Reflectance and Ellipsometry of Metal/Electrolyte Interfaces BY M. STEDMAN Division of Inorganic and Metallic Structure National Physical Laboratory Teddington Middlesex Received 1st October 1970 The improving sensitivity and increasing use of optical reflection techniques in the study of metals and semiconductors in contact with electrolytes makes it timely to review the interpretation of such measurements. The surface charge on the conductor the layer of solvent molecules forming the compact layer the adsorption of ions on the electrode as well as the distribution of ions in the diffuse layer are all features of the electrical double layer which can contribute to optical measurements. Models of these features are described which facilitate computation of their optical effects and speci- men results are presented.The fact that all of these features may make comparable contributions to optical measurements is illustrated for the system mercury+aqueous sodium fluoride and the predicted contributions are compared with experimental results. The measurement of optical change on the reflection of light from a surface ha been used increasingly as a route to the optical parameters of the media at or near the surface. The changes measured may be in intensity (reflectometry) or in the polarization parameters (ellipsometry). Often the optical parameters are not of primary interest but are used as means to probe structure near the surface. Whilst the refinement of instrumentation has taken place rapidly our ability to interpret the measurements remains problematic. Those who make optical measurements on electrodes have to deal with a parti- cularly complicated situation in that the structure of the metal/electrolyte interface has various features with differing dependencies on electrode potential.There has been a tendency in interpreting optical measurements on electrodes to focus attention on to just one feature of double layer structure and to interpret the total optical change in terms of change in that feature only as though all else remained constant. This is often unjustified and it is becoming clear that all aspects of double layer structure in both the metal and the electrolyte phases must be considered. It is timely to survey the range of possible contributions to optical measurements on electrodes and to review the models available for predicting optical effects based on our present ideas of double-layer structure.The discussion that follows will be restricted to interfaces at equilibrium and the effects of Faradaic processes will not be considered. OPTICAL PROPERTIES OF THE DOUBLE LAYER DEFINITIONS The optical parameters used in this paper follow the definitions and sign conven- tions recommended by Muller (Nebraska Symposium 1968). Optical effects are quoted either as changes in the elliptical parameters A and t,b or as relative changes of reflectance AR/R for perpendicular (s) and parallel (p) polarizations. 64 M. STEDMAN 65 BASIC REQUIREMENTS OF A N OPTICAL MODEL The simplest model of a metal/electrolyte interface is one in which the media are completely homogeneous and in which the bulk properties of the metal and electrolyte are applicable up to their interface.This hypothetical model serves as a reference state the optical properties of which can be calculated from the bulk parameters. Structural features of the double layer cause the refractive index to be modified in the region of the interface and deviation from the conceptual reference state can be characterized by the profile of (complex) refractive index with distance from the electrode surface. For the purposes of optical calculation it is convenient to express the profile in stepped form so that the interface region is represented by one or more homogeneous films. The optical properties can then be calculated in the usual way by application of the exact Drude equations. In practice relative rather than absolute optical measurements are made and the electrochemist is mainly interested in the optical changes that occur with electrode potential.Such changes will be classified as those associated with changes occurring in the metal and those in the electrolyte solution. CHANGES I N THE METAL Reflection spectroscopy in which field modulation is applied to the sample through contact with an electrolyte has been widely used during the last decade to study the electronic structure of semiconductors. Generally the magnitude of the effect observed has made it reasonable to neglect the changes in the electrolyte. Recently similar though smaller effects have been observed in metals and have been studied by Hansen and P r o ~ t a k ~ Buckman