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

Liu Shi-Yuan Zhang Chuan-Wei Gu Hua-Yong Shen Hong-Wei

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

Liu Shi-Yuan, Zhang Chuan-Wei, Gu Hua-Yong, Shen Hong-Wei
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  • Abstract views:  4711
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  • Received Date:  27 December 2007
  • Accepted Date:  25 February 2008
  • Published Online:  20 September 2008

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

  • 1. (1)华中科技大学数字制造装备与技术国家重点实验室,武汉 430074; (2)武汉光电国家实验室光电材料与微纳制造研究部,武汉 430074

Abstract: 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.

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