Surface electronic structures of Ba overlayers on W(100), W(110), and W(111)

The total energy distributions (TEDs) in field emission (FE) and photofield emission (PFE) and the work functions have been measured at room temperature for Ba adsorbed on W(100), W(110), and W(111) in the range of coverage from 0 to 1 ML (monolayer). We observe two initial state peaks and three final state peaks on $\mathrm{W}(100)∕\mathrm{Ba}$, six initial state peaks and one final state peak on $\mathrm{W}(110)∕\mathrm{Ba}$, and two initial state peaks and two final state peaks on $\mathrm{W}(111)∕\mathrm{Ba}$. We extend the full-potential linear augmented plane wave method for the electronic structures of periodic lattices to calculate the emission current in FE and surface PFE at a metal-adsorbate-vacuum interface. Our calculations account for the energies of all of the initial state features observed experimentally in FE and surface PFE from clean W(100), in PFE and angle-resolved inverse photoemission spectroscopy from $\mathrm{W}(100)∕\mathrm{Ba}$ at 1 ML, and for all of the peaks observed in FE, surface PFE, and photoemission from $\mathrm{W}(110)∕\mathrm{Ba}$ at 0.6 ML and from $\mathrm{W}(111)∕\mathrm{Ba}$ at 1 ML. The $d{z}^{2}$-like surface states of the Swanson hump [L. W. Swanson and L. C. Crouser, Phys. Rev. Lett. 16, 389 (1966)] of clean W(100) hybridize with $s$-like states of the $c(2\ifmmode\times\else\texttimes\fi{}2)$ overlayer and are shifted by $\ensuremath{-}1.60\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ to yield a prominent peak in PFE. An isolated Ba $c(2\ifmmode\times\else\texttimes\fi{}2)$ layer is found to be weakly metallic; the metallicity is greatly enhanced when it is adsorbed on a W(100) substrate. The TEDs in PFE from the atomically less dense overlayer $\mathrm{W}(110)∕\mathrm{Ba}$ $(2\ifmmode\times\else\texttimes\fi{}2)$ are dominated by substrate-overlayer interactions, while those from the atomically denser overlayer $\mathrm{W}(111)∕\mathrm{Ba}$ $(1\ifmmode\times\else\texttimes\fi{}1)$ are dominated by interactions within the overlayer. Our results yield evidence that above $1∕3$ ML Ba coverage on W(111), which corresponds to a commensurate $({3}^{1∕2}\ifmmode\times\else\texttimes\fi{}{3}^{1∕2})R30\ifmmode^\circ\else\textdegree\fi{}$ overlayer, the interstitial sites fill in randomly to form a commensurate $(1\ifmmode\times\else\texttimes\fi{}1)$ overlayer at 1 ML coverage.