Variable-range hopping conduction in epitaxial CrN(001)

Epitaxial CrN(001) layers, grown by dc magnetron sputtering on MgO(001) substrates at growth temperatures $T_s$ $=$ 550–850 °C, exhibit electronic transport that is dominated by variable-range hopping (VRH) at temperatures <120 K. A transition from Efros-Shklovskii to Mott VRH at 30 ± 10 K is well described by a universal scaling relation. The localization length decreases from 1.3 nm at $T_s$ $=$ 550 °C to 0.9 nm for $T_s$ $=$ 600–750 °C, but increases again to 1.9 nm for $T_s$ $=$ 800–850 °C, which is attributed to changes in the density of localized states associated with N vacancies that form due to kinetic barriers for incorporation and enhanced desorption at low and high $T_s$, respectively. The low-temperature transport data provide lower limits for the CrN effective electron mass of $4.9m_e$, the donor ionization energy of 24 meV, and the critical vacancy concentration for the metal-insulator transition of 8.4 $\times$ 10${}^{19}$ cm${}^{-3}$. The room temperature conductivity is dominated by Hubbard band states near the mobility edge and decreases monotonically from 137 Ω${}^{-1}$cm${}^{-1}$ for $T_s$ $=$ 550 °C to 14 Ω${}^{-1}$cm${}^{-1}$ for $T_s$ $=$ 850 °C due to a decreasing structural disorder, consistent with the measured x-ray coherence length that increases from 7 to 36 nm for $T_s$ $=$ 550 to 850 °C, respectively, and a carrier density that decreases from 4 $\times$ 10${}^{20}$ to 0.9 $\times$ 10${}^{20}$ cm${}^{-3}$, as estimated from optical reflection and Hall effect measurements. The absence of an expected discontinuity in the conductivity at ∼280 K suggests that epitaxial constraints suppress the phase transition to a low-temperature orthorhombic antiferromagnetic phase, such that CrN remains a cubic paramagnetic insulator over the entire measured temperature range of 10–295 K. These results contradict previous experimental studies that report metallic low-temperature conduction for CrN, but support recent computational results suggesting a band gap due to strong electron correlation and a stress-induced phase transition.

Figure 1

(a) XRD ω−2θ scan from a 1-μm-thick CrN/MgO(001) sample. The inset shows a corresponding ω-rocking curve for the CrN 002 reflection at 2θ $=$ 43.26°. (b) Width ${\Gamma }_{\omega }$ of the CrN 002 rocking-curve peak and the in-plane XRD coherence length ${\eta }_{\left|\right|}$ vs $T_s$.

Figure 2

(a) Conductivity σ at room temperature (290 K) and 10 K vs the growth temperature $T_s$ $=$ 550–850 °C of 140-nm-thick CrN/MgO(001) layers. (b) Semilog plot of the CrN conductivity vs reciprocal temperature. The open symbols represent the measured data for samples grown at different $T_s$. The solid lines are the result from nonlinear curve fitting, using Eqs. (9) and (10).

Figure 3

Conductivity σ of three CrN/MgO(001) layers grown at $T_s$ $=$ 550, 700, and 850 °C, plotted on a log-scale vs (a) $T^{-1/4}$ and (b) $T^{-1/2}$. The lines are obtained from linear fitting in the temperature ranges of 50–120 K and 10–25 K for (a) and (b), respectively.

Figure 4

Localization length ξ vs $T_s$. The right $y$ axis indicates the corresponding lower limit for the N-vacancy concentration $N_v$.

Figure 5

Log-log plot of the normalized conductivity vs normalized temperature for all samples. The solid line corresponds to the scaling function in Eq. (10).

Figure 6

Optical reflectance $R$ vs wavelength from 140-nm-thick CrN/MgO(001) layers grown at $T_s$ $=$ 550–850 °C, measured with an incident angle of 45°.