Atypically small temperature-dependence of the direct band gap in the metastable semiconductor copper nitrideCu3N

Abstract

The temperature-dependence of the direct band gap and thermal expansion in the metastable anti-${\mathrm{ReO}}_{3}$ semiconductor ${\mathrm{Cu}}_{3}\mathrm{N}$ are investigated between 4.2 and 300 K by Fourier-transform infrared spectroscopy and x-ray diffraction. Complementary refractive index spectra are determined by spectroscopic ellipsometry at $300\phantom{\rule{4pt}{0ex}}\mathrm{K}$. A direct gap of $1.68\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ is associated with the absorption onset at $300\phantom{\rule{4pt}{0ex}}\mathrm{K}$, which strengthens continuously and reaches a magnitude of $3.5\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ at $2.7\phantom{\rule{4pt}{0ex}}\mathrm{eV}$, suggesting potential for photovoltaic applications. Notably, the direct gap redshifts by just $24\phantom{\rule{4pt}{0ex}}\mathrm{meV}$ between 4.2 and $300\phantom{\rule{4pt}{0ex}}\mathrm{K}$, giving an atypically small band-gap temperature coefficient $d{E}_{\text{g}}/dT$ of $\ensuremath{-}0.082\phantom{\rule{4pt}{0ex}}\mathrm{meV}/\mathrm{K}$. Additionally, the band structure, dielectric function, phonon dispersion, linear expansion, and heat capacity are calculated using density functional theory; remarkable similarities between the experimental and calculated refractive index spectra support the accuracy of these calculations, which indicate beneficially low hole effective masses and potential negative thermal expansion below $50\phantom{\rule{4pt}{0ex}}\mathrm{K}$. To assess the lattice expansion contribution to the band-gap temperature-dependence, a quasiharmonic model fit to the observed lattice contraction finds a monotonically decreasing linear expansion (descending past ${10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ below $80\phantom{\rule{4pt}{0ex}}\mathrm{K}$), while estimating the Debye temperature, lattice heat capacity, and Gr\uneisen parameter. Accounting for lattice and electron-phonon contributions to the observed band-gap evolution suggests average phonon energies that are qualitatively consistent with predicted maxima in the phonon density of states. As band-edge temperature-dependence has significant consequences for device performance, copper nitride should be well suited for applications that require a largely temperature-invariant band gap.