Optical and transport measurement and first-principles determination of the ScN band gap

The electronic structure of scandium nitride is determined by combining results from optical and electronic transport measurements with first-principles calculations. Hybrid functional Heyd-Scuseria-Ernzerhof (HSE06) calculations indicate a 0.92 eV indirect \ensuremath{\Gamma} to $X$ band gap and direct transition energies of 2.02 and 3.75 eV at $X$ and \ensuremath{\Gamma} points, respectively, while ${G}_{\mathrm{o}}{W}_{\mathrm{o}}$ and $G{W}_{\mathrm{o}}$ methods suggest 0.44\char21{}0.74 eV higher gap values. Epitaxial ScN(001) layers deposited on MgO(001) substrates by reactive sputtering exhibit degenerate $n\text{-type}$ semiconductor properties with a temperature-independent electron density that is varied from $N=1.12\ensuremath{-}12.8\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$ using fluorine impurity doping. The direct optical gap increases linearly with $N$ from 2.18 to 2.70 eV, due to a Burstein-Moss effect. This strong dependence on $N$ is likely the cause for the large range (2.03\char21{}3.2 eV) of previously reported gap values. However, here extrapolation to $N=0$ yields $2.07\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ for the direct $X$ point transition of intrinsic ScN. A reflection peak at $3.80\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ is independent of $N$ and in perfect agreement with the HSE06-predicted peak at 3.79 eV, associated with a high joint density of states (DOS) near the \ensuremath{\Gamma} point. The electron mobility at 4 K is $100\ifmmode\pm\else\textpm\fi{}30\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{Vs}$ and decreases with temperature due to scattering at polar optical phonons with characteristic frequencies that decrease from 620 to $440\ifmmode\pm\else\textpm\fi{}30\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, with increasing $N$, due to free carrier screening. The transport and DOS electron effective mass, determined from measured intra- and interband transitions, respectively, are $0.40\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.16em}{0ex}}{m}_{\mathrm{o}}$ and $0.33\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.16em}{0ex}}{m}_{\mathrm{o}}$, in good agreement with the first-principles predictions of ${m}_{tr}=0.33\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}{m}_{\mathrm{o}}$ and ${m}_{\mathrm{DOS}}=0.43\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}{m}_{\mathrm{o}}$. The ScN refractive index increases with increasing $h\ensuremath{\nu}=1.0\ensuremath{-}2.0\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ from 2.6\char21{}3.1 based on optical measurements and from 2.8\char21{}3.2 based on the calculated dielectric function. An overall comparison of experiment and simulation indicates (i) an overestimation of band gaps by $\mathit{GW}$ methods, but (ii) excellent agreement with a deviation of \ensuremath{\le}0.05 eV for the hybrid functional and (iii) a value for the fundamental indirect gap of ScN of $0.92\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$.