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 that can produce defects. One cause of the problem is nonuniform absorption of thermal radiation, especially in patterned wafers, where the optical properties vary across the surface of the wafer. Recent developments in RTP have lead to the use of millisecond-duration heating cycles, where light with very high power density is used to heat the surface of the wafer. Pattern effects are especially important here, because there is very little time for thermal diffusion to even out temperature distributions during the heating cycle. There have been very few studies on the radiative properties of patterned wafers, especially for the structures expected to be used on advanced semiconductor devices. The feature size is already below 100 nm and is comparable or smaller than the wavelengths of radiation (200–1000 nm) emitted by the flash-lamps typically used for millisecond processing. Hence, this work is devoted to a parametric numerical study of the radiative properties of patterned wafers with the smallest dimension down to 30 nm. The effects of wavelength, wave polarization, and angle of incidence on selected periodically patterned wafers are presented. The methods include the rigorous coupled wave analysis (RCWA) and the effective medium approach (EMA). RCWA is used to obtain exact solutions of Maxwell’s equations, and EMA is used to approximate the periodic structures as a planar multilayer structure with an effective dielectric function. This study provides an assessment of the applicability of EMA for simulations of radiative properties of patterned wafers.

1.
“International Technology Roadmap for Semiconductors 2004 Update,” Semiconductor Industry Association, (http://public.otrs/net).
2.
Gelpey, J. C., Elliott, K., Camm, D., McCoy, S., Ross, J., Downey, D. F., and Arevalo, E., 2002, “Advanced Annealing for Sub-130nm Junction Formation,” in Rapid Thermal and Other Short-Time Processing Technologies III, P. J. Timans, E. Gusev, F. Roozeboom, M. C. O¨ztu¨rk and D.-L. Kwong, Eds., (The Electrochemical Society, Pennington), pp. 313–324.
3.
Skorupa
W.
,
Yankov
R. A.
,
Anwand
W.
,
Voelskow
M.
,
Gebel
T.
,
Downey
D. F.
, and
Arevalo
E. A.
,
2004
, “
Ultra-Shallow Junctions Produced by Plasma Doping and Flash Lamp Annealing
,”
Materials Science and Engineering B
,
114
, pp.
358
361
.
4.
Lindsay, R., Pawlak, B. J., Henson, K., Satta, A., Severi, S., Lauwers, A., Surdeanu, R., McCoy, S., Gelpey, J., Pages, X., and Maex, K., 2004, “Integration of Low and High Temperature Junction Anneals for 45nm Cmos,” in Advanced Short-Time Thermal Processing for Si-Based CMOS Devices II, M. C. O¨ztu¨rk, E. P. Gusev, L. J. Chen, D.-L. Kwong, P. J. Timans, G. Miner and F. Roozeboom, Eds., (The Electrochemical Society, Pennington), pp. 145–156.
5.
Nishinohara
K. T.
,
Ito
T.
, and
Suguro
K.
,
2004
, “
Improvement of Performance Deviation and Productivity of Mosfets with Gate Length Below 30 Nm by Flash Lamp Annealing
,”
IEEE Transactions on Semiconductor Manufacturing
,
17
, pp.
286
291
.
6.
Bentini
G. G.
, and
Correra
L.
,
1983
, “
Analysis of Thermal Stresses Induced in Silicon During Xenon Arc Lamp Flash Annealing
,”
Journal of Applied Physics
,
54
, pp.
2057
2062
.
7.
Madou, M. J., 1997, Fundamentals of Microfabrication, CRC Press, Boca Raton, FL.
8.
Hebb
J. P.
, and
Jensen
K. F.
,
1998
, “
The Effect of Patterns on Thermal Stress During Rapid Thermal Processing of Silicon Wafers
,”
IEEE Transactions on Semiconductor Manufacturing
,
11
, pp.
99
107
.
9.
Tada
H.
,
Abramson
A. R.
,
Mann
S. E.
,
Miaoulis
I. N.
, and
Wong
P. Y.
,
2000
, “
Evaluating the Effects of Thin Film Patterns on the Temperature Distribution of Silicon Wafers During Radiant Processing
,”
Optical Engineering
,
39
, pp.
2296
2304
.
10.
Liu
J.
,
Zhang
S. J.
,
Chen
Y. S.
,
2003
, “
Prediction of Radiative Properties of Patterned Silicon Wafers by Solving Maxwell’s Equations in the Time Domain
,”
Numerical Heat Transfer Part B: Fundamentals
,
44
, pp.
329
345
.
11.
Liu
J.
,
Zhang
S. J.
, and
Chen
Y. S.
,
2004
, “
Rigorous Electromagnetic Modeling of Radiative Interactions with Microstructures Using the Finite Volume Time-Domain Method
,”
International Journal of Thermophysics
,
25
, pp.
1281
1297
.
12.
Moharam
M. G.
,
Pommet
D. A.
,
Grann
E. B.
, and
Gaylord
T. K.
,
1995
, “
Stable Implementation of the Rigorous Coupled-Wave Analysis for Surface-Relief Gratings - Enhanced Transmittance Matrix Approach
,”
Journal of the Optical Society of America A
,
12
, pp.
