Atomic-Scale Structure of a Liquid MetalâInsulator Interface - The

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Atomic-Scale Structure of a Liquid Metal-Insulator Interface Lilach Tamam,† Diego Pontoni,‡ Tommy Hofmann,§ Benjamin M. Ocko,§ Harald Reichert,‡,^ and Moshe Deutsch*,† †

Physics Department and Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel, ‡ESRF, 6 rue Jules Horowitz, Grenoble, France, §Condensed Matter Physics & Materials Science Department, ur Metallforschung, Brookhaven National Laboratory, New York 11973, and ^Max-Planck-Institut f€ Heisenbergstrasse 3, D-70569 Stuttgart, Germany

ABSTRACT The structure of the liquid Hg/sapphire interface was measured with angstrom-scale resolution by high-energy X-ray reflectivity. The atomic Hg layering found at the interface is less pronounced than at the Hg/vapor interface, showing a twice-shorter decay length with depth, and a weaker peak/valley density contrast. We also find a near-interface, 8 ( 3 Å thick layer, the density of which, although depth-varying, is enhanced, on average, by 10 ( 5% relative to the bulk. The enhancement is assigned to a 0.13 ( 0.05 e/atom charge transfer from the Hg to the substrate, somewhat less than theory. The unexplained anomalous temperature dependence previously reported for the mercury/vapor density profile is absent here, implying a nonstructural origin for the anomaly. SECTION Surfaces, Interfaces, Catalysis

T

he special nature of the free surface of a liquid metal has long been recognized.1,2 The surface, separating a conducting bulk from an insulating vapor, gives rise to a steep gradient in the charge density and in the corresponding interface-normal electric field.3,4 Macroscopically, this yields a surface tension orders of magnitude higher5 than that of organic van der Waals liquids6 and water. Microscopically, it induces a near-surface atomic layering, which decays over a depth of a few atomic layers. Predicted in the 1970s,2-4 the layering was confirmed experimentally only in 1995 by X-ray reflectivity (XR) in Hg and Ga,7,8 and has since been shown to be universal for all liquid metals and alloys studied to date.9-11 Simulations suggest that layering should occur in all liquids at temperatures below about 1/10 of the liquid's critical temperature, if not preempted by bulk freezing.12-14 The present study explores by XR measurements whether surface layering in liquid metals persists when the vapor is replaced by a solid. Only two X-ray studies of such interfaces have been published to date. One of these studies, of molten Pb and In in contact with Si, uncovered the presence of a 20-30 Å thick interfacial layer 30% denser than the bulk metal.15 This intriguing effect has been assigned to the nature of these semiconductor/metal Schottky contacts, where a large (0.8 e/atom) charge transfer from the metal to the semiconductor leads to a size reduction of the surface-adjacent metal ions, and to a strong compressing field across the interface. The density enhancement was not observed when Si was replaced by an insulator, Al2O3.15 However, the maximum wavevector transfer, qz = 0.5-0.9 Å-1, used in those measurements was 3-to-6-fold smaller than the qz ≈ 3 Å-1 range employed in the present measurements, a range

r 2010 American Chemical Society

required to observe surface-induced layering or a dense interfacial layer only a few angstroms thick.15 The second earlier study investigated the Ga/diamond interface16 with qz e 2 Å-1. It had insufficient range to reach the expected7 layering peak of Ga at qz = 2.4 Å-1 and did not even show a rise toward such a peak at its high-qz end.17 The measured XR curve was interpreted as showing Ga dimer layering at the interface with a 7% density enhancement over the bulk for the first layer.16,18 A simpler interpretation, a single 7 Å thick interfacial layer of a density 20% higher than bulk Ga, but no layering, was rejected as being unphysical. Since diamond is a group IV semiconductor, like Si, the rejected interpretation may in fact be consistent with the Schottky contact Pb/Si and In/Si measurements discussed above. Thus, no evidence for or against liquid metal layering at a solid interface has been clearly resolved in the two available X-ray studies. The study presented here is the first that attains atomic resolution, and thus allows addressing that question. Our study also impacts the atomic structure of oxide/metal interfaces, where, despite their ubiquity and importance in the chemical industry, materials science, nanotechnology, and microelectronics,19 there are no atomic-scale, high-resolution X-ray studies published for any such interface. Theory suggests that the structure and associated properties of the metal/Al2O3 interfaces should depend on the surface termination (Al-terminated, Al2-terminated or O-terminated), Received Date: January 8, 2010 Accepted Date: February 26, 2010 Published on Web Date: March 05, 2010

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DOI: 10.1021/jz1000209 |J. Phys. Chem. Lett. 2010, 1, 1041–1045

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Figure 1. (a) Measured (symbols) and box-model-fitted (lines) XR curve of the Hg/Al2O3 interface at T = 12 C. Inset: Experimental setup and reflection geometry. kout, kin, qz = kout - kin = (4π/λ) sin R and R are the reflected and incident rays' wavevectors, the surface-normal wavevector transfer, and the grazing incidence angle. (b) Electron density profiles of the fitted models in panel a.

