Conduction mechanism and shallow donor properties in silicon-doped $\varepsilon \text{-G}{\mathrm{a}}_2{\mathrm{O}}_3$ thin films: An electron paramagnetic resonance study

The defects in Si-doped ε-${\mathrm{Ga}}_2{\mathrm{O}}_3$ epitaxial layers have been investigated by electron paramagnetic resonance (EPR) spectroscopy. The results show that Si doping introduces a single, paramagnetic defect, attributed to Si incorporation on the tetrahedral gallium lattice site. It is a spin $S=1/2$ center with an axial $g$ tensor with principal values of $g//c=1.9573$ and $g\perp c=1.9591$. The temperature dependence of the EPR parameter demonstrates that it is a shallow effective mass donor, which is at the origin of the $n$-type conductivity. The EPR spectrum is modified by motional narrowing effects, the analysis of which allows one to reveal different transport regimes, including localization, hopping conductivity, and ionization in the conduction band when the temperature is raised from $T=4\mathrm{K}$ to room temperature. Partial electrical compensation and donor clustering are equally evidenced by the EPR results, which are confirmed by correlated electrical transport measurements. Silicon is thus a promising dopant for the formation of highly conductive $n$-type ε-${\mathrm{Ga}}_2{\mathrm{O}}_3$.

Figure 1

$\varepsilon \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ structure representation. The structure contains three nonequivalent Ga sites—two distorted octahedral Ga sites $({\mathrm{Ga}}_1,{\mathrm{Ga}}_2)$ and one distorted tetrahedral Ga site $\left({\mathrm{Ga}}_3\right)$—and two nonequivalent oxygen sites $({\mathrm{O}}_1,{\mathrm{O}}_2)$. Please note, that the two octahedral ${\mathrm{Ga}}_{1,2}$ sites are different from the crystallographic point of view [5], but when occupied by donor impurities, they give rise to equivalent donor states.

Figure 2

X-ray-diffraction pattern of the Si-doped ε-${\mathrm{Ga}}_2{\mathrm{O}}_3$ epitaxial layer (black) and the comparison with an undoped sample (blue) and a β-${\mathrm{Ga}}_2{\mathrm{O}}_3$ substrate (red).

Figure 3

Room-temperature EPR spectrum (circle) for the $B//c$ axis (red) and $B\perp c$ axis (blue); the spectra are characterized by a Lorentzian line shape (red line) and linewidth of $\mathrm{\Delta }Bpp=0.90$ and 0.99 G, respectively.

Figure 4

Angular variation of the effective $g$ factor for a rotation of the magnetic field from $B//c$ to $B\perp c$. $T=300\mathrm{K}$ (black) and $T=4\mathrm{K}$ (red); angular variation around the $c$ axis (blue) is at $T=300\mathrm{K}$.

Figure 5

EPR spectra for $T=295\mathrm{K}$ (circle, red) and $T=4\mathrm{K}$ (diamond, blue); the lines are fit with Lorentzian line shapes (line) for the $B//c$ axis.

Figure 6

(a) Temperature dependence of the EPR linewidth $\mathrm{\Delta }{B}_{pp}$ between room temperature and $T=4\mathrm{K}$ for the $B//c$ axis. (b) Temperature dependence of the EPR signal intensity obtained by double integration of the experimental spectrum. (c)Temperature dependence of the effective $g$ factor for $B//c$.

Figure 7

Inverse of the EPR signal intensity vs temperature.

Figure 8

EPR linewidth (dot) $ln\left(\mathrm{\Delta }{B}_{pp}\right)$ vs $T^{-1}$, and simulation (inset, red lines) of the high-temperature part with an Arrhenius law.

Figure 9

EPR linewidth $ln\left(\mathrm{\Delta }{B}_{pp}\right)$ vs $T^{-0.25}$ (circle), and simulation (red, blue lines) corresponding to a 3D VRH hopping processes in two temperature regions.

Figure 10

Logarithm of the conductivity (in ${\mathrm{\Omega }}^{-1}\mathrm{c}{\mathrm{m}}^{-1})$ vs $T^{-1/4}$. Lines: Linear fits of the data at high (red) and low (blue) temperatures. The estimated slopes are ${T_0}^{0.25}=(10.8\pm 0.1){\mathrm{K}}^{0.25}$ in the 50- to 100-K temperature range and ${T_0}^{0.25}=\left(5.2\pm 0.2\right){\mathrm{K}}^{0.25}$ in the range 50 to 10 K.

Figure 11

Principal values and axes of the $g$ tensor of shallow donors in three ${\mathrm{Ga}}_2{\mathrm{O}}_3$ polytypes: Si and Sn donors in the β polytype, Si donor in the ε polytype, and Sn donor in the α polytype.