1077
1086
.
13.
Palik, E. D., 1998, Handbook of Optical Constants of Solids, Academic Press, San Diego, CA, Vol. 1.
14.
Jellison
G. E.
, and
Modine
F. A.
,
1994
, “
Optical Functions of Silicon at Elevated Temperatures
,”
Journal of Applied Physics
,
76
, pp.
3758
3761
.
15.
Lautenschlager
P.
,
Garriga
M.
,
Vina
L.
, and
Cardona
M.
,
1987
, “
Temperature Dependence of the Dielectric Function and Interband Critical Points in Silicon
,”
Physical Review B
,
36
, pp.
4821
4830
.
16.
Halison
I. H.
,
1965
, “
Interspecimen Comparison of the Refractive Index of Fused Silica
,”
Journal of the Optical Society of America
,
55
, pp.
1205
1209
.
17.
Rooseboom, F., 1996, Advances in Rapid Thermal and Integrated Processing, Kluwer Academic Publishers, Dordrecht, the Netherlands.
18.
Li
L. F.
,
1996
, “
Use of Fourier Series in the Analysis of Discontinuous Periodic Structures
,”
Journal of the Optical Society of America A
,
13
, pp.
1870
1876
.
19.
Zhang
D. W.
,
Lu
Z. W.
,
Yu
W. X.
, and
Li
F. Y.
,
2002
, “
Electromagnetic Diffraction Analysis of Columned Grid Gratings
,”
Journal of Optics A
,
4
, pp.
180
186
.
20.
Moharam
M. G.
,
Grann
E. B.
,
Pommet
D. A.
, and
Gaylord
T. K.
,
1995
, “
Formulation for Stable and Efficient Implementation of the Rigorous Coupled-Wave Analysis of Binary Gratings
,”
Journal of the Optical Society of America A
,
12
, pp.
1068
1076
.
21.
Garnett
J. C. M.
,
1906
, “
Colours in Metal Glasses, in Metallic Films, and in Metallic Solutions - II
,”
Philosophical Transactions of the Royal Society of London A
,
205
, pp.
237
288
.
22.
Bruggeman
D. A. G.
,
1935
, “
Calculation of Various Physics Constants in Heterogenous Substances I. Dielectricity Constants and Conductivity of Mixed Bodies from Isotropic Substances
,”
Annalen Der Physik
,
24
, pp.
636
664
.
23.
Zhang, Z. M., Fu, C. J., and Zhu, Q. Z., “Optical and Thermal Radiative Properties of Semiconductors Related to Micro/Nanotechnology,” in Advances in Heat Transfer, vol. 37. New York: Academic press, 2003, pp. 179–296.
24.
Rytov
S. M.
,
1956
, “
Electromagnetic Properties of a Finely Stratified Medium
,”
Soviet Physics JETP
,
2
, pp.
466
475
.
25.
Gaylord
T. K.
,
Glytsis
E. N.
, and
Moharam
M. G.
,
1987
, “
Zero-Reflectivity Homogeneous Layers and High Spatial-Frequency Surface-Relief Gratings on Lossy Materials
,”
Applied Optics
,
26
, pp.
3123
3135
.
26.
Sentenac
A.
, and
Greffet
J. J.
,
1994
, “
Design of Surface Microrelief with Selective Radiative Properties
,”
International Journal of Heat and Mass Transfer
,
37
, pp.
553
558
.
27.
Lalanne
P.
, and
LemercierLalanne
D.
,
1996
, “
On the Effective Medium Theory of Subwavelength Periodic Structures
,”
Journal of Modern Optics
,
43
, pp.
2063
2085
.
28.
Kikuta
H.
,
Ohira
Y.
,
Kubo
H.
, and
Iwata
K.
,
1998
, “
Effective Medium Theory of Two-Dimensional Subwavelength Gratings in the Non-Quasi-Static Limit
,”
Journal of the Optical Society of America A
,
15
, pp.
1577
1585
.
29.
Carr
D. W.
,
Sullivan
J. P.
, and
Friedmann
T. A.
,
2003
, “
Laterally Deformable Nanomechanical Zeroth-Order Gratings: Anomalous Diffraction Studie by Rigorous Coupled-Wave Analysis
,”
Optics Letters
,
28
, pp.
1636
1638
.
30.
Lee, B. J., Zhang, Z. M., Early, E. A., DeWitt, D. P., and Tsai, B. K., 2005 (in press), “Modeling Radiative Properties of Silicon with Coatings and Comparison with Reflectance Measurements,” Journal of Thermophysics and Heat Transfer.
31.
Incropera, F. P., and DeWitt, D. P., 2002, Fundamentals of Heat and Mass Transfer, 5th ed. J. Wiley, New York.
32.
Born, M., and Wolf, E., 1999, Principles of Optics, 7th ed. Cambridge University Press, Cambridge, UK.
33.
Hessel
A.
,
Oliner
A. A.
,
1965
, “
A New Theory of Woods Anomalies on Optical Gratings
,”
Applied Optics
,
4
, pp.
1275
1297
.
This content is only available via PDF.
You do not currently have access to this content.