The major theme of our past self-assembly work has been using real-time microscopic observations of thermal fluctuations to analyze the pattern formation mechanisms in the 1-100nm size regime. We have studied several systems in which the ordering is particularly dramatic. In collaboration with Sandia/New Mexico, we have analyzed fluctuations of the co-existing low- and high-density Pb phases that appear on Cu(111) surfaces exposed to Pb [1]. As illustrated by the low energy electron microscope images in Figure 1, the patterns depend remarkably on temperature and Pb coverage. With scanning tunneling microscopy (STM) we studied the ordering of another system, S-induced holes in Ag films on Ru [2,3]. In collaboration with A. Schmid (LBNL), we analyzed spin-polarized LEEM (SPLEEM) observations of magnetic-domain fluctuations on Fe/Cu(001). In collaboration with S. Helveg and F. Besenbacher (Aarhus Univ., Denmark), we analyzed stripe phases that appear in the O/Pt(110) system [4].
Figure 1. LEEM observations of the self-assembled patterns that occur after depositing increasing amounts of Pb on Cu(111). The dark phase is a random Pb-Cu surface alloy, the bright phases is a Pb overlayer phase. The temperature is 675K and the field of view is 4 µm.
By combining theory and experiment, we have quantitatively determined the forces responsible for self-assembly in these systems. In general, domain patterns on surfaces are caused by a competition between short-ranged atomic attractions and longer-ranged repulsions. There are many sources, however, for the repulsions. For example, our analysis shows that the Pb/Cu system is a surface-stress-domain system in which repulsions arise from the interference of bulk elastic relaxations: these relaxations relieve surface stress at domain boundaries [5]. We also determined that surface stress controls domain formation in the S-induced holes in Ag films on Ru [2]. However, the source of the repulsions turns out not to be bulk relaxations. Instead, stress in this system is relieved by generation of dislocations in the Ag film. By analyzing the thermal vibrations of the hole array shown in Figure 2, we measured the long-range repulsions. By comparison with 2-D Frenkel-Kontorova models of the dislocations, we showed that the repulsion arises from interactions between dislocations in the film. In related work, we have found that the O/Pt system also orders to relieve surface stress. By analyzing how the size of magnetic domains of Fe/Cu film depends on temperature and applied magnetic fields, we found that magnetic dipole repulsion accounts for the pattern formation.
Since the forces responsible for self-assembly can now be understood, we believe that making useful surface structures using self-assembly will depend upon having very fast surface diffusion. To form ordered patterns with very large periodicities, considerable mass transport must occur. Thus, our most recent efforts have concentrated on understanding the detailed kinetic pathways by which surface phases self-assemble and on understanding the mechanisms of enhanced surface diffusion.
Figure 2. Self-assembly of a triangular vacancy lattice in an atomic layer of Ag on Ru.
(a) Intermediate state of the lattice formation. New (smaller) S-filled holes are created "in place" to extend the existing local hole arrays. For more information, see the Ag on Ru S-deposition movie below. (b) Superposition of two STM images acquired 12 seconds apart. The red and the blue lines show long-wavelength vibrations in the lattice. (c) The time-correlation function of the nearest-neighbor (NN) hole-pair separation is strongly temperature dependent, as expected for thermal vibrations. (d) Histogram of the fluctuations in NN-hole separations from which the restoring forces holding each vacancy in place are quantified. See the Vibrations of a Lattice at Room Temperature and the Vibrations of a Lattice at T=80C movies below.
In fact, we have found that systems can self-assemble in several distinct ways, with the mass transport occurring through unanticipated processes. Our work has established that patterns can form either "in place" or through the motion of highly mobile domains. For example, real-time observation shows that the hole arrays in Ag form in-place at room temperature by a sequence of fast dislocation reactions (Figure 2) [3]. That is, pattern formation occurs by fast dislocation motion within the film, not, as first thought, by highly mobile holes meandering until they crystallize into a lattice [1]. In contrast, the Pb/Cu and Sn/Cu systems are clear examples of self-assembly occurring by highly mobile domains moving into ordered patterns. Thus, to understand self-assembly in these systems, the mechanisms of domain mobility must be understood. To self-assemble, domains many nanometers in size must move many microns. This motion requires considerable mass transport within the domains.
To obtain fast diffusion in a domain requires a high density of diffusing species and low diffusion barriers. Our recent study of S-induced mass transport on Cu(111) suggests a way to systematically enhance surface diffusion. We find that less than 1/100th of a monolayer of S enhances Cu mass transport by many orders of magnitude (Figure 3) [6]. For example, we can easily observe Ostwald ripening of 2-D islands at temperatures as low as -60°C, which would take many years to occur on a clean surface. We attribute this mass transport enhancement to the fact that Cu bound in mobile Cu-S clusters on the surface has a much lower formation energy than simple Cu adatoms on Cu(111). In fact, by comparing experiment to theoretical models of diffusion in such a two-component system, we showed that enough Cu-S clusters exist so that mass transport is limited by the rate at which Cu and S react, rather than by diffusion of the clusters themselves. Since mobile clusters have been observed in several systems, this mechanism might explain many observations of adsorbate-enhanced diffusion and provide a way to purposely speed up nanoscale self-assembly. Surprisingly, even some large particles can readily diffuse on a surface.
Figure 3. (a). Plot showing that Cu islands decay over 100 times faster with about 1/100th ML of S on the surface. (b). Mass-transport acceleration scales as 3rd power of S coverage, establishing that Cu3S3 clusters are responsible for acceleration.
Finally, we have elucidated the nanometer-scale patterns that strained films can assume on square-symmetry substrates [7] and have analyzed the patterns that steps form as they move during growth on a strained surface [8].
[1] R. Plass, J.A. Last, N.C. Bartelt, G.L. Kellogg, Nanostructures - Self-assembled domain patterns, Nature 412, 875 (2001).
[2] K. Thuermer, R.Q. Hwang, and N.C. Bartelt, Surface self-organization caused by dislocation networks, Science 311, 1272 (2006).
[3] K. Thuermer, C.B Carter, N.C. Bartelt, and R.Q. Hwang, Self-Assembly via Adsorbate-Driven Dislocation Reactions, Physical Review Letters 92, 106101 (2004).
[4] S. Helveg, W.X. Li, N.C. Bartelt, S. Horch, E. Laegsgaard, B. Hammer, and F. Besenbacher, Role of surface elastic relaxations in an O-induced nanopattern on Pt(110)-(1x2), Physical Review Letters 98, 115501 (2007).
[5] R. van Gastel, R. Plass, N.C. Bartelt, G.L. Kellogg, Thermal motion and energetics of self-assembled domain structures: Pb on Cu(111), Physical Review Letters 91, 055503 (2003).
[6] W.L. Ling, N.C. Bartelt, K. Pohl, J. de la Figuera, R.Q. Hwang and K.F. McCarty, Enhanced self-diffusion on Cu(111) by trace amounts of S: Chemical-reaction-limited kinetics, Physical Review Letters 93, 166101 (2004).
[7] J.C. Hamilton, Overlayer strain relief on surfaces with square symmetry: Phase diagram or a 2D Frenkel-Kontorova model, Physical Review Letters 88, 126101 (2002).
[8] F. Léonard, J. Tersoff, Competing step instabilities at surfaces under stress, Applied Physics Letters 83, 72 (2003).