Pattern scaling effect on the radiative properties of wafer’s surface

Abstract

This paper presents a parametric study of the radiative properties of patterned wafers with a polysilicon gate array on the Si substrate, considering the effect of wavelength and polarization. The finite-difference time-domain (FDTD) method was employed to examine the pattern scaling effect on the spectral absorptance via numerical solutions of the Maxwell’s equations. The effective medium theory (EMT) was also used to help explain the absorptance predictions. While the gate sizes are very small compared to wavelength, the results show rather unusual phenomena. The absorptance calculated by EMT is in agreement with FDTD in the cases with small gate and period sizes. With the increase of period and decrease of the ratio of the gate width to the grating period, both EMT and FDTD results for the TM (transverse magnetic) mode approach to pure silicon since the grating effect diminishes. However, the error of EMT results for the TE mode in some cases becomes considerable due to the limitation of EMT, which requires the period to be significantly smaller than the wavelength. Besides, the TE (transverse electric) absorptance curve separates from that of plain Si when the wavelength equals the grating period, this is because the gate can interact with its neighbering region by diffraction and the diffraction effects are weak, when the wavelength is small. The peak absorptance can be attributed to the thin film effect. It shows that a slight increase in the gate height can drastically increase the absorptance and the increased gate height shifts the peak absorptance to longer wavelength due to the increase of optical path length in the effective thin film. This work is of great importance for optimization of advanced annealing techniques in semiconductor manufacturing.