使用白光干涉儀以基因演算法從反射光譜振幅計算光學常數

Calculation of optical constants from reflected spectral amplitude with Genetic Algorithm by white light interferometer

蕭義勝(Yi-sheng Siao)

指導教授 ： 李正中

國立中央大學/理學院/光電科學研究所/碩士(2011年)

摘要

基因演算法應用在數值分析上一直有傑出的表現，本論文將基因演算
法應用於反推薄膜光學常數，在單層膜且沒有吸收時，可以很精確的反推
出薄膜光學常數。
本論文用五種樣本測量光譜並使用基因演算法擬合光學常數，並將多
次擬合後的光學常數取平均值，將計算出的光譜與測量光譜比較，使用的
材料有Ta2O5、Nb2O5、以及SiO2，其中Ta2O5 與Nb2O5 折射率與厚度較大，
因此在基因演算法中所設定的上下限可以比較廣，薄膜折射率範圍可以在1
到3而薄膜厚度範圍可以在1到1000nm，而SiO2樣本折射率與厚度均較小，
造成光譜沒有轉折點較難擬合，因此將薄膜折射率範圍設定在1.4 到1.5 時
才能得出正確的薄膜厚度。
本論文中的Ta2O5 與Nb2O5 材料，折射率精確度可以優於2%，膜厚精
確度可優於1%，但總體而言擬合的折射率與厚度誤差均小於5%，而SiO2
材料經修正範圍後，擬合出的折射率誤差更可以小於1%，厚度誤差小於
3%。
同一片薄膜樣本，其表面厚度也不一定會各點完全相同，橢圓偏振儀
只能測量出薄膜上某一點的薄膜光學常數，本論文使用白光干涉儀的快速
測量光譜搭配基因演算法的精確擬合，可以將二維的薄膜各點厚度求出 ，
將來可以應用在工業上的快速測量與大面積的測量，減少測量時間成本。

關鍵字

白光干涉儀 ； 薄膜光學常數 ； 基因演算法

並列摘要

The genetic algorithm (GA) is excellent at solving global numerical
optimization problems. We propose GA to acquire optical constant of thin films
from spectral amplitude retrieved using Fourier transform of the Interferogram.
The optical parameters such as refractive index and thickness of thin films
are essential for comparison of samples which are produced using different
methods. These optical parameters are usually determined by photometric
methods or Ellipsometer. The optical thickness, the product of refractive index
and thickness determine the spectrum of the thin films. As optical constant in
multiple of quarter wave we can find spectrum peaks. Under the condition when
the single layer sample has larger optical thickness, we can acquire the optical
parameters accurately through GA.
In this study, we select five samples which are different materials and
thickness and use GA to fit the spectrum to acquire the optical parameters of
each sample. We use GA to fit the spectrum 1000 times and use the average
optical parameters to calculate the spectrum comparing with the measured
spectrum. We use three material Ta2O5, Nb2O5 and SiO2 as the samples. The
refractive index of Ta2O5 and Nb2O5 are higher than SiO2, so it is easy for GA to
acquire the optical constants under a wide range of the optical parameters. For
Ta2O5 and Nb2O5, we set the range of refractive index between one to three and
the thickness between 1 nm to 1000 nm. For SiO2, we change the range of
refractive index between 1.4 to 1.5.
The minimum errors of the calculated refractive index of Ta2O5 and Nb2O5
are smaller than 2% and the thickness are smaller than 1%. The total errors of
the optical parameters are smaller than 5%. The errors of the calculated
refractive index of SiO2 are smaller than 1% and the thickness are smaller than
3%.
The same thin film sample would have different optical parameters on its
two-dimensional surface. The Ellipsometer only measure one point on the thin
film at a time and it cost at least thirty minute in a process. In this study, we use
white-light interferometer with GA to measure the two-dimensional optical
parameters on the thin film surface in a short time.

並列關鍵字

Genetic Algorithm ； optical costant ； optical properties ； white light interferometer

參考文獻

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[3] R. E. Denton, et al., "The determination of the optical constants of thin films

from measurements of reflectance and transmittance at normal incidence,"

[4] J. C. Manifacier, et al., "A simple method for determination of the optical