  We study the mechanism leading to the metallization of the $\beta$-SiC(001)
Si-rich surface induced by hydrogen adsorption. We analyze the effects of band
bending and demonstrate the existence of a quasi-2D electron gas, which
originates from the donation of electrons from adsorbed hydrogen to bulk
conduction states. We also provide a simple model that captures the main
features of the results of first-principles calculations, and uncovers the
basic physics of the process.
