Electron paramagnetic resonance of boron acceptors in isotopically purified silicon

The electron paramagnetic resonance (EPR) linewidths of B acceptors in Si are found to reduce dramatically in isotopically purified ${}^{28}\text{S}\text{i}$ single crystals. Moreover, extremely narrow substructures in the EPR spectra are visible corresponding to either an enhancement or a reduction in the absorbed microwave on resonance. The origin of the substructures is attributed to a combination of simultaneous double excitation and spin relaxation in the four level spin system of the acceptors. A spin population model is developed which qualitatively describes the experimental results.

Figure 1

(a) The level schemes of B acceptors. An externally applied magnetic field splits the heavy (light) hole subband into two energy states $|\pm 3/2⟩$ $\left(|\pm 1/2⟩\right)$. We refer to each level as $|1⟩-|4⟩$ in the order shown. On top of the EPR-allowed transitions defined by $\Delta m=1$, the experimentally observed nominally EPR-forbidden transitions $\Delta m=2$ and $\Delta m=3$ are also shown. (b) EPR spectra recorded at $T=3.0\text{K}$ on ${}^{28}\text{S}\text{i}:\text{B}$ and ${}^{\text{nat}}\text{S}\text{i}:\text{B}$ samples showing the $\Delta m=1$ and 2 transitions.

Figure 2

EPR spectra of the intersubband $\Delta m=1$ resonance (a) and the $\Delta m=2$ resonance (b) in ${}^{28}\text{S}\text{i}:\text{B}$ for $H\parallel \left[100\right]$. The upper spectrum in each figure was measured at $T=3.2\text{K}$, $\nu =9.38\text{GHz}$ and a microwave power of $P=0.2\text{mW}$. The lower spectra were measured at $T=1.8\text{K}$, $\nu =9.56\text{GHz}$, and $P=0.002\text{mW}$. The values of $P$ were chosen to achieve the same microwave excitation rate $w$ in the two resonators used. Solid lines show the results of numerical fittings composed of two Lorentzian lines, which are separately shown as dashed and dotted lines. $H_0$ is the resonance field of each signal. The amplitudes of the spectra were normalized. The insets show the integrated absorption spectra in the magnetic field region of the substructures in arbitrary units.

Figure 3

Contour plots obtained by the population model described in the text for (a) $\Delta m=1$ and (b) $\Delta m=2$. The contour lines indicate a relative intensity (in %) of the substructure lines as compared to the intensity of the broad underlying transition. Negative and positive intensities correspond to a suppression (dip) and an enhancement (peak) of the microwave power absorptions, respectively. The negative region is shown shaded. The parameters used in the calculation were $T=3\text{K}$, $\nu =9.4\text{GHz}$, and ${\gamma }_{14}/w={\gamma }_{12}/w=1$, with $w$ being the resonant microwave excitation rate. The dashed line represents the assumed correlated temperature dependence of ${\gamma }_{13}$ and ${\gamma }_{23}$ in ${}^{28}\text{S}\text{i}:\text{B}$ as discussed in the text.