The concept of rapid thermal processing has many potential applications in microelectronics manufacturing, but the details of chamber design remains an active area of research. In this work the influence of lamps radius on the thermal stresses in a wafer during the cooling process is studied in detail. Since the equations governing the present thermal-elastic system are coupled in nature, the solution for the temperature and stresses must proceed simultaneously by using a fully implicit finite difference method. After the thermal stresses are obtained, the optimum lamps radii for various heights of the chamber under the constant power ramp-down control scheme are determined based on the maximum shear stress failure criterion. The shortest cooling time that can significantly reduce the thermal budget and dopant redistribution is also predicted by applying the maximum stress control scheme. The result obtained is useful in the design of a reliable rapid thermal processor based on a more practical consideration, thermal stress.

1.
Gyurcsik
,
R. S.
,
Riley
,
T. J.
, and
Sorrell
,
F. Y.
,
1991
, “
A Model for Rapid Thermal Processing: Achieving Uniformity Through Lamp Control
,”
IEEE Trans. Semicond. Manuf.
,
4
(
1
), pp.
9
13
.
2.
Roozeboom, F., 1992, Manufacturing Equipment Issues in Rapid Thermal Processing, Academic Press, New York.
3.
Hu
,
S. M.
,
1969
, “
Temperature Distribution and Stresses in Circular Wafers in a Row During Radiative Cooling
,”
J. Appl. Phys.
,
40
(
11
), pp.
4413
4423
.
4.
Lord
,
H. A.
,
1988
, “
Thermal and Stress Analysis of Semiconductor Wafers in a Rapid Thermal Processing Oven
,”
IEEE Trans. Semicond. Manuf.
,
1
(
3
), pp.
105
114
.
5.
Young
,
G. L.
, and
McDonald
,
K. A.
,
1990
, “
Effect of Radiation Shield Angle on Temperature and Stress Profiles During Rapid Thermal Annealing
,”
IEEE Trans. Semicond. Manuf.
,
3
(
4
), pp.
176
182
.
6.
Campbell
,
S. A.
, and
Knutson
,
K. L.
,
1992
, “
Transient Effects in Rapid Thermal Processing
,”
IEEE Trans. Semicond. Manuf.
,
5
(
4
), pp.
302
307
.
7.
Hebb
,
J. P.
, and
Jensen
,
K. F.
,
1998
, “
The Effect of Patterns on Thermal Stress During Rapid Thermal Processing of Silicon Wafers
,”
IEEE Trans. Semicond. Manuf.
,
11
(
1
), pp.
99
107
.
8.
Bentini
,
G.
,
Correra
,
L.
, and
Donolato
,
C.
,
1984
, “
Defects Introduced in Silicon Wafers During Rapid Isothermal Annealing: Thermoelastic and Thermoplastic Effects
,”
J. Appl. Phys.
,
56
(
10
), pp.
2922
2929
.
9.
Dilhac
,
J. M.
,
Nolhier
,
N.
,
Ganibal
,
C.
, and
Zanchi
,
C.
,
1995
, “
Thermal Modeling of a Wafer in a Rapid Thermal Processor
,”
IEEE Trans. Semicond. Manuf.
,
8
, pp.
432
439
.
10.
Cho
,
Y. M.
,
Paulraj
,
A.
,
Kailath
,
T.
, and
Xu
,
G.
,
1994
, “
A Contribution to Optimal Lamp Design in Rapid Thermal Processing
,”
IEEE Trans. Semicond. Manuf.
,
7
, pp.
34
41
.
11.
Huang
,
C. J.
,
Yu
,
C. C.
, and
Shen
,
S. H.
,
2000
, “
Selection of Measurement Location for the Control of Rapid Thermal Processor
,”
Automatica
,
36
(
5
), pp.
705
715
.
12.
Huang
,
I.
,
Liu
,
H. H.
, and
Yu
,
C. C.
,
2000
, “
Design for Control Temperature Uniformity in Rapid Thermal Processor
,”
Korean J. Chem. Eng.
,
17
(
1
), pp.
111
117
.
13.
Sorrell
,
F. Y.
,
Fordham
,
M. J.
,
O¨ztu¨rk
,
M. C.
, and
Wortman
,
J. J.
,
1992
, “
Temperature Uniformity in RTP Furnaces
,”
IEEE Trans. Electron Devices
,
39
(
1
), pp.
75
80
.
14.
Campbell
,
S. A.
,
Ahn
,
K. L.
,
Kanutson
,
K. L.
,
Liu
,
B. Y. H.
, and
Leighton
,
J. D.
,
1991
, “
Steady-State Thermal Uniformity and Gas Flow Patterns in a Rapid Thermal Processing Chamber
,”
IEEE Trans. Semicond. Manuf.
,
4
(
1
), pp.
14
20
.
15.
Huff, H. R., and Goodall, R. K., 1995, “Challenges and Opportunities for Dislocation Free Silicon Wafer Fabrication and Thermal Processing: An Historical Review,” Proc. 3rd Int. Rapid Thermal Processing Conf., Amsterdam, The Netherlands, Aug. 30–Sept. 1, pp. 9–40.
16.
Shishiguchi, S., Mineji, A., Matsuda, T., and Saito, S., 1997, “Boron Implanted Shallow Junction Formation by High-Temperature/Short-Time/High Ramping Rate (400°C/sec) RTA,” VLSI Tech. Symp., pp. 89–90.
17.
Collart, E. J. H., de Cock, G., Murrel, A. J., and Foad, M. A., 1998, “Characterization of Low Energy Boron Implantation and Fast Ramp-Up Rapid Thermal Annealing,” Mat. Res. Soc. Symp. Proc., Vol. 525, pp. 227–235.
18.
Incropera, F. P., and Dewitt, D. P., 1981, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York.
19.
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H., 1984, Computational Fluid Mechanics and Heat Transfer, McGraw-Hill.
20.
Reismann, H., and Pawlik, P. S., 1980, Elasticity, John Wiley & Sons, New York.
21.
Boley, B. A., and Weiner, J. H., 1960, Theory of Thermal Stresses, John Wiley & Sons, New York.
22.
Lin
,
S.
, and
Chu
,
H. S.
,
2000
, “
Thermal Uniformity of 12-in Silicon Wafer During Rapid Thermal Processing by Inverse Heat Transfer Method
,”
IEEE Trans. Semicond. Manuf.
,
13
(
4
), pp.
448
456
.
23.
Nowinski, J. L., 1978, Theory of Thermoelasticity With Application, Sijthoff & Noordhoff.
24.
Miyazaki
,
N.
,
Uchida
,
H.
,
Munakata
,
T.
, and
Fujioka
,
K.
,
1992
, “
Thermal Stress Analysis of Silicon Bulk Single Crystal During Czochralski Growth
,”
J. Cryst. Growth
,
125
, pp.
102
111
.
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