Time-Dependent Capture Numbers with Repulsive Pair Interactions: Cu/Cu(111) and Ge/Si(001)
- PDF / 624,489 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 16 Downloads / 157 Views
W2.1.1
Time-Dependent Capture Numbers with Repulsive Pair Interactions: Cu/Cu(111) and Ge/Si(001) J. A. Venables1,3, H. Brune2 and J. Drucker1 1
Department of Physics & Astronomy, Arizona State University, Tempe AZ 85287-1504, U.S.A. 2 Institut de Physique des Nanostructures, EPFL, CH 1015 Lausanne, Switzerland. 3 School of Chemistry, Physics & Environmental Science, University of Sussex, Brighton, U.K.
ABSTRACT Recent experiments and calculations have shown that weak repulsive interactions between adsorbate atoms may shift nucleation kinetics from the well-known diffusion limit towards the attachment-limited case. The distinctions between diffusion- and attachment-limited kinetics are clarified, and the increased importance of the transient nucleation regime in the latter case is shown to be due to a combination of delayed nucleation and reduced capture. A time-dependent interpolation scheme between attachment- and diffusion-limited capture numbers is proposed, and tested against KMC simulations. Using this scheme to interpret recent STM results on Cu/Cu(111), bounds on the maximum adatom-adatom potential repulsive energy of 12±2 meV are deduced. Time-dependent effects also occur in the growth and ripening of strained Ge islands on Si(001), and the similarities and differences between these two systems are discussed. RATE EQUATIONS CONTAINING SELF-CONSISTENT CAPTURE NUMBERS Rate equations have been used successfully to analyze data, notably of the nucleation density nx, as a function of experimental variables, usually the flux F (or equivalently deposition rate R) and the substrate temperature T [1-3]. The reaction rates in each equation, e.g. for the single adatom density n1, are of the form 2σ1D1n12 (for the rate of adatoms forming pairs) or σxD1n1nx (for the rate of adatoms joining stable clusters). In these terms σ1 and σx are capture numbers, and D1 is the single-adatom diffusion coefficient. This paper discusses the determination of capture numbers, when there may be barriers for attachment of adatoms to other adatoms and to clusters. The full mathematical and computational details are given in a companion paper [4]. Although the distinction between diffusion-limited and attachment-limited kinetics is generally well known, there have not been many explorations of such issues in connection with epitaxial crystal growth. But several recent Scanning Tunneling Microscopy (STM) experiments at low temperatures on smooth metal surfaces [5,6] and associated ab-initio calculations [7,8] have highlighted attachment-limited behavior, due to the presence of repulsive barriers between adatoms. In particular, we show that capture numbers exhibit these two limits, and indicate how the two limits can be combined to give generally applicable, including time-dependent, forms. Repulsive barriers modify the results of conventional (sometimes called classical) nucleation theory (CNT), by extending the transient nucleation regime to higher dose. New formulae are given for the capture numbers on the assumption of radial symmetry
Data Loading...
