Void formation in screen-printed local aluminum contacts modeled by surface energy minimization

- New analytical model for void formation based on surface energy minimization.
- Model is able to describe geometry dependence of voids.
- Significantly deeper BSFs for bifacial PERC+ cells (8 µm) compared to PERC (4 µm).
- BSF depths can be modeled by the amount of screen printed Al-Paste.

We demonstrate that the presence of voids in local aluminum rear contacts of PERC solar cells reduces the Al-BSF depths when compared to filled contacts. However, since voided contacts still exhibit a shallow Al-BSF we conclude that voids form during the re-crystallization process of the Al-BSF and thus at a point in time during furnace firing, where the aluminum is liquid. We propose an analytical model for void formation which takes into account the surface energies of the silicon wafer, the liquid aluminum as well as the aluminum-oxide shells of the screen-printed aluminum layer. Using geometrical approximations the model predicts that voids occur if the contact height exceeds a certain value. Scanning electron microscope cross-section measurements demonstrate that indeed voids are observed only for contact heights larger than 21 µm. The physical reason is, that in case of large contact heights the Al melt energetically favors to wet the large surface area of the aluminum-oxide shells instead of the relatively small area of the silicon wafer surface. We find that so-called PERC+ solar cells with Al fingers as rear contacts instead of full-area Al layers exhibit significantly smaller contact heights and hence exhibit almost no voids. Additionally, PERC+ solar cells exhibit much deeper Al-BSFs compared to PERC cells over a large range of rear contact widths. Using a new analytical model for Al-BSF formation, we find that the different Al-BSF depths are described solely by the different amount of Al paste printed to the rear side of PERC and PERC+ cells. Consequently, the PERC+ cells achieve low contact recombination and high efficiencies of 21.1% for narrow contact lines around 50 µm width, whereas PERC solar cells obtain highest efficiencies of 21.2% for 80 µm wide contact lines.