Relaxation Process of Ionized Impurity Pairs in Silicon

The relaxation mechanism of the ionized impurity pairs in silicon, in which the direct absorption process occurs, was analyzed. The hopping of carriers in the surrounding impurity pairs gives rise to the fluctuating electric field at the homopolar pair. The effect of the fluctuating field on the relaxation time between the bonding and the antibonding states of the homopolar pair was calculated by the density-matrix method. It was revealed that the magnitude of the relaxation time $\tau$ for 9 Gc/sec at 10°K is ${10}^{-9\mathrm{}}$ sec, in agreement with the experiments. $\frac{1}{\tau }$ calculated is approximately proportional to the temperature $T$ in the high temperature range and has stronger temperature dependence than $T$ in the low temperature range. This behavior is also in good agreement with the experiments. The temperature dependence of the relaxation time was compared with the temperature dependence of the hopping conductivity and the results obtained were consistent.