First principles study of the Cu(100), Cu(110) and the Cu(111) surface

Extended abstracts !

I

I

I

I

I

I

o.81 0

>

0 0

0 0

CD

0

"-'0.5

0.2 I

0.2

I

I

I

0.3

coverage

I

I

I

0.4

0.5

(ML)

Figure I. Activation energy of surface diffusion of Ga on Ge(100).

The STM observation suggests that Ga atoms on Si(100) 2 x l form rows oriented parallel to the dimerization direction of Si atoms at low coverages and have one-dimensional mobility across the Si dimer rows 1. Since the Ge(100) surface has a structure similar to Si(100), anisotropic behavior of the surface diffusion will be expected. In the present measurement, we could not find any evidence for the anisotropy or other dynamical properties such as phase transitions.

Acknowledgement This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture.

References i j Nogami, J Vac Soc Japan, 32, 593 (1989). 2 T Honda, T Okano and Y Tuzi, J Phys (Paris), C6, 257 (1988). 3 R Gomer, Surface Sci, 38, 373 (1973).

First principles study of the Cu(lO0), Cu(llO) and the Cu(lll) surface T Rodacht, K P Bohnent and K M Ho:~, tKernforschunoszentrum

Karlsruhe, Institut fiir Nukleare Festkrrperphysik, P.O. Box 3640, D-7500 Karlsruhe, FRG ; ~Ames Laboratory--U.S. Department of Energy and Department of Physics, Iowa State University, Ames, Iowa 50011, USA

Over the past few years there has been substantial progress in measuring surface relaxations and surface phonons. Especially the noble metals have attracted a lot of attention since they allow to study how the interaction of localized d-electrons and delocalized s-p electrons influences surface properties. Cu with the narrowest d-band among all noble metals has been studied extensively. LEED, high (HEIS) and medium energy ion scattering (MEIS) studies as well as SPLEED studies have been carried out for the low index Cu-surfaces. Thus the surface structure is

well known. High resolution EELS and He scattering measurements have also given detailed information about the surface phonon spectrum. However the structural studies as well as the phonon measurements revealed the need for theoretical work to interpret these data in simple physical terms. So far a systematic study of the low index surfaces of Cu has been carried out only within the framework of the embedded atom method. These results seem to depend critically on the underlying fit to bulk properties. Thus there is the need for first principles total energy calculations which have been applied successfully to a variety of metal surfaces. Our calculations were performed by use of the first-principles pseudopotential approach within the local-density-functional formalism. The only approximations made in these calculations are the local-density approximation for treating the exchangecorrelation energy of the electrons', the frozen-core approximation, and the Born-Oppenheimer approximation. Details of the method can be found elsewhere 2. F o r dealing effectively with the narrow d-bands a real space formulation for the localized part of the charge density was used. To test the norm conserving pseudopotential extensive studies of bulk properties were carried out. The results were in excellent agreement with experiment 3. The surface calculations were performed using the periodic slab geometry with seven atomic layers separated by three layers of vacuum. Details will be given in a forthcoming publication 3. Relaxations for the three low index surfaces are given in Table 1. For C u ( l l 0 ) all experiments support a value of Ad12 = ( - 7.5 -t- 1.5)~ and Ad2s = (2.5 _-/-1.5)~ 4 which is in excellent agreement with the theoretical results, the accuracy of which is roughly 0.5 ~ of the interlayer spacing. The results for Cu(100) seem to contradict the experiment where strong second layer effects are found. However a detailed analysis of the R-factor as given in ref 5 shows that also Adt2 -- - 2~o and Ad23 ~ 0 ~ is compatible with the measured I - V curves. Unfortunately so far only LEED studies have been carried out for this surface. F o r Cu(111), where only small effects are calculated, the agreement with experiment is again excellent. Comparing with results obtained with the semiempirical embedded-atom method (EAM) there is generally qualitative agreement. More cannot be expected since apparently the uncertainty inherent in the EAMapproach is of the order of at least 2 - 3 ~ of the interlayer distance as can be seen from comparing results from refs 6 and 7. Having determined the equilibrium geometry surface interand intraplanar force constants were calculated for the Cu(100) surface at high symmetry points. This was done by distorting the equilibrium geometry appropriately. Having obtained the surface force constants the dynamical matrix for a slab 50 layers thick was set up. The coupling between the inner layers of the slab is described using force constant matrices determined from measured bulk phonon dispersion curves s whereas the couplings involving the surface region are determined from our microscopic calculations. Solving for the eigenvalues and eigenvectors of the slab gives surface modes and their eigenvectors without approximations. Results for the X-point are given in Table 2. As can be seen the agreement with available experimental information is of the order of 0.1 THz. A detailed analysis of these results as well as results for other Cu surfaces will be given in a forthcoming publication s . Results from calculations within the EAM-method are similar however EAM-calculations by different groups differ up to 0.5 THz 9" lo. 751

Extended abstracts

Table l. Multilayer relaxation for the Cu(100), Cu(110) and Cu(111) surfaces. Results are given in % of interlayer distance ( - , inward; + , outward relaxation). For comparison are also given experimental results and results of embedded atom calculations Our calculations LEED

