Gain Coefficient Process Dependency of Focusing and Leveling Sensor

Fig. 3. Change of gain coefficient with film thickness. (a) First-order gain coefficient; (b) second-order gain coefficient; (c) third-order gain coefficient; (d) fourth-order gain coefficient; (e) fifth-order gain coefficient

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Fig. 4. Theoretically simulated results of measurement error varying with film thickness. (a) Using standard bare silicon wafers for calibrating; (b) using silicon wafer with specific process film on surface for calibrating

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Fig. 5. Physical picture of silicon wafer coated with SiO₂ film

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Fig. 6. Comparison of experimental and simulation results. (a) Variation of measurement error with film thickness; (b) variation of first-order gain coefficient with film thickness

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Table 1. Silicon substrate, refractive index, and Cauchy coefficient of photoresist in simulation model
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Table 1. Silicon substrate, refractive index, and Cauchy coefficient of photoresist in simulation model
Material Refractive index at 800 nm Cauchy coefficient
N₁ N₂ /μm^-2 N₃ /μm^-4
PAR870 1.46 1.45815 0.015861 0.000550
PI6133 1.52 1.49930 0.007264 -0.000210
TAI7092 1.50 1.49760 0.010078 0.000775
SiO₂ 1.47 - - -
Si 3.68 - - -

Table 2. Measurement error caused by change of each gain coefficient
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Table 2. Measurement error caused by change of each gain coefficient
Coefficient Initial value Change value Measurementerror /nm
α₁ 4.0014 0.1800 62.8
α₂ -0.0013 0.0014 1.8
α₃ 1.6321 0.2000 5.3
α₄ 0.0223 0.0300 1.8
α₅ 2.2373 0.6500 1.8

Table 3. Gain coefficient of each order for SiO₂ film thicknesses of 0, 250, and 690 nm
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Table 3. Gain coefficient of each order for SiO₂ film thicknesses of 0, 250, and 690 nm
SiO₂ film thickness /nm Coefficient
α₁ α₂ α₃ α₄ α₅
0 4.0014 -0.0013 1.6321 0.0223 2.2373
250 4.1081 -0.0018 1.7560 0.0335 2.6501
690 4.0647 -0.0017 1.7057 0.0312 2.4659

Table 4. Maximum measurement error and first-order gain coefficient for different SiO₂ film thickness

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Table 4. Maximum measurement error and first-order gain coefficient for different SiO₂ film thickness

Experimental No.	SiO₂ thickness /nm	α₁	Measurement error 1at 1.25 μm /nm	Measurement error 2at 1.25 μm /nm
1	49.2	4.0109	22.9	8.7
2	100.5	3.9709	2.8	-6.6
3	150.3	3.9875	10.9	0.2
4	201.2	4.1058	48.6	-7.1
5	253.8	4.1200	55.9	-11.3
6	305.8	4.0138	23.3	-1.1
7	357.7	3.9712	11.6	0.5
8	406.7	3.9607	7.7	12.6
9	455.6	3.9485	0.7	-2.7
10	502.8	3.9432	14.2	15.3
11	549.3	3.9614	-2.2	-1.4
12	592.3	3.9918	18.7	-2.7
13	651.5	4.0274	31.2	6.6
14	695.4	4.0618	36.6	-4.1
15	757.8	4.0471	33.3	0.6
16	807.6	3.9684	24.3	6.0

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Shengsheng Sun, dan Wang, Mingcheng Zong. Gain Coefficient Process Dependency of Focusing and Leveling Sensor[J]. Acta Optica Sinica, 2022, 42(4): 0412002

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Aug. 9, 2021

Accepted: Aug. 31, 2021

Published Online: Jan. 29, 2022

The Author Email: Sun Shengsheng (sunshengsheng@ime.ac.cn), Zong Mingcheng (zongmingcheng@ime.ac.cn)

DOI:10.3788/AOS202242.0412002

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Silicon substrate, refractive index, and Cauchy coefficient of photoresist in simulation model

Table 1. Silicon substrate, refractive index, and Cauchy coefficient of photoresist in simulation model

Table 2. Measurement error caused by change of each gain coefficient

Table 2. Measurement error caused by change of each gain coefficient

Table 3. Gain coefficient of each order for SiO2 film thicknesses of 0, 250, and 690 nm

Table 3. Gain coefficient of each order for SiO2 film thicknesses of 0, 250, and 690 nm

Table 4. Maximum measurement error and first-order gain coefficient for different SiO2 film thickness

Table 4. Maximum measurement error and first-order gain coefficient for different SiO2 film thickness

Table 3. Gain coefficient of each order for SiO₂ film thicknesses of 0, 250, and 690 nm

Table 3. Gain coefficient of each order for SiO₂ film thicknesses of 0, 250, and 690 nm

Table 4. Maximum measurement error and first-order gain coefficient for different SiO₂ film thickness

Table 4. Maximum measurement error and first-order gain coefficient for different SiO₂ film thickness