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通过对样品薄膜表面的SEM测量,发现d1~d6样品的TiO2薄膜表面形貌基本相同,即旋涂薄膜表面形貌基本不受旋涂层数影响。图 1是d3样品的SEM表面形貌图。从图 1中可以看出,薄膜表面较均匀的分布着溶胶-凝胶方法制备的薄膜中常见的孔隙,薄膜表面整体比较平整,在薄膜表面观察不到明显的裂纹存在。
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椭偏光谱测量技术作为一种灵敏的、非接触、无损测量技术,通过测量偏振光经过样品反射或透射后偏振态的改变得到椭偏光谱,然后根据样品结构建立结构模型,对结构模型中的材料选择合适的色散模型,对椭偏光谱进行拟合分析,来获取样品的光学参量,是一种间接测量技术。在通常的反射测量情况下,椭偏参量ρ定义如下[17-18]:
$ \rho=\frac{r_{p}}{r_{s}}=\tan \varPsi \exp (\mathrm{i} \varDelta) $
(1) 式中,rp和rs分别代表p光和s光的振幅反射系数;tanΨ是振幅反射系数比的模,Ψ∈[0°, 90°];Δ是振幅反射系数比的幅角,Δ∈[0°, 360°]。UVISEL型椭偏光谱仪光路元件的设置顺序为氙灯光源、起偏器、样品、光弹调制器、检偏器、单色仪,在起偏器、光弹调制器、检偏器相对入射平面的方位分别为45°, 0°, 45°的设置情况下,椭偏光谱中间参量Is, Ic分别为:
$ I_{\mathrm{s}}=\sin (2 \varPsi) \sin \varDelta $
(2) $ I_{\mathrm{c}}=\sin (2 \varPsi) \cos \varDelta $
(3) 椭偏参量Ψ和Δ由Is和Ic算得出,因此Ψ,Δ为间接参量,非直接测量参量,同时受限于sin(2Ψ)在Ψ接近45°时随Ψ变化不明显,计算误差较大,以及数值上关于45°的镜像效应,在椭偏光谱拟合分析中通常采用对Is, Ic色散曲线进行拟合的方法,而不是对Ψ, Δ色散曲线进行直接拟合计算。
采用起偏器、光弹调制器、检偏器相对入射平面的方位分别为45°,0°,45°的设置,在70°入射角下,分别测量了d1~d6样品在1.55eV~4.00eV区间的椭偏反射光谱。
考虑到TiO2薄膜含有一定的孔隙率,且SEM观察到的薄膜表面形貌基本不受旋涂层数影响,建立了如图 2所示的样品结构模型,用来对样品的椭偏光谱进行拟合分析。在材料色散模型选择中,单晶硅、SiO2天然氧化层均为常规标准材料,采用标准参考文件,环境空气取折射率n=1,空气消光系数k=0。TiO2层的色散模型采用New Amorphous色散模型,该色散模型是由Fourouchi & Bloomer的Amorphous模型发展来的[18],该色散模型可以看作是能带带隙之上的单振子模型,带隙之下消光系数k=0,视为无吸收,折射率n和消光系数k可以分别表示为:
$ n(\omega)=n_{\infty}+\frac{B\left(\omega-\omega_{j}\right)+C}{\left(\omega-\omega_{j}\right)^{2}+\varGamma_{j}^{2}} $
(4) $ k(\omega)=\left\{\begin{array}{l} \frac{f_{j}\left(\omega-\omega_{\mathrm{g}}\right)^{2}}{\left(\omega-\omega_{j}\right)^{2}+\varGamma_{j}^{2}}, \left(\omega>\omega_{\mathrm{g}}\right) \\ 0, \left(\omega \leqslant \omega_{\mathrm{g}}\right) \end{array}\right. $
(5) $ B=\frac{f_{j}}{\varGamma_{j}}\left[\varGamma_{j}^{2}-\left(\omega_{j}-\omega_{\mathrm{g}}\right)^{2}\right] $
(6) $ C=2 f_{j} \varGamma_{j}\left(\omega_{j}-\omega_{\mathrm{g}}\right) $
(7) 式中,n∞为长波折射率,ωg为带隙能量,ωj为最大吸收能量,fj为振子强度,Γj为展宽因子。
图 3a、图 3b分别是对d1~d6样品椭偏光谱Is, Ic色散曲线的测量和拟合结果。可以看出,在1.55eV~4.00eV波段内,拟合得到的Is与Ic色散曲线与实测曲线均吻合较好。
Figure 3. Results of elliptic polarization measurement and fitting of TiO2 thin films with different spin coating layers
表 1为拟合得到的不同旋涂层数的TiO2薄膜的厚度和孔隙率结果。可以看出,在实验采用的旋涂参量下,TiO2薄膜每层旋涂的厚度约为8.9nm,旋涂层数的增加与薄膜厚度的增加成较好的线性关系,因此可以在一定程度上通过控制旋涂层数实现对薄膜厚度的控制。同时可以看到, 薄膜的孔隙率均为15%~16%,即薄膜孔隙率基本不随旋涂层数变化,这与SEM观察到的不同旋涂层数样品表面形貌基本相同是一致的。
Table 1. Thickness and porosity of TiO2 thin films with different spin coating layers
sample thickness/nm TiO2/% void/% d1 8.88 84.2 15.8 d2 17.50 84.8 15.2 d3 27.08 84.7 15.3 d4 36.06 84.4 15.6 d5 44.26 84.1 15.9 d6 53.58 84.2 15.8 椭偏光谱拟合得到的TiO2薄膜New Amorphous色散模型中参数值如表 2所示。
Table 2. Fitted parameter values of new amorphous dispersion model
parameter value n∞ 1.9417520±0.2259548 ωg/eV 3.1120360±0.0452856 fj/eV 0.2010251±0.0538058 ωj/eV 4.1955300±0.0326773 Γj/eV 0.4761398±0.0235010 拟合得到的TiO2薄膜的带隙ωg≈3.1eV,这一参量跟参考文献[19]和参考文献[20]中TiO2薄膜的带隙ωg≈2.9eV~3.2eV相吻合。
