Liquid gallium and the eutectic gallium indium (EGaIn) alloy: Dielectric functions from 1.24 to 3.1 eV by electrochemical reduction of surface oxides

Liquid metals based on gallium are promising materials for soft, stretchable, and shape reconfigurable electromagnetic devices. The behavior of these metals relates directly to the thicknesses of their surface oxide layers, which can be determined nondestructively by ellipsometry if their dielectric functions ε are known. This paper reports on the dielectric functions of liquid gallium and the eutectic gallium indium (EGaIn) alloy from 1.24 to 3.1 eV at room temperature, measured by spectroscopic ellipsometry. Overlayer-induced artifacts, a continuing problem in optical measurements of these highly reactive metals, are eliminated by applying an electrochemically reductive potential to the surface of the metal immersed in an electrolyte. This technique enables measurements at ambient conditions while avoiding the complications associated with removing overlayers in a vacuum environment. The dielectric responses of both metals are closely represented by the Drude model. The EGaIn data suggest that in the absence of an oxide the surface is In-enriched, consistent with the previous vacuum-based studies. Possible reasons for discrepancies with previous measurements are discussed.

Metals that are liquid at or near room temperature are particularly attractive for soft, stretchable, and reconfigurable electronics because they maintain electrical functionality during stretching, compression, and deformation.¹ Gallium-based alloys provide ideal alternatives to mercury for these applications, because liquid gallium (Ga) has low toxicity,² low bulk viscosity,³ negligible vapor pressure, and is an excellent electrical conductor. These properties have enabled numerous applications for Ga-based liquid metals, especially the eutectic alloy eutectic gallium indium (EGaIn) (75 wt. % Ga, 25 wt. % In), for electronics and optics.⁴ Examples include but are not limited to microfluidic electrodes,^5,6 pumps,⁷ conductive elastomers,^8,9 soft diffraction gratings,¹⁰ stretchable wires,^11,12 self-healing circuits,^13–15 reconfigurable antennas,^16–18 heat transfer fluids,^19,20 and sensors.^21,22 Their properties can also be used in new ways to pattern metals,^23,24 including inkjet printing²⁵ and 3D printing.²⁶ 

Here, we report dielectric function data $ε=ε1+iε2$ for liquid Ga and EGaIn from 1.24 to 3.1 eV obtained by ellipsometry. Knowledge of ε for these metals is important for a number of optical applications,²⁷ including those involving metamaterials^28–30 and liquid plasmonics.^31,32 In addition, these data are essential for optically determining the thicknesses of films that form on the surface of these metals, including not only the natural oxide but also non-native oxides, graphene and other 2D materials,^33,34 thiols,³⁵ and other self-assembled monolayers.³⁶ 

To accurately determine the dielectric function of a material by ellipsometry, overlayers, including oxides, must be completely removed. At the same time, the surface must be uniform and flat. Liquid Ga rapidly forms a passivating oxide layer in the presence of partial pressures of oxygen beyond the ppm range.³⁷ Here, we prepare and maintain oxide-free surfaces by applying a reductive voltage bias with the sample in an electrolyte. This simple method also avoids the need to use expensive and labor-intensive ultrahigh vacuum equipment, including windows that can change optical properties in response to flange-induced stresses and pressure differences. At the same time, these data are obtained under conditions more closely characteristic of microfluidic³⁸ and hydrogel devices.^39,40 This approach also makes it possible to make in situ measurements while modifying surfaces or growing nanostructures⁴¹ by chemical and electrochemical deposition.

Previous reports on the dielectric functions of liquid Ga and EGaIn show that these metals exhibit nearly free electron-like Drude behavior, although some differences occur in scale. This can be understood from the experimental limitations that follow from the high reactivity of these metals to oxygen (leading to the need to compensate for window strain for samples in ultrahigh vacuum^42–45) or from corrections of pseudodielectric function data $⟨ε⟩=⟨ε1⟩+i⟨ε2⟩$ for the presence of an oxide skin for the measurements made in dry N₂.^46–48 These limitations do not occur in the present work.

Ellipsometric measurements require a uniform and flat surface. Because liquids tend to form curved surfaces to minimize surface energy, we have taken steps to flatten the surface of the metal. We wet the metal to a copper film, as outlined schematically in Figure 1. First, a solution of acetic acid and NaCl was used to remove the native oxide from a copper substrate. A drop (∼1 g) of liquid metal (Ga purity 99.99% Ga, or EGaIn 75.5 wt. % Ga 24.5 wt. % In) was then placed on the substrate in 1 M HCl. The acid removes the Ga oxide, promoting the wetting of the liquid metal to the copper, which occurs at 80 °C. The Ga/Ga-oxide interface remains copper-free during the time scales of our experiments, as determined by energy dispersive spectroscopy (EDS) measurements (see supplementary material Fig. S1) and corroborated by X-ray photoelectron spectroscopy measurements (not reported). The sample was then transferred to a measurement cell with strain-free windows fixed at angles of 70° with respect to the surface normal of the sample. Setting the ellipsometric angles of incidence and reflectance both equal to 70° ensured that the optical beams were normal to the windows on both entrance and exit sides.

