Optimization strategies for parametric analysis of thin-film reflectivity spectra

• Published in: IEEE transactions on instrumentation and measurement Vol. 52; no. 5; pp. 1635 - 1639
• Main Authors: Schlaf, M., Hagras, H., Sands, D.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-10-2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computational modeling; Fourier transforms; Genetic algorithms; Infrared spectra; Mathematical analysis; Mathematical models; Minima; Optical films; Optical refraction; Optical variables control; Optimization; Reflectivity; Simulated annealing; Spectra; Studies; Thin films; Transistors
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2003.817921

Near-normal incidence Fourier transform infrared reflection spectra are utilized to determine the optical properties and thickness of thin films. A parametric model of the refractive index for the wavelength range is used in conjunction with three optimization algorithms to determine the global minimum of these complex functions. The simple downhill simplex algorithm can find the global minimum quickest but only if the starting parameters are such that local minima are not encountered on route, and for more complex optical functions, the usefulness decreases. The simulated annealing optimization and genetic algorithms are able to find global minima reproducibly but are seen best as complementary rather than competitive. Genetic algorithms are limited in accuracy according to the number of bits used to encode the solution, and the speed of computation decreases with increasing bits. Simulated annealing is a random process and tends to be slower initially, but any desired accuracy can be achieved by adjusting the random step length as the algorithm proceeds.