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 E_F of point defects in silicon (Si) crystals during the cooling process of the Czochralski (CZ) method were studied by first principles analysis. E_F of several charge states of vacancy (V) and interstitial Si (I) was calculated as a function of the Fermi level. E_F 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-V_n or As-V_n complex formation was greater than that of stable V_n complex formation from isolated P or As atoms and vacancies.