Complete wetting transitions at the liquid-vapor interface of gallium-bismuth alloys: Single-wavelength and spectroscopic ellipsometry studies

Abstract

Complete wetting transitions at the liquid-vapor interface of ${\mathrm{Ga}}_{x}{\mathrm{Bi}}_{1\ensuremath{-}x}$ alloys (${x}_{\mathrm{Ga}}=0.915$, 0.88, 0.8, 0.67, and 0.57) have been investigated by ellipsometry. For this purpose we have developed a UHV apparatus equipped with an in situ phase modulation ellipsometer. The setup allows cleaning of the alloy surface under UHV conditions. Spectroscopic ellipsometry $(0.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}\ensuremath{\leqslant}h\ensuremath{\nu}\ensuremath{\leqslant}4.65\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ at various constant temperatures and time-dependent measurements at a constant energy of $2.75\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, while the sample was continuously cooled down, are utilized. These complementary approaches promise access to the functional form of the wetting film thickness with temperature as complete wetting is approached. A multistage analysis is introduced to extract the film thickness from single-wavelength ellipsometry. For a careful analysis of the spectra, it was necessary to reinvestigate the complex dielectric functions of the pure components bismuth and gallium. The spectra of the alloys have been modeled using an effective medium approximation for the liquid $\mathrm{Ga}\ensuremath{-}\mathrm{Bi}$ bulk phase covered by a film of liquid bismuth. In our particular sample geometry, the wetting film thickness grows from one or two atomic layers to about $30\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}50\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ within a few K as one approaches the demixing regime. The data show the proposed logarithmic divergence of $d$, typical for short range interactions. In the temperature and composition range studied they do not agree with the functional form proposed for long range intermolecular interactions.