and others. The work of Hansen and Prostak is of particular interest to electrochemists and they have proposed a simple theory to explain their observations on the potential dependence of the internal reflectance of 50 A gold film electrodes.First the change in the charge on the electrode is expressed as a fractional change in the density of free electrons in a thin surface layer. region is dominated by the free electron contribution the change in electron density can be related to a change in the plasma frequency; this implies a frequency shift of the spectrum and a change in the complex refractive index can be derived. Qualitative support for the theory is strong particularly in the close resemblance of the modulation spectrum to the derivative of the reflectance spectrum of gold. The main quantitative test of the theory that was published concerned the variation of ARJR for angles of incidence between 61 and 76" at 4800A and for a particular potential sweep.Some comments should be made on this test. First the optical constants of gold (viz. 1.80-1.98i) used for computation differ seriously from those referred to in the literature (ca 1.25-1.89 and indeed from those previously reported by Hansen.6 Secondly no computed results were sho,wn for comparison with the observed data for the relative change in reflectance for parallel polarization AR,/R,. When this is done using the same optical data considerable divergence from the observed curve is found. Finally the sign of the AR/R results of Hansen is inconsistent with the direction of the potential step he used and with the changes quoted for the optical constants. One concludes that a more searching test of the theory over a much wider range of conditions is desirable.However there is no reason to doubt the basic soundness of the theory which will provide a most useful guide for predicting the optical behaviour of metal electrodes at least in the free electron regions of their spectra. This is illustrated in fig. 1 which shows the results of applying the theory to mercury and gold ; optical Since the spectrum of gold in the 5000 s4-3 66 ELLIPSOMETRY OF METALIELECTROLYTE INTERFACES effects at 5461 are shown as AA At,,$ and AR/R. Results are restricted to external reflection from the metal. Although internal reflection can be more sensitive for the majority of metals it is unlikely that one can attain the exceedingly thm yet continuous films required by the technique.The full curves show the behaviour predicted for an increase of surface change of 10 pC cm-2 and assume no change in the electrolyte. The broken curves show the behaviour predicted for an increase of solution refractive index of 0.03 in a layer 6A thick and assume no change in the metal. These values were chosen as typical experimental ones but the graphs can be appropriately scaled for any other size of increase. Such graphs provide a useful comparison of the contributions to the total optical effect to be expected from changes in the metal and changes in the electrolyte and can help to select the conditions most appropriate for studying a particular feature of double-layer structure. Absolute reflectances (R and R,) should also be considered particularly if cells with multiple reflections are planned.0 -0 02 . . b b o 90 Angle incidence (deg) -+ 3 a \ \ I -0'04 i j \ I I 0 90 90 4 0 90 01 ' /- A- 0 90 0 90 angle incidence (deg.) FIG. l.-Computed optical effects as a function of angle of incidence. - change only in the metal AqM = + 10 pC cm-2 in 5 A layer. -- change only in the electrolyte An = f0.03 in 6 A layer. Refractive indices electrolyte 1.33 gold 0.495-2.46i mercury 1.600-4.75i. Wavelength 5461 A. CHANGES I N THE ELECTROLYTE First we consider the effects of changes in solvent structure. THE COMPACT LAYER.-The structure of the layer of solvent dipoles comprising the compact or inner double layer differs from that of the solvent in the bulk solution and varies with electrode potential. Evidence for the detailed structure of the inner layer has been scanty and ambiguous and only recently has the use of temperature and pressure as experimental variables in double-layer measurements made possible the derivation of surface excess entropies and volumes.Such measurements reported by Hills Payiie and Hsieh ' 9 * have clarified some aspects of inner layer structure at least for a few simple aqueous electrolytes. The contribution that the inner layer may make to optical measurements on electrodes does not seem to have been discussed in the literature. Three aspects M. STEDMAN 67 of the layer need to be considered viz. orientation of the solvent molecules thickness of the layer and