Design and Preparation of a 6-Channel Fan-Shaped Integrated Narrow-Band Filter in the Mid-Infrared Band

Abstract

A six-channel fan-shaped integrated narrow-band filter on a silicon substrate was designed on the basis of the Fabray–Perot (FP) theory and was fabricated using e-beam thermal evaporation. The central wavelength was modulated by modifying the FP cavity thickness using the combination mask method. Germanium and zinc sulfide were selected as the high and low refractive index film materials, respectively. Its average peak transmission reached 83.3%, the cut-off transmittance was less than 1%, and the full width at half maximum (FWHM) changed from 55 and 94 nm, and the central wavelength positioning accuracy error was less than 0.35%. Furthermore, transmittance was also calculated inversely, using the thickness of each layer of films, in order to deduce the reason of the decrease in peak transmittance. Thickness deviation of each layer and interface scattering contributed to the decrease of peak transmittance. Compared with the same type of products in the market, our filter showed better properties than that of some published and commercial filter.

1. Introduction

Integrating many spectral channels on one optic system is generally called multispectral technology [1,2]. It is an important method to acquire spectral information and has been used widely in scientific experiments, biomedical, agricultural production, remote sensing and defense [3,4,5,6]. Multispectral imaging systems are evolving toward miniaturization, light weight, and higher integration, especially in special applications such as airborne and spaceborne platforms [7,8]. Herein, bandpass filters play a key role in multispectral imaging system. Compared to a single-channel bandpass, multi-channel infrared integrated filters have enabled the system to have a small size and simplified structure, and be lightweight [9].

Much work has been made to develop a single-channel bandpass filter, so most of these filters working in visible and near infrared could be bought easily in the market [10,11,12,13]. The 3–5 μm area is an important window in the infrared band, and it has important application significance in the military [14,15]. In this band, however, less work has been made to fabricate multi-channel narrow-band filter on a whole substrate.

Usually, the Fabray–Perot (FP) theory is used to design multi-channel infrared integrated filter on a single substrate where a multi-channel could be realized by changing the thickness or refractive index of the spacer layer by using complex processes of etching [16,17], photolithography [18], etc. Alternately, nanocavity injected with varying refractive index liquid materials have been proved to modify the optic thickness of a space layer and then obtain a multi-channel [19]. Some people prepared a linear variable filter in using the dual ion beam sputtering method where the thickness of space layer could be linearly changed by adjusting the deposition rate [20]. In the published work, the peak transmittance (T_max) ranged from 30% to 65% [21,22,23], and even that of single-channel could only reach to 70% [24]. Therefore, it is necessary to develop multi-channel infrared integrated filters on a single substrate with a high T_max.

In this work, we proposed to adjust the optical thickness of a spacer layer for developing a high-transmission 6-channel fan-shaped integrated narrow-band filter on a single substrate based on the FP interferometer theory. Here, the spacer layer was modified by a fan-shaped hard mask ensuring the position accuracy of the central wavelength and a high transmittance; error analyses were also included. In the end, compared to the same type of filter indicators on the market, it showed a big advantage.

2. Basic Principle and Film Design

The FP interferometer was composed of a spacer in the middle and two parallel plates outside. The inner surfaces of the plate were coated with the same high-reflectivity film and its reflectivity determined the peak transmittance. The central transmittance wavelength could be selected with a changing thickness of the spacer layer. In an FP narrow-band filter layer system, the plates and spacer could all be substituted by high reflective films and dielectric layers, respectively; its structure is shown in Figure 1.

Transmittance of central wavelength was as following [25]:

$$T=T_0/\left(1+F{\sin }^2\mathsf{\theta }\right)$$

(1)

in Equation (1),

$$T_0=T_1{T}_2/{\left(1-\sqrt{R_1{R}_2}\right)}^2$$

(2)

$$F=4\sqrt{R_1{R}_2}/{\left(1-\sqrt{R_1{R}_2}\right)}^2$$

(3)

$$\mathsf{\theta }=\left({\mathsf{\phi }}_1+{\mathsf{\phi }}_2-2\mathsf{\delta }\right)/2$$

(4)

where R₁ and R₂, T₁ and T₂ are the reflectance and transmittance of the films stack, respectively; φ₁ and φ₂ are the reflective phases of the films stack; δ equal to 2πndcosθ/λ, which is the phase thickness of the spacer layer; n is the refractive index of a single layer film; d is the physical thickness of a single layer film and λ is the reference wavelength. R₁ and R₂, T₁ and T₂ are all functions of n, d, and λ [25]. Here, we only considered the case of normal incidence of light. The λ₀ of the maximum transmittance was determined by Equations (5) and (6).

$${\mathsf{\theta }}_0=\left({\mathsf{\phi }}_1+{\mathsf{\phi }}_2-\frac{4\mathsf{\pi }}{\mathsf{\lambda }}nd\right)/2=-k\mathsf{\pi }$$

(5)

$${\mathsf{\lambda }}_0=\frac{2nd}{\left[k+\frac{\left({\mathsf{\phi }}_1+{\mathsf{\phi }}_2\right)}{2\mathsf{\pi }}\right]}=\frac{2nd}{m}$$

(6)

where k is a natural number, m is the order of interference equal to k + (φ₁ + φ₂)/(2π).

