Open AccessA fast algorithm for reflectivity calculation of micro/nano deep trench structures by corrected effective medium approximation
Author(s) -
Shiyuan Liu,
Hua-yong Gu,
Chuanwei Zhang,
Shen Hong-Wei
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.5996
Subject(s) - trench , materials science , shallow trench isolation , optics , physics , nanotechnology , layer (electronics)
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.