The cell was then filled with a solution of 0.1 M NaCl. Potentials were established and measured with a three-electrode WaveNow potentiostat using a reference electrode. The cathode was attached to the copper substrate and the anode to a platinum wire in solution. The potentiostat recorded both voltage and current.

Spectroscopic ellipsometric data were obtained from 1.24 to 3.1 eV using a J.A. Woollam Co. VASE rotating-analyzer ellipsometer at an angle of incidence of 70°. Data were obtained equally spaced in wavelength at various positive and negative polarizer and analyzer angles, then averaged to improve accuracy. The liquid-Ga data were obtained with the sample at 35 °C to ensure that it was well above the Ga melting point of ∼30 °C. The EGaIn data were obtained at room temperature. Both liquid metals are sufficiently opaque in the spectral range so that there is no contribution from the copper substrate to the optical data. The dielectric functions ε of the metals themselves were determined directly using the two-phase (ambient/substrate) model together with optical data for the water ambient.⁴⁹ The resulting pseudodielectric functions $⟨ε⟩=⟨ε1⟩+i⟨ε2⟩$ are therefore expected to be an accurate representation of the actual bulk dielectric functions of the metals. Otherwise, the preparation of bare metal surfaces typically requires the use of sophisticated vacuum processing. The appeal of the present technique includes not only the ease of implementation at room temperature but also that it can be done with common laboratory equipment.

Figure 2 shows the real and imaginary parts of ⟨ε⟩ for liquid Ga averaged over six runs on different days. These data are tabulated for ease of use in Table S1 of the supplementary material. All six sets of data fall well within the experimental uncertainty, indicating that our procedure leads to consistent results. Previous work demonstrated the effectiveness of using electrical biases to either eliminate or grow oxide skins.^38–40 According to the Pourbaix diagram, an open-circuit potential of at least −1.2 V vs. SHE (standard hydrogen electrode) is sufficient to remove the oxide at neutral pH conditions.⁵⁰ The current densities that achieve this for Ga ranged from 0.21 to 0.31 mA/cm² at potentials of −1.22 V and −1.33 V, respectively. The formation of bubbles (presumably hydrogen) on the Ga surface occurred at current densities greater than 0.31 mA/cm², which established an upper limit.

Removal of the oxide by electrochemical reduction was visually apparent: the result is a pristine, mirror-like surface. In addition, in the absence of the oxide, the ellipsometric data becomes consistent and reproducible. Being amphoteric, the oxide can also be removed⁵⁰ using acidic or basic pH solutions. The dielectric function of pure Ga immersed in 0.07 M HCl was also measured in the absence of current to confirm the validity of our technique. The dielectric values agreed within the experimental uncertainty with those from the electrochemical reduction. This result provides an additional evidence that the electrochemical reactions remove the oxide, and that the voltage does not skew the measurement.

We further assess the results using the Drude free-electron model

where E is the photon energy, $Ep$ is the plasma energy, and $γ$ is the broadening parameter. Table I lists these parameters for the two liquid metals. The absence of interband features is consistent with the lack of long-range order, in contrast to the situation for the metals in their solid phases. Hence, these liquid metals are essentially Drude-like.⁴⁶ 

We next compare our results for Ga to data^43,45,47,48 from other sources to assess the discrepancies and to determine the best possible values of ε for this material. Sources of discrepancies can be attributed to instrumentation, including window strain in vacuum measurements, and the inadvertent presence of overlayers (or the improper correction of their effects). All available data in the 1.24 to 3.1 eV spectral range are shown in Fig. 3. While all results are in basic agreement, systematic differences do occur. For example, our $ε1$ data are generally more negative than those reported elsewhere, and our $ε2$ data more positive.

We first consider the effect of an oxide overlayer, since the reactivity of liquid Ga makes this the most likely source of error. The red curves in Fig. 3 show the dielectric functions we would have obtained if our samples had been covered with a 1 nm thick layer of β-Ga₂O₃ instead of being oxide-free.⁴⁹ This thickness is reasonable, because a ∼1 nm (Ref. 51) surface oxide forms in vacuum conditions if the partial pressure of oxygen is ∼1 × 10⁻⁹ atm.³⁷ We confirm these curves by observing a large decrease in the absolute values of the fitted dielectric functions when we measure the Ga sample without removing the oxide (see supplementary material Fig. S2; further characterization of the oxide on Ga will be presented in a subsequent publication). All other data show evidence of an overlayer. This is not surprising even for samples prepared and maintained in UHV, unless the measurements are done relatively quickly after preparation. It is definitely not surprising for cases where samples are maintained in a N₂ atmosphere during both preparation and measurement.⁴⁸ Because this value suppression is seen for all data in Fig. 3, we conclude that oxides on our samples are either absent or thinner than those on the other samples.

