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.
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