Ad34

-9.27 2.77 - - 1.08

Cu(100)

Ad12 Ad23 Ad3,,

-3.02 0.08 - 0.24

Cu(11 I)

Ad12 Ad23 Ad34

- 1.27 -0.64 -0.26

Cu(110)

Ad12 Ad23

SPLEED

-8.5 I1 2.3

-5.312 3.3 - 1.25 0.9

-0.715

Table 2. Surface phonon frequencies of the Cu(100) surface at the Xpoint. The results are given in THz. For comparison are also given experimental results and results of embedded atom calculations

X

Mode

Our calculations

SI $4 $5 $6

2.31 3.10 3.43 6.19

Experiment

Embedded atom method Nelson et al 9 Luo et al 1°

3.2414

2.09 2.99 6.08

2.13 3.25 3.21 5.55

References I p Hohenberg and W Kohn, Phys Rev, 136, B864 (1964); W Kohn and L J Sham, Phys Rev, 140, Al133 (1965). 2 K M Ho and K P Bohnen, Europhys Lett, 4, 345 (1987) and references given therein. 3 T Rodach, K P Bohnen and K M Ho, to be submitted. '* M Copel, T Gustafsson, W R Graham and S M Yalisove, Phys Rev, 1333, 8110 (1986). 5 D M Lind, F B Dunning, G K Waiters and H L Davis, Phys Rev, B35, 9037 (1987). 6 S M Foiles, M I Baskes and M S Daw, Phys Reo, B33, 7983 (1986). 7 T Ning, Q Yu and Y Ye, Surface Sci, 206, L857 (1988). a R M Nicklow, G Gilat, H G Smith, L J Raubenheimer and M K Wilkinson, Phys Rev, 164, 922 (1967). 9 j S Nelson, E C Sowa and M S Daw, Phys Rev Lett, 61, 1977 (1988). 1o Luo Ningsheng, Xu Wenlan and S C Shen, Solid State Commun, 67, 837 (1988). i1 D L Adams, H B Nielsen and J N Anderson, Surface Sci, 128, 294 (1983). 12 1 Stensgaard, R Feidenhans'l and J E Serensen, Surface Sci, 128, 281 (1983). 13 S A Lindgren, L Walld6n, J Rundgren and P Westrin, Phys Rev, B29, 576 (1984). 14 M Wuttig, R Franchy and H Ibach, Solid State Commun, 57, 445 (1986).

752

Experiment HEIS

MEIS

Embedded atom method Foiles et al6 Ning et al 7

-7.54 2.5

-4.93 0.23

-8.73 1.56 -- 1.20

- 1.44 - 0.33

-3.79 - 0.54 0.02

- 1.39 -0.05

-2.48 -0.04 0.00

On the structure and dynamics of thin Ar films on Pt(111) P Zeppenfeld, U Becher, K Kern, R David and G Comsa, lnstitut fiir Grenzfliichenforschung and Vakuumphysik, Kernforschunosanlage Jiilich, 5170 Jiilich, FRG The structure and lattice dynamics of thin Ar films physisorbed on P t ( l l l ) have been investigated using He-diffraction and inelastic He-scattering. The He-scattering apparatus is described in detail elsewhere 1. Structural information is obtained by monitoring the total scattered He-intensity as a function of the wave-vector transfer Q parallel to the surface. The total scattering angle being fixed at 0~ + 0f = 90 °, Q, is varied by rotating the sample and thereby changing both incident and outgoing angles 0 i and 0 r simultaneously. P h o n o n spectra are recorded by Time-of-Flight analysis of the scattered He-beam. In the experiments reported below a He-beam energy of 18.3 meV has been used, resulting in an overall wave-vector and energy resolution o f A Q = 0.02 A - 1 and AE = 0.32 meV, respectively. Ar is adsorbed on the Pt(l 11) surface from the 3D-gas phase at low surface temperatures (~-20 K). The Ar coverage is readily obtained by monitoring the specularly reflected He-intensity 2. Ar adsorbs on the clean P t ( l l l ) surface in a hexagonal solid phase aligned with respect to the substrate. In the submonolayer regime a structural phase transition of the physisorbed Ar layer is observed at a coverage 19 ~- 0.75 (19 = 1 refering to full m o n o layer coverage): At lower coverage (19 < 0.6) the first order diffraction peak of the Ar-phase is centered at Q = 1.90 A - l , corresponding to a lattice parameter a = 3.81 A. U p o n increase of the Ar coverage a second first-order diffraction peak at Q = 1.96 A - x emerges, corresponding to an Ar-phase with lattice parameter a = 3.70 A i.e. slightly compressed with respect to the first. While the intensity of the first peak continuously decreases upon further Ar-adsorption, the second peak at Q = 1.96 A becomes more intense. At 19 = 0.75 the two diffraction peaks have about equal intensities while above 19 > 0.9 the first peak has vanished and only the second one is observed. The discontinuous change of the diffraction peak position and the observed phase coexistence indicate that this phase tran.sition is of first order. Since a discontinuous transition between two incommensurate (floating) phases as a function of coverage is not likely to occur, we have looked for c o m m e n s u r a t e s t r u c t u r e s - - i n particular for