Quantitative study of adsorbate-adsorbate interactions of hydrogen on the Si(100) surface

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The equilibrium spatial distribution of hydrogen atoms adsorbed on the clean $\mathrm{Si}(100)\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}1$ surface under ultrahigh vacuum conditions has been investigated by means of scanning tunneling microscopy (STM). Singly occupied dimers, doubly occupied dimers, and clusters of adjacent doubly occupied dimers along a dimer row are observed. Through the evaluation of large-area STM images, a quantitative assessment of the prevalence of the different adsorbate configurations has been obtained for a range of hydrogen coverages from 0.03 to 0.59 monolayers. At moderate coverages, most of the hydrogen adatoms are found in doubly occupied dimers, while a relatively small number are present as singly occupied dimers or as part of clusters of doubly occupied dimers. The interaction between doubly occupied dimers was examined by determining the experimental size distribution of clusters and the spatial correlation function for the doubly occupied dimers. A nearest-neighbor interaction model is compared with experiment within analytic approximations and through full Monte Carlo simulations. The model is found to agree well with the experimental results. An effective pairing energy of $\ensuremath{\varepsilon}=0.31\ifmmode\pm\else\textpm\fi{}0.04\mathrm{eV}$ and an effective clustering energy of $\ensuremath{\omega}=0.04\ifmmode\pm\else\textpm\fi{}0.01\mathrm{eV}$ are inferred. These results are independent of any hypothesis concerning the adsorption/desorption pathways, but have implication for possible pathways and their kinetics.