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

Complete wetting transitions at the liquid-vapor interface of ${\mathrm{Ga}}_x{\mathrm{Bi}}_{1-x}$ 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 $(0.8\mathrm{eV}⩽h\nu ⩽4.65\mathrm{eV})$ at various constant temperatures and time-dependent measurements at a constant energy of $2.75\mathrm{eV}$, 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 $\mathrm{Ga}-\mathrm{Bi}$ 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 $30\mathrm{\AA }\text{to}50\mathrm{\AA }$ 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.

Figure 1

High temperature Ga-rich part of the $\mathrm{Ga}-\mathrm{Bi}$ phase diagram (solid lines) (Refs. 6, 7). Vertical dashed lines show the experimental paths of time-dependent and spectroscopic experiments. Full circles present measurements where no wetting film was detected, open circles present measurements where a wetting film has formed. CP is the critical point at $x_{\mathrm{Ga},\mathrm{c}}=0.7$ and $T_{\mathrm{c}}=263°\mathrm{C}$. Dashed-dotted lines describe interfacial passages for two kinetic measurements described in Figs. 7, 8 along the paths $A_1{B}_1{B}_{2}CMD$ for $x_{\mathrm{Ga}}>x_{\mathrm{Ga},\mathrm{c}}$ and $A_2{B}_{2}CMD$ for $x_{\mathrm{Ga}}<x_{\mathrm{Ga},\mathrm{c}}$, respectively.

Figure 2

Experimental setup of the phase modulation ellipsometer (UVISEL, Jobin Yvon) connected to the homemade UHV chamber: ①, pumping system, turbo and ion pumps $\left({10}^{-9}\mathrm{mbar}\right)$; ②, sample height adjustment along $z$ axis; ③, micrometer screws to tilt the whole apparatus in the $xz$ and $yz$ planes; ④, vibration damping system; ⑤, Mo crucible with the liquid alloy on the heater; ⑥, Ar sputter gun; ⑦, wobble stick and mechanical cleaning device; ⑧ and ⑨, modulator and analyzer heads of the ellipsometer.

Figure 3

Real and imaginary parts of the dielectric function for pure liquid Ga: ●, this work at $256°\mathrm{C}$ [see also Table (a)]; solid lines, free-electron Drude fit to ●; ◇, $250°\mathrm{C}$ (Ref. 21); ◻, $850°\mathrm{C}$ (Ref. 20).

Figure 4

Real and imaginary parts of the dielectric function for pure liquid Bi: ●, this work at $289°\mathrm{C}$ [see also Table (b)]; solid lines, free-electron Drude fit to ●; dashed-dotted line, $285°\mathrm{C}$ (Ref. 23); ◇, $390°\mathrm{C}$ (Ref. 22); and ◻, $500°\mathrm{C}$ (Ref. 20).

Figure 5

Primary experimental data—intensities $I_S$ and $I_C$. Upper section: $I_S$ and $I_C$ measured at $293°\mathrm{C}$ for a ${\mathrm{Ga}}_{0.88}{\mathrm{Bi}}_{0.12}$ alloy; solid lines show the fit within the framework of the two-phase model with an EMA used as substrate. Middle section: Variation of $I_S$ at temperatures approaching the liquid-liquid coexistence line shown as difference relative to $I_S$ $(293°\mathrm{C})$ to magnify the effect with temperature; solid lines present the three-phase model fits with EMA for the Ga-rich alloy as substrate and pure liquid Bi as film. Lower section: Same presentation for $I_C$.

Figure 6

Thickness of the wetting film approaching the liquid-liquid coexistence line $(\Delta T=T-T_{\mathrm{coex}})$ for $x_{\mathrm{Ga}}=0.915$ (◻,◇—two runs, same sample); 0.88 (●) and 0.8 (▿). Error bars represent the uncertainty of the three-phase model fit only.

Figure 7

Time-dependent measurements at $h\nu =2.75\mathrm{eV}$ on continuous cooling of a ${\mathrm{Ga}}_{0.8}{\mathrm{Bi}}_{0.2}$ alloy: upper part—cooling curves for heater and crucible; lower part—ellipsometric angles $\Psi$ (◻) and $\Delta$ (엯). On cooling along path $A_1{B}_1{B}_{2}CMD$ (see also Fig. 1) the following phases are exposed to the light beam at the surface of the sample: homogeneous liquid region $A_1\to B_1$ (region I), within miscibility gap $B_1\to B_2\to C$ (region II), crucible temperature stays almost constant at the monotectic temperature $222°\mathrm{C}$ (region III), afterward the sample continues to cool down further on path $M\to D$ (region IV).

Figure 8

Time-dependent measurements at $h\nu =2.75\mathrm{eV}$ on continuous cooling of a ${\mathrm{Ga}}_{0.57}{\mathrm{Bi}}_{0.43}$ alloy: upper part—cooling curves for heater and crucible; lower part—ellipsometric angles $\Psi$ (◻) and $\Delta$ (엯). Cooling proceeds in a similar way as described in Fig. 7, but along the path $A_2{B}_{2}CMD$. The disturbance at $\sim 3.5\mathrm{h}$ is discussed in text.

Figure 9

$x_{\mathrm{Ga}}=0.8$: thickness of the wetting film versus $\Delta \mu$ and versus $T$ (inset) extracted from single-wavelength measurements corresponding to region I in Fig. 7. The solid line is a fit of $d$ proportional to $\ln \left(\Delta {\mu }^{-1}\right)$.

Figure 10

$x_{\mathrm{Ga}}=0.8$: thickness of the wetting film versus $\Delta \mu$ and versus $T$ (inset) extracted from single-wavelength measurements corresponding to region IV in Fig. 7. The solid line is a fit of $d$ proportional to $\ln \left(\Delta {\mu }^{-1}\right)$.

Figure 11

$x_{\mathrm{Ga}}=0.88$: thickness of the wetting film versus $\Delta \mu$ extracted from ellipsometric spectra in the homogeneous phase region above the demixing gap. 엯, this work; solid line, fit according to $d\propto \ln \left(\Delta {\mu }^{-1}\right)$; ◻, data of Huber et al. as scanned from their Fig. 3b in Ref. 11 (error bars correspond to symbol size); dashed line, fit according to $d\propto \ln \left(\Delta {\mu }^{-1}\right)$. Inset: Same data presented as $d$ versus $\ln \left(\Delta {\mu }^{-1}\right)$.