its density or compression. Orientation per se seems unlikely to contribute as a first-order effect. To argue in simple terms the ray reflected from the substrate travels through the film in two directions encountering the dipoles both head first and tail first.The optical effect arising from the interference of this ray with that reflected from the top of the dipole film will thus be similar for the two dipole orientations (see fig. 2). The influence of the orientated dipoles on the sur- rounding media may lead to second-order effects. More important are the inter- related aspects of layer thickness and compression. Hills and Payne have derived ;- FIG. 2. surface excess entropies and volumes as a function of surface charge; they estimate that as the surface charge on mercury in contact with 0.1 N aqueous sodium fluoride increases from -10 to about + 2 0 ~ C c m - ~ a compression of ca. 17 % occurs in the water layer.This is typical of the compressions estimated for a range of aqueous electrolytes onm ercury.8 For a similar compression of bulk water and taking the density as 1.21 g ~ m - ~ the refractive index is 1.405.9 Although the unidirectional compression of the inner layer is not exactly equivalent to the bulk compression of water we may use the bulk refractive index to predict the optical effect. Thus for the system with optical constants Ytelectrolyte 1.334 nfilm 1.405 dfilm 4A n,,,,,(niercury) 1.603-4.729i wavelength 5461 A incidence 70° we compute the following optical changes with respect to the (filmless) reference state AA - 0. 120° A$ 0.013" ARJR 9.07 x These results indicate that the contribution of the inner layer to optical measurements is well within the sensitivity of modern instruments and should not be neglected without careful consideration.ARJR - 3.6 x THE DIFFUSE DOUBLE LAYER.-The excess surface charge on an electrode (metal plus adsorbed ions) is compensated by an ionic atmosphere or diffuse layer composed of ions with concentration excesses or deficiencies with respect to their values in the bulk solution and which are held in equilibrium by the interplay of coulombic and thermal forces ; the profiles of ion concentrations with distance from the electrode surface can be predicted by the Gouy-Chapman theory. The optical effect of the diffuse layer has been discussed.1o The crux of the problem is the conversion of ion concentrations to solution refractive indices and this was done by application of the Lorenz-Lorentz equation using ion refractivities and volumes.Ideally the concentration profiles would then be expressed in a stepped form and the diffuse layer would be approximated as a multi-layered film; in practice treatment as a 68 ELLIPSOMETRY OF METAL/ELECTROLYTE INTERFACES single homogeneous layer suffices. Typically the variation of optical effect with surface charge exhibits asymptotes characteristic of the refractivities and volumes of the dominating ions; maximum curvature occurs near the zero of surface charge. An example in which the optical effect is expressed as AA is shown in fig. 3 curve (b). Since the diffuse layer is a mirror of the charge on the electrode optical methods could provide a route to potentials of zero charge. 4M (@ Cm-*) FIG. 3.-Change of A with surface charge 4M for aqueous sodium fluoride solutions on mercury.Angle of incidence 70" ; wavelength 5461 A. Top Experimental results for a range of concentrations. Bottom Computed results for 0.1 N NaF. Curve a field effect in the metal ; b diffuse double layer ; c inner layer ; d (a + b) ; e (a + b + c). In solutions of sodium and potassium salts it is usually the anion which makes the larger contribution to the refractive index. Typical optical effects of the diffuse layer are as follows for a change in the net surface charge from 0 to +20 pC cm-2 on mercury in contact with 0.1 M aqueous potassium chloride AA - 0.06" A$0.0067" (wavelength 5461 A angle of incidence 70"). ADSORBED IoNs.-The problem of calculating the optical effect of adsorbed ions is similar to that encountered in calculating the effect of ions in the diffuse layer viz.the conversion of surface concentrations of ions to a film refractive index. The method used by the author for the diffuse double layer and referred to above can easily be extended to include adions by simply adding their concentrations to those M. STEDMAN 69 of the ions in the diffuse double layer and forming a single equivalent layer for optical calculation ; detailed equations have been published. O Chiu and Genshaw l1 have adopted a slightly different approach in which they use ion refractivity and volume in the Lorenz-Lorentz equation to derive the " refractive