Figure 2. (a) Measured, Fresnel-normalized, XR curve R/RF of the Hg/Al2O3 interface at T = 12 C (symbols), and fit (solid line) by the model described in the text. The dashed lines are curves calculated with shorter (blue) and longer (red) layering decay lengths, as discussed in the text. (b) Fitted density profile (solid line), and its components (dashed lines): independent top layer (red), first three gaussians (blue), DC sum (black), and Al2O3 (green). (c) Comparison of the profile in panel b (solid, 0.5 upshifted) with the Hg/vapor profile8 (dashed).

stoichiometry, and coverage (isolated atoms or a full metal film).19-22 A transfer of 0.2 e/atom is predicted, from the Al2O3 to the metal for Al-termination, and in reverse for Otermination.23-25 This may give rise to a compression of the interface-adjacent liquid metal layer, of an unknown magnitude, extension, and depth variation. The measured XR curve (Figure 1) is strongly modulated, with a period of Δqz ≈ 1.3 Å-1. Simplistically, Δqz could be assigned to a dense interfacial layer, d = 2π/Δqz = 4.8 Å thick. However, attempts (Figure 1) to fit the measured XR curve by a one-box model of such a layer, with or without interfacial roughness σ, were unsuccessful. Even a two-box model, which fits R well for qz e 1.3 Å-1 at a cost of doubling the number of fit parameters, fails at higher qz's. Several other few-box models also failed to fit the measured R(qz) over the full qz range. An inspection of the Fresnel-normalized R/RF in Figure 2a reveals the reason for this failure. The higher-qz peak of this double-humped curve at qz ≈ 1.7 Å-1 is clearly more intense than the low-qz peak at qz ≈ 0.4 Å-1. Similar to same-parity peaks in conventional powder diffraction, for a single dense interfacial slab, the higher the qz-position of a peak in a R/RF


curve, the lower its intensity. A plausible way for the 1.7 Å-1 peak to be more intense than the 0.4 Å-1 peak, as observed here, is through a Bragg-like intensity enhancement by multiple reflections from several interfacial layers. This explanation implies the occurrence of mercury layering at the interface. While nonlayered box models comprising 2-3 boxes of particular height ratios can also be made to yield an enhanced second peak, the full measured R/RF curve could not be fit with such models, as discussed above. As the number of boxes increases, the fit improves. However, the resultant boxmodel density profiles progressively approach the layered interface model discussed below, implying again the high probability for the occurrence of layering. It should also be noted that the R/RF >1 value of the first peak implies an interfacial density higher than the bulk. Motivated by these considerations, by the theoretical, general-principles prediction of liquid layering at a solid wall,26-28 and by the observed Hg/vapor interfacial layering,8-11 we employed a modified distorted crystal (DC) model, successfully used to describe the layering at liquid

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metal/vapor interfaces.8,29 This model treats the liquid Hg as a sum over atomic layers, represented by gaussians of varying widths σn. The Al2O3 interface, at d0, is represented by an error function of width σs: 3 Fa d1 -z2 =2σ2a X Fn d1 -ðz -nd1 Þ2 =2σ2n pffiffiffiffiffiffi FðzÞ ¼ pffiffiffiffiffiffi e þ e 2πσa n ¼1 2πσ n 2 !3 ¥ X 2 d F z -d 2 0 5 pffiffiffiffiffiffi e -ðz -ndÞ =2σn þ s 41-erf pffiffiffi þ F¥ 2 2π σ 2 σ n s n ¼4

