Temperature-dependent band gap, interband transitions, and exciton formation in transparent $p$-type delafossite ${\mathrm{CuCr}}_{1-x}$${\mathrm{Mg}}_x$${\mathrm{O}}_2$ films

Temperature-dependent interband transitions and exciton excitations of sol-gel derived ${\mathrm{CuCr}}_{1-x}$${\mathrm{Mg}}_x$${\mathrm{O}}_2$ $(2\%\le x\le 8\%)$ films have been investigated by transmittance spectra (8–300 K) and photoluminescence (PL) spectra (77–300 K). An abnormal dependence of the optical band gap with the temperature has been found for the films with $x=0.02$ and 0.04. At the low-temperature region, the gap energy shows a redshift trend with decreasing temperature. It is due to the strong Cr $3d\text{−}\text{O}$ $2p\text{-Cu}$ $3d$ interaction in the upper part of the valence band, which can be weaken by heavily Mg doping. The spin-orbit interactions of ${\mathrm{Cr}}^{3+}$ ions in an octahedral environment make the $3d$ states more disperse, which can contribute to the relatively high conductivity. A well-defined low-energy absorption has been assigned to the spin-allowed $3d$ $\to$ $3d$ transition. Moreover, a strong exciton excitation around 1.8 eV has been observed due to the naturally low-dimensional structure of the delafossite, which can be modulated by temperature and hole concentration.

Figure 1

(a) Transmittance spectra for the ${\mathrm{CuCr}}_{1-x}$${\mathrm{Mg}}_x$${\mathrm{O}}_2$ films at room temperature. (b) Transmittance spectra for ${\mathrm{CuCr}}_{0.98}$${\mathrm{Mg}}_{0.02}$${\mathrm{O}}_2$ at the temperatures of 8, 120, 220, and 300 K. (c) An enlarged spectral region for the films with $x=0.02$ and 0.08 near the absorption edge at different temperatures.

Figure 2

Plot of ($\alpha h\nu$)${}^2$ vs the photon energy for the determinations of direct optical band-gap energies for the (a) ${\mathrm{CuCr}}_{0.98}$${\mathrm{Mg}}_{0.02}$${\mathrm{O}}_2$ and (b) ${\mathrm{CuCr}}_{0.96}$${\mathrm{Mg}}_{0.04}$${\mathrm{O}}_2$ films.

Figure 3

(a) Temperature-dependent $E_{\mathrm{OBG}}^{\mathrm{dir}}$ for the ${\mathrm{CuCr}}_{1-x}$${\mathrm{Mg}}_x$${\mathrm{O}}_2$ films are plotted with the best-fitting lines. (b) Absorption spectra for all ${\mathrm{CuCr}}_{1-x}$${\mathrm{Mg}}_x$${\mathrm{O}}_2$ films at room temperature. The inset shows the absorption spectra for the ${\mathrm{CuCr}}_{0.98}$${\mathrm{Mg}}_{0.02}$${\mathrm{O}}_2$ film at 8 K.

Figure 4

The Urbach energy $E_U$ determined from ln$\alpha$ vs photon energy at room temperature. Note that the inset shows temperature dependence of $E_U$ for the ${\mathrm{CuCr}}_{0.98}$${\mathrm{Mg}}_{0.02}$${\mathrm{O}}_2$ film.

Figure 5

Electronic band diagram for the ${\mathrm{CuCr}}_{1-x}$${\mathrm{Mg}}_x$${\mathrm{O}}_2$ films was applied to explain the experimental results.

Figure 6

(a) Photoluminescence spectra for the ${\mathrm{CuCr}}_{0.02}$${\mathrm{Mg}}_{0.98}$${\mathrm{O}}_2$ film in the energy region from 1.798 eV to 1.812 eV at different temperatures. (b) Emission spectra in an enlarged energy region from 2.05 eV to 2.45 eV at different temperatures.