Two-Dimensional Phase Transition Mediated by Extrinsic Defects

Abstract

We have investigated the ͑ p 3 3 p 3 ͒ to ͑3 3 3͒ phase transition in the a phase of Sn͞Ge(111) with variable temperature STM at temperatures between 30 and 300 K. Point defects in the Sn film stabilize localized regions of the ͑3 3 3͒ phase, where the size is characterized by a temperature dependent length (exponential attenuation). The inverse of the attenuation length is a linear function of temperature showing that the phase transition occurs at 70 K. At low temperature a density wave mediated defect-defect interaction realigns the defects to be in registry with the ͑3 3 3͒ domains.Structural phase transitions belong to a group of phenomena, which are strongly related to surface symmetry and its lowering. In many cases a prediction of the order and universality class of an anticipated phase transition can be made based solely on the knowledge of the space group of the surface or adsorbate structure [1]. This idealized picture is rarely achieved in the real world, where defects and imperfections in the surface break the symmetry. Various types of surface phase transitions have been reported in the literature [2,3], and even though an atomistic picture of the phase nucleation process has remained elusive, it is generally believed that this process involves defects and impurities [4,5]. Since the energy differences between different phases on a surface are usually very small, a slight perturbation of this energy balance, coupled with the broken symmetry induced by an imperfection, can affect not only the transition temperature but also the temperature dependence of the order parameters near the critical point. For example, consider a system with a charge density wave (CDW) instability. Electrons in the normal state will screen charged impurities, producing an attenuated CDW or Friedel oscillation near the impurity sites. The ion cores follow the local charge rearrangement and, consequently, the normal-state symmetry is broken locally and short-range CDW order develops. The electronic response to the external perturbation [6], x͑q, T ͒, depends on the temperature, leading to the intriguing proposition that defects will in general affect the evolution of long-range ordering. Tosatti and Anderson concluded that "a CDW can be regarded as unattenuated Friedel oscillations" [7].There is indeed evidence that imperfections have a strong influence on surface phase transitions. For example, the anticipated second-order phase transition on a Si(100) surface from a ͑2 3 1͒ to a c͑4 3 2͒ structure is not sharp [8]. This behavior was qualitatively reproduced by Monte Carlo simulations based on an Ising spin model [9,10]

Low Temperature Disordered Phase ofα−Pb/Ge(111)

“…1(d)), all the Pb atoms are equivalent except small distortions pinned around defects. This local distortion has the same characteristics as reported for the Sn/Ge system [11][12][13]16]. At 90 K in (e), large (3×3) domains and sharp domain walls are present, indicating the new LRO is fully developed.…”

“…Fig. 1(d) shows a honeycomb structure developing around the Ge defects [12,13,16]. The range of this defect induced density wave is temperature dependent [12,16] and is responsible for the high temperature tail seen in both order para meters ∆Z and , blurring a clear definition of T 1 .…”

The next 25 years of surface physics

“…It is cute, and the pictures made the cover of Nature, but that is all there is. This is surface Melechko's realization that the defects were controlling and intimately involved in this CDW transition has attracted the attention of the CMP community, because now the surface scientist can address fundamental questions, at the atomic scale, associated with defect mediated 2D phase transitions [23][24][25]. The arrows in Fig.…”

“…The white lines on this figure show that, even at RT, the presence of a Ge defect wants to create a honeycomb structure and the vacancy a hexagonal distortion. Melechko observed that as he dropped the temperature the spatial extent of the damped CDW increased, growing until the damped CDW waves from different defects overlapped, giving very intricate interference patterns in the STM images [23,24]. The experimental observations lead to the construction of the following ansatz to fit the experimental images:…”

“…A sampling grid (80 AÂ80 A) slightly smaller than the average CDW domain size (100 AÂ100 A) was used to quantify the defect alignment on a large number of STM images at RT [23,24]. If all of the defects were on two of the three lattices, the probability P C was defined to be 1, and if they were equally distributed on three lattices, then P C ¼ 0.…”