Unified method for measuring entropy differences between coexisting surface phases using low energy electron microscopy

Abstract

We demonstrate the ability of low energy electron microscopy (LEEM) to extract fundamental information in surface phase transitions during in situ observations of complex semiconductor surfaces. We utilize established LEEM techniques and develop a methodology that enables us to calculate the surface entropy difference using only LEEM measurements without the need for external characterization. We demonstrate the effectiveness of the unified method by monitoring the phase coexistence during the first-order transition between the $c\phantom{\rule{0.16em}{0ex}}(8\ifmmode\times\else\texttimes\fi{}2)$ and $(6\ifmmode\times\else\texttimes\fi{}6)$ phases on the surface of GaAs(001) at a range of temperatures relevant for epitaxy. The coexistence behavior with temperature and the fluctuations of phase boundaries are measured and analyzed to obtain the entropy difference and stress difference between the phases. The calculated values show that the entropy difference is not large enough to stabilize the $(6\ifmmode\times\else\texttimes\fi{}6)$ phase with respect to the $c\phantom{\rule{0.16em}{0ex}}(8\ifmmode\times\else\texttimes\fi{}2)$ by itself, suggesting that the elastic relaxation during the coexistence between the two phases is necessary to stabilize the $(6\ifmmode\times\else\texttimes\fi{}6)$ phase.