ELEMENTARY MODEL OF DIRECT BONDING AT LOW TEMPERATURE
The simplest model of the joining kinetics at the stage of isolated interface voids shrinking is developed. The model basic assumptions are described, as well as also the kinetic equations in the mono-size approximation are derived.
There are tThree main stages of the process can be represented distinguished when two surfaces with a small roughness are in contact with each other (tens-of-nanometer-order irregularities) and fall under pressure:
1. At the first stage, several isolated contacts are formed. Their number and contact area increases with time due to the capillary pressure and external pressure effect.
2. At the next stage, the formation of a two-phase quasi-directional contact zone, consisting of two interpenetrating percolation clusters – a contact cluster and a pore cluster – can be expected.
3. At the third stage, one can expect the formation of almost complete contact aside from a certain number of isolated pores at the interface. These pores ripen and selfheal (recover) withover time, mainly due to the capillary pressure effect.
The present article is devoted to a simple model of the third stage. The Gibbs-Thomson equations for capillary effect is reformulated for the case of rectangular voids. Chemical potentials for various facets of finite sizes are found. Difference of the surface diffusivities along different facets is taken into account. Balance of grain-boundary diffusion fluxes and surface diffusion fluxes are also taken into account. The proposed model is only the first step to describe the compound joining kinetics at its last stage.
Subsequent research will focus on:
1. Accounting for evolving pore size distribution. The ripening of interfacial poresPore coalescence proceeds due to vacancy exchangeexchange by by diffusion via theacross their outer surface (cont contact interface.)
2. Designing a model with a rigorous solution for the ‘real’ stress distribution (the real contact stress distribution) around realistic pore structures (irregular, nont-rectangular shape)
3. Detailed and comprehensive three-stage compound analysis.
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