High-accuracy, midinfrared (450 cm-1≤ω≤4000 cm-1) refractive index values of silicon -: art. no. 123526
High-accuracy, midinfrared (450 cm-1≤ω≤4000 cm-1) refractive index values of silicon -: art. no. 123526
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DOI：
10.1063/1.1923612
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发表时间：
2005-06-15
影响因子：
3.2
通讯作者：
Amirtharaj, PM
中科院分区：
文献类型：
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作者：
Chandler-Horowitz, D;Amirtharaj, PM
使用傅里叶变换红外（FTIR）透射光谱数据测量硅的折射率的真实的和虚部n（ω）和k（ω）作为光子频率ω的函数。需要对晶片的厚度t进行精确的机械测量，并使用两个FTIR光谱：一个高分辨率（Δ ω =0.1至0.5 cm（-1））产生主要取决于t和n（ω）的典型通道光谱（法布里-珀罗条纹），另一个低分辨率（Δ ω =4.0 cm（-1））产生主要取决于t和k（ω）的吸收光谱。开发了一种程序，首先获得高分辨率光谱的n（ω）的初始估计值，然后从具有最小测量漂移的更快的低分辨率光谱计算k（ω）。然后将初始n值和最终k值一起用作拟合高分辨率光谱的起始点数据。一个以前推导出的传输公式收敛入射光束用于拟合。使用该程序确定的n（ω）的精度主要取决于样品厚度t的测量误差，并且k（ω）由从取样和取样方法获得的绝对透射值的精度决定。我们的结果与先前公布的值为n（Ω）和k（Ω）在450-4000-cm（-1）的光谱区域进行了比较。报告的n（Ω）不确定度为+/- 10（-4）绝对值，比公布值好10倍。n（欧米茄）的值范围从4000 cm（-1）（拉姆=2.5 μ m）处的3.4400到450 cm（-1）（拉姆=22.222 μ m）处的3.4169。k（Ω）值的标准差为
The real and imaginary parts of the refractive index, n(omega) and k(omega), of silicon were measured as a function of photon frequency omega using Fourier transform infrared (FTIR) transmission spectral data. An accurate mechanical measurement of the wafer's thickness, t, was required, and two FTIR spectra were used: one of high resolution (Delta omega=0.1 to 0.5 cm(-1)) yielding a typical channel spectrum (Fabry-Perot fringes) dependent mainly on t and n(omega), and one of low resolution (Delta omega=4.0 cm(-1)) yielding an absorption spectrum dependent mainly on t and k(omega). A procedure was developed to first get initial estimates for n(omega) for the high-resolution spectrum and then calculate k(omega) from the faster low-resolution spectrum with minimal measurement drift. Then both initial n and final k values were used together as starting point data for a fit to the high-resolution spectrum. A previously derived transmission formula for a convergent incident beam was used for the fit. The accuracy of n(omega) determined using this procedure is mostly dependent upon the measurement error in the sample thickness t and k(omega) is dominated by the accuracy of the absolute transmission values obtained from a sample-in and sample-out methods. Our results are compared with previously published values for n(omega) and k(omega) in the 450-4000-cm(-1) spectral region. The reported uncertainty in n(omega) is +/- 10(-4) absolute, a factor of 10 better than published values. The values of n(omega) range from 3.4400 at 4000 cm(-1) (lambda=2.5 mu m) to 3.4169 at 450 cm(-1) (lambda=22.222 mu m). The k(omega) values had a standard deviation of