Phase-field-crystal modeling of the (2x1)-(1x1) phase-transitions of Si(001) and Ge(001) surfaces

TL;DR

This paper introduces a phase-field-crystal model to simulate the (2x1)-(1x1) phase transitions on Si(001) and Ge(001) surfaces, successfully reproducing experimental observations and providing insights into the temperature-dependent dimerization process.

Contribution

The paper presents a novel 2D phase-field-crystal model specifically for surface phase transitions, capturing the coexistence of different dimerization states and the temperature dependence of the transition.

Findings

Simulated dimerization patterns match STM images.

The model predicts a first-order phase transition between temperatures.

Dimerization varies with temperature, consistent with experiments.

Abstract

We propose a two-dimensional phase-field-crystal model for the (2$\times$1)-(1$\times$1) phase transitions of Si(001) and Ge(001) surfaces. The dimerization in the 2$\times$1 phase is described with a phase-field-crystal variable which is determined by solving an evolution equation derived from the free energy. Simulated periodic arrays of dimerization variable is consistent with scanning-tunnelling-microscopy images of the two dimerized surfaces. Calculated temperature dependence of the dimerization parameter indicates that normal dimers and broken ones coexist between the temperatures describing the charactristic temperature width of the phase-transition, $T_L$ and $T_H$, and a first-order phase transition takes place at a temperature between them. The dimerization over the whole temperature is determined. These results are in agreement with experiment. This phase-field-crystal approach is applicable to phase-transitions of other reconstructed surface phases, especially semiconductor $n\times$1 reconstructed surface phases.