Study of Impurity Distributions (Mainly Lithium in Silicon) Using ac Hopping Conduction

Abstract

The results of previous studies on ac impurity conduction are applied in an attempt to study the distribution of impurities when this is not random. The present study applies mostly to the distribution of lithium in silicon, but a few other situations are also examined. A possibility is presented, on a theoretical basis, to determine experimentally the complete distribution function of the distances between minority impurities and their nearest-neighbor majority impurities. It is found, however, that the experimental methods which are required must be more sensitive than methods thus far employed. A less quantitative method for determining the distribution is also proposed. It utilizes previously derived similarity relations which make it possible to compare experimental results on one sample with results on another where the distribution is known to be random. The latter have been reported in the literature by S. Golin. This method is used successfully in the present paper. The following cases are examined: (1) All the impurities are added to the melt before crystallization. (2) Acceptors are added to the melt, but the donors (lithium) are diffused into the crystallized material at 400\ifmmode^\circ\else\textdegree\fi{}C. All the data, except for Golin's samples which serve as the standard, refer to silicon. The experimental data for the first category are taken from the literature. For the second category they are reported in this paper. The results are as follows: Materials where all the impurities were introduced before crystallization indicate that the distribution of impurities is random, or very close to it. In lithium-doped samples, the randomness of the distribution depends on various conditions. A dramatic difference between oxygen-poor and oxygen-rich samples is observed. Oxygen-rich samples, $n$- or $p$-type, always exhibit a random distribution. This indicates that oxygen inhibits the mobility of lithium. In oxygen-poor samples, $n$- and $p$-type, the distribution depends on the temperature from which the samples were quenched. When this temperature is in excess of 200\ifmmode^\circ\else\textdegree\fi{}C, the distribution is again random, or very close to it. For lower temperatures, the distribution deviates from random. To explain the results, one has to assume either pairs with relatively large separations compared to those occurring in the theory of Reiss, Fuller, and Morin,r with traps of the nature described by Tanaka and Fan. The latter is found to be the likely explanation. The distance of closest approach between the lithium and boron atoms in silicon is calculated to be 2.87\ifmmode\pm\else\textpm\fi{}0.03 \AA{}, in good agreement with Morin's results on aluminum and lithium.