1. Introduction

The successful manufacture of a complex optical multilayer coating can be difficult at times because the main problem is how to control the layer thicknesses accurately [1-2]. There exists a great variety of different monitoring techniques such as quartz crystal monitoring and optical monitoring. Quartz crystal monitoring is used widely in the deposition of metal films and filters, but it can not offer the real time deposition error compensation in the remaining layers. Optical monitoring techniques, which are extensively applied in optical multilayer deposition system, can be subdivided into monochromatic monitoring [3-11] and wideband monitoring techniques [12, 13].

Among the optical monitoring techniques, turning point monitoring (TPM) method, in which the deposition layer stops at an extremum of the optical signal, is most commonly used for single wavelength monitoring of quarter-wave optical coatings [2]. Furthermore, TPM method can be modified to monitor the deposition of nonquarter-wave films by changing the monitoring wavelength, so that each layer terminates at the turning point [4]. The advantage of TPM method is that it has a strong error self-compensation mechanism in production of various narrow bandpass filters [5]. However, the precision for single-layer thickness monitored by TPM is low. An alternative method, which is inherently more accurate and called the level monitoring method [6], involves the termination of the layer at a point remote from a turning value where the signal changes much more rapidly. Previously, there were many reports on the improvement of optical monitoring techniques [7-11]. Tikhonravov et al. chose a sequence of monitoring wavelengths for monochromatic monitoring to reduce the effect of accumulation of thickness errors [7]. Lee et al. enhanced the monitoring precision of optical coating with the most sensitive monitoring wavelengths [9].

In this paper, a new method based on the use of dual wavelengths monitoring (DWM) is proposed. Using the DWM method, the layer thickness error can be compensated and the sensitivity at every terminating point is high. There is no need to change the monitoring wavelength for every layer. The advantage of this method for the quarter-wave and nonquarter-wave coatings is demonstrated by theoretical simulation and experimental results.

2. Method

In the manufacture of optical coatings, there are many sources of errors, including variation of substrate temperature, noise of the system, thickness errors of layers and refractive index errors of materials [4, 14]. In order to gain the simulated results accord with the experimental results, the refractive indices at different wavelengths for Zinc Sulfide (ZnS) film deposited by electron beam evaporation and Magnesium Fluoride (MgF₂) film deposited by thermal evaporation were calculated from all normal incidence transmittance data [15]. In the following simulation and experiment, refractive index is regarded as a constant during deposition.

Assuming that the dielectric layers in an optical multilayer structure are isotropic and nonabsorbing, and the film growth is steady. The characteristic matrix at normal incidence condition is given by [8]

where θ and n(λ) are the phase thickness and refractive index of the current layer respectively. α and β are the real and imaginary parts of the equivalent admittance at the beginning point of the current layer, respectively. λ is the monitoring wavelength. Additionally, n(λ) at different wavelengths can be fitted by Cauchy function. The Cauchy function is

The parameters of ZnS film are k ₁=2.212, k ₂=7.648×10⁴ nm², and k ₃=6.6×10⁹ nm⁴. The parameters for MgF₂ film are k ₁=1.354, k ₂=6.165×10³ nm² and k ₃=-3.22×10⁸ nm⁴.

The admittance for the considered layer at the monitoring wavelength can be written as below:

where ${\alpha }^{\prime }=\frac{\alpha }{n\left(\lambda \right)},{\beta }^{\prime }=\frac{\beta }{n\left(\lambda \right)}$ . The reflectivity of the film can be obtained by

For a nonabsorbing material, the center of the admittance circle is always located on the real admittance axis. The admittance can be calculated using the following formula [9]:

The sensitivity, which is the variation of reflectivity as the change of the optical thickness, can be described as follows:

 

Fig. 1. Sensitivity as a function of monitor wavelength on terminating point of the film with structure S/HLHLHLH/A: (a) high index layer “H”, (b) low index layer “L”.

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The film with structure S/HLHLHLH/A is used as an example. n(λ) of the substrate is 1.52 and the reference wavelength is 600 nm. n(λ) of H (ZnS) and L (MgF₂) materials is given by Eq. (2). The sensitivity of each layer at different wavelengths was calculated by Eq. (6) and the results are shown in Fig. 1. As indicated in Fig. 1, the maximum sensitivity for each layer locates at different wavelengths, and the sensitivity at the reference wavelength (600 nm) is zero. Comparing Fig. 1(a) with Fig. 1(b), it is found that the sensitivity of H layer is higher than that of L layer.

The layer thickness error can not be avoided during deposition process even if having a steady deposition environment and precise monitor system. In the DWM method, the thickness error will be compensated as in TPM method. Two chosen monitoring wavelengths should be shorter than the reference wavelength, so that the deposition process will go through at least one turning point, and each terminating point will stop at the quite sensitive position. We select 420 nm, where the sensitivity is high (as shown in Fig. 1), as the monitoring wavelength of the first, second, fifth and the sixth layers, and use 480 nm wavelength to monitor the other layers. The starting point, turning point and terminating point can be calculated by Eq. (4). Supposing that the first layer, which monitor wavelength is 420 nm, terminates too late and the transmittance at the terminating point changes from 0.778 to 0.798, so the physics thickness calculated by Eq. (4) varies from 65.6 to 67.3 nm correspondingly. In order to compensate the thickness error, the admittance loci pattern of 600 nm can be analyzed as shown in Fig. 2. In this case, the admittance locus of the first layer arrives at A2, rather than A1 due to the overshoot thickness error. This leads the second layer to start from A2 and must stop at the turning point B1 to insure that the coating error can be compensated and do not affect the following layers. As show in Fig. 2, the imaginary part of admittance for the first two layers must be zero at point B1. Therefore, the physics thickness of second layer will be changed from 109.6 to 108.2 nm as the calculation from Eq. (4). The starting point, termination point and turning point of the second layer with 420 nm monitor wavelength, can be obtained by Eq. (4). Repeat above steps until the coating is completed.

