Patent ID: 7920999

Claim:
A method of predicting internal gettering behavior in a silicon substrate, comprising the steps of: determining, with an arithmetic device, a generation rate Is of a contaminant heavy metal silicide nuclei at a surface of oxygen precipitates from an arithmetic expression, Is =(4 πRs*DC ( t )) Z ( T )ρ exp(−Δ G*/kbT ) wherein Rs* is a critical nuclei radius of the contaminant heavy metal silicide; D is a diffusion coefficient of a contaminant heavy metal; C(t) is a concentration of the contaminant heavy metal within a silicon wafer at a time t; 4πRs*DC(t) is a frequency at which contaminant heavy metal atoms come into contact with a critical nuclei by diffusion; Z(t) is a Zeldovich factor; ρ is a density of an atom site on the surface of the oxygen precipitates; ΔG* is a free energy change of a system at the time when the contaminant heavy metal silicide are formed on the surface of the oxygen precipitates; kb is a Boltzmann's constant; T is absolute temperature; ρ exp(−ΔG*/kbT) is an equilibrium density of the critical nuclei; determining with an arithmetic device a density Ns(t) in an effective gettering site during an internal gettering heat treatment from an arithmetic expression, Ns ( t )=∫ t=0 t=t Is ( t )4 πR 2 ( N−Ns ( t )) dt wherein Is is a nucleic generation rate R is a radius of the oxygen precipitates; N is a density of the oxygen precipitates; calculating with an arithmetic device a time change ∂C(t)/∂t of the contaminant heavy metal concentration by assigning the determined density Ns(t) to an arithmetic expression, ∂ C ( t )/∂ t =−4 πRD ( C ( t )− C eq ) Ns ( t ) wherein R is the radius of the oxygen precipitates; D is the diffusion coefficient of the contaminant heavy metal; C(t) is the concentration of the contaminant heavy metal within the silicon wafer at a time t; C eq is a solubility of the contaminant heavy metal; and repeating the above arithmetic calculations with an arithmetic device, using a finite difference method to predict a residual concentration C(t) of the contaminant heavy metal at an arbitrary time t.