Microwave Absorption in Silicon at Low Temperatures

Abstract

The microwave conductivity of $p$-type and $n$-type silicon was studied at low temperatures at \ensuremath{\sim}9000 Mc/sec. Samples measured had impurity concentrations ranging from 6.7\ifmmode\times\else\texttimes\fi{}${10}^{15}$ to 2.2\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. In the impurity conduction range, the microwave conductivity varies much more slowly than the dc conductivity, becoming orders of magnitude larger in comparison at 4.2\ifmmode^\circ\else\textdegree\fi{}K. Furthermore, the conductivity showed strong non-Ohmic characteristics in all the samples. The experimental results indicated that the microwave conductivity in the low-concentration range consists of two parts, one the conductivity due to direct absorption process in ionized impurity pairs, which shows saturation at low electric-field intensity, and the other, the conductivity due to hopping process, which does not show a non-Ohmic character. A simple theory of the microwave absorption in the ionized impurity pairs was developed, supporting the experimental conclusions. Theory gives a microwave conductivity due to the direct absorption process of the right order of magnitude and the same temperature dependence as measured. But the relaxation time calculated for the pairs is too long compared with the experimental results. The measured hopping conductivity was compared with calculation and reasonable agreement was obtained. The ratio of the conductivity due to the direct absorption process to the hopping conductivity was calculated and requires that a value for the effective Bohr radius of the boron impurity of 20 \AA{} must be used in stead of the 13 \AA{} obtained from hydrogenic approximation.