-
包络法是一种根据薄膜在一定光谱范围内的透射光谱曲线及其包络线计算薄膜光学参数的方法,由Manifacier J C提出,并由Swanepoe R加以修正和发展[12-13]。该方法可根据薄膜的透射率光谱同时计算出薄膜的折射率和厚度以及消光系数。通过测试样片的透射率光谱曲线,然后用包络法计算薄膜厚度和折射率。在透射率光谱曲线中,最大透射率值由
${T}_{\rm max}$ 表示,最小值由${T}_{\rm min}$ 表示,基底的折射率用$ {n}_{s} $ 表示,空气折射率用$ {n}_{0} $ 表示,当薄膜没有吸收(k=0)时,有:当
$ {n}_{f}>{n}_{s} $ 时,$$ {T}_{\rm max}={T}_{\lambda /2}={T}_{s}=\frac{2{n}_{s}}{{n}_{s}^{2}+1} $$ (1) 当
$ {n}_{f}<{n}_{s} $ 时,$$ {T}_{\rm min}={T}_{\lambda /2}={T}_{s}=\frac{2{n}_{s}}{{n}_{s}^{2}+1} $$ (2) 当k
$ \ne $ 0时,考虑到基片后表面反射的影响,有:$$ \frac{1}{{T}_{\rm max}}-\frac{{R}_{s}}{{T}_{s}}\left[1+\frac{\chi }{16{n}_{0}{n}_{s}{n}_{f}^{2}\alpha }\right]=\frac{{\left({C}_{1}+{C}_{2}\alpha \right)}^{2}}{16{n}_{0}{n}_{s}{n}_{f}^{2}\alpha } $$ (3) $$ \frac{1}{{T}_{\rm min}}-\frac{{R}_{s}}{{T}_{s}}\left[1+\frac{\chi }{16{n}_{0}{n}_{s}{n}_{f}^{2}\alpha }\right]=\frac{{\left({C}_{1}-{C}_{2}\alpha \right)}^{2}}{16{n}_{0}{n}_{s}{n}_{f}^{2}\alpha } $$ (4) 式中:
${R}_{s}$ 为基底的反射率;${T}_{s}$ 为基底的透射率;$ \alpha $ 为吸收系数;$ {n}_{0} $ 为空气折射率;$ {n}_{f} $ 为薄膜折射率。$$ \chi =4{n}_{s}{n}_{f}{\left({n}_{0}+{n}_{f}\right)}^{2}-4{n}_{s}{n}_{f}{\left({n}_{0}-{n}_{f}\right)}^{2}{\alpha }^{2}-16{n}_{0}{n}_{s}{n}_{f}^{2}\alpha $$ $$ {c}_{1}=\left({n}_{0}+{n}_{f}\right)\left({n}_{f}+{n}_{s}\right) $$ $$ {c}_{2}=\left({n}_{0}-{n}_{f}\right)\left({n}_{f}-{n}_{s}\right) $$ 然后可以求得薄膜的初始折射率:
$$ {n}_{f}=\sqrt{N+\sqrt{{N}^{2}-{{n}_{s}}^{2}}} $$ (5) 式中:
$N=2{n}_{s}\left(\dfrac{{T}_{\rm max}-{T}_{\rm min}}{{T}_{\rm max}{T}_{\rm min}}\right)+\dfrac{{{n}_{s}}^{2}+1}{2}$ 。根据极值点处的折射率和波长可求得膜层厚度:
$$ d=\frac{{\lambda }_{1}{\lambda }_{2}}{2\left[n\left({\lambda }_{1}\right){\lambda }_{2}-n\left({\lambda }_{2}\right){\lambda }_{1}\right]} $$ (6) $$ 2nd=m\lambda $$ (7) 式中:
$ d $ 为厚度平均值;$ m $ 为极值个数;$ n $ 为薄膜的折射率。然后利用这些值进一步验证每对极值点处的$ \lambda $ 和$ n $ 。最后采用不同的色散模型进行反演拟合获得全波段的$ n $ 。公式(8)用于计算薄膜的吸收系数$ \alpha $ ,其中$ d $ 表示沉积薄膜的厚度,x由公式(9)给出:$$ \alpha =-\frac{\mathrm{ln}\left|x\right|}{d} $$ (8) $$ x=\frac{\sqrt{{{E}_{m}}^{2}-\left({n}^{2}-1\right)\left({n}^{2}-{{n}_{s}}^{2}\right)}}{{\left(n-1\right)}^{2}\left(n-{{n}_{s}}^{2}\right)} $$ (9) 式中:
$ n $ 为薄膜的折射率。$$ {E}_{m}=\frac{8{n}^{2}{n}_{s}}{{T}_{\rm max}}+\left({n}^{2}-1\right)\left({n}^{2}-{{n}_{s}}^{2}\right) $$ (10) 并且可以通过公式(11)计算出薄膜的消光系数:
$$ k=\frac{\alpha \lambda }{4\pi } $$ (11) 包络法用于计算薄膜光学常数的初始值,它只能准确计算出薄膜极值点处的折射率和消光系数,无法计算出整个波段的光学常数,所以需要经过选择色散模型对计算出来的初始值进行一个全波段的拟合,拟合出全波段的光学常数。文中运用包络法进行前期的数据计算,从而得到色散模型拟合的初始值。
-
通过数据处理将分光光度计和傅里叶变换红外光谱仪测得的光谱曲线整合到一张图内,得到YbF3单层薄膜在0.4~14 μm光谱范围内的透射率光谱曲线,如图1所示。
图 1 不同基底温度下沉积的YbF3薄膜实测透射率光谱曲线
Figure 1. Transmittance spectra curves of YbF3 thin films deposited at different substrate temperatures
从图1中可以看出,在3 μm和6 μm处有两个明显的吸收峰,根据其他文献可知,这是由于存在水汽吸收峰导致的[14],所以在进行光学参数反演时对吸收峰处的数据进行处理,去除异点数据,然后再进行反演拟合,这样可以得到较为准确的光学常数。采用包络法计算得到色散模型拟合的初始值,折射率拟合采用Cauchy色散关系。
$$ n\left(\lambda \right)={A}_{0}+\frac{{A}_{1}}{{\lambda }^{2}}+\frac{{A}_{2}}{{\lambda }^{4}} $$ (12) 式中:A0、A1、A2为无量纲参数;λ以μm为单位。消光系数拟合采用Exponential负指数函数拟合表达式:
$k\left(\lambda \right)={B}_{1}{\rm exp}\left(\dfrac{{B}_{2}}{\lambda }\right)$ 。拟合柯西参数为A0=1.4809,A1=4.2256×10−3,A2=−6.8813×10−5,B1=2.65218×10−4,B2=−4.628332×10−1。反演计算不同基底温度下YbF3薄膜的光学常数如图2所示。图 2 不同基底温度下沉积的YbF3薄膜的光学常数
Figure 2. Optical parameters of YbF3 thin films deposited at different substrate temperatures
由图2可知,基底温度对YbF3薄膜光学常数有一定影响,随着基底温度的升高,薄膜折射率略有增加。
为了验证色散模型拟合的光学常数的准确性,对基底温度为100 ℃条件下得到的YbF3薄膜样片进行椭偏测试,测试得到的光学常数(0.4~1.6 μm)与色散模型拟合的光学常数(0.4~14 μm)进行对比,如图3所示。
图 3 不同方法下获得的YbF3薄膜的光学常数
Figure 3. Optical constants of YbF3 thin films obtained by different methods
由图3可知,运用两种方法得到的光学常数曲线基本一致,为了进一步对色散模型得到的光学常数进行验证,将其代入TFCalc光学薄膜设计软件中,计算其在0.4~14 μm内的透射率光谱曲线,并将计算得到的透射率光谱曲线与实测的透射率光谱曲线进行对比,如图4所示。
图 4 TFCalc计算的透射光谱曲线与实测透射率曲线比较
Figure 4. Comparison of the transmission spectrum curve calculated by TFCalc and the measured transmission curve
从图4中可以看出,计算得到的透射率光谱曲线与实测的透射率光谱曲线仅在3 μm和6 μm左右处有微小差别,在其余波段均吻合较好,其中在3 μm和6 μm左右处存在水汽吸收峰,证明了色散模型拟合得到的光学常数的准确性。
-
同样,通过处理分光光度计和傅里叶变换红外光谱仪进行测量的透射率光谱曲线,可以得到YF3单层薄膜在0.4~14 μm光谱范围内的透射率光谱曲线,如图5所示。
图 5 不同基底温度下沉积的YF3薄膜实测透射率光谱曲线
Figure 5. Transmittance spectra of YF3 thin films deposited at different substrate temperatures
从图5中可以看出,在3 μm和6 μm处有两个吸收峰,这是由于存在水吸收峰导致的,同样在优化反演时将水吸收峰处的异点数据排除,不予进行计算。
由色散模型反演计算可以得到不同基底温度下YF3薄膜的光学常数,如图6所示。
图 6 不同基底温度下沉积的YF3薄膜的光学参数
Figure 6. Optical parameters of YF3 thin films deposited at different substrate temperatures
由图6可知,沉积温度对YF3薄膜光学参数有一定影响,随着基底温度的升高,折射率也会略有增加。
