On the Role of Surface Diffusion in Stress Relaxation During Electromigration
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Abstract We report on the role of surface diffusion involved in relaxation of electromigration (EM) induced compressive stresses in relation to hillock growth and EM behavior of interconnects. Two competing mechanisms of EM stress relaxation by material transport onto the surface are considered. The first is hillocking by threshold diffusional creep (TCH), with rather large blocks of material (grains or group of grains) involved in plastic flow. The second mechanism, atomic diffusion hillocking (ADH), is presumed to be a nonthreshold one, and represents atomic grain boundary (GB) diffusion stimulated by the hydrostatic stress gradient in the direction normal to the film surface. The latter process involves surface diffusion because GB diffusional flux onto the surface must be coupled with the flux of redistribution of the atoms over the surface. If ADH acts rapidly, this should prevent the build-up of the matter at the down-wind (anode) end of the stripe, and thus, eliminate the Blech EM threshold resulting from the stress-gradient along the stripe. The question as to whether GB diffusion capable of transporting atoms pushed by electron wind along the stripe is also effective in relieving compressive stress by GB migration of the surplus atoms in the normal direction, has remained open up to now. The problem is especially acute for short or/and narrow lines separated into short polycrystalline segments, where the Blech threshold effects are critical to EM reliability. We derived the main features of the EM behavior in drift velocity test geometry assuming that both TCH and ADH are operative. The result can be compared with available and future experimental observations in order to reveal if and when the ADH mechanism with surface diffusion involved works. 1. Analysis and Discussion In the analysis that follows we assume that GB network is the main diffusion pathway for electrotransport and that all relevant materials properties are isotropic. 1-1. Stress Relaxation by Threshold Creep According to the conventional view on the Blech problem, the EM flux divergence at the anode end of the stripe (x=0) results in EM induced compressive stresses a(x), which can relax by hillock growth if a (x) exceeds some threshold stress, at. The process of hillock growth was rationalized recently [1-3] in terms of diffusional creep with threshold at = Gb/d, with G being the shear modulus, b, the Burgers vector of GB dislocations acting as sinks for atoms at the root of growing hillock, and d, the grain size. The hillock distribution, across the stripe (i.e. in the y-direction) was presumed to be uniform, and with this approximation of "extended hillocks", the film thickening rate Ii is given by [1,2]: h(x)/ho =[a(x)- at]/1,
a(x) > at,
(1)
where h0 is the initial thickness of the film and tI is effective creep viscosity. It was also shown that the anode stress a(0) always exceeded at, the stress experienced non-linear drop in the hillocked zone, 0 < x < Lx, where a(x) > at, and decayed linearly outside this zone at L _> x >_Lx. (He
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