Step Capillary Waves and Equilibrium Island Shapes on Si(001)

Abstract

From low-energy electron microscopy measurements of step fluctuations and equilibrium 2D island shapes on Si(001), We determine the temperature dependence of the ${S}_{A}$ and ${S}_{B}$ step edge stiffnesses, free energies, and mobilities. A capillary wave analysis of step stiffnesses is in quantitative agreement with the 2D island shapes, demonstrating the direct relation between equilibrium thermal fluctuations and equilibrium structure. The analysis also suggests that step free energies vanish at \ensuremath{\sim}1200\ifmmode^\circ\else\textdegree\fi{}C, providing direct evidence for a roughening transition. The combined exploration of step dynamics and equilibrium island shapes yields new insight into the basic thermodynamics of Si(001).