According to the principle mentioned above, six-channel filters working in a wavelength range of 3.5–4.6 μm were designed with reference wavelength of 4 μm, by optimizing the basic film layer structure of G|HLHL aH LHLH|A. Herein, A and G represents air and silicon substrate with indices of 1 and 3.5, respectively. H is Ge materials with a refractive index of 4. L is ZnS materials with a refractive index of 2.17. Their optic thickness are all λ/4. Ge used to be a spacer layer and the coefficient of a was set to modify the thickness of the spacer. Moreover, a suitable matching layer of ZnS was prepared near the substrate to get a high transmittance.

Design films based on the FP theory, the basic layer system, was determined and shown as follows:

G|0.9364L1.087H0.9692L0.9924H0.944L aH 0.6678L1.4277H0.8455L0.9546H|A

The interval between the adjacent center wavelengths was designed to be 150 nm apart, and the corresponding physical thickness difference of the spacer layer was 60 nm. The spectra are shown in Figure 2.

The peak transmittance of each channel could reach 95% or more, and the cutoff transmittance was less than 1%, the full width at half maximum (FWHM) was between 47 and 55 nm. A linear relation between peak wavelength and spacer layer thickness was determined and shown in the inset picture of Figure 1, which obeyed Equation (6).

3. Experiments

The structure of the 6-channels narrow-band filter is shown in Figure 3. Each channel occupied a sector angle of 60° with a center wavelength from 3.675 to 4.425 μm. The three hard masks shown in Figure 4 were designed to realize the 6 channels. Substrate was Si wafer purchased from Zhejiang Lijing Optoelectronics (Hangzhou, China), with a thickness of 0.4 mm and a diameter of 50.8 mm.

First, low reflection films were deposited on silicon substrates and then a 900-nm Ge-film spacer layer was added. Next, two channels, shown in Figure 5c, could be obtained by depositing 180 nm of Ge film with a mask (Figure 4a), and then two 60-nm Ge-film layers were prepared under No. 2 mask and No. 3 mask, respectively. After this, we could get 4 and 6 channels, as shown in Figure 5d,e, respectively. Last, an up-reflective film was prepared, as shown in Figure 5f.

Generally, plating a low refractive index film on a high refractive index substrate is the effective road to increase the transmittance. The ideal single layer antireflection film has an optical thickness of λ/4, and its refractive index needs to satisfy $n_1^2=n_0\times n_2$ [25]. Where, $n_0$ is the refractive index of the incident medium, $n_1$ is the refractive index of the film and $n_2$ is the refractive index of the substrate. The refractive index of Y₂O₃ almost satisfies the above equation, so this film with a λ/4 thickness was deposited on the back surface of the Si substrate. The deposition parameters are shown in

Table 1. Material deposition parameters.

Material	Base Pressure Vacuum (Pa)	Temperature (°C)	Evaporation Rate (nm/s)
Ge	1.3 × 10−3	120	0.3
ZnS	3 × 10−3	105	0.4
Y2O3	2 × 10−3	250	0.4

. The deposition rate and thickness were all controlled by using the quartz crystal film thickness controller manufactured by the Shanghai Moringtech Company (Shanghai, China). The gold-plated crystal oscillator was purchased from JJK companies (Albuquerque, NM, USA).

4. Results Discussion and Comparison

Transmission spectra of these samples were all measured by using a vacuum infrared Fourier spectrometer with a type of VERTEX 70V manufactured by BRUKER (Billerica, MA, USA). Its basic measurement optic structure diagram and sample holder are shown in Figure 6a,b, respectively. During measurement, spectral resolution could reach to 2 cm⁻¹, when using an MIR source and each channel was scanned 16 times, to reduce the error. Peak wavelength was determined to a wavelength with maximum spectral transmittance. In order to eliminate the influence of water vapor and other impurities in the air, the measurements were all carried out in a vacuum environment with a pressure less than 0.2 mbar. Incident light with an incident angle near zero and a beam diameter of 2 mm was used to carry out transmittance measurement. The sample and transmittance spectra are shown in Figure 6c,d, respectively.

