GENERAL, DISCUSSION Dr. D. den Engelsen (Philips Rex. Lab., Eindhoven) said: Langmuir-Blodgett layers have been used before in order to test the validity of the Drude linear approxi- mation of the exact ellipsometric equati0ns.l. We studied Langmuir-Blodgett layers of various compounds of which the unsaturated fatty acid docosenoic acid CH3(CH2),CH=CH(CH2), ,COOH will now be considered. Monolayers of the cis- and the trans-conformation were spread on triply-distilled water (pH = 5.5, temp. 21"C), containing 2 x M CdC12 in some experiments. From known sur- face pressure against area diagrams of spread monolayers of these acids it was concluded that the Langmuir-Blodgett experiment should be done at 20 dyn/cm. Only one monolayer of both compounds could be transferred to the surface of a hydrophylic solid. Experiments to increase the number of deposited monolayers failed, e.g., for a hydrophobic surface there was no attachment. For the ellipsometric measurements we deposited the acids on polished, etched silicon plates.' The effect of the Si02 layer of about 30A thick was accounted for in the calculations. Since the refractive index could not be determined from one monolayer, we assumed the same refractive index of 1.50 for the two conformations. From the measured 6A values a layer thickness of 30.5 A was calculated for the trans- compound and 21.3 A for the cis-compound. A variation of k0.05 in the refractive index changes these values by about 1 A. The cis-acid probably has a lower refractive index than the trans due to the poorer packing, which leads to about 22 A for cis, whereas 30.5A undoubtedly is the upper limit for trans. From molecular models one deduces a maximum layer thickness of the cis-compound of about 25 A ; therefore these boomerang-shaped molecules are tilted, i.e., the line connecting the two extremities is not normal to the surface. Molecular models indicate a layer thickness of about 30 A for the trans ; thus the trans-molecules are not tilted. The surface pressure against area diagrams of the two acids on water at 20dyn/cm indicate cross-sections of the trans and cis of, 20 and 30A2/molecule respectively. This leads to a volume of 600 A3/molecule for trans- and a slightly greater volume for cis-docosenoic acid. Dr. W. Plieth (Free University, Berlin) said: A detailed picture of the adsorption of some compounds is given in fig. 3 of the paper by Meyer and Sparnaay. A dissociation into four particles has been assumed for adsorption of CH3SH and CH3X on a (1 1 1)-face. A dissociation into three particles occur on a (100)-face. Moreover, three different radicals, CH3-, CH2= and CHE, are formed on the surface. describes the bond between a surface and an adsorbed molecule as mutual effects between the electron system of the adsorbed molecule and an unknown number of surface atoms. Therefore, the compensation The MO-theory of chemisorption Mertens, Theroux and Plumb, J. Opt. Suc. Amer., 1963,53, 788. Hall, J. Plzys. Cliem., 1965, 69, 1654. to be published. Gaines, InsolubIe Monolayers at Liquid-gas Interfaces, (Interscience, 1966), p. 236. Archer, J. Opt. SOC. Amer., 1962, 52, 960. T. B. Grimley, Proc. Phys. Soc., 1958, 72, 103 ; Ado. CataZysis, (Academic Press, New York), 1960,12, 1. 45 Published on 01 January 1970. Downloaded by TECHNISCHE UNIVERSITEIT EINDHOVEN on 03/07/2015 14:44:44. View Article Online / Journal Homepage / Table of Contents for this issue
Transcript
GENERAL, DISCUSSION
Dr. D. den Engelsen (Philips Rex. Lab., Eindhoven) said: Langmuir-Blodgett layers have been used before in order to test the validity of the Drude linear approxi- mation of the exact ellipsometric equati0ns.l. We studied Langmuir-Blodgett layers of various compounds of which the unsaturated fatty acid docosenoic acid CH3(CH2),CH=CH(CH2), ,COOH will now be considered. Monolayers of the cis- and the trans-conformation were spread on triply-distilled water (pH = 5.5, temp. 21"C), containing 2 x M CdC12 in some experiments. From known sur- face pressure against area diagrams of spread monolayers of these acids it was concluded that the Langmuir-Blodgett experiment should be done at 20 dyn/cm. Only one monolayer of both compounds could be transferred to the surface of a hydrophylic solid. Experiments to increase the number of deposited monolayers failed, e.g., for a hydrophobic surface there was no attachment.
