THE INFLUENCE OF SURFACE VIBRATIONS ON THE EQUILIBRIUM DOPING OF A SEMICONDUCTOR

We calculate the distribution coefficient of impurities in a system of gas + crystal. It is shown that the qualitative change in the vibrational spectrum of the crystal due to the presence of surface modes, and of localized and quasi-localized impurity modes, significantly changes the equilibrium concentration of impurities in the crystal, at a given temperature, by as much as an order of magnitude or more. A "stiff" adsorbed monolayer impedes the incorporation of impurities in the crystal, while a "soft" adsorbed monolayer facilitates the incorporation of the impurities into the crystal. The appearance of high frequency localized modes in the vibrational spectrum due to light impurity atoms, impedes the incorporation of these impurities in the crystal and leads to a decrease of the distribution coefficient for given values of the atomic force constants and the temperature. The presence of low frequency quasi-localized modes due to heavy impurity atoms facilitates the incorporation of these impurities into the crystal, and increases the distribution coefficient for given values of the atomic force constants and the temperature.