Defect behavior during growth of heavily phosphorus doped Czochralski silicon crystals (II): Theoretical study

Recent studies including our own report (I) have revealed that heavily phosphorus (P) doped Czochralski-silicon (HP-Cz-Si) exhibits peculiar defect behaviors during crystal growth. HP-Cz-Si crystals with a low resistivity of around 0.6 mΩ cm (P concentration of 1.3 × 1020 P cm−3) have interstitial-type stacking faults (SFs) and dislocations, which degrade device characteristics. The purpose of this paper is to clarify what causes the defect behavior in HP-Cz-Si through theoretical calculations. The thermal equilibrium concentrations of substitutional P (Ps), interstitial P (Pi), and (Ps)n-vacancy (V) clusters (n = 1−4) were determined by using density functional theory (DFT) calculations. The concentrations of Pi ([Pi]) and (Ps)nV ([(Ps)nV]) balanced with the given Ps concentration ([Ps]) were obtained as a function of the total P concentration ([P]) and the temperature. On the basis of the calculated results those can quantitatively explain our experimental results in the report (I), we propose a defect model that accurately represents HP-Cz-Si crystal growth. The main feature of the model is that the incorporated Pi atoms at the solid/liquid interface around [Pi] = 1017 Pi cm−3 cause the formation of SFs and dislocations during the HP-Cz-Si crystal growth with around [P] = 1020 P cm−3. Furthermore, DFT calculations were performed for Pi segregation on the SF and for the photoelectron spectra of P 1s measured by hard x-ray photoelectron spectroscopy to explain the other experimental results in the report (I).