For the ellipsometric measurements we deposited the acids on polished, etched silicon plates.' The effect of the Si02 layer of about 30A thick was accounted for in the calculations. Since the refractive index could not be determined from one monolayer, we assumed the same refractive index of 1.50 for the two conformations. From the measured 6A values a layer thickness of 30.5 A was calculated for the trans- compound and 21.3 A for the cis-compound. A variation of k0.05 in the refractive index changes these values by about 1 A. The cis-acid probably has a lower refractive index than the trans due to the poorer packing, which leads to about 22 A for cis, whereas 30.5A undoubtedly is the upper limit for trans. From molecular models one deduces a maximum layer thickness of the cis-compound of about 25 A ; therefore these boomerang-shaped molecules are tilted, i.e., the line connecting the two extremities is not normal to the surface. Molecular models indicate a layer thickness of about 30 A for the trans ; thus the trans-molecules are not tilted. The surface pressure against area diagrams of the two acids on water at 20dyn/cm indicate cross-sections of the trans and cis of, 20 and 30A2/molecule respectively. This leads to a volume of 600 A3/molecule for trans- and a slightly greater volume for cis-docosenoic acid.
Dr. W. Plieth (Free University, Berlin) said: A detailed picture of the adsorption of some compounds is given in fig. 3 of the paper by Meyer and Sparnaay. A dissociation into four particles has been assumed for adsorption of CH3SH and CH3X on a (1 1 1)-face. A dissociation into three particles occur on a (100)-face. Moreover, three different radicals, CH3-, CH2= and CHE, are formed on the surface.
describes the bond between a surface and an adsorbed molecule as mutual effects between the electron system of the adsorbed molecule and an unknown number of surface atoms. Therefore, the compensation
The MO-theory of chemisorption
Mertens, Theroux and Plumb, J. Opt. Suc. Amer., 1963,53, 788. Hall, J. Plzys. Cliem., 1965, 69, 1654. to be published. Gaines, InsolubIe Monolayers at Liquid-gas Interfaces, (Interscience, 1966), p. 236. Archer, J. Opt. SOC. Amer., 1962, 52, 960. T. B. Grimley, Proc. Phys. Soc., 1958, 72, 103 ; Ado. CataZysis, (Academic Press, New York), 1960,12, 1.
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of" dangling bonds " on a surface by undissociated molecules is possible. A dissocia- tion can be combined with the adsorption but it is not necessary for the saturation of the surface bonds. In many cases the bonds in the adsorbed molecule may only become weaker.
The experimental results of the authors can be interpreted by the MO-theory. A number of six atoms on a (1 11)-face and a number of two atoms on a (100)-face are occupied in the adsorption bond by one adsorbed molecule. Weakening of intermolecular bonds or perhaps a dissociation into CH3- and SH- or X- can explain the other results.
Dr. J. Mchtyre (Bell Telephone Lab., N.J.) said: For purposes of correlation, eqn (1) and (2) in Hansen's paper represent specialized cases of the general first-order relations for the fractional reflectivity change produced by thin film deposition (cf. eqn (2) of ref. (2). For example, on noting that the quantity <t3 - <fl = -n: = t3 -cl, which in this case is real, and also that Im t2 = 2n,k2 = n2a,A/2n the form of eqn (1) is evident by inspection, except for a difference in sign. This sign difference results from the use of different definitions for A,, 2, and <,. In the general relations of McIntyre and Aspnes,l the Nebraska convention was followed, with 2, = nj - ik,, etc., so that i t j , t j and g j are complex conjugates of the analogous quantities in Hansen's paper. These conventions must be adhered to rigorously to obtain the same final numerical result.
