ANALYTICAL APPROXIMATIONS FOR THE DISTRIBUTIONS OF SUBSTITUTIONAL TRANSITION METAL DEFECTS IN SILICON FLOAT ZONE CRYSTALS

摘要

It is reported about the formation rate of substitutional transition metal (TM) defects (M_s) in dislocated (D) and dislocation-free (DF) 0.8 inch FZ crystals. Theoretical and experimental results are presented for the metals Cu, Ni, Co, Ag, Pd (group Ⅰ) and Rh, Au, Pt, Ir (group Ⅱ). It is shown, that the frozen-in concentration Ns(0) can be determined by solving the Frank-Turnbull rate equation. For a given vacancy distribution Cv(T), characterized by its dependence on temperature, all dopants can be arranged according to their binding energies EB, which are connected with characteristic temperatures T_c. Calculations of N_s(0) are performed by integration with the steepest descent method for D-crystals considering different cooling rates and additionally for vacancy dominated (Ⅴ) and interstitial dominated (Ⅰ) regions of DF-crystals. It is shown, that the void and swirl formation in Ⅴ- and Ⅰ-regions have a strong influence on N_s(0) in most cases. From a comparison between theoretical and experimental results the binding energies 2.0 to 2.5 eV (group Ⅰ) and 2.6 to 3.0 eV (group Ⅱ) are derived. The reduced concentrations N_s(0)/N_D as observed in Ⅴ-regions, for example, are in the range between 3-10~9-4) and 1 for E_B = 2 up to 3 eV, where ND is the total TM doping concentration.