PHYSICAL REVIEW B VOLUME 36, NUMBER 6 15 AUGUST 1987-II Work function of metals upon alkali-metal adsorption: Overlayer relaxation P. A. Serena, J. M. Soler, and N. Garcia Inder P. Batra IBM Research Diuision, Almaden Research Center E33/80I, 650 Harry Road, San Jose, California 95120 (Received 6 April 1987) The work function of metals is lowered upon alkali-metal adsorption and this lowering (A4) is known to be coverage dependent. Using standard jellium-model calculations, we show that if the metal-overlayer distance is assumed to increase with coverage, the experimental behavior of AN is much better reproduced. In particular the minimum work function is increased and shifted to higher coverages, in agreement with experimental results. The increase of distance with coverage also leads to an energetically more stable configuration. The adsorption of alkali metals on metal surfaces has been studied for a long time. ' ' A rather complete list of references can be found in a recent paper by Wimmer et al. ' The change in work function AN depends on coverage 6 and shows universal behavior on almost all metallic substrates. ' On semiconducting substrates the behavior may be somewhat different" but it is not yet ful- ly established. Alkali-metal adsorption at low coverage leads to a rapid decrease of the work function. Then at a critical coverage 6, the curve shows a minimum. Even- tually at higher coverages one reaches the characteristic value of the overlayer. The correct physics of this behav- ior is contained in the model proposed by Gurney' in 1935. At low coverage the valence level of the alkali- metal adatom is only partially occupied leading to a large dipole moment which lowers the work function. With in- creasing coverage the adatom valence-level occupancy in- creases and hence the work-function lowering goes through a minimum. The general shape of the work- function-change curve is thus reasonably explained. A fundamental understanding of the work function of clean surfaces and the changes occurring due to adsorp- tion has been provided by the density-functional calcula- tions of Kohn, Lang, Smith, and Ying. ' Quantitative values have been obtained using the simplified scheme of the jellium model. The full-potential linearized augmented-plane-waves (FLAPW) method for slabs of real atoms has been applied by Wimmer et al. ' More re- cently Ning et a/. have used a combination of slab and jellium approaches. Whereas the general shape of AN as a function of coverage is quite well reproduced, the criti- cal coverage at which A4 goes through a minimum is usually underestimated. In the present report we present results based on stan- dard jellium-model calculations. A crucial new element, however, is the introduction of a coverage-dependent metal-overlayer distance. At low coverages, where the alkali-metal atom is more or less an ion, we choose the ionic radius to estimate the metal-overlayer distance. At high coverages, when metallization sets in, it is more ap- propriate to use the atomic radius. At intermediate cover- ages our results are based on a linear interpolation. Our motivation for choosing such a model is derived from a recent first-principles total-energy calculation for the Al-Ge system. ' The calculation was done for two different coverages and it was concluded that the over- layer metallization was in fact accompanied by overlayer-substrate distance relaxation. More recently experimental evidence for such a distance relaxation has also been presented. ' Furthermore, Muscat and Ba- tra, ' using an Anderson model Hamiltonian approach, have also studied non-self-consistently the effect of dis- tance relaxation. Wimmer et al. ' have noted an almost linear dependence of the change in work function with overlayer distance at a fixed coverage. Thus the evi- dence seems to be rather persuasive to incorporate the overlayer-substrate vertical distance as a parameter in the work-function calculations. This is the subject of the present Brief Report. In our calculation the substrate is described by the jelli- um model. The alkali-metal adatom is also replaced by a jellium slab of width d with coverage dependence obtained from d (6) =d, „„+(d„„— d, ,„)6, where d;, „ is tv ice the alkali-metal ionic radius and d„, „ is the distance between the most compact planes in the bulk alkali metal. The adatom slab is centered at —, 'd(6) and the height of the jellium increases according to the in- crease of 6. We notice that the model of Lang is simply obtained by taking 6=1 in Eq. (1), as the value of d is kept fixed in his model. The results are obtained by solv- ing for the system of two jellium materials (substrate and adsorbate) self-consistently in the local-density approxima- tion (LDA). Figure 1 shows our typical calculated results for the work function as a function of coverage. The example chosen corresponds to the substrate r, =2. 07 a. u. (Al) and with Cs as the overlayer. It is well known that jellium- 36 3452 1987 The American Physical Society