With regard to the discussion of thin films in multilayer systems, the importance of employing the linear-approximation relations should be emphasized in those cases where phase change effects are important since these equations are exact, to first order in d/A, and take anomalous phase change effects into account. As an example, consider the effects produced by deposition of a very thin transparent film on a highly reflecting substrate in a gaseous ambient medium (n, = 1.0; n2 = 1.3, k , = 0.0; 123 = 3.0, k3 = 30.0; d/A = 1 . 0 ~ In this case, a plot of (AR/R),l against 41 exhibits a very sharp peak with a maximum of +2.0 x when cP1 = 89". In contrast, an absorbing film with identical refractive index and an extinction coefficient k , = 0.1 (characteristic of a moderately strong infra-red absorption band) produces a broader peak of opposite sign, with a maximum in (AR/R)II = -2.3 x at 41 = 87". The existence of the anomalous effect produced by the transparent film is not intuitively obvious and is not evident from Hansen's relations for the reflection absorbance All. The effect is clearly predicted, however, by eqn (2b) of ref. (2). Physically, it originates from the rapid variation of the phase change on reflection at the metal substrate, 611, near the principal angle (88"). This effect is of importance in studies of the electro-reflectance effect in metals caused by double-layer refractive index modulation. that this is one of the principal sources of the optical modulation effects observed by Walker,5-6 which he attributed to the electrochemical generation of solvated electrons. The relatively large magni- tude of this phase-shift effect near grazing incidence may also be of utility in optical studies of the structure of the double layer at the electrode-solution interface.
In fact, it has been proposed
Dr. B. Cahan (Case Western Reserve University) said: Hansen has stated in his earlier papers and in this discussion that he arranged his thin gold films for use in the
J. D. E. McIntyre and D. E. Aspzes, Surface Sci., 1971, 24,417. J. D. E. McIntyre and D. M. Kolb, Disc. Faraday Soc., 1970, in press. R. Muller, Surface Sci., 1969, 16, 14. J. D. E. McIntyre, to be published. D. C. Walker, Can. J. Chern., 1966,44,2226 ; 1967,45, 807. D. C. Walker, Aital. Chenz., 1967, 39, 896.
ATR electromodulation experiments so that the excess electrons stayed in the metal. I fail to see how this is possible. There is a basic fundamental error in the hypothesis that it is possible to establish an excess of charge inside a metal. The only place excess charge can accumulate macroscopically is at the surface. Any excess charge inside the electrode must immediately flow out through the connecting lead wire, since the Fermi levels of the two metals in contact are equal. If this were not the case, his equations would lead to the impossible conclusion that the electromodulation effect is dependent on thickness and would go to zero for bulk gold.
Prof. M. J. Dignam (University of Toronto) said: I report on recent developments that have occurred in the field of reflection spectroscopy at the University of Toronto. My collaborators in this work are Dr. B. Rao, Mr. M. Moskovits and Mr. R. Stobie. We have designed and built an automated, wavelength scanning, ellipsometer which operates in the range 0.5-5 p with a wavelength resolution of about 20A and an angular precision of about 0.01'. To test the capabilities of our technique, we have conducted studies on methanol adsorbed on vacuum-deposited gold films using a flow system, and hydrogen as the carrier gas. The results from one such study are shown in fig. 1. They were obtained for an angle of incidence of 80" and following four reflections. During measurements on the film covered surface, the relative pressure of methanol was maintained at 0.05 to within a few per cent, so that no more than a monolayer coverage is expected.
v)
cd a .- 2 c .- 4 I 3
0.06
0.04 -
0.02 -
0.00 3.2 3.3 3.4 3.5 3.6
wavelength pm FIG. 1 .-Ellipsometric spectrum for methanol adsorbed on silver.
