We present first-principles density-functional calculations for the adsorption of water on the Ge(100) surface. The dissociation of water molecules into OH and H species is energetically favored over the molecular adsorption, where O forms a bond to the down atom of the Ge dimer, similar to the case of Si(100). However, on Ge(100) the energy barrier for water dissociation is calculated to be $\ensuremath{\sim}0.49\mathrm{eV},$ which is significantly larger than our previous value (0.15 eV) on Si(100). Since the molecular adsorption on Ge(100) has a relatively smaller adsorption energy of 0.33 eV compared to that (0.57 eV) on Si(100), adsorbed water molecules on Ge(100) prefer desorption rather than dissociation upon being thermally activated. This result provides an explanation for the experimental observations on Ge(100), where water does not stick easily at room temperature.
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