A method based on admittance diagram called Admittance Real-time Monitoring, ARM, was proposed to monitor multilayer coatings. This optical monitoring method is highly sensitive and capable to compensate for thickness errors. The sensitivities of ARM were compared with that of the conventional method by using runsheet diagram. The in situ error compensation of ARM showed a great improvement in the optical performance when utilized in an anti-reflection coating process.
© 2008 Optical Society of America
Various monitoring methods have been developed to control the thickness of thin-film deposition . The turning point method, TPM, which is the most popular and developed method, has the advantage of error compensation for quarterwave stacks [2,3]. For nonquarterwave stacks, the wavelength of the monitoring system is expected to change to the one which is appropriate for monitoring each individual layer. The capability of the hardware clearly limits the method .
Another method, based on a single wavelength, called the level monitoring method , is suitable for monitoring nonquarterwave multilayers. According to error analysis, the monitor plate must be precoated for error compensation. Several numerical methods[6,7] and the optimum trigger point method then have been developed to improve the performance, sensitivity and compensation[8,9] associated with the TPM and the level method. These monitoring methods are based on the use of runsheet diagram to control the thickness of films, according to transmittance or reflectance. Therefore, the refractive index, n, extinction coefficient, k, and thickness, d, are not independently determined in real time. To real time determination of n, k and d, ellipsometry and phase extraction methods have been proposed [10–12].
In this article a new optical monitoring method based on an admittance diagram, called Admittance Real-time Monitoring, ARM, is proposed and its sensitivity is compared with that of TPM. The admittance diagram showed better than the runsheet diagram in monitoring because of it has higher sensitivity, and offers more physical and visual information. The diagram is obtained from the locus of the effective admittance, plotted during the deposition.
For a nonquarterwave layer, the target value in the runsheet may possible be obtained, even when the refractive index during the process is unexpected. Although the refractive index was wrong, the terminal phase, δ, could still be formed, yielding the wrong thickness, according to Eq. (1). Therefore, the error is not presented in the runsheet, as the diagram that is based on transmittance, T, or reflectance provides no phase information.
In the case of ARM, the admittance locus deviates from the expected value if the refractive index is incorrect. Equation (2) presents the center, C and the radius, R, of the effective admittance locus, where “y” and “ys” represent the refractive index of the thin-film and the substrate, respectively.
ARM offers two important advantages, high sensitivity and error compensation, helping operators make layers with an appropriate thickness, to deliver the required optical performance. The admittance diagram and runsheet diagram offer very different sensitivity as defined by Eq. (3).
The sensitivities, Sx and Sy are correspondent to x-coordinate and y-coordinate, respectively. Δi denotes the difference between neighboring data points and Wi denotes the difference between two extreme values, where “i” represents x or y, as shown in Fig. 1.
Equation (3) is used to plot the density of data-dots and is more useful than the slope of curve for comparing sensitivities. A zero slope indicates zero-sensitivity in the runsheet diagram, but it is not zero in the admittance diagram. The sensitivities of the monitoring diagram, runsheet and admittance, for the same film stacks, were then plotted. Figure 2 plots the sensitivity based on the runsheet data, while Fig. 3 is based on the admittance diagram. The deposition-rate is assumed herein to be constant, since it is not difficult to control the deposition rate within accuracy of ±0.1nm/sec.
A stable deposition rate causes Δx in the runsheet to be always constant, indicating that the Sx versus optical thickness is horizontal. Figure 2 plots Sy in the runsheet diagram. Three curves reveal different distributions for the same material and thickness, a quarterwave high-index film H, on different precoatings: none, HL and HLHL. With different precoatings, the highest sensitivity increases and the corresponding thickness shifts to the shorter value.
Figures 3(a) and 3(b) show the same case analyzed by using admittance. It is more sensitive and the sensitivity peak increases more rapidly for different precaotings than that in the runsheet. The thickness corresponded to the highest sensitivity shifts to the longer value, the quarterwave.