For nonquarter-wave multilayer coating, the layer thickness error also can be compensated by the DWM method. As discussed above, assuming the imaginary part of admittance for current layer to be zero, we can get the reference wavelength of current layer. So the compensated thickness of current layer can be obtained by Eq. (4) from this reference wavelength. Then the starting, extremum and terminating points with monitoring wavelength can be calculated by Eq. (4).

 

Fig. 2. Admittance locus of 600 nm of the first two layers.

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Fig. 3. Spectrum of the film with structure S/HLHLHLH/A monitored by different methods with a 0.5% standard deviation error.

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3. Simulation

Computer simulation allows us to observe, step by step, the information of film assemblies [16]. Simulation techniques, therefore, are particularly suited for the evaluation of control techniques. We can apply them to a simple quarter-wave S/HLHLHLH/A multilayer coating, and compare the DWM method with the other monitoring method. The refractive indices for substrate, ZnS and MgF₂ are 1.52, 2.288 and 1.368 respectively, and the reference wavelength is 600 nm. Suppose that each layer has a 0.5% standard deviation error in transmittance. As an example, the first, second and the sixth layers have negative deviations, the others have positive deviations. The simulated spectra of the films were calculated by a software for design of optical coatings. Moreover, the thickness error compensation introduced in section 2 could be taken into account. The spectrum of the film monitored by the DWM, level monitoring and TPM methods is shown in Fig. 3.

As indicated in Fig. 3, the spectral performance monitored by the DWM method, where we select 420 nm and 480 nm as the two monitoring wavelengths, is much better than those monitored by the other methods. Since the transmittance varies slowly with respect to thickness near a turning point, a 0.5% error in transmittance may cause a relatively large thickness error. The spectrum, therefore, monitored by TPM method deviates greatly from the theoretical design. For the level monitoring method, we select 420 nm as monitor wavelength. As can be seen from Fig. 1(b), the termination point of the fourth layer is located at turning point, where the 0.5% error of transmittance induces a 12.8 nm optical thickness error, which will seriously affect the spectral performance.

4. Experimental results

4.1 Quarter-wave multilayer coating

The experimental example is the film with structure S/HLHLHLH/A. ZnS and MgF₂ layers were deposited by electron beam evaporation and thermal evaporation, respectively. For the DWM method, experimental parameters such as the monitoring wavelength, starting point, extremum point and terminating point are presented in Table 1. The measured transmittances of the films were measured by a Perkin-Elmer lambda-950 spectrophotometer.

The theoretical (T_theo) and measured (T_meas) transmittances of the films are shown in Fig. 4. Comparing Fig. 4(a) with Fig. 4(b), it is obvious that the spectral performance of the film monitored by the DWM method is better than that monitored by TPM method. Additionally, we use a merit function to evaluate the spectral characteristic of the films. The merit function (f) is defined as:

Based on the data in Fig. 4, the value of f can be calculated by Eq. (7). The results show that f of the DWM method is 0.394, which is better than that (0.923) of TPM method.

Table 1. Experimental parameters of the structure S/HLHLHLH/A.

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4.2 Nonquarter-wave multilayer coating

The DWM method not only can be used in quarter-wave coating, but also can be used in nonquarter-wave coating. We take a 13-layer longwave-pass filter as an example. The structure design can be specified by the formulas below, and the reference wavelength is 600 nm.

S/0.938H 0.741L 0.98H 1.051L 1.01H 1.044L 0.957H 0.993L 0.97H 1.057L 1.14H 0.896L 0.597H

Two wavelengths of 420 nm and 494 nm were chosen as the two monitoring wavelengths. The sensitivity of each layer was calculated by Eq. (6). The starting point, extremum point and terminating point were obtained by Eq. (4). Theoretical and experimental spectra of the filter are shown in Fig. 5. As presented in Fig. 5, the performance achieved by the DWM method is much better than that obtained by TPM method. For the DWM method, transmittance is lower than 1.5% in the wavelength from 550 to 650 nm, and it is larger than 95% in the wavelength between 760 and 1000 nm. This result clearly confirms that the DWM method is superior to TPM method in the optical coating monitoring.

 

Fig. 4. Theoretical and measured transmittances of the film with structure S/HLHLHLH/A monitored by (a) the DWM method and (b) TPM method.

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Fig. 5. Spectrum of a longwave-pass filter monitored by the DWM method and TPM method.

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5. Conclusion

A new monitoring method based on the dual wavelengths monitoring has been proposed. Two appropriate wavelengths, which are chosen according to the sensitivity of each layer, are used to monitor the deposition process, so that each terminating point has a high sensitivity. The advantages of the DWM method are that the layer thickness error can be compensated, and the monitoring wavelengths need not be changed for each layer. The theoretical analyses and experimental results have demonstrated the advantages of the DWM method. For both the quarter-wave multilayer and the nonquarter-wave multilayer optical coatings, spectral performance of the film monitored by the DWM method is better than that of the film monitored by TPM method. It is believed that the DWM method can be also useful to manufacture various other types of optical coatings.