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Multipoint Cauchy method (MCM) is presented to investigate the refractive index and dispersion for each of Ge20Sb15Se65 and Ge28Sb12Se60 chalcogenide thin films at any wavelength in the transmission spectrum based on the regional approach method and Cauchy fitting. We theoretically calculate and compare the refractive index and dispersion curves obtained by using six different models. The results show that the most accurate results are obtained by the MCM. Two Ge—Sb—Se films are prepared by magnetron sputtering experimentally, and transmission spectrum curves are measured by Fourier infrared spectrometer, the noise is removed by segmental filtering and then the refractive index, dispersion, absorption coefficient, and optical band gap of the two films ina range of 500–2500 nm are obtained by the MCM. The results show that the refractive index of Ge28Sb12Se60 film is larger than that of Ge20Sb15Se65 film, which is caused by the higher polarizability and density of the former. The refractive indexes of both films decrease with wavelength increasing, so the long waves travel faster than short waves in the two films. The optical band gap of Ge28Sb12Se60 film (1.675 eV) is smaller than that of Ge20Sb15Se65 film (1.729 eV), and the corresponding wavelengths of the two are 740.3 nm and 717.2 nm. Finally, the microstructures of the two films are characterized by Raman spectra, and the reasons why the two chalcogenide films have different optical properties are explained from the bonding properties between the atoms.
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Keywords:
- infrared chalcogenide film /
- Cauchy model /
- optical properties /
- microstructure
[1] Rode A V, Zakery A, Samoc M 2002 Appl. Surf. Sci. 197 481
[2] Yamada N, Ohno E, Akahira N 1987 Jpn. J. Appl. Phys. 26 61
[3] Afonso C N, Solis J, Catalina F 1992 Appl. Phys. Lett. 60 3123
Google Scholar
[4] Yang Z, Wilhelm A A, Lucas P 2010 J. Am. Ceram. Soc. 93 1941
[5] Hilfiker J N, Singh N, Tiwald T 2008 Thin Solid Films 516 7979
Google Scholar
[6] Alias M S, Dursun I, Saidaminov M I 2016 Opt. Express 24 16586
Google Scholar
[7] Rodenhausen K B, Schmidt D, Kasputis T 2012 Opt. Express 20 5419
Google Scholar
[8] Onodera H, Awai I, Ikenoue J 1983 Appl. Opt. 22 1194
Google Scholar
[9] Zhang G, Sasaki K 1988 Appl. Opt. 27 1358
Google Scholar
[10] Wang H 1994 Fiber Integr. Opt. 13 293
Google Scholar
[11] 顾晓明, 贾宏志, 王铿 2009 光学仪器 31 89
Google Scholar
Gu X M, Jia H Z, Wang K 2009 Optical Instruments 31 89
Google Scholar
[12] Aqili A K S, Maqsood A 2002 Appl. Opt. 41 218
Google Scholar
[13] Chambouleyron I, Martinez J M, Moretti A C 1997 Appl. Opt. 36 8238
Google Scholar
[14] 宗双飞, 沈祥, 徐铁峰, 陈昱, 王国祥, 陈芬, 李军, 林常规, 聂秋华 2013 62 096801
Google Scholar
Zong S F, Shen X, Xu T F, Chen Y, Wang G X, Chen F, Li J, Lin C G, Nie Q H 2013 Acta Phys. Sin. 62 096801
Google Scholar
[15] Verma K C, Sharma P, Negi N S 2008 Appl. Phys. B 93 859
Google Scholar
[16] Song S, Dua J, Arnold C B 2010 Opt. Express 18 5472
Google Scholar
[17] Sharma N, Sharda S, Sharma V 2012 Mater. Chem. Phys. 136 967
Google Scholar
[18] Yahia I S, Shapaan M, Ismail Y A M 2015 J. Alloys Compd. 636 317