We next consider whether misalignment errors might explain discrepancies in data. All data in Fig. 3 except those of Schulz were obtained with some version of ellipsometry. We use the rotating-analyzer configuration to establish general scales of errors. We use the two-phase (substrate/ambient) model and the data of Fig. 2 to calculate the normalized cosine and sine Fourier coefficients $α2$ and $β2$⁠, respectively, of the detected optical signal for a polarization angle $P=30°$⁠, an angle of incidence $θ=70°$⁠, and a reference analyser azimuth angle $A=0°$⁠, incorrectly adding 1° to each in turn. We then invert the equations to calculate ε with the nominally correct values.

The results are shown in Fig. 4. The black curves are the data of Fig. 2. The red, green, and blue curves are the values of $ε$ with the $1°$ errors in P, θ, and A, respectively.

As can be seen, no single effect works in isolation; that is, any given source of error modifies both $ε1$ and $ε2$⁠. Summarizing the changes at 1.24 eV as linear equations, and including the effect of an overlying oxide as well, we have

Equation (2) show that the effect of 1 nm of oxide can also be simulated by making an alignment error of nearly 1° in θ. This is considerably beyond typical alignment errors, and hence, the oxide explanation is more likely. The good and bad agreements with $ε1$ and $ε2$⁠, respectively, of the Teshev and Shebzhukhov (TS) results are inconsistent with an oxide alone, but can be realized with a combination of errors of the order of 1°. The most likely explanation here is window strain, noting that windows in ultrahigh-vacuum chambers are a problem unless shown otherwise or special configurations are used.⁵² We believe that the discrepancies seen in the Freyland results are also due to window strain, since these measurements were also obtained with the sample in UHV. Although our data were obtained with the optical beams passing through windows, our measurements were made with everything at atmospheric pressure under conditions where we could verify the absence of strain artifacts independently, and ensure that nothing would change under operating conditions.

The data of Schulz require a separate comment. These were deduced from double-beam reflectance measurements coupled with interference data relative to a deposited Al reference, where the liquid Ga sample contacted the hypotenuse face of a right prism and the reference was total internal reflection. The accuracy limitation here is expected to be a combination of the use of reflectance as a probe and a deposited Al film as a reference. It is almost impossible to prepare optical-reference-grade Al films by evaporation unless it is done in ultrahigh vacuum. Unfortunately, no measurements of both TE and TM polarized light were done to verify these assumptions. If the results were identical, which is the case at an incidence angle of 45°, it would have verified that the reference was optical-grade.

In Figure 5, we present the real and imaginary parts of the dielectric function ⟨ε₁⟩ + i⟨ε₂⟩ for liquid EGaIn with the oxide removed electrochemically. The pseudodielectric function is different than that of pure Ga, being much closer to previously reported dielectric-function spectra of pure solid In (see supplementary material Fig. S3).^53–55 We were unable to find literature data for liquid indium, and its melting point of 156.6 °C is beyond the capability of our electrochemical bath. Evidence of In enrichment at the surface of the EGaIn alloy has been previously demonstrated in high vacuum.^56–58 Previous measurements by ion-scattering and Auger spectroscopy data show that the surface monolayer is at least 94 at. % In.⁵⁷ This is attributed to the ∼30% lower surface energy of In at its melting point.⁵⁶ Such surface In enrichment has yet to be observed in ellipsometric data. After exposure to air, the metal interface of EGaIn reverts back to its expected alloy composition.⁵⁸ As a consequence, the oxide-free spectrum of EGaIn cannot be used to model configurations when oxides are present. We discuss this challenge in a future publication.

Our pseudodielectric-function data for the dielectric functions of liquid Ga and liquid EGaIn are taken under conditions where native oxides are absent, and hence should be an accurate representation of the actual bulk dielectric functions of these materials. The tabulated dielectric values for the liquid metal can enable the ellipsometric measurement of the thickness of the oxide skin and other coatings that form on these liquid metals and to provide optical properties for researchers who study their optical applications.

See supplementary material for the EDS spectrum of the gallium surface, the tabulated pseudodielectric function for gallium and EGaIn, the pseudodielectric function of the native gallium oxide, and the pseudodielectric function of oxide-free EGaIn compared to that of pure indium.

The authors acknowledge the use of the Analytical Instrumentation Facility (AIF) at North Carolina State University, which was supported by the State of North Carolina and the National Science Foundation. The authors gratefully acknowledge the primary support by NSF Research Triangle MRSEC on Programmable Soft Matter (DMR-1121107) and partial support by NSF (CBET-1510772). We also thank Ron Synowicki at J.A. Woollam Company for helpful discussions. We also thank Professor Jan Genzer for access to his laboratory and for helpful discussions.