It can be shown theoretically that for a good reflecting substrate and not too large angles of incidence, the amplitude function, In (tan $/tan $),* is to a good approximation proportional to the reflectance absorbance for p-polarized light, the proportionality factor being 2.303/2. (A full paper discussing various aspects of i.-r. ellipsometric spectroscopy is in press.') The C-H stretching bands are clearly
* 4 and A have their usual meaning with the " bar " referring to bare substrate conditions. M. J. Dignam, B. Rao, M. Moskovits and R. W. Stobie, Can. J, Chem., in press.
displayed in the amplitude plot of fig. 1 with four of the five peak frequencies in excellent agreement with those obtained by Byholder and Wyatt for methanol adsorbed onto a silica supported dispersion of iron. Since making these measurements, instrument sensitivity has been increased about five-fold. It is evident that sufficient sensitivity is available for observing the absorption bands from single reflection measurements, and hence that the technique can be used for studying adsorption on single crystal faces.
Ellipsometric spectroscopy has a number of advantages over conventional reflec- tion spectroscopy. It is more sensitive to the properties of the adsorbed molecules while at the same time being much less sensitive to absorption of light within the adjacent gas or solution phase. It is also much less sensitive to light intensity and detector drift. That ellipsometric spectroscopy has not been used extensively before now is due undoubtedly to the extreme tediousness of manual ellipsometric measure- ments and data reduction procedures. Our present instrument produces readings in digital form on paper tape at the rate of one per second, thus overcoming both problems. Details of the instrument will be published in the near future.
Dr. M. Stedman (Nat. Phys. Lab., Teddington) said: The proposal of Cahan et ai. for detecting a double layer of refractive index lower than that of the bulk solution is interesting. However, any realistic model of a double layer would feature refractive index gradients, which would affect computations particularly in critical angle regions. How would the reflectance effect behave for inhomogeneous films?
I have attempted to find the reflectance effect reported in the paper of Cahan et al. using my computer programmes which are based on the exact equations and provide output with a numerical resolution of 1 in lolo. The principal cases I have examined SO far are nrnetal = 0.495-2.46i(gOld), Ylfilm = 1.33, nelectrolyte = 1.34 and 1.38, dfilm = lOA, A = 5461 A. Output was either in the form of absolute reflec- tance or of the reflectance ratio Rf i lm present/I?film absent (= 1 + AI?/R) for p and s polarizations, tabulated for ranges of angle of incidence. The only effect discovered was a small deviation from the general trend of reflectance at angles immediately below the critical angle. This consisted of an increase in reflectance which did not exceed lo-* (in terms of AR/R) occurring over a range of about 0.003' ; in addition, there appeared to be a sharp drop in reflectance back to its original trend, occurring at the critical angle.
As the critical angle is approached the Fresnel coefficients approach unity : r s 2 3 + 1, rz3+ - 1, where the subscripts 1, 2, 3 refer to electrolyte, film, substrate. The total reflection coefficient is defined by Rs = (rsz +r13 exp)/(l +ri2r;3 exp) where exp is an exponential term dependent on film thickness and nearly equal to one in the present case. Both the numerator and denominator become small and numerical resolution is lost at this stage of computation. For example, for the system mentioned above with nl = 1.34, we find at = 82.9958' (0, = 82.9960'), r ; , = 0.9928 and r i3 and exp are very close to one, and numerical resolution in computed Rs drops to about 1 in lo8 (normally 1 in lolo). I conclude that the deviations detected in reflectance near the critical angle did not exceed the uncertainty of computation, and hence are probably artefacts. Theoretical considerations indicate that a slight change in the slope of reflectance curves may occur at the critical angle, but this was not detected in the computed results within the available accuracy. I would welcome the general com- ments of the authors, and would like to know whether their results are related to mine. It would be helpful for the theory of their effect to be clarified, to have some
G. Byholder and W. V. Wyatt, J. Phys. Chem., 1966,70, 1745.
It is important to consider the accuracy of comptuation.
specific quantitative examples of their computed effect, and to know the numerical resolution of their computer.
