Using first principles calculations and Monte Carlo simulations, we have examined the validity of the Ising model widely used for the order-disorder phase transition on Si(001)-2×1. Our study suggests that not only dipole-dipole interactions of asymmetric dimers but also subsurface layer strains play an important role in determining the energetics for different surface configurations. Without consideration of the strain effect the Ising model can miscalculate the phase transition significantly. Including the strain effect, a new model Hamiltonian predicts a transition temperature range of 170-200 K, in good agreement with experimental observations (∼200 K). However, the new model still cannot reproduce streak patterns (well above the transition temperature) as seen in low-energy electron diffraction. We discuss a possible reason for the disagreement.
Bibliographical noteFunding Information:
The authors acknowledge the Welch Foundation (Grant No. F-1535) for their financial support of this work.
- Density functional calculations
- Ising models
- Monte Carlo simulations
- Surface structure, morphology, roughness, and topography
- Surface thermodynamics (including phase transitions)