Determination of the thickness and optical constants of amorphous silicon

The rigorous expression for the transmission of a thin absorbing film on a transparent substrate is manipulated to yield formulae in closed form for the refractive index and absorption coefficient. A procedure is presented to calculate the thickness to an accuracy of better than 1% with similar accuracies in the values of n. A method to correct for errors due to slit width is also given. Various formulae to calculate the absorption coefficient accurately over almost three orders of magnitude are discussed. Only data from the transmission spectrum are used and the procedure is simple, fast and very accurate. All formulae are in closed form and can be used on a programmable pocket calculator.