Google Scholar
[19] Xiao C, Song B, Jin Y 2019 Opt. Laser Technol. 120 105708
Google Scholar
[20] Jin Y, Song B, Jia Z 2017 Opt. Express 25 440
Google Scholar
[21] Jin Y, Song B, Lin C 2017 Opt. Express 25 31273
Google Scholar
[22] 高静, 于峰, 葛廷武 2014 红外与激光工程 43 3368
Google Scholar
Gao J, Yu F, Ge Y W 2014 Infrared and Laser Engineering 43 3368
Google Scholar
[23] Pernick B J 1983 Appl. Opt. 22 1133
Google Scholar
[24] 王申浩, 陶宗明, 杨蕾, 张辉 2017 大学物理实验 30 58
Wang S H, Tao Z M, Yang L, Zhang H 2017 College Physics Experiment 30 58
[25] Tatian B 1984 Appl. Opt. 23 4477
Google Scholar
[26] Swanepoel R 1983 J. Phys. E: Sci. Instrum. 16 1214
Google Scholar
[27] Fu Y Z, Cheng G G, Wang Q 2012 Mater. Sci. Technol. 20 145
[28] 张巍, 陈昱, 付晶, 陈飞飞, 沈祥, 戴世勋, 林常规, 徐铁峰 2012 61 056801
Google Scholar
Zhang W, Chen Y, Fu J, Chen F F, Shen X, Dai S X, Lin C G, Xu T F 2012 Acta Phys. Sin. 61 056801
Google Scholar
[29] Afzal M Z, Krämer M, Bukhari S S 2013 International Workshop on Camera-Based Document Analysis and Recognition (Cham: Springer) pp139−149
[30] Chen J, Jönsson P, Tamura M 2004 Remote Sens. Environ. 91 332
Google Scholar
[31] Hoang T, Vangala R R 1996 U.S. Patent 5 6
[32] Wang S, Patenaude F, Inkol R 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings IEEE 3 III-III
[33] Wei W H, Wang R P, Shen X 2013 J. Phys. Chem. C 117 16571
Google Scholar
[34] Tauc J 1970 Mater. Res. Bull. 5 721
Google Scholar
[35] Jackson K, Briley A, Grossman S 1999 Phys. Rev. B 60 14985
Google Scholar
[36] Holubova J, Cernosek Z, Cernoskova E 2007 J. Optoelectron. Adv. Mater. 1 663
[37] Wang Y, Matsuda O, Inoue K 1998 J. Non-Cryst. Solids 232 702
[38] Bhosle S, Gunasekera K, Boolchand P 2012 Int. J. Appl. Glass Sci. 3 205
Google Scholar
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图 1 镀在透明二氧化硅玻璃衬底上的薄膜结构示意图
Figure 1. Schematic of the structure of a thin film coated on a transparent silica glass substrate.
图 2 在有限玻璃基板上的Si-H薄膜的透射率曲线
Figure 2. Transmittance curve of Si-H thin film on finite glass substrate.
图 3 六种不同模型得到的薄膜折射率和色散比较
Figure 3. Comparison of refractive index and dispersion of thin film obtained by six different models.
图 4 六种色散模型(包含多点柯西法)得到的折射率和色散与真实值差值随波长变化关系 (a)折射率差与波长的关系; (b)色散差与波长的关系
Figure 4. Relation between the refractive index and the dispersion obtained by six dispersion models (include MCM) and the true value as a function of wavelength: (a) Δn vs. wavelength; (b) ΔD vs. wavelength.
图 5 五种滤波方法去噪声比较 (a) Adjacent averaging方法; (b) Savitaky-Golay方法; (c) percentile filter方法; (d) FFT filter方法; (e)分段拟合法
Figure 5. Comparison of five filtering methods to reduce noise: (a) Adjacent averaging method; (b) Savitaky-Golay method; (c) percentile filter method; (d) FFT filter method; (e) piecewise fitting method.
图 6 利用改进的Swanepoel方法获得的具有上下切线包络的透射曲线 (a) Ge20Sb15Se65薄膜; (b) Ge28Sb12Se60薄膜
Figure 6. Transmission curve with upper and lower tangent envelopes obtained by using the improved Swanepoel method: (a) Ge20Sb15Se65 film; (b) Ge28Sb12Se60 film.
图 7 Ge-Sb-Se薄膜的折射率和色散 (a)折射率与波长的关系; (b) 色散与波长的关系
Figure 7. Refractive index and dispersion of Ge-Sb-Se films: (a) Refractive index vs. wavelength; (b) dispersion vs. wavelength.
