Low-temperature diffusion of implanted sodium in silicon

We have studied the low-temperature diffusion of sodium atoms implanted (at primary ion energy $E$ = 300 keV to total doses within $\Phi$ = 5 $\times$ 10$^{14}$–3 $\cdot$ 10$^{15}$ cm$^{-2}$) in single-crystalline silicon grown by the method of float-zone melting (fz-Si) with low oxygen concentration $N_{\mathrm{O}}$ and by the Czochralski method in the presence of magnetic field ($m$Cz-$n$-Si and $m$Cz-$p$-Si) with $N_{\mathrm{O}}\approx$ 5 $\times$ 10$^{17}$ cm$^{-3}$. The diffusion was studied at annealing temperatures within $T_{\mathrm{ann}}$ = 500–420$^\circ$C for periods of time $t_{\mathrm{ann}}$ = 72–1000 h. It is established that the temperature dependence of the diffusion coefficient $D(10^{3}/T)$ of sodium in fz-Si in a broad range of $T_{\mathrm{ann}}$ = 900–420$^\circ$C obeys the Arrhenius law with $E_{\mathrm{fz}}$ = 1.28 eV and $D_{0}$ = 1.4 $\cdot$ 10$^{-2}$ cm$^{2}$/s. The same parameters are valid for the implanted sodium diffusion in $m$Cz-Si in the interval of $T_{\mathrm{ann}}$ = 900–700$^\circ$C. However, at lower temperatures, the values of $D$ in $m$Cz-Si are lower than to those in fz-Si, which is related to the formation of more complicated Na–O$_{n}$ ($n>$ 1) complexes in the former case. Estimation of the diffusion activation energy of these complexes yields $\Delta E\approx$ 2.3 eV.