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First-principles calculations of Cu(001) thin films quantum size effect in surface energeti



First-principles calculations of Cu(001) thin ?lms: quantum size e?ect in surface energetics and surface chemical reactivities
Bo Sun,1 Ping Zhang,1, ? Suqing Duan,1 Xian-Geng Zhao,1 Jun

ren Shi,2 and Qi-Kun Xue2
1

arXiv:cond-mat/0701294v1 [cond-mat.mes-hall] 13 Jan 2007

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China 2 Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China First-principles calculations of Cu(001) free-standing thin ?lms have been performed to investigate the oscillatory quantum size e?ects exhibited in surface energy, work function, atomic relaxation, and adsorption energy of the cesium adsorbate. The quantum well states have been shown and clari?ed at particular k-points corresponding to the stationary extrema in bulk Brillouin zone, which are in good agreement with experimental observations. The calculated surface energetics and geometry relaxations are clearly featured by quantum oscillations as a function of the ?lm thickness of the ?lm with oscillation periods characterized by a superposition of long and short length scales. Furthermore, we have investigated Cs adsorption onto Cu(001) thin ?lms as a function of the ?lm thickness. Our systematic calculated results clearly show the large-amplitude quantum oscillations in adsorption energetics, which may be used to tailor catalysis, chemical reactions and other surface processes in nanostructured materials.
PACS numbers: 73.61.-r, 73.20.At, 73.21.Ac,

I.

INTRODUCTION

When the thickness of thin metal ?lms approaches the nanoscale, the oscillatory quantum size e?ects (QSEs) associated with electronic con?nement and interference will occur1,2,3,4 due to the splitting of the energy-level spectrum into subbands normal to the plane of the ?lms, i.e., the quantum well (QW) states. These QW states lead to strongly modi?ed physical properties and thus have been the subject of numerous experimental investigations in recent years5,6 . For example, the QW states are found to be responsible for an unusual metallic ?lm growth pattern7,8,9,10 , and for the thickness-dependent stability11 observed in the experiment. The QW states are directly connected to the oscillation in the exchange coupling between two magnetic materials across a nonmagnetic spacer layer of various thickness12 , and to giant magnetoresistance13,14,15,16 . Moreover, the QW states also give rise to an oscillatory phonon-electron coupling as the ?lm thickness varies, and thus a?ect the transition temperature of the superconductivity17,18 . Experimentally, the characterization of the QW states are commonly measured using angle-resolved photoemission spectroscopy (ARPES) and the scanning tunneling microscopy (STM). ARPES can be used to study the band structure along any direction of the surface Brillouin zone (BZ), while STM o?ers the possibility to study local structures, such as islands, chains, dots, etc. Using the scanning tunneling spectroscopy (STS) technique, in which the di?erential conductance (dI/dV ) is measured, one can reliably determine the energy of quantized electronic states in the range of approximately 1 eV below and above the Fermi level. Theoretically, a number of approaches have been used in the past in order to describe the electronic properties, in particular the QW states, in ultrathin metallic ?lms. Quasi-one-dimensional models, such as a square well potential19 or the phase ac-

cumulation model (PAM)20 , have been successfully used to interpret the energies of QW states. More sophisticated methods have also been used, such as the tightbinding approach21 and layer-Korringa-Kohn-Rostoker approach22,23 . In a few systems the QW states have been investigated by self-consistent density-functional calculations24,25,26,27,28,29,30,31 . There are strong reasons to use the ab initio methods. First, there are no adjustable parameters, and a wide range of calculated structural and electronic properties o?er the possibility of a detailed comparison with experiments. Also, quantities such as the expected STM pro?les and the amplitudes of the wave functions of the QW states, which cannot be obtained in simple approaches, can be calculated. In this paper we report our ?rst-principles calculations of the QSE in a speci?c QW system, i.e., the Cu(001) freestanding thin ?lms. Previous QSE studies concerning Cu(001) are mainly focused on the oscillations in magnetic interaction between the two ferromagnetic layers in fcc M /Cu/fcc M (001) sandwich structures where M denotes the ferromagnetic material. It has been demonstrated that the Cu(001) ?lms have a long length scale of 5.6 monolayer (ML) and a short length scale of 2.6 ML of oscillation periods for magnetic coupling in the [001] direction, corresponding to spanning vectors at the belly and neck of the bulk Cu Fermi surface respectively32,33,34,35 . Recent experimental e?orts have been focused on the new band structure properties of QW states in Cu(001) system36,37,38,39,40,41,42,43,44 . On the other side, the QSE of Cu(001) associated with its energetics was scarcely considered up to now. In particular, there is no clear experimental or theoretic evidence of the interplay between the di?erent oscillation periods of Cu(001) ?lms by the belly and neck extrema in bulk Cu Fermi surface. In this paper we present a detailed ?rstprinciples study of the surface energetics of the Cu(001) free standing thin ?lms. The QW states corresponding to the stationary extrema in bulk BZ are studied in detail.

2 The oscillations of the energetics versus the Cu(001) ?lm thickness are identi?ed and the corresponding oscillation periods are explained. We ?nd that the quantum interference of the QW states with di?erent in-plane wave vectors result in a superposion between long- and shortlength oscillating periods. The other purpose in this paper is to investigate the QSE character in surface adsorption energetics for a representative system in order to shed light on the e?ect of the QW states on the surface reactivities. Since the adsorption property is closely characterized by the chemical bonding between the adsorbate and the surface of the substrate, thus when the substrate is ultrathin, the QSE in the substrate will also in?uence the behavior of the surface adsorption. Here we address a particular adsorbate system, i.e., Cs/Cu(001), as a case study to manifest the QSE in surface adsorption properties. Due to its simple electronic structure and active chemical properties which is intrinsic for alkali metals, Cs is a unique adsorbate on metal surfaces, and has been extensively studied. Concerning Cs adsorption on Cu metal surfaces, the recently published articles45,46,47,48,49,50 mainly focus on the investigation of electronic, dynamic, and geometry properties of Cs layers on Cu(111). The nature of interaction between the Cs adatom and Cu(001) ?lm has been studied both via ?rst-principles pseudopotential calculations51 or throu