图 8 Ge-Sb-Se薄膜的吸收特性 (a) 吸收系数与波长的关系; (b) 强吸收区域中吸收系数与光子能量乘积的平方根与光子能量之间的关系
Figure 8. Absorption characteristics of Ge-Sb-Se films: (a) Absorption coefficient vs. wavelength; (b) square root of the product of the absorption coefficient and photon energy vs. the photon energy in the strong absorption region.
图 9 Ge-Sb-Se薄膜的拉曼光谱
Figure 9. Raman spectrum of Ge-Sb-Se film.
表 1 六种折射率模型
Table 1. Six models of refractive index.
名称 模型 Cauchy $n = A + \dfrac{B}{{{\lambda ^2}}} + \dfrac{C}{{{\lambda ^4}}}$ 二阶归一化标准Sellmeier $n = \sqrt {1 + \dfrac{{A \cdot {\lambda ^2}}}{{{\lambda ^2} - B}} + \dfrac{{C \cdot {\lambda ^2}}}{{{\lambda ^2} - D}}} $ 三阶归一化标准Sellmeier $n = \sqrt {1 + \dfrac{{A \cdot {\lambda ^2}}}{{{\lambda ^2} - B}} + \dfrac{{C \cdot {\lambda ^2}}}{{{\lambda ^2} - D}} + \dfrac{{E \cdot {\lambda ^2}}}{{{\lambda ^2} - F}}} $ 二阶非标准形式的Sellmeier $n = \sqrt {A + \dfrac{{B \cdot {\lambda ^2}}}{{{\lambda ^2} - C}} + D \cdot {\lambda ^2}} $ Conrady $n = A + \dfrac{B}{\lambda } + \dfrac{C}{{{\lambda ^{3.5}}}}$ Herzberger $n = A + B \cdot {\lambda ^2} + C \cdot {\lambda ^2} + \dfrac{D}{{\left( {{\lambda ^2} - 0.028} \right)}} + \dfrac{E}{{{{\left( {{\lambda ^2} - 0.028} \right)}^2}}}$ 
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表 2 由图2中数据获得的λ, TM和Tm的值以及通过改进后的Swanepoel方法计算的n和d值
Table 2. Values of λ, TM, and Tm obtained in Fig. 2 and the values of n and d calculated by the improved Swanepoel method
λ TM Tm n d m0 m n0 d0 972.4 0.9202 0.5007 2.9173 6.001 6.0 2.9169 1000.0 911.2 0.9199 0.4904 2.9613 6.501 6.5 2.9611 1000.0 859.0 0.9193 0.4801 3.0066 1000.0 7.002 7.0 3.0062 1000.0 814.1 0.9183 0.4697 3.0527 1000.4 7.501 7.5 3.0526 1000.1 774.9 0.9165 0.4591 3.0996 1000.1 8.002 8.0 3.0993 1000.0 740.5 0.9134 0.4485 3.1471 999.5 8.502 8.5 3.1468 1000.0 710.0 0.9080 0.4376 3.1951 999.7 9.002 9.0 3.1947 1000.0 682.8 0.8984 0.4260 3.2435 999.4 9.502 9.5 3.2430 999.9 658.4 0.8818 0.4132 3.2921 1000.2 10.002 10.0 3.2917 1000.0 636.3 0.8530 0.3982 3.3410 999.3 10.503 10.5 3.3402 999.9 616.3 0.8050 0.3796 3.3898 999.6 11.003 11.0 3.3893 999.9 598.1 0.7252 0.3546 3.4335 1020.4 11.483 11.5 3.4387 1001.6 581.3 0.6127 0.3191 3.4878 1000.6 12.002 12.0 3.4874 1000.0 565.9 0.4595 0.2678 3.5368 981.9 12.502 12.5 3.5365 1000.0 551.7 0.2879 0.1965 3.5856 1001.6 13.001 13.0 3.5857 1000.1 注: $ \qquad \quad \overline d = 1000.2;{\sigma _1} = 7.58;\overline {{d_0}} = 1000.1;{\sigma _0} = 0.40$.
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表 A1 六种模型的系数
Table A1. Coefficients of six models.