将表 2中所得的参量代入New Amorphous色散模型中,得到TiO2薄膜的折射率n和消光系数k色散曲线,如图 4所示。
由图 4可见,在1.55eV~4.00eV波段内,TiO2薄膜的折射率处于2.1~3.0之间,薄膜对于3.1eV以下波段消光系数k=0,是无吸收的。
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椭偏光谱作为一种薄膜光学常数的间接测量方法,对拟合结果可靠性有必要进行验证。由椭偏光谱拟合得到的折射率色散及薄膜厚度等光学常数结果,通过计算可以反演得到样品的理论反射光谱,将理论反射光谱与实测反射光谱进行比较,两者的符合程度是检验椭偏光谱拟合结果可靠性的便捷方法之一。
在椭偏光谱测试中,起偏器方位45°、光弹调制器方位0°、检偏器方位45°,由琼斯矩阵分析可知, 探测器得到的直流信号与入射光强、样品反射率成正比。实验中以单晶硅片为参考基片,与椭偏光谱测量共角度70°下,原位测量了样品相对单晶硅的反射光谱Rr,得到了样品实际反射率色散曲线Rf,换算过程中单晶硅片理论反射率RSi的计算采用了单晶硅理论复折射率色散值并考虑了单晶硅表面天然氧化层的影响。
图 5为根据椭偏光谱拟合所得光学常数通过薄膜干涉理论计算反演得到反射谱与原位共角实测反射谱的对比。从图中可以看到,不同厚度样品的理论反射率曲线与实测反射率曲线在峰位、形状上总体吻合均较好,表明对椭偏光谱拟合的结果是可靠的。同时注意到,反演得到的反射率曲线与实测反射率曲线在强度值上最大有3%左右的偏差,可以认为这是由薄膜表面及内部孔隙界面散射所致,同时表面微尘散射和氙灯光源强度的稳定性也会影响反射率测量值的大小。
基于原位共角椭偏与反射谱的TiO2薄膜光学常数分析
Analysis of optical constants of TiO2 thin film based on in-situ common angle ellipsometry and reflection
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摘要: 为了分析溶胶-凝胶法制备的TiO2薄膜的光学常数,采用旋涂法制备了多层TiO2薄膜,利用扫描电镜对表面形貌进行了分析,利用椭圆偏振光谱对薄膜的折射率色散和孔隙率进行了拟合分析,并利用原位共角反射光谱对拟合结果进行了验证,得到了TiO2薄膜厚度、孔隙率和折射率色散曲线。结果表明,TiO2薄膜厚度与旋涂层数成线性关系,薄膜孔隙率约为15%且与旋涂层数无关,New Amorphous色散模型可以较好地拟合溶胶-凝胶旋涂方法制备的TiO2薄膜在1.55eV~4.00eV波段的椭偏光谱。该研究为溶胶-凝胶法制备的TiO2薄膜的光学常数测量提供了参考。Abstract: In order to analyze the optical constants of the TiO2 thin film prepared by the sol-gel method, multi-layer TiO2 thin films were prepared by spin-coating, and the surface morphology was analyzed by scanning electron microscopy. The refractive index dispersion and porosity of the film were analyzed by ellipsometry. The fitting analysis was carried out, and the fitting results were verified by in-situ common-angle reflectance spectroscopy. The TiO2 thin film thickness, porosity, and refractive index dispersion curves were then obtained. The results show that the thickness of the TiO2 thin film has a linear relationship with the number of spin coatings. The porosity of the film is about 15% and has nothing to do with the number of spin coatings. The New Amorphous dispersion model can fit the ellipsometric spectrum of TiO2 thin film prepared by the sol-gel spin coating method in the 1.55eV~4.00eV band. This study provides a reference for the measurement of the optical constants of the TiO2 thin film prepared by the sol-gel method.
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Key words:
- spectroscopy /
- optical constants /
- spectroscopic ellipsometry /
- TiO2 thin film
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Table 1. Thickness and porosity of TiO2 thin films with different spin coating layers
sample thickness/nm TiO2/% void/% d1 8.88 84.2 15.8 d2 17.50 84.8 15.2 d3 27.08 84.7 15.3 d4 36.06 84.4 15.6 d5 44.26 84.1 15.9 d6 53.58 84.2 15.8 Table 2. Fitted parameter values of new amorphous dispersion model
parameter value n∞ 1.9417520±0.2259548 ωg/eV 3.1120360±0.0452856 fj/eV 0.2010251±0.0538058 ωj/eV 4.1955300±0.0326773 Γj/eV 0.4761398±0.0235010 -
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