3. Experiment and results
This system we used is a plasma-assisted sputter deposition system with a transmission optical monitoring system, which receives the light energy that passes through the samples, and the effective admittance can be instantly obtained during the process. Figure 4 represents the layout of the optical monitoring system with a monitoring program which shows both the runsheet and the admittance diagram in real time. The system contains a fast (1.25M S/s) and precise (12 bit A–D converter) data acquisition system. Figure 5 represents the main procedure in the monitoring program. The process of the admittance generated from transmittance in real time is depended on simplex algorithm with some assumptions and restrictions, such as the tolerance of refractive index is assumed ±0.05, the tolerance of extinction coefficient is assumed ±0.01, the refractive index must be positive, and so on. These limitations are based on the stable deposition rate, small extinction coefficient, and at normal incidence, during the sputtering deposition. Then the simplex algorithm enables us to find an effective admittance that is close to the actual value.
Two parameters about noise we defined to appraise the signal in the deposition process. S/N decides the data stream is reliable or not, defined by Eq. (4). Because the data stream can not be divided into signals and noise, the monitoring system regards the average as signal. Equation (5) is used to appraise the stability of data stream in long time.
In the following experiment, the deposition time of one layer is about 5 minutes. The Stability is requested to be smaller than 0.00125 in 20 minutes, and the S/N is requested to be larger than 220 for every transmittance data sourced from 100 acquiring signals.
A four-layers anti-reflection filter with of layer structure: Glass| H(13nm)/L(32 nm)/H(120nm)/L(85nm)|air was coated and monitored at the wavelength, 570nm. The termination of the first layer was at transmittance of 90.363%, as shown in Fig. 6(a), the value was very close to the desired transmittance (90.365%), as shown in Fig. 6(b). There is small error 0.002% and hard to see from runsheet. This tiny difference arose from the change in the refractive index during the coating process, as shown in the magnified part of the first layer in Fig. 7. It was easily observed in the real-time admittance diagram, denoted as B and b in Fig. 7.
The following three layers were terminated based on effective admittance with compensation[13,14]. To compensate for the error in the first layer, a series of thickness modifications were introduced, to make the final locus end at E in Fig. 7, the theoretical design point, by applying admittance real-time monitoring. Figure 7 displays the admittance diagram, which consists the simulated loci, thin-solid loci, and the experimental loci, bold-dotted loci. Figures 8 plots the optical performance obtained by using the conventional runsheet monitoring method and ARM.
This investigation presented a monitoring method that is based on the admittance diagram and showed the advantages of ARM. ARM enables the monitoring of the index error and is more sensitive than the conventional runsheet method. Moreover, the clear visual information in the admittance diagram is a powerful tool for determining the most appropriate thickness of the next layer to compensate error. The compensation effect of an antireflection coating is better than that of the conventional method was demonstrated.
The authors thank the National Science Council of Taiwan, for financially supporting this research under Contract No. NSC95-2221-E-008-115-MY3. and NSC94-2622-E-008-017.
References and links
3. C. J. Van der Laan, “Optical monitoring of nonquarterwave stacks,” Appl. Opt. 25, 759 (1986). [CrossRef]
6. C. C. Lee, K. Wu, C. C. Kuo, and S. H. Chen, “Improvement of the optical coating process by cutting layers with sensitive monitoring wavelengths,” Opt. Exp. 13, 4854–4861 (2006). [CrossRef]
7. C. Zhang, Y. Wang, and W. Lu, “Single-wavelength monitoring method for optical thin-film coating,” Opt. Eng. 43, 1439–1444 (2004). [CrossRef]
9. H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin film monitoring systems,” Opt. Acta 24, 907–930 (1977). [CrossRef]
10. J. Lee and R. W. Collins, “Real-time characterization of film growth on transparent substrates by rotatingcompensator multichannel ellipsometry,” Appl. Opt. 37, 4230–4238 (1998). [CrossRef]
11. S. Dligatch, R. Netterfield, and B. Martin, “Application of in-situ ellipsometry to the fabrication of multilayered coatings with sub-nanometre accuracy,” Thin Solid Films 455–456, 376–379 (2004). [CrossRef]
12. C. C. Lee, K. Wu, S. H. Chen, and S. J. Ma, “Optical monitoring and real time admittance loci calculation through polarization interferometer,” Opt. Exp. 15, 17536–17541 (2007). [CrossRef]
13. Y. J. Chen, “Optical monitoring of thin-film through admittance diagram,” Master Thesis of the National Central University, Taiwan (2004).
14. B. J. Chun and C. K. Hwangbo, “Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance,” Opt. Exp. 14, 2473–2480 (2006). [CrossRef]