A B C D E F Cauchy 2.6006 2.9900 × 105 2.4107 × 108 二阶归一化标准Sellmeier 6.0592 1.3837 × 105 0.5371 1.3837 × 105 三阶归一化标准Sellmeier 11.1212 6.4542 × 104 5.9297 6.4455 × 104 –11.3546 –4.9139 × 104 二阶非标准形式的Sellmeier –30.1052 36.8509 4.3322 × 104 –0.0079 Conrady 2.3534 502.8603 1.2718 × 109 Herzberger 4.3450 –3.1408 × 10–8 1.7525 × 10–12 3.0038 × 105 9.0228 × 1010
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表 A2 利用六种模型和多点柯西法得到的折射率与真实值的差
Table A2. Difference between refractive index obtained by using six models, MFM, and real value.
λ Δncauchy ΔnSel2 ΔnSel3 Δnsel2非 ΔnConrady ΔnHerzberger ΔnMCM 580 –0.0002 0.0018 –0.0005 –0.0003 –0.0007 –0.0050 –0.0001 600 –0.0003 –0.0107 –0.0007 –0.0005 –0.0014 0.0081 –0.0002 620 –0.0004 –0.0180 –0.0008 –0.0006 –0.0016 0.0162 –0.0002 640 –0.0004 –0.0216 –0.0007 –0.0006 –0.0015 0.0201 –0.0003 660 –0.0004 –0.0226 –0.0006 –0.0005 –0.0012 0.0207 –0.0003 680 –0.0004 –0.0218 –0.0005 –0.0005 –0.0008 0.0186 –0.0003 700 –0.0004 –0.0197 –0.0003 –0.0004 –0.0003 0.0146 –0.0003 720 –0.0004 –0.0167 –0.0002 –0.0003 0.0001 0.0091 –0.0003 740 –0.0004 –0.0131 –0.0001 –0.0003 0.0005 0.0028 –0.0003 760 –0.0004 –0.0090 0.0000 –0.0002 0.0008 –0.0038 –0.0003 780 –0.0004 –0.0047 0.0000 –0.0002 0.0010 –0.0103 –0.0003 800 –0.0004 –0.0002 0.0000 –0.0002 0.0011 –0.0160 –0.0003 820 –0.0004 0.0043 0.0000 –0.0002 0.0011 –0.0207 –0.0003 840 –0.0003 0.0089 0.0000 –0.0002 0.0009 –0.0238 –0.0003 860 –0.0003 0.0134 –0.0001 –0.0002 0.0007 –0.0249 –0.0003 880 –0.0003 0.0178 –0.0002 –0.0002 0.0004 –0.0236 –0.0003 900 –0.0003 0.0222 –0.0003 –0.0002 –0.0001 –0.0196 –0.0003 920 –0.0002 0.0264 –0.0004 –0.0003 –0.0006 –0.0123 –0.0003 940 –0.0002 0.0305 –0.0006 –0.0004 –0.0012 –0.0014 –0.0003 960 –0.0002 0.0345 –0.0007 –0.0004 –0.0019 0.0134 –0.0003 $\begin{aligned}{\text{注}}:\; & \Delta {n_{{\rm{Cauchy}}}} = 0.0003;\sigma {n_{{\rm{Cauchy}}}} = 0.0002;\Delta {n_{{\rm{Sel2}}}} = 0.0253;\sigma {n_{{\rm{Sel2}}}} = 0.0273;\\ &\Delta {n_{{\rm{Sel3}}}} = 0.0006;\sigma {n_{{\rm{Sel3}}}} = 0.0010;\Delta {n_{{\rm{Sel}}2{\simfont\text{非}}}} = 0.0005;\sigma {n_{{\rm{Sel}}2{\simfont\text{非}}}} = 0.0005;\\ & \Delta {n_{{\rm{Conrady}}}} = 0.0016;\sigma {n_{{\rm{Conrady}}}} = 0.0022;\Delta {n_{{\rm{Herzberger}}}} = 0.0226;\sigma {n_{{\rm{Herzberger}}}} = 0.0225;\\ & \Delta {n_{{\rm{MCM}}}} = 0.0002;\sigma {n_{{\rm{MCM}}}} = 0.0001 .\end{aligned}$
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表 3 多点柯西法获得的两种薄膜多个波长处的折射率
Table 3. Refractive index at multiple wavelengths of two thin films obtained by MCM.