Miss M. A. Barrett (University of Bristol) (communicated); I have searched, by computation, for the effect described in the paper by Cahan et al. of a marked drop in R, near the critical angle for films of lower refractive index than the electrolyte. The constants used for the tests included : Ytmetal 0.495-2.463, 1.3-2.5i, and 2-2i; nfilrn from 1.15 to 1.329 with a thickness of 5 A ; neIectrolyte 1.33 and 1.38 ; wavelength 5461 A. The angle of incidence was increased in steps of 0.05" from 75" to 90". R,, increased monotonically and almost linearly in this range. Alternatively, Ylfilm was increased in steps of 0.001 from 1.31 to 1.329. In both cases, there was only a slight irregularity in the general rate of change of R,, and R, as the critical angle was passed. Under the most favourable conditions the effect did not exceed the sixth decimal place; the accuracy of the computations would be seven significant figures at best. A more detailed comparison of our computations would be valuable.
Dr. B. D. Cahan, Miss J. Horkans and Prof. E. Yeager (Case Western Reserve University) (conzmunicated) : We thank Miss Barrett and Miss Stedman for their communications which prompted us to uncover an unfortunate error in the equations used in the computer programme which predicted the anomalous behaviour at glanc- ing angles of incidence. With a corrected programme, the calculation of reflectivity at high angles no longer yields this effect. Experimental data showing peculiarities in the reflectivity of gold in 1N CF,COONa at 89.5", which were originally believed to confirm the predicted behaviour, are now unexplained.
Dr. R. Parsons (University of Bristol) said: I would suggest that the reason that no hydrogen is visible on gold electrodes is that the amount of hydrogen adsorbed on gold is very small. At the reversible potential Breiter, Knorr and Volkl estimated that the coverage with adsorbed hydrogen was about 4 %.
Dr. A. Bewick (University of Southampton) said: In the paper of Cahan et al., it is pointed out that the derivative reflectivity curve for gold, fig. 3, is considerably broader than that calculated by Hansen and Prostak. It is suggested that this is due to the neglect of the effect of surface states in the metal. In view of this, I wonder if it is wise in this context to use the reflectivity curve obtained at 0.0 V in 1N HClO,, when at this potential the surface will possess a certain amount of adsorbed hydrogen. The adsorbed atoms will presumably be associated with surface states or might even induce surface states where none existed in the absence of the chemi- sorbed species, as pointed out by Grimley2 and Koutecky.3
In reply to Parsons' comment, I would suggest that the effect of 4 % of adsorbed hydrogen on the width of the derivative reflectivity curve might well be measurable.
Dr. B. Cahan (Case Western Reserve University) said: In reply to Bewick, the relative electroreflectivity (1 /R)(aR/aE), in fig. 2, not the derivative reflectivity (l/R)(dR/aA), in fig. 3, is wider than calculated by Hansen and Prostak. Indeed, Hansen and Prostak predict that the reflectivity curve should be similar to (l/R) (aR/aL),. The (1 /R)(dR/aE), curves show this broadness at all potentials ; 0.2, 0.6 and 1.0 V have been shown in fig. 2 as representative. Concerning the effect of
Breiter, Knorr and Volkl, 2. Elektrochem., 1955, 59, 681.
hydrogen on the (1 /R)(aR/a& curves, if any, these curves were practically identical at all potentials between the potentials of visible H2 gas evolution and oxide forma- tion. We emphatically agree with the point about the effect of adsorbed species on surface states. It is specifically because of this interaction that optical methods have such high sensitivity in the study of adsorption.
Prof. M. J. Sparnaay (Enschede, Netherlands) said: Concerning fig. 5 in the paper of Cahan et al., what kind of surface states have they in mind? While there will be Tamm states at the metal/vacuum interface is this, also the case at the metal/ electrolyte interface ? Do they also have independent evidence for surface states in these systems ?
Dr. B. I). Cahan (Case Western Reserve University) said: In reply to Sparnaay, the surface states we have in mind in fig. 5 are those originating from the truncation of the lattice as well as from specific chemical interactions with liquid-phase species. Independent evidence is available for such surface states within semiconductor electrodes but it is difficult to cite non-controversial independent evidence for metal electrodes.
