Patent ID: 7016819

Claim:
An automated simulation method for determining enhanced generation recombination rate due to trap-to-band tunnelling in a semiconductor device using the Dirac coulombic tunnelling integral, comprising the steps of: assigning the variable C to the ratio of the Poole-Frenkel barrier lowering energy (ΔE fp ) divided by the energy range for which tunnelling can occur (ΔE n ); assigning the value (C+1)/2 to a variable v and performing a second order Taylor's series expansion of the Dirac coulombic tunnelling integral around v to determine a maximum value (u max ) for the variable u of the integral; determining if the value for u max , is less than C, is between C and 1 or is more than 1; assigning the value of C to the variable v if u max is less than C; assigning the value of U max to the variable v if u max is between C and 1; assigning the value of 1 to the variable v if u max is more than 1; reducing the Taylor's series expansion of the Dirac coulombic tunnelling integral to an error function; reducing the error function to simple exponential functions by applying rational approximations to the error function; and calculating the enhanced generation recombination rate due to trap-to-band tunnelling in a semiconductor device using the said simple exponential functions; wherein said method determines the leakage current in a polysilicon Thin Film Transistor.