Diffusion of Gold into Silicon. W-Shaped Concentration Profiles of Gold
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DIFFUSION OF GOLD INTO SILICON. W-SHAPED CONCENTRATION PROFILES OF GOLD. A.V.VAYSLEYB, J.MALINSKY Department of Material Science, School of Mines, Columbia University, N.Y. 10027
ABSTRACT Diffusion of gold atoms into silicon crystals was considered. It was shown that Wshaped gold profiles in silicon can be explained in the framework of both the dissociative and the kickout mechanisms. During the last 20 years the diffusion of gold atoms into silicon crystals was actively studied. Nevertheless, so far this Au-Si pair constantly demonstrates new property. Lately, it was discovered [1] that at relatively short time intervals, the gold concentration profiles are W-shaped compared to U-shaped ones at long time interval. It was explained with the assistance of the kickout diffusion mechanism in the presence of extended defects in the Si crystal. In the present communication we wish to show that W-shaped profiles can be explained in the framework of both the dissociative and the kickout diffusion mechanisms with a few modification equations given in [2-4]. Let us consider a plain silicon plate having thickness d, whose both surfaces are covered with thin Au layers. When the sample is heated to the temperature above 900K, AuSi diffusion occurs. Since, the solubility of gold into silicon is low, we can assume that the Au concentration does not change at the boundary. In the presence of inhomogeneously distributed extended defects, such as swirls and vacancy clusters, the set of equations describing the diffusion kinetics of gold in silicon on taking into account both the dissociative and the kickout mechanisms can be written as follows:
9•Csklcs + kAcc d aI I dc ý2v &L=~DI d'c ox2
-k3ClCs+k4ci
(1) (2)
-k22cic +kISV(3) c-
dc ' -D - DtdX Idc k 3 ctcs C +k 4 ci --,l()(\I A(x'(c,
cc
(4)
Here cs and ci are gold concentrations in the positions of substitution and interstices, respectively, cv is vacancy concentration, cI is the Si interstitial concentration, c(X ((x=i,V,I,s) are the corresponding thermodynamic equilibrium concentrations. Coefficients kj (j=1,2,3,4) are the constants of the recombination and dissociation:
k, =k 2 ci
,CcV/C ,k 2 = 4rR(Di +Dv),k
3
= 47rRD,,k 4
= k3 c
c/cS
(5)
where Da (a=i,V,I) are the corresponding diffusivities. On the right side of Eq.(l) the diffusion term is omitted because DsI
the approximate solution of Eq.(7) can be written as
follows:
C= {1 + CoU1 (x,t)exp[-Pj(x)tl(
,J
(12)
where uI has the same form as uv with the change Dv by DI, fl 1(X) is proportional P1 (X) which describes inhomogeneous distribution of dislocations or swirls in the sample. Near the edges and in the middle of the sample we have
1 + c 0ý7_r-•,t
,
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