from the Hg to the Al2O3 suffices to account for the observed density increase. For a given enhancement, the presence of any compressing interfacial field will reduce the estimated charge transfer. Theory agrees with the direction, but predicts a somewhat larger charge transfer.23-25 The smaller peak-valley contrast, and the roughly twiceshorter decay length of the layering oscillations (Figure 2c) indicate a less pronounced layering than that at the free surface.8,29 However, attempts to completely eliminate the layering, or fix the decay length at the 5 Å of the Hg/vapor interface, invariably resulted in poor fits, particularly for qz > 1 Å-1. This is well demonstrated in Figure 2a by the large disagreement of the dashed lines with the measured R/RF. These lines are model-calculated, keeping all parameters at the best-fit values listed above, but increasing (red) or decreasing (blue) the layering decay length σh only by 5%. Note that the lower-q peak in Figure 2 is not influenced at all, but the large-q peak, where layering is supposed to contribute strongly, is indeed significantly altered, implying great sensitivity to the existence and decay length of the layering. Thus, we conclude that the measured XR curves support the persistence of a layering at the Hg/solid Al2O3 interface, albeit a less pronounced one than that at the Hg/vapor interface. Note that, since sapphire is a wide bandgap insulator, the charge transfer implies overcoming a barrier. Thus, electron density spillover from the mercury into the sapphire is expected to be smaller than that into the vapor phase. This increased charge confinement should enhance the interfaceadjacent layering peaks in the electron density, as indeed observed in simulations of an insulating-layer-covered liquid Cs surface.34,35 The observation here of the opposite effect, a reduction in the layering peaks, implies a lowering of the barrier for charge transfer, which most likely results from chemical bonding between the metal and the sapphire. Such bonding has been demonstrated for Cu, Ag, and Au in ab initio density-functional calculations, and is shown to consist of a complex combination of interactions: electrostatic, polarization, and orbital hybridization.23,36 In the absence of similar calculations for the Hg/sapphire interface, one can only speculate on the exact nature of the bonding in our system. Note, however, that a strong ionic bonding would have created a highly localized layer of sapphire-bound mercury atoms, and consequently a sharp first peak in the Hg electron density. Since a rather broad peak is observed instead (Figure 2b), the bonding may include a significant hybridization component which would reduce the peak by charge redistribution and delocalization. Clearly, ab initio density functional calculations for this system are called for to help clarify these preliminary and tentative suggestions. The surfaces of all liquids are theoretically predicted to be roughened by thermally excited capillary waves (CWs),37 the amplitude of which is predicted by CW theory to be σT ∼ (T/γ)1/2, where γ is the surface tension.38 All liquid surfaces measured to date conform to this T-dependence, except for Hg, where σT was experimentally found to increase with T faster than the CW theory prediction.29 Figure 3 shows the measured XR curves of the Hg/vapor interface at two different temperatures (symbols). The XR curve calculated for T = 25 C from the measured T = -26 C XR curve using

ð1Þ The first term represents an independent top layer at z = 0, of adjustable width σa and amplitude Fa, as for the Hg/vapor interface.8,29 The first sum has a layer spacing d1 different from the underlying layer spacing, d, and independent amplitudes Fn, to mimic, respectively, layer compression and interfacial density enhancement. Fs = 1.178 e/Å3 and F¥ = 3.25 e/Å3 are the bulk Al2O3 and Hg electron densities. σ2n = nσh2 þ σ20, where σ0 is common to all layers and σh determines the layering decay length as n increases and the individual gaussians progressively merge to form a z-independent F¥.8,29 The XR corresponding to F in eq 1 was calculated from the master equation R(qz) = R RF(qz)|(F¥-Fs)-1 [dF(z)/dz] exp(iqzz)dz|2.30,31 The model in eq 1 is highly flexible. An extensive search was carried out to find a minimal set of fit parameters with physically acceptable values, that will allow a good agreement with the measured R, while fixing the other parameters at independently determined values. These searches used the Hg/vapor parameter values8,29 as the starting point, gradually increasing the number and choice of the parameters varied in the fit. This process allowed identifying features common to all fits, and provided error estimates for the fitted values. The final number of fit parameters used here (4 plus 3 fixed values) is comparable to the 6-7 fit parameters used in the fits in refs 8, 29, and 32. The best-fit model (line, Figure 2a) exhibits an excellent agreement with the measured R/RF (symbols). The resultant density profile (solid line) is shown in panel b, and compared in panel c with that of the Hg/vapor interface8 (dashed line). To minimize the number of adjustable parameters, σ0 = 0 was chosen, yielding a fitted width for F1 of σh = 1.15 Å, roughly twice the 0.5 Å of the Hg/vapor interface8,29 and close to the fixed σs = σa = 1 Å. d = 2.74 Å was fixed at the Hg/vapor value.8,29 F1,2,3 ≈ 3.9 e/Å3, FR ≈ 2.9 e/Å3, and d0 = 0.8 ( 0.2 Å were fitted. The fixed d1 = 2.66 Å was obtained from the observed density enhancement (see below). Two features stand out in the fitted profile in Figure 2c: an increased near-interface average electron density, and a distinct layering. Integration over the profile yields a 10 ( 5% average increase in F over F¥ in a layer 8 ( 3 Å thick, both considerably smaller than the 30% and 20-30 Å of the Schottky contacts discussed above.15 Also, while the Schottky layer's density is z-independent,15 Figure 2b exhibits a nonconstant average density for the enhancement layer, the exact z variation of which is masked by the layering oscillations. A 10% density enhancement corresponds to a Δr/r = (ΔF/F)/3 ≈ 3% atomic radius contraction. The known ionic radius dependence on the ionization state33 indicates that a transfer of 0.13 ( 0.05 e/atom


