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 Gamma to X band gap and direct transition energies of 2.02 and 3.75 eV at X and Gamma points, respectively, while G(o)W(o) and GW(o) methods suggest 0.44-0.74 eV higher gap values. Epitaxial ScN(001) layers deposited on MgO(001) substrates by reactive sputtering exhibit degenerate n-type semiconductor properties with a temperature-independent electron density that is varied from N = 1.12-12.8 x 10(20) cm(-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 (2.03-3.2 eV) of previously reported gap values. However, here extrapolation to N = 0 yields 2.07 +/- 0.05 eV for the direct X point transition of intrinsic ScN. A reflection peak at 3.80 +/- 0.02 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 Gamma point. The electron mobility at 4 K is 100 +/- 30 cm(2)/Vs and decreases with temperature due to scattering at polar optical phonons with characteristic frequencies that decrease from 620 to 440 +/- 30 cm(-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 +/- 0.02m(o) and 0.33 +/- 0.02m(o), in good agreement with the first-principles predictions of m(tr) = 0.33 +/- 0.05m(o) and m(DOS) = 0.43 +/- 0.05m(o). The ScN refractive index increases with increasing h nu = 1.0 - 2.0 eV from 2.6-3.1 based on optical measurements and from 2.8-3.2 based on the calculated dielectric function. An overall comparison of experiment and simulation indicates (i) an overestimation of band gaps by GW methods, but (ii) excellent agreement with a deviation of <= 0.05 eV for the hybrid functional and (iii) a value for the fundamental indirect gap of ScN of 0.92 +/- 0.05 eV.