index " of the adsorbed ion. This notional refractive index of the adion is then combined linearly with the refractive index of the solvent in proportion to surface coverage.The combined refractive index is taken to apply to a layer of thickness equal to the length of the adion. However difficulty can arise with ions of low refractivity. For example application of the method to the fluoride ion leads to an imaginary refractive index although the ion is clearly not absorbing. For ions of larger refractivity the two methods appear to lead to similar results. For example the optical effect of a monolayer of bromide ions (reckoned at q1 = - 105 pC cm-') on mercury for optical conditions and data as previously given is computed as follows; (first figure method of the author; second that of Chiu and Genshaw) AA -0.526" -0.634" A$ 0.060" 0.058". More typically for a change in surface charge (qm) from 0 to +20 pC cm-2 the change in bromide ion adsorption (qi) would be about - 26 pC cm-2 and the associated contribution of the bromide adions to the optical effect would be AAN -0.15" A$-0.015" A'RP/RP- 1 x AR,/R,- 1 - x 10-4.It is probable that these models give a useful guide to the optical effect of ions in the double layer. However it is not obvious that the use of ion refractivities derived from measurements on dilute bulk solutions is valid for ions in the double layer environment. Furthermore the process of adsorption not only changes the ion adsorbed but may also significantly modify the substrate e.g. by partial charge transfer. INTERFACE BETWEEN MERCURY AND AQUEOUS SODIUM FLUORIDE This system is a useful one to study and discuss because of the simplifying absence of specific ion adsorption. EXPERIMENTAL The ellipsometer operated at 5461 A and had the usual polarizer/quarter-wave plate/ samplelanalyzer configuration.The circles could be read to less than 0.01" and Faraday cell modulation could be applied on both arms of the instrument. Manual setting was facilitated by inspection of the photomultiplier output trace whilst continuous automatic balancing could be obtained through feedback from phase sensitive detectors. A fused- silica cell with 70" faces contained a mercury pool as the working electrode; a Teflon lid carried nitrogen feeds a platinum counter electrode and a saturated calomel electrode in a probe as a reference. All of the chemicals were freshly distilled or otherwise purified. The cell was driven by a modified 1 A Chemical Electronics potentiostat and the usual procedure was to step from - 1.5 V (sce) to the desired potential and back.Effects of impurity adsorp- tion and of the disturbance of the surface of the mercury pool on stepping the potential were obviated by extrapolation of the optical effect to the start of the step. RESULTS Experimental results for a range of concentrations are presented in fig. 3. Potentials have been converted to surface charges using the data of Russel. Optical effect is shown as change in A relative to the value at zero surface charge. Also shown are the optical effects for a 0.1 N solution as computed from the models 70 ELLIPSOMETRY OF METAL/ELECTROLYTE INTERFACES presented earlier. The inner layer contribution is based on the value previously derived and the shape of the curve follows that given by Hills and Payne for the surface excess volume.The contribution from the metal derives from the data shown in fig. l(d) and is expected to be linear with charge. The diffuse layer contri- bution has been previously computed by the author.1° Combined effects were obtained by addition of the component effects although strictly a multilayer computa- tion should be made for each surface charge. DISCUSSION All of the features of double-layer structure that have been discussed above can contribute to optical measurements in greater magnitude than the sensitivity of modern instruments. Thus any of these features is open to study by optical methods ; equally none should be completely neglected in interpreting results. This has been illustrated by the computations for mercury/aqueous sodium fluoride which predict comparable contributions from the surface charge on the metal and from the inner and diffuse layers in the electrolyte.As would be expected the experimental results presented as a function of surface charge are not very dependent on electrolyte concentration. Comparison of the experimental results with the theoretical ones (fig. 3) shows that the sum of the metal and diffuse layer contributions (curve (d)) reproduces the trend and magnitude of the observations quite well. Inclusion of the inner layer contribution (curve (e)) does not alter the trend