Modeling the formation of local highly aluminum-doped silicon regions by rapid thermal annealing of screen-printed aluminum

The formation of local highly aluminum-doped (Al-p ⁺) regions by rapid thermal annealing (firing) of screen-printed aluminum strongly depends on the temperature profile and the contact geometry. We measure the local Al-p ⁺ layer thickness W _Al-p+ as a function of the point and line contact size. Using quantitative yet simple analytical modeling, the time-dependent silicon concentration in the Al melt is described by elementary differential equations. From this we calculate W _Al-p+ and find agreement with the measurements. In contrast to the formation of full area Al-p ⁺ layers we find a smaller silicon concentration at the end of the firing process compared to the equilibrium concentration. This is a result of the process dynamics such as the dissolution rate of solid silicon and the transport of silicon in the Al melt.