Comparison of algorithms used for evaluation of ellipsometric measurements- Random search, genetic algorithms, simulated annealing and hill climbinggraph-searches

On the base of an extended criteria function and two different point select ion strategies, two hill climbing searches were applied in ellipsometry, an d were compared with the well known random search (RS), genetic algorithms (GA) and simulated annealing (SA) to evaluate ellipsometric measurements. F or the evaluation of an ellipsometric measurement an adaptive optical model has to be assumed because of the lack of the inverse equations. Finding th e appropriate parameters of the optical model of the plan-parallel thin lay er-structure by minimising the difference (error) between the measured and the simulated (computed with the optical model) spectra leads to a classica l global optimisation task. To demonstrate the methods, spectroscopic ellip sometric samples were evaluated using two different types of optical models : separation by implantation of oxygen and electrochemically prepared porou s silicon. The ellipsometric evaluation gives real examples to demonstrate the difficulties and the differences among the evaluating possibilities and capabilities. The results prove that the well-known gradient method (Leven berg-Marquardt) needs some pre-searches to give enough reliability, because of the hilly error surfaces. The comparison also shows that by increasing the complexity of the optical model, and thus the number of the parameters and the dimensions of the search space, the difference of convergence speed (effectiveness) and reliability between RS and the more complicated method s also increase. (C) 2000 Elsevier Science B.V. All rights reserved.