Dr. J. McIntyre (Bell Telephone Lab., N.J.) said: A number of models have now been proposed to account for the electroreflectance (ER) effect in metals. For the group Ib metals, Cu, Ag and Au, which exhibit pronounced features in their reflec- tivity spectra, the dominant effect in the AR/R spectrum at low angles of incidence is due to a perturbation of the electronic properties of the metal in its surface region. A striking feature of the experimental ER spectra of metals such as Ag and Au,l for external reflection at < 45", is that the signal R-laR/aEproduced by modulation of the electrode potential E is everywhere negative over the photon energy range 1-6 eV. The semi-empirical rigid shift models of Hansen and Prostak,2 however, predict an ER spectrum which resembles the derivative of the reflectivity spectrum. Thus, for a metal such as Ag, which has a deep minimum in R at 3.85 eV, peaks of both signs should appear. Similarly, if the Fermi level of the metal were modulated by the field together with its plasma frequency, the values of the inter-band components of the dielectric constant at the absorption edge, corresponding to the excitation of an electron from a d-band to the Fermi surface, would undergo changes opposite in sign to those of the free-electron components. Such behaviour should also produce ER peaks of opposite sign. Models based on a simple frequency shift of the optical constants are therefore not generally applicable, and experimental deviations from their predictions are not necessarily attributable to a gross distortion of the optical constants of the surface layer of the metal, as proposed by Cahan, Horkans and Y eager (CHY).
In an attempt to resolve these fundamental discrepancies and to provide a theo- retical basis for optical investigations of the surface electronic properties of metals, McIntyre and Aspnes (MA) proposed a model based on a first-order approximation for the reflectance change of a two-phase system produced by the generation of a very thin intermediate phase. In this model it is implicitly assumed that the Fermi level is not modulated by the field and that bound electronic states are also unaffected;
J. D. E. McIntyre, paper presented at the Electrochem. SOC. Meeting (New York, 1969), abstr. no. 231. A. Prostak and W. N. Hansen, Phys. Rev., 1967,160, 600 ; 1968,174, 500. J. D. E. McIntyre and D. E. Aspnes, Bull. Arner. Phys. Soc., 1970, 15, 366; in press. J. D. E. McIntyre and D. E. Aspnes, Surface Sci., 1971, 24, 417.
the ER effect of metals is attributed to a modulation of the density of the free electron wave-function tails at the metal surface. The mean perturbation of the metallic dielectric constant %, in this region is given by
where tf is the free-electron component of ern, N is the free-electron density of the bulk metal and ANs is the excess surface electronic charge required to shield the applied field. It results, therefore, that to first order in d/A (cf. eqn (2) of ref. (l)), the ER effect is independent of the transition layer thickness.
The MA theory predicts that the ER effect should closely approximate the (positive definite) dielectric loss function, Im (Q; l) and quantitatively accounts for the observed features of the ER spectrum of Au, including the non-zero response in wavelength regions well-removed from the main peak at 2.6 eV (as noted by CHY) and the uniform sign.
The success of this free-electron model in accounting for the features of the experi- mental ER spectra of Ag and Au suggests that surface states of the metal do not contribute significantly to the ER effect. This implies that the orbitals of the 5d core electrons in the Au surface atoms are either " stiff " or are well-shielded from the applied external field by the 6s conduction-band electrons. Experimental deviations from the predictions of the simple free-electron theory, however, may furnish further information concerning the one-electron wave functions of the surface metal atoms.
The shape of the pseudo-plasma edge for Au is determined by the combined contributions of intraband and interband transitions to the complex dielectric con- stant. Examination of analyzed dielectric response function curves for Au 2 p
reveals that the edge shape is mainly determined by the real part of thefree electron contribution, which varies rapidly and non-linearly with frequency in this energy region. Surface states may be expected to make a relatively small contribution compared to the bulk metal layer of ca. 200A thickness which is sampled by the incident radiation. The dip in R at 640nm in fig. 3 of CHY is not seen in the reflectivity of thin gold films deposited on very smooth substrates. It appