Theoretically Modeling Of Ellipsometric Response From Randomly Micro-rough Surfaces

Optical constants of materials are basically physical parameters to analyze the interaction between light and substance,the precise measurement of which plays a significant role in the accurate simulation and analysis of micro-scale radiation heat transfer and radiative properties.With the computer technique and machining precision developed rapidly,the technology of spectroscopic ellipsometry(SE)has been rapidly developed and wildly applied to evaluate optical constants and thin film thickness of samples,owning to its fast,precise,and non-destructive advantages.The data analysis of SE is mainly based on Fresnel equation,which only describes the reflection performance for perfectly smooth surfaces.Because the SE is quite sensitive to surface structures,the surface roughness can result in errors of SE measurement.Aiming at the problem,from two perspectives this dissertation theoretically study the model fitting the SE parameters of micro-rough surfaces.One is on the basis of the effective medium approximation,and another is the direct inversion via Mueller matrix.Both methods are helpful to modify the errors from rough surfaces and obtain accurate optical constants.On the basis of the fact that the average cross-section mixture of the solid materials and air is inhomogeneous along the height of surface roughness,the work proposed the layered effective medium approximation(LEMA)model to fit the SE parameters of Gaussian distributed randomly micro-rough surfaces.The finite-difference time-domain(FDTD)method is utilized to simulate the SE parameters of Gaussian distributed randomly micro-rough surfaces,and the rigorous coupled-wave analysis(RCWA)method is used to calculate the SE parameters of the LEMA model.The limitation of the LEMA model is performed that it cannot capture the influence of the correlation length(?)on the SE parameters.In addition,this work reveals that the natural weakness of the LEMA model may be overwhelmed by changing the total thickness of model.Via data fitting,the mathematical relationship between the thickness of the LEMA model and the characteristic parameters of micro-rough surfaces has been found.Furthermore,the results from the ellipsometric experiment agree well with the calculations from the LEMA model,which gives a good support to the validity of the LEMA model.However,it is found that the fitting precision of the LEMA model exists uncertainty as materials change.Mueller matrix contains more metrical information than the SE parameters.Factors including the relative surface roughness,the correlation length,optical constants and incident light are considered to study their effect on the specular part of Mueller matrix of micro-rough surfaces.It is found that the change of relative surface roughness and correlation length has no influence on the element m01 of Mueller matrix.The value of m01 is mainly influenced by optical constants of materials.Besides,the value of m01 increases with the refractive index n and extinction coefficient k rising.When the root mean square roughness ? keeps constant,both the relative surface roughness and ?/? are proportional to the value of m23.In addition,with k changing,the intercept alters but the proportionality coefficient keeps constant.The values of m22 and m23 of micro-rough surfaces are greater than those of smooth surfaces.Simultaneously,as the value of k changes,the curves of m22 and m23 of both surfaces have the same variation trend.These results may facilitate the direct inversion of utilizing Mueller matrix to the topographies of micro-rough surfaces and optical constants of materials.