The channel information is shown in

Table 2. The 6-channel information.

Channel	T1	T2	T3	T4	T5	T6
Peak position (nm)	3670	3817	3962	4114	4260	4410
Transmittance (%)	76.5	82.5	85.7	84.8	86.7	84.3
FWHM (nm)	55.98	55.64	60.27	69.3	79.64	93.53

. The peak wavelength was located in the range of 3.5–4.6 μm, and the peak transmittance varied from 76.5% to 86%. The average FWHM of the six channels was about 50 nm.

The test results showed that the peak transmittance was slightly lower than the design value. Thus, an SEM cross-section of the first channel filter was tested; shown in Figure 7a, and the space layer thickness of channel 2–6 are also show in Figure 7b–f. Details of the thickness difference of each layer are included in

Table 3. Theoretical thickness and test thickness difference table.

Film Number	Design Thickness (nm)	Test Thickness (nm)	Deviation (nm)
1	432.04	427	−5.04
2	271.75	278	−6.25
3	447.15	437	10.15
4	248.11	248	0.11
5	435.54	427	8.54
6	900	893	7
	960	948	12
	1020	1010	10
	1080	1070	10
	1140	1120	20
	1200	1180	20
7	308.11	466	−157.89
8	356	218	138
9	390.06	397	−6.94
10	238.65	238	0.65

.

According to the results of the tested thickness, the calculated transmittance spectrum of the six channels was acquired; as shown in Figure 8a. The calculated curve T_max was 14% lower than that of the design, and 5% more than that of test. The peak wavelength position of measurement were determined to be a linear relation, similar to that of the design from Figure 8b. The maximum position difference was about 10 nm and the corresponding relative error was less than 0.35%. Furthermore, we found that the thickness error of layer 7 and 8 showed a giant deviation, as compared to the theory. Therefore, we plotted the transmittance curves with the tested and theoretical thickness of layer 7 and 8, respectively, as shown in Figure 8c,d. It can be observed from Figure 8c that the tested T_max dropped to 82% with a thickness deviation of 138 nm, but the peak wavelength was maintained here. However, as seen in Figure 8d, the decrease of T_max was only 3% with a 157 nm thickness deviation, but the displacement of the peak wavelength could be up to 60 nm. Based on the analysis above, it was known that the film thickness deviation was the main cause of the decrease of T_max and the error of positioning, and each layer played a different role in peak transmittance and wavelength.

Film scatter also caused a decrease in transmittance, and was usually divided into in-body scattering and surface scattering [26,27]. In-body scattering was due to the difference in refractive index caused by the columnar structure (circle 2) and gap (circle 1) of the evaporated film, as shown in Figure 9.

Table 4. Optical properties comparison table.

Company Name	Peak Wavelength (nm)	Base Material	Filter Channel Characteristics	Positioning Accuracy (nm)	Peak Transmittance
Spectrogon	3700	Silicon	Single-channel	±20	75%
	3860	Sapphire	Single-channel	±20	60%
	4120	Sapphire	Single-channel	±20	70%
	4270	Sapphire	Single-channel	±25	70%
	4275	Sapphire	Single-channel	±15	70%
	4515	Sapphire	Single-channel	±20	70%
HB-Optical	2100	–	Single-channel	±10	75%
	2200	–	Single-channel	±10	75%
Alluxa	1064	Silicon	Single-channel	–	85%
In this work	3675	Silicon	6 channels integration	±10	76.5%
	3825			±10	82.5%
	3975			±10	85.7%
	4125			±10	84.8%
	4275			±10	86%
	4425			±10	84.3%

shows a comparison of the commercial products [28,29,30] and our filter. Most of the products were single-channel narrow-band filters, and the peak position deviation was between ±15 and ±20 nm. However, the peak position deviation in this work was between ±5 and ±15 nm, and the peak position error (Δλ/λ₀, Δλ, and λ₀ were the positioning accuracy and peak wavelength, respectively) was controlled within 0.13%–0.35%, which were far less than the same type of products in the market. In this work, the average peak transmittance could go up to 83%, which was greater than the others.

5. Conclusions

In our work, a 6-channel narrow-band filter with higher optical properties was developed on the basis of the FP theory, using three hard masks, to modify spacer thickness. The average peak transmittance was more than 83%, the cutoff transmittance was less than 1%, peak positioning accuracy error was less than 0.35% and a passband half-width varying from 55 to 94 nm, were observed. These properties are better than that of a commercial filter. In the test results section, a single factor analysis showed that the deviation of Ge and ZnS film thickness was the main reason for the decrease in T_max and the location error, respectively. The combination of the two factors would greatly reduce the peak transmittance and the location accuracy of the central wavelength.