基于修正等效介质理论的微纳深沟槽结构反射率快速算法研究

利用等效介质理论和严格耦合波理论研究比较微纳米级高深宽比深沟槽结构的红外反射谱，提出一种对等效折射率加入色散修正项的深沟槽结构反射率快速算法. 通过超越色散方程分析和大量计算发现，加入的等效折射率色散修正项与波长的平方成反比，并且与深沟槽结构的材料、周期和占空比有关. 这种新的计算方法可以非常精确地获得高深宽比深沟槽结构的反射率，而且明显提高了运算速度，在复杂深沟槽结构基于模型的红外反射谱测量中具有重要的应用价值，可以应用于微电子和微机电系统制造过程中高深宽比微纳深沟槽结构刻蚀进度的在线实时监测. 关键词： 深沟槽结构 严格耦合波理论 等效介质理论 反射率

A fast algorithm for reflectivity calculation of micro/nano deep trench structures by corrected effective medium approximation

This paper proposes a fast algorithm for reflectivity calculation of micro/nano scale high-aspect-ratio deep trench structures by the novel method of corrected effective medium approximation (CEMA). Extensive comparative investigation on the infrared reflection spectra of deep trench structures by means of effective medium approximation (EMA) and rigorous coupled-wave analysis (RCWA) reveals that the RCWA based method is accurate but time consuming while the EMA based calculation is much faster but less accurate. The proposed CEMA method is based on EMA but a dispersion corrected factor is added to calculate the refractive index of each effective medium. The dispersion corrected factor is found to be in inverse proportion to the square of the wavelength, and relates to the period, material and void fraction of trench structures. Simulations carried out on a lot of complex multi-layered trench structures, such as the bottle trench structure, demonstrate that the CEMA method is not only fast in calculation but also accurate enough in comparison with the RCWA based method. It is expected that the proposed CEMA method can be applied to deep trench measurement by model-based infrared spectroscopy (MBIR), thus has further potential applications such as real time etching process monitoring of micro/nano scale high-aspect-ratio deep trench structures in manufacturing microelectronics and microelectromechanical system (MEMS) devices.