Analytical Model for Calculating Trapped Charge in a－Si：H and Its Relative Error Analysis

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Analytical Model for Calculating Trapped Charge in a-Si:H and Its Relative Error Analysis

Using a Taylor series expansion for the Fermi-Dirac occupation function,an accurate analytical model is developed for calculating the trapped-charge density in a-Si: H considering deep and tail states simultaneously without simplification.This is followed by the investigation of the relative errors of the localized trapped charge density in a-Si:H at all temperatures as a function of the quasi-Fermi level in the band gap calculated from three published analytical models and our above model. The results suggest that the relative errors of all these models increase notably as Efn is very closed to Ec(e.g.,-0.01 eV< Efn-Ec).It is also noticed that the relative errors of all above models become larger normally the greater is the value of temperature.A detailed analysis indicates that each model has its own applicability with various temperatures and various positions of the Fermi level.