminish for $n\to n_{\text{c}}$ and is likely proportional to the same factor. On the metallic side of the Mott transition ($n>n_{\text{c}}$) the low-temperature transport changes from the Efros-Shklovskii hopping to the Mott variable-range hopping, manifesting the closure of the Efros-Shklovskii Coulomb gap at the Mott transition. At high temperatures, the conductance still exhibits localized transport for both $n>n_{\text{c}}$ and $n<n_{\text{c}}$, but, surprisingly, in the latter case with a linear temperature dependence as $n$ approaches $n_{\text{c}}$. We identify this transport regime as the anomalous variable-range hopping of the nondegenerate conduction electrons moving in disorder, which does not originate from Si doping. Our optical data indeed show that the conduction-band states are localized by extra disorder due to the oxygen vacancies, which is also confirmed by the chemical composition data. Finally, the room-temperature Seebeck data confirm the nondegenerate electron transport and also indicate merging of the donor band into the conduction band at the Mott transition.

Close

PrevNext

View figure in article

• Electrical conductivity
• Doped semiconductors
• Scanning electron microscopy
• Secondary ion mass spectrometry
• Transport techniques
• X-ray photoelectron spectroscopy