From this presentation James Webb Space Telescope (JWST) Technology Discussion For APPEL Forum, dated August 7, 2008, I see this:
- Low $\alpha_S$/$\epsilon_H$ to minimize absorbed solar heat load
- Metallic coatings have $\alpha_S$/$\epsilon_H$ > 1
There's more detail in Technology Development for Large Deployable Sunshield to Achieve Cryogenic Environment, but I haven't found a free source for that one, so you'll just have to take my word for it. Here's a handy diagram from that paper:

$\alpha_S$ is solar absorptance, and $\epsilon_H$ is the emissivity of the material. I can't perfectly identify the meaning of the H subscript, but "hemispherical" seems plausible.
If I've understood correctly, the low $\alpha_S/\epsilon_H$ value helps ensure a low steady-state temperature of the outermost layer, but the paper assumes that the reason for using such a coating is so obvious to its intended audience that it doesn't explain in any further detail. As I'm not an engineer or familiar with the issues of things warming up in sunlight I can't be certain.
Silicon was chosen due to its high emissivity and robustness to environmental conditions prior to launch. Germanium was also considered, but:
Germanium has been used in
applications in the past and has
the proper thermal properties.
However, there are issues
identified with property
degradation due to humidity
effects. The coating also has high
electrical resistance causing a
need for complicated
supplemental grounding on a large
membrane in space