Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2006-03-21
2006-03-21
Rodriguez, Paul L. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S013000, C716S030000
Reexamination Certificate
active
07016819
ABSTRACT:
An automated simulation method for determining the enhanced generation-recombination rate due to trap-to-band tunnelling in a semiconductor device using the Dirac coulombic tunelling integral and to a simulator for carrying out the method are disclosed. The method and simulator are, for example, particularly useful in the modelling of characteristics such as leakage current in polysilicon TFTs, which leakage current can, for example, seriously degrade pixel voltage in active matrix display devices. The simulator embodies the method, which method comprises the steps of: assigning the variable C to the ratio of the Poole-Frenkel barrier lowering energy (ΔEfp) divided by the energy range for which tunnelling can occur (ΔEn); 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 (umax) for the variable u of the integral; determining if the value for umaxis less than C, is between C and 1 or is more than 1; assigning the value of C to the variable v if umaxis less than C; assigning the value f umaxto the variable v if umaxis between C and 1; assigning the value of 1 to the variable v if umaxis 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.
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Craig Dwin
Oliff & Berridg,e PLC
Rodriguez Paul L.
Seiko Epson Corporation
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