波长/nm Ge20Sb15Se65薄膜 Ge28Sb12Se60薄膜 Texp TM m n Texp TM m n 600 0.2449 0.2682 8.7331 2.6902 0.0009 0.0253 13.3793 2.8670 620 0.3463 0.4036 8.0131 2.6530 0.0417 0.0726 12.7620 2.8259 640 0.4987 0.5496 7.4160 2.6208 0.1107 0.0957 12.2073 2.7902 660 0.4749 0.6845 6.9106 2.5929 0.2449 0.2519 11.7057 2.7592 680 0.7724 0.7891 6.4760 2.5685 0.2914 0.3957 11.2495 2.7320 700 0.6566 0.8552 6.0972 2.5472 0.5222 0.5266 11.0259 2.7081 750 0.9088 0.9096 5.7634 2.5041 0.7469 0.7853 10.1068 2.6597 800 0.6160 0.9219 5.4665 2.4720 0.6155 0.9123 9.3455 2.6233 900 0.6199 0.9321 4.9602 2.4285 0.8667 0.9681 8.1494 2.5735 1000 0.7666 0.9388 4.5433 2.4014 0.7547 0.9735 7.2448 2.5420 1100 0.8085 0.9429 4.1932 2.3835 0.6124 0.9773 6.5316 2.5210 1200 0.7580 0.9455 3.8945 2.3711 0.9678 0.9805 5.9523 2.5062 1300 0.6850 0.9472 3.6364 2.3622 0.6186 0.9813 5.4709 2.4955 1400 0.9418 0.9480 3.4109 2.3556 0.9556 0.9806 5.0638 2.4875 1500 0.7814 0.9482 3.2121 2.3506 0.7282 0.9801 4.7145 2.4813 1600 0.6521 0.9479 3.0356 2.3466 0.6430 0.9800 4.4112 2.4765 1700 0.7244 0.9474 2.8776 2.3435 0.8853 0.9800 4.1452 2.4726 1800 0.8914 0.9470 3.1213 2.3410 0.9383 0.9801 3.9099 2.4694 1900 0.9384 0.9470 2.9544 2.3389 0.7164 0.9801 3.7002 2.4668 2000 0.8249 0.9476 2.8046 2.3372 0.6282 0.9800 3.5121 2.4647 2100 0.7121 0.9491 2.6694 2.3358 0.6868 0.9800 3.2838 2.4628 2200 0.6614 0.9518 2.5468 2.3345 0.8411 0.9801 3.1325 2.4613 2300 0.6679 0.9559 2.4349 2.3335 0.9705 0.9804 2.9947 2.4599 2400 0.7188 0.9617 2.3326 2.3326 0.9441 0.9809 2.8686 2.4588
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表 4 Ge-Sb-Se薄膜拉曼光谱中对应的振动模式
Table 4. Vibration modes in the Raman spectrum of Ge-Sb-Se system.
拉曼峰位/cm–1 振动模式 160 Se2Sb-SbSe2结构中的Sb—Sb同极键的振动 170 Ge2Se6/2结构中的Ge—Ge同极键的伸缩振动 197 SbSe3/2三角锥结构中的Sb—Se键的E1模式振动 203 共顶角GeSe4/2四面体中的Ge—Se键的V1模式振动 215 共边GeSe4/2四面体中的Ge—Se键振动 235 Sen环结构中的Se—Se键振动 256 Sen链结构中的Se—Se键振动 270 Ge-GemSe4-m结构中的Ge—Ge同极键的振动 303 GeSe4四面体的F2型不对称振动
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[1] Rode A V, Zakery A, Samoc M 2002 Appl. Surf. Sci. 197 481
[2] Yamada N, Ohno E, Akahira N 1987 Jpn. J. Appl. Phys. 26 61
[3] Afonso C N, Solis J, Catalina F 1992 Appl. Phys. Lett. 60 3123
Google Scholar
[4] Yang Z, Wilhelm A A, Lucas P 2010 J. Am. Ceram. Soc. 93 1941
[5] Hilfiker J N, Singh N, Tiwald T 2008 Thin Solid Films 516 7979
Google Scholar
[6] Alias M S, Dursun I, Saidaminov M I 2016 Opt. Express 24 16586
Google Scholar
[7] Rodenhausen K B, Schmidt D, Kasputis T 2012 Opt. Express 20 5419
Google Scholar
[8] Onodera H, Awai I, Ikenoue J 1983 Appl. Opt. 22 1194
Google Scholar
[9] Zhang G, Sasaki K 1988 Appl. Opt. 27 1358