为了验证色散模型拟合的光学常数的准确性,对基底温度为100 ℃条件下得到的YF3薄膜样片进行椭偏测试,测试得到的光学常数(0.4~1.6 μm)与色散模型拟合的光学常数(0.4~14 μm)进行对比,如图7所示。
由图7可知,运用两种方法得到的光学常数曲线基本一致,同样将色散模型得到的光学常数代入TFCalc光学薄膜设计软件中,计算其在0.4~14 μm内的透射率光谱曲线,如图8所示。
图 8 TFCalc计算的透射光谱曲线与实测透射率曲线比较
Figure 8. Comparison of the transmission spectrum curve calculated by TFCalc and the measured transmission curve
从图8中可以看出,计算得到的透射率光谱曲线与实测的透射率光谱曲线仅在3 μm和6 μm左右处有微小差别,在其余波段均吻合较好,其中在3 μm和6 μm左右处存在水汽吸收峰。证明了色散模型拟合得到的光学常数的准确性。事实证明,运用包络法和色散模型结合的方法求解宽光谱范围内的光学常数是可行的。
-
用原子力显微镜(AFM)在非接触模式下分别测量了两种红外低折射率薄膜的表面粗糙度,对于每种材料至少检查四个不同的位置。图9显示了两种红外低折射率薄膜表面的形貌。膜层表面形貌比较均匀,当镀制束流较大时膜层表面会有溅射点。总体而言,薄膜的均方根粗糙度仍然较低,只有某些点显示出最大峰值。对于红外薄膜而言,使用电子束热蒸发法制备的薄膜可以有很好的表面形貌。
Inverting optical constants of YbF3 and YF3 thin films in the ultra-wide spectrum from 0.4 to 14 μm
-
摘要: 为了获得红外低折射率材料的光学常数,采用电子束热蒸发技术在多光谱硫化锌基底上以不同的基底温度分别制备了单层氟化钇(YF3)和氟化镱(YbF3)薄膜。通过分光光度计和傅里叶变换红外光谱仪分别测试其在可见至远红外波段的透射率光谱曲线,使用包络法和色散模型拟合相结合的方法对其在可见至红外波段的光学常数进行了反演,得到了其在0.4~14 μm波段内的折射率与消光系数。采用椭偏测试结果验证了YF3和YbF3薄膜在0.4~1.6 μm波段内的光学常数正确性;将拟合得到的光学常数代入TFCalc 膜系设计软件,计算得到的单层薄膜的透射率光谱曲线与实测的光谱曲线吻合较好。实验结果表明,该方法获得的在超宽光谱0.4~14 μm范围内的光学常数准确、可靠。Abstract: In order to obtain the optical constants of infrared low refractive index materials, single-layer yttrium fluoride (YF3) and ytterbium fluoride (YbF3) thin films were prepared on multispectral zinc sulfide substrates by electron beam thermal evaporation technique at different substrate temperatures. Spectrophotometer and Fourier transform infrared spectrometer were used to test the transmittance spectra of the optical parameters from visible to far-infrared bands, and the refractive index and extinction coefficient in the band of 0.4-14 μm were obtained by using the combination of envelope method and dispersion model fitting. The accuracy of the optical constants of YF3 and YbF3 films in the band of 0.4-1.6 μm was verified by the ellipsometry test results. The obtained optical constants were substituted into the TFCalc film design software, and the calculated transmittance spectrum curve of the monolayer film was in good agreement with the measured spectrum curve. The experimental results show that the optical constants obtained by this method are accurate and reliable in the ultra-wide spectral range of 0.4-14 μm.
