First Principles Analysis of Formation Energy of Point Defects and Voids in Silicon Crystals during the Cooling Process of Czochralski Method (Dopant Type and Concentration Dependence)

Abstract

The effects of p-type (B) or n-type (P or As) dopant concentration on the formation energy EF of point defects in silicon (Si) crystals during the cooling process of the Czochralski (CZ) method were studied by first principles analysis. EF of several charge states of vacancy (V) and interstitial Si (I) was calculated as a function of the Fermi level. EF of the most stable state of V and I in Si crystals was estimated by considering the dependence of the Fermi level on crystal temperature. The V concentration was found to decrease in p-type but to increase in n-type Si crystals when dopant concentration was higher than about 1×1019 atoms/cm3. This explains the reported experimental results for void formation behavior in Si crystals, i.e., void formation is suppressed by an increase in p-type dopant concentration above about 1×1019 atoms/cm3, but is enhanced by an increase in n-type dopant concentration to about 3×1019 atoms/cm3. Other calculations showed that, at the initial stage of void formation, the reduction of the total energy of stable P-Vn or As-Vn complex formation was greater than that of stable Vn complex formation from isolated P or As atoms and vacancies.