but predicts too large an optical effect. Since the bases of the calculations of the metal and diffuse layer contributions are straightforward whilst those of the inner layer effect are speculative it is likely that the latter effect was over-estimated.This is not surprising since compression of water in the compact layer is manifestly different from bulk compression. The observed deviations at high surface charges from the general trend of the results do not correlate with any of the predictions. The complementary observation of A$ as a function of charge would be revealing since the ratio of the metal and electrolyte contributions would be different (fig. l(e)). The present conclusion is that theory and experiment are in reasonable accord but detailed interpretation must await the refinement of both. Much of this paper has been concerned with the conversion of structural data to optical effects; most experimentalists wish to effect the reverse process. A question that arises is whether there are any situations in which double-layer structure may be neglected.In the formation of thick films e.g. in corrosion and passivation studies and generally in any study of extended Faradaic processes changes in A and $ may be many degrees and double-layer effects may well be negligible. However calculation before rejection is always a wise rule. The study of specific ion adsorption is a more difficult case since the change in A may be only a few tenths of a degree. The results of Chiu and Genshaw on the adsorption of the bromide ion on mercury from potassium bromide solutions are of particular interest as excellent agreement with existing adsorption data l 3 was reported without any allowance for the double layer being made. The data of Lawrence Parsons and Payne l 3 show that the net charge (qM+qi) on the electrode is always negative so that the dominant ion in the diffuse layer is always the cation (which has the lower refractivity).This fortuitous situation leads to the expectation that the diffuse layer will have only a small optical effect in this particular case. However a contribution from the metal similar to that already calculated would be expected as well as some contribution from the inner layer. The former would be about 0.05 to 0.1" for the range of potentials used in this work compared with the experimental changes of up to 0.25". Interpretation thus seems less clear than was supposed by Chiu and Genshaw. M. STEDMAN 71 A serious criticsm of all the models used in this paper is that matter in the double layer is treated as though it were the same as bulk matter although in a thin layer.Refinement of these models will require insight into how the properties of substances are modified at interfaces. Unfortunately such information is only likely to be accessible in those experiments for the interpretation of which we need the data. Another dissatisfying feature of the treatment is the division of the double layer into separate components. Such division is neither experimentally possible nor uniquely definable. We may manipulate the double layer but it retains an essential unity. Combining these thoughts with modern views of discreteness in the double layer leads one to seek a microscopic approach to optical calculations. Strachan14 and Sivukhin l 5 have treated molecular films as collections of Hertzian oscillators in their studies of optical reflectance.Perhaps their pioneering work should be taken up again and developed in this context. It is a pleasure to acknowledge many helpful discussions with my colleagues Dr. M. E. Peover and Dr. R. J. King. The work described was carried out at the National Physical Laboratory. Recent Developments in Ellipsometry ; ed. N. M. Bashara A. B. Buckman and A. C. Hall (North- Holland Publishing Co. Amsterdan 1969). R. H. Muller ref. (l) p. 14 and 29. W. N. Hansen ref. (l) p. 205. W. N. Hansen and A. Prostak Phys. Rev. 1968,174,500. A. B. Buckman; ref. (l) p. 193. W. N. Hansen I.S.A. Trans. 1965 4,267. ' G. J. Hills and R. Payne Trans. Faruday SOC. 1965 61 326. S. Hsieh Ph.D. Thesis (University of Southampton 1969). Y. B. Zel'olovith S. B. Kormer M. V. Sinitsyn and K. B. Yushko Soviet Phys. Doklady 1961 6,494. (Note two printing errors in fig. 2 the q- $+I ordinate extends to 0.006" ; in fig. 3 the ordinate extends from 1.332). l o M. Stedman Chern. Phys. Letters 1968 2,457. I 1 Y-C. Chiu and M. A. Genshaw J. Phys. Chem. 1968,72,4325. l 2 C. D. Russel J. Electroanal. Chern. 1963,6,486. l 3 J. Lawrence R. Parsons and R. Payne J. Electroanal. Chern. 1968,16,193. I4 C . Strachan Proc. Cambr. Phil. SOC. 1932 29 116. I s D. V. Sivukhin Soviet Phys. JETP 1956 3 269.