Solid State Communications, Vol. 67, No. 6, pp. 643-645, 1988. 0038-1098/88 $3.00 + .00 Printed in Great Britain. Pergamon Press plc STRUCTURE OF THE ct PHASE OF Ge(1 1 1) ~ × x/C3-Pb J.N. Carter, V.M. Dwyer and B.W. Holland Department of Physics, University of Warwick, Coventry, CV4 7AL, UK (Received 24 March 1988 by C.W. McCombie) The structure of the ~ phase of the Ge(1 1 1) v/3 x x/'3-Pb system is determined by energy minimisation with respect to the structural parameters using a charge self-consistent empirical tight-binding method. We find that the lead atoms lie above the second layer Ge atoms, in agreement with X-ray diffraction studies. The top layer of Ge is strongly contracted towards the bulk. THERE is currently strong interest in the structure of metal overlayers on semiconductor surfaces and the Pb/Ge(1 1 1) systems is an attractive example to study because it is known that Pb does not penetrate signifi- cantly into the Ge surface, so the structural possibili- ties are restricted, simplifying the interpretation of experimental data. It was established several years ago [1-4] that at a coverage of 0 = 1/3 a~,/-3 x ~ R 30 ° structure is formed by Pb on Ge(1 1 1) and it was proposed that the Pb overlayer consisted of one atom per unit cell as earlier suggested by Estrup and Morrison [5] for the Pb overlayer on Si(1 1 1). This was named the ~ phase to distinguish it from the more complex strutures seen at higher coverages [1-4, 6]. The question then arises as to how this overiayer sits on the surface, i.e. what is the adsorbate/substrate registry? If we assume that the system has a three-fold rotation axis, at least for the projection of the structure on the surface plane, there are only three possibilities, as shown in Fig. 1. The Pb atom may sit above a top layer Ge atom (7"1 site), above a second layer Ge atom (T4 site) or above a fourth layer Ge atom (//3 site). Feidenhans'l et aL [7] studied the system using surface X-ray diffraction and concluded that the T4 site was the true one, which is in harmony with energy minimisation calculation [8, 9] on the similar structures for A1 and Sn on Si(1 1 1). The X-ray work involved the measurement of reflec- tions on the surface plane only and therefore it was only possible to determine the projection of the struc- ture on the surface plane. Our aim in this Communica- tion is to determine by energy minimisation calcula- tions, not only the site in which the Pb atom sits, but the full three dimensional structure including relaxa- tion of Ge atoms normal to the surface. We make our calculations of the total energy of the system by using a charge self-consistent empirical tight binding cluster method developed by the authors [10] for semiconductor surfaces. The basis used is that of the sp 3 hybrids and dangling hybrids that appear artificially due to truncation of the cluster are sat- urated by adding hydrogen atoms. The one-electron energy is calculated by diagonalising the tight binding Hamiltonian, whose matrix elements are determined empirically after the manner of Harrison [11]. The difference between ion-ion and electron-electron en- ergies is written as a sum of contributions from the bonds [12] and found for each type of bond from the bond energy as a function of length as determined by an accurate quantum chemistry cluster calculation. An approximate charge self-consistency is imposed by calculating the charge on each atom and adjusting the term values on each atom to take account of the Figure 1 (~ Top layer Ge 2ncl layer Ge ' _ +') Pb TI H3 T4 Fig. 1. The three clusters representing the possible sites for Pb adsorption. The numbering system for the inequivalent top Ge atoms in the Tl case is shown, and the arrows for the T4 and//3 cases show the allowed relaxation directions in the surface plane. 643