Spin dynamics of exchange-coupled nitrogen donors in heavily doped $n$-type $15R$ SiC monocrystals: Multifrequency EPR and EDMR study

Semiconductor devices based on $15R$ silicon carbide (SiC) show improved properties compared to other polytypes. Here, we report the investigation of nitrogen-doped $15R$ SiC monocrystals with $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ using multifrequency electron paramagnetic resonance (EPR) and electrically detected magnetic resonance (EDMR) spectroscopic methods in the microwave (MW) frequency range from 9.4 to 328.84 GHz and in the temperature range from 4.2 to 300 K. A single intensive $S$ line with $S=1/2$, at $g_{\perp }=2.0026\left(2\right)$, and $g_{\parallel }=2.0043\left(2\right)$ dominates the EPR spectrum in $15R$ SiC at $T<160$ K and was attributed to the exchange-coupled nitrogen (N) donors substituting quasicubic “$k1$” site having the deeper energy level in $15R$ SiC lattice. From the analysis of the temperature behavior of the integral intensity, magnetic field position, intensity, shape, and width of the $S$ line, it was concluded that at $T<90$ K, the exchange coupling occurs between localized donor electrons, while at $T=90-150$ K the interaction between exchange-coupled N donors and conduction electrons takes place. In the temperature interval from 20 to 160 K, the $S$-line EPR width was characterized by a two-phonon Orbach relaxation process with the activation energy of $\sim 6.5$ meV corresponding to the valley-orbit splitting values for N donors in $15R$ SiC. The variable-range hopping regime obeying the $T^{1/4}$ law was found to take place at $T<20$ K leading to the appearance of the $S$ line in the EDMR spectrum at low temperatures. The appearance of the EDMR signal from exchange-coupled N donors is caused by the EPR-induced temperature-increase mechanism and the spin-flip hops process. The results obtained from MW conductivity measurements agree with EPR and EDMR data. The temperature variation of MW conductivity was described by several processes, including the electron-hopping process between N donor impurity atoms at $T<50$ K with activation energy ${\varepsilon }_3=1.5$ meV, electron transitions between Hubbard bands at $T=50–100$ K; the transition of the electrons from the donor energy levels to conduction band with ionization energy ${\varepsilon }_1=32$ meV at $T=100–200$ K and scattering of the conduction electrons by ionized donors occurred at the temperature higher than 200 K.

Figure 1

Crystal structure of $15R$ SiC drawn in vesta 3.5.2 program [27] using the data from Ref. [28] The c axis is along the [0001] direction.

Figure 2

(a) Temperature dependence of MW loss $\left(\mathrm{\Delta }\right)$ and frequency shift (δ) measured in $15R$ SiC monocrystals with $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$. (b) Temperature dependence of the natural logarithm of MW conductivity estimated from Eq. (1). Dots are experimental data; solid red and blue lines represent the result of fitting with Eq. (2).

Figure 3

High-frequency EPR spectra (${\nu }_0=328.84$ GHz) measured in $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ at $\mathbf{B}\parallel \mathbf{c}$ and $\mathbf{B}\perp \mathbf{c} \left(T=8\mathrm{K}\right)$. Solid black lines are experimental spectra; solid red lines are the sum of simulated components. Inset shows the detailed view of simulated components at $\mathbf{B}\parallel \mathbf{c}$.

Figure 4

Temperature dependence of $X$-band EPR spectra measured in $15R$ SiC monocrystals with $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ at $\mathbf{B}\parallel \mathbf{c}$ (a) and $\mathbf{B}\perp \mathbf{c}$ (b), ${\nu }_0=9.398$ GHz.

Figure 5

Temperature variation of spin susceptibility obtained from the analysis of $X$-band EPR $S$ line obtained for $15R$ SiC monocrystals with $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}, \mathbf{B}\parallel \mathbf{c}$. Dots are experimental data; solid blue and red lines correspond to the result of fitting with Eqs. (4) and (5).

Figure 6

(a) Result of the fitting of experimental $X$-band EPR spectrum from $S$ line in $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ using Dysonian line shape by Eq. (6) and Eq. (7). $T=140$ K, $\mathbf{B}\perp \mathbf{c}$. (b) Temperature variation of the $A/B$ ratio of the $S$ line obtained from the fitting of $X$-band EPR spectra in $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ using Eqs. (6) and (7) at $\mathbf{B}\parallel \mathbf{c}$ (solid squares) and $\mathbf{B}\perp \mathbf{c}$ (open circles).

Figure 7

Temperature dependence of $g_{\parallel }, g_{\perp }$, and averaged $g$ values $\left(g_{\mathrm{av}}\right)$ for $S$ line obtained in $15R$ SiC monocrystals with $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim {510}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ from the fitting of $X$-band EPR spectra using Eqs. (6) and (7).

Figure 8

(a) Temperature variation of the $S$-line width obtained from the fitting of $X$-band EPR spectra in $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ using Eqs. (6) and (7). Open blue circles are experimental data at $\mathbf{B}\parallel \mathbf{c}$, solid black squares are experimental data at $\mathbf{B}\perp \mathbf{c}$, and solid red lines are fitting with Eq. (9). Inset shows the temperature range of the EPR linewidth minimum at 20 K for both principal magnetic field orientations. (b) Natural logarithm of $\mathrm{\Delta }{B}_{pp}$ vs $T^{-1/4}$ in the temperature interval from 5 to 20 K. Solid black squares are experimental data at $\mathbf{B}\perp \mathbf{c}$; solid red line is fitting with Eq. (8).

Figure 9

(a) Comparison of EPR and EDMR spectra of $S$ line measured in $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ at ${\nu }_0=9.702$ GHz and ${\nu }_0=100$ GHz, $T=7$ K, $\mathbf{B}\perp \mathbf{c}$. (b) Temperature variation of EDMR spectra intensity of $S$ line measured at ${\nu }_0=100$ GHz, $\mathbf{B}\perp \mathbf{c}$, The solid line results from the fitting with Eq. (20).

Figure 10

Theoretical estimation of hopping probability $\left(W_{ij}\right)$ vs distance between donors $R_{ij}$ at different temperatures ($T=20$, 5, and 1 K) using Eq. (10) for $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$. Curves were normalized to their maximum value.

Figure 11

Power dependence of the $S$-line EDMR signal amplitude measured in $15R$ SiC monocrystals having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ at ${\nu }_0=100$ GHz and $T=7$ K. Dots are experimental data; the solid line is the result of fitting with Eq. (21).

Figure 12

(Adapted from Ref. [24]) Mechanism responsible for the appearance of S-line EDMR signal in the VRH regime in $15R$ SiC having $\left(N_{\mathrm{D}}–N_{\mathrm{A}}\right)\sim 5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$.