Reaction Diffusion Model

3.1 Reaction Diffusion Model

As the fabrication of a semiconductor device today as back then consists of more and more single layer depositions, often being followed by an annealing step, hydrogen as “the” passivation agent was suggested to play a key role in the first modeling attempt dating back to 1977 [13]. In the so-called reaction-diffusion model Jeppson et al. assumed the breaking of hydrogen-bonds at the interface via a thermally and field-activated process under stress. This reaction-limited stress phase is schematically depicted in Fig. 3.1 (taken from [55]) and can be described with the kinetic rate equation at the interface after [56, 57, 58, 31] as

∂N ---it-= kf(N0 − Nit)− krNitX1it∕a ∂t

(3.1)

where $N0$ denotes the total amount of interface states, $Nit$ the fraction of dangling bonds thereof (not yet passivated), and $Xit$ the interfacial hydrogen concentration. The rates $k f$ and $k r$ describe the forward (depassivation) and reverse (passivation) process with a kinetic exponent $a$ considering the “size” of the diffusing species.

Figure 3.1: From Top to Bottom: Schematic view of the atomic hydrogen reaction-diffusion model during stress and relaxation. During the short initial phase, the interface region enters equilibrium. When in equilibrium, the degradation is dominated by the diffusion of hydrogen. As the stress is removed, the hydrogen diffuses back to the interface.

3.1.1 Stress Phase
3.1.2 Back Diffusion of Hydrogen during Recovery

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