Ellipsometric Metrology Of Ultrathin Films: Dual Angle Of Incidence

Abstract

Single angle of incidence ellipsometrie measurements have been extended to dual angle measurements on our newly constructed multi-method precision ellipsometer in order to better determine the optical constants of a substrate. Following the measurement error analysis that was prescribed in an earlier paper for single angle of incidence and fixed wavelength measurements, the results for dual angle of incidence are presented here. Using an Explicit Error Analysis (EEA) method, involving the differentials of the measurable optical constants of the surface, it is possible to find a well-defined pair of incident angles to perform the measurement. Without a measurement error analysis, there would be no way of knowing what the absolute measurement uncertainty is or which angles of incidence could provide optimum measurement conditions. As in the case of single angle of incidence measurement where we were able to select an optimum angle of incidence to assure the highest measurement accuracy, the dual angle of incidence measurement also predicts optimum angles of incidence. It was found that in the case of single angle of incidence ellipsometry the principal angle of incidence can sharply define the optimum angle for measuring bare substrates and very thin films on a substrate. Likewise, for the dual angle of incidence measurement, there can also be two sharply defined angles for certain sample surface models. Here we present a dual angle ellipsometric measurement of the real part of the refractive index of a silicon substrate at the wavelength of 632.8 nm. A silicon dioxide film thickness between 125 and 150 nm and the two angles of incidence, 68 and 72 deg, optimized this measurement. The real part of the refractive index of the silicon substrate was found to be 3.865 ± 0.001.