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albeit 3-fold smaller in magnitude and in layer thickness than that found in Pb/Si and In/Si Schottky contacts.15 An ∼3% ionic diameter contraction due to a small, 0.13 ( 0.05 e/atom charge transfer from the Hg to the Al2O3 would account for this enhancement, somewhat smaller than the 0.2-0.3 e/ atom theoretical prediction.23,24 The measured XR curves do not vary with T over a large, 70 C range. This suggests that the anomalous T dependence of the Hg/vapor and Hg/electrolyte interfaces' density profiles29 is not of a structural origin, but may rather originate in some novel thermally activated fluctuation effect of the liquid surface. Similar measurements for other liquid metal/solid substrate combinations should provide further insight into the structure and underlying physics of these scientifically and technologically important interfaces.

EXPERIMENTAL METHODS We employed a high-energy, high-intensity, microfocused X-ray beam to study by XR the interface between Hg, a liquid metal forming no dimers and resisting oxidation even at an ambient atmosphere,8,29 and an ultra smooth (0001)Al2O3 substrate, which is an insulator, not a semiconductor. Measurements were done at beamline ID15A, ESRF, using the HEMD instrument,39-41 at an X-ray energy of E = 70 keV and an ∼5 1011 photons/s flux in a 5 20 μm2 (V H) focal spot. A sealed and thermostatted sample cell was used, with Hg (Merck, triple distilled, 99.999% pure) held in a 15 mm diameter KelF trough. The 10 10 0.5 mm3 substrate was lowered in vacuum onto the Hg. Identical results were obtained under dry nitrogen, in line with many studies using a Hg Langmuir trough, which maintained a clean Hg surface for several days under similar conditions.42-44 The cleaning procedure of the Al2O3, (a sequence of solvents, piranha, and UV irradiation under oxygen45), yielded a clean, Oterminated Al2O3 surface.19 For each sample and temperature T, XR curves were measured at several lateral sample positions. The measured qz e 3 Å-1 range (Figure 1) significantly exceeds those of previous studies, and extends well beyond the Hg/vapor interface's layering peak,8 qz = 2.2 Å-1, thus providing atomic-scale resolution.

Figure 3. Measured T-dependence of XR curves for the Hg/vapor and Hg/Al2O3 interfaces.

CW theory (line) is observed to lie significantly higher than the measured one (symbols), clearly demonstrating that the actual σT is significantly higher than that predicted by CW theory. A similar anomaly has been recently observed in measurements of the electrocapillary effect at the Hg/electrolyte interface (unpublished results). A possible explanation for this anomaly is that the standard CW theory is indeed valid, but the intrinsic F(z) has some additional T-dependence. Alternatively, F(z) could remain T-independent, as found for all other liquid metals to date, and the deviation may be due to a new surface roughening effect not included in the standard CW theory. No theoretical explanation exists at present for this unique, intriguing effect. Replacing the vapor phase by a solid, as done here, eliminates the CWs, and thus replaces the CW roughness of the free surface by the T-independent static σs of the Al2O3 surface. Thus, any T variation of the XR curve of the Hg/Al2O3 interface is bound to result from a T-dependence of the intrinsic F(z). As Figure 3 demonstrates, no such dependence is found for a large relative-T variation of ΔT/T = 22%. It is therefore highly likely that the anomalous T variation of the Hg/vapor interface is not due to a T-induced variation in the intrinsic F(z), but is rather due to a novel thermal fluctuation effect unaccounted for by CW theory. In conclusion, this study provides for the first time strong evidence that the atomic layering detected at the Hg/vapor interface8 also persists at the Hg/solid Al2O3 interface. However, the layering is found here to decay twice as fast with depth. A density enhancement is also found at the interface,


AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: [email protected].

ACKNOWLEDGMENT This work was supported by the US-Israel

Binational Science Foundation, Jerusalem (M.D.). Brookhaven National Laboratory (BNL) is supported by DOE Contract DEAC02-76CH0016. We thank ESRF for beamtime at ID15A.

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