A physics-based analytical solution to the surface potential of polysilicon thin film transistors using the Lambert W function

A physics-based analytical solution to the surface potential of polysilicon thin film transistors (poly-Si TFTs) using the Lambert W function has been derived from poly-Si TFTs implicit surface potential equation without any empirical smoothing functions. The analytical solution eliminates the need for the complex iterative computation and is very accurate with absolute error only in nanovolt range. Its high accuracy is proved by a comparison of calculating the surface potential under various bias conditions with respective numerical results and also by the fact that the characteristics of the surface potential derivative with respect to the gate voltage show no splits and peaks. A poly-Si TFTs charge sheet model based on this precise analytical surface potential solution is developed and the results are verified using the experimental data.