-
-
[1] Liu Huasong, Fu Xuan, Wang Lishuan, et al. Characterization of optical properties of weak absorption thin film [J]. Infrared and Laser Engineering, 2013, 42(8): 2108-2114. (in Chinese) doi: 10.3969/j.issn.1007-2276.2013.08.032 [2] Feng Yidong, Yu Tianyan, Liu Dingquan. Influence of deposition process on reliability of YbF3 thin films [J]. Acta Optica Sinica, 2018, 38(7): 0731002. (in Chinese) [3] Xu Lingmao, He Yanchun, Zheng Jun, et al. Infrared optical properties of yttrium fluoride thin films at low temperature [J]. China Surface Engineering, 2019, 32(4): 151-155. (in Chinese) [4] Zhang Yaoping, Zhang Yundong, Ling Ning, et al. Effect of substrate temperature on defects and optical properties of YbF3 thin films [J]. Optical Instruments, 2006(1): 93-96. (in Chinese) doi: 10.3969/j.issn.1005-5630.2006.01.020 [5] Ling Xiulan, Huang Wei. Effects of process parameters and deposition methods on defects of ZnS/YbF3 thin films [J]. Optical Instruments, 2006, 28(5): 71-74. (in Chinese) [6] Wang Duoshu, Li Youlu, Li Kaipeng, et al. Research method of the temperature characteristic of infrared thin-films [J]. Infrared and Laser Engineering, 2018, 47(4): 0404006. (in Chinese) [7] Li Wei, Jin Chengyu. Elliptic polarization data analysis method for thin film materials [J]. Chinese Journal of Spectroscopy Laboratory, 2010, 27(1): 66-76. (in Chinese) doi: 10.3969/j.issn.1004-8138.2010.01.014 [8] Amotchkina T, Trubetskov M, Hahner D, et al. Characterization of e-beam evaporated Ge, YbF3, ZnS, and LaF3 thin films for laser-oriented coatings [J]. Applied Optics, 2020, 59(5): A40. doi: 10.1364/AO.59.000A40 [9] Liu H, Li S, Chen D, et al. Study on broadband optical constants of yttrium fluoride thin films deposited by electron beam evaporation [J]. Optik - International Journal for Light and Electron Optics, 2019, 205: 163548. [10] Ji Yiqin, Liu Huasong, Zhang Yanmin. Measurement and analysis of optical film constants [J]. Infrared and Laser Engineering, 2006, 35(5): 513-518. (in Chinese) doi: 10.3969/j.issn.1007-2276.2006.05.003 [11] Li Kaipeng, Wang Duoshu, Li Chen, et al. Study on optical thin film parameters measurement method [J]. Infrared and Laser Engineering, 2015, 44(3): 1048-1052. (in Chinese) doi: 10.3969/j.issn.1007-2276.2015.03.047 [12] Zhong Disheng, Wang Luqhuan, Yu Yingzhi. Measurement of optical constants of thin films by spectrophotometry [J]. Journal of Liaoning University (Natural Science Edition), 1996(2): 1-13. (in Chinese) [13] Shen Weidong, Liu Xu, Zhu Yong, et al. Determination of optical constants and thickness of semiconductor thin films using transmittance test curve [J]. Acta Semiconductors, 2005(2): 335-340. (in Chinese) doi: 10.3321/j.issn:0253-4177.2005.02.022 [14] Qin Yang, Zhang Rongfu. Preparation of ytterbium fluoride films at different temperatures [J]. Optical Instruments, 2018(3): 40-94. (in Chinese)