Google Scholar
[10] Wang H 1994 Fiber Integr. Opt. 13 293
Google Scholar
[11] 顾晓明, 贾宏志, 王铿 2009 光学仪器 31 89
Google Scholar
Gu X M, Jia H Z, Wang K 2009 Optical Instruments 31 89
Google Scholar
[12] Aqili A K S, Maqsood A 2002 Appl. Opt. 41 218
Google Scholar
[13] Chambouleyron I, Martinez J M, Moretti A C 1997 Appl. Opt. 36 8238
Google Scholar
[14] 宗双飞, 沈祥, 徐铁峰, 陈昱, 王国祥, 陈芬, 李军, 林常规, 聂秋华 2013 62 096801
Google Scholar
Zong S F, Shen X, Xu T F, Chen Y, Wang G X, Chen F, Li J, Lin C G, Nie Q H 2013 Acta Phys. Sin. 62 096801
Google Scholar
[15] Verma K C, Sharma P, Negi N S 2008 Appl. Phys. B 93 859
Google Scholar
[16] Song S, Dua J, Arnold C B 2010 Opt. Express 18 5472
Google Scholar
[17] Sharma N, Sharda S, Sharma V 2012 Mater. Chem. Phys. 136 967
Google Scholar
[18] Yahia I S, Shapaan M, Ismail Y A M 2015 J. Alloys Compd. 636 317
Google Scholar
[19] Xiao C, Song B, Jin Y 2019 Opt. Laser Technol. 120 105708
Google Scholar
[20] Jin Y, Song B, Jia Z 2017 Opt. Express 25 440
Google Scholar
[21] Jin Y, Song B, Lin C 2017 Opt. Express 25 31273
Google Scholar
[22] 高静, 于峰, 葛廷武 2014 红外与激光工程 43 3368
Google Scholar
Gao J, Yu F, Ge Y W 2014 Infrared and Laser Engineering 43 3368
Google Scholar
[23] Pernick B J 1983 Appl. Opt. 22 1133
Google Scholar
[24] 王申浩, 陶宗明, 杨蕾, 张辉 2017 大学物理实验 30 58
Wang S H, Tao Z M, Yang L, Zhang H 2017 College Physics Experiment 30 58
[25] Tatian B 1984 Appl. Opt. 23 4477
Google Scholar
[26] Swanepoel R 1983 J. Phys. E: Sci. Instrum. 16 1214
Google Scholar
[27] Fu Y Z, Cheng G G, Wang Q 2012 Mater. Sci. Technol. 20 145
[28] 张巍, 陈昱, 付晶, 陈飞飞, 沈祥, 戴世勋, 林常规, 徐铁峰 2012 61 056801
Google Scholar
Zhang W, Chen Y, Fu J, Chen F F, Shen X, Dai S X, Lin C G, Xu T F 2012 Acta Phys. Sin. 61 056801
Google Scholar
[29] Afzal M Z, Krämer M, Bukhari S S 2013 International Workshop on Camera-Based Document Analysis and Recognition (Cham: Springer) pp139−149
[30] Chen J, Jönsson P, Tamura M 2004 Remote Sens. Environ. 91 332
Google Scholar
[31] Hoang T, Vangala R R 1996 U.S. Patent 5 6
[32] Wang S, Patenaude F, Inkol R 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings IEEE 3 III-III
[33] Wei W H, Wang R P, Shen X 2013 J. Phys. Chem. C 117 16571
Google Scholar
[34] Tauc J 1970 Mater. Res. Bull. 5 721
Google Scholar
[35] Jackson K, Briley A, Grossman S 1999 Phys. Rev. B 60 14985
Google Scholar
[36] Holubova J, Cernosek Z, Cernoskova E 2007 J. Optoelectron. Adv. Mater. 1 663
[37] Wang Y, Matsuda O, Inoue K 1998 J. Non-Cryst. Solids 232 702
[38] Bhosle S, Gunasekera K, Boolchand P 2012 Int. J. Appl. Glass Sci. 3 205
Google Scholar
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