Thermally Induced Stresses and Strains in Laser Processing of Thin Films
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THERMALLY INDUCED STRESSES AND STRAINS IN LASER PROCESSING OF THIN FILMS Judah A. Tuchman, Lisa P. Welsh and Irving P. Herman Department of Applied Physics, Columbia University, New York, NY 10027
ABSTRACT The stresses and strains induced in thermal laser processing of substrates and thin films on substrates, are obtained in terms of single integrals by solving the thermoelastic equations using a Gaussian profile laser as the heating source. This analysis is applied to silicon thin films on fused silica and sapphire substrates. In part, this study shows that defects can form in the films because the stresses induced during high temperature laser processing of silicon and similar materials can exceed the yield stress under certain experimental conditions.
INTRODUCTION During laser processing of surfaces, thermal heating will cause the formation of stresses
*and strains throughout the heated material, which must be analyzed because of their potential long term effects. In the extreme case, damage to the material system may result by the formation of defects. However, even the creation of built-in-stresses and strains without defects can alter properties. For example, laser-induced elastic strains will perturb phonon frequencies, thereby complicating in-situ temperature measurements by Raman microprobe analysis [1]. In this paper, solutions of the thermoelastic equations for local heating of isotropic substrates by a TEM00 Gaussian laser beam are presented. These solutions are extended to the case of thin films on substrates, as in Reference [1], to assess potential contributions to material damage by defect formation.
SOLUTION - THERMOELASTIC EQUATIONS The temperature rise due to a focused laser beam with cylindrical symmetry, has been obtained by Lax [21 by solving the heat flow equation under steady state conditions. In the particular case of a TEMOO Gaussian beam with power P0 , beam waist o0, and intensity I(r, z = 0) = P0 e- r/2(1) X60)2
MaLRes. Soc. Symp. Proc. Vol.130. 01969 Materials Research Society
334
TableJ Total strains and residual stresses in a substrate heated by a gaussian laser beam.
r =- coJ (Jo(XR) - -LR-) F(X) [A(X) exp(-XZ) - B(X) exp(-WZ) - C(X)Z exp(-XZ)] dX jI(XR) FpZd C& = - Oof F(;L) [A(;L) exp(-;Z) - B(X) exp(-WZ)- C(;)Z exp(--)]dX 00rW
-A()ex(Z)-
JJ= Jo(XR)F(;>)[(2-B(X)-AoL))exp(-a)-W2B(o)exp(-WZ) Offs=
-
-
C( )Z exp(-4Z)] dC
0 Jo(LR)F(X) [(2W -I)B(X) exp(-XZ) - 72 B(.) exp(-WZ) - C(X)Z exp(-XZ)]dX + aoj J1(XR) (X)[A(x) exp(-a) - B(L) exp(-WZ) - C(X)Z exp(-;LZ)] dX W2-~X2
2W
a= 0 Jo(.R)F(X) [(A(X) + B(;L)(l- 2•v)) exp(-XZ) + - aoj J 1-R) F(X)[A(X) exp(-;XZ)
-
B(;L) exp(-WZ)
-
BQL) exp(-WZ)] d
C(;.)Z exp(-;.Z)] d;X
Jo(;R)F(L) [B(X)(exp(-XZ) - exp(-WZ)) - C(X)Z exp(-XZ)] dX 1Oo
oy =
l+v 2o&W 1 . Tmax , 1-v Itl+v
where
and A(XL) =-3(W+2X)(I'v)(W-)2
,
B(X) =
(W2.;2)2
E - Co and C(X) 2
2 2
(W -; )
=
(W+;,)(W 2 -; 2)
Table II Total strains and residual stresses in a laser heated thin film on a substrate.
er¶(r)
-
f (r, z=0)
64o(r) z--0) "== eS(r, vl+v(f)
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