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TECHNICAL PAPERS

# Radiative Properties of Patterned Wafers With Nanoscale Linewidth

[+] Author and Article Information
Y.-B. Chen

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Z. M. Zhang1

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332zzhang@me.gatech.edu

P. J. Timans

Mattson Technology, Fremont, CA 94538

1

Corresponding author.

J. Heat Transfer 129(1), 79-90 (Jun 08, 2006) (12 pages) doi:10.1115/1.2401201 History: Received January 31, 2006; Revised June 08, 2006

## Abstract

Temperature nonuniformity is a critical problem in rapid thermal processing (RTP) of wafers because it leads to uneven diffusion of implanted dopants and introduces thermal stress. One cause of the problem is nonuniform absorption of thermal radiation, especially in patterned wafers, where the optical properties vary across the wafer surface. Recent developments in RTP have led to the use of millisecond-duration heating cycle, which is too short for thermal diffusion to even out the temperature distribution. The feature size is already below $100nm$ and is smaller than the wavelength $(200–1000nm)$ of the flash-lamp radiation. Little is known to the spectral distribution of the absorbed energy for different patterning structures. This paper presents a parametric study of the radiative properties of patterned wafers with the smallest feature dimension down to $30nm$, considering the effects of temperature, wavelength, polarization, and angle of incidence. The rigorous coupled wave analysis is employed to obtain numerical solutions of the Maxwell equations and to assess the applicability of the method of homogenization based on effective medium formulations.

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## Figures

Figure 1

Parameters of selected cases, where dG and dT are the depths of gate and trench, respectively, and lG, lP, and lT are the lengths of gate, pitch, and trench

Figure 2

Optical constants of silicon at 25, 700, and 910°C: (a) refractive index, and (b) extinction coefficient

Figure 3

Schematic drawing for the TE wave incidence on a grating layer, showing the reflected diffraction orders j=−2, −1, 0, and 1

Figure 4

Calculated normal, spectral absorptance for plain Si(A‐1) and SiO2-coated Si(A‐2) at 25, 700, and 910°C

Figure 5

Spectral absorptance predicted using RCWA for cases with gratings at 910°C at θ=0 and 45deg: (a) case A-3; (b) case B-1; (c) case B-2; and (d) case B-3

Figure 6

Comparison of the absorptance predicted by different methods at 910°C: (a) TE wave for case A-3; (b) TM wave for case A-3; (c) TE wave for case B-1; (d) TM wave for case B-1; (e) TE wave for case B-3; and (f) TM wave for case B-3

Figure 7

Effect of incidence angle on the absorptance at 910°C for cases without gates: (a) TE wave for case A-1; (b) TM wave for case A-1; (c) TE wave for case A-2; (d) TM wave for case A-2; (e) TE wave for case A-3; and (f) TM wave for case A-3

Figure 8

Effect of incidence angle on the absorptance at 910°C for cases with gates: (a) TE wave for case B-1; (b) TM wave for case B-1; (c) TE wave for case B-2; (d) TM wave for case B-2; (e) TE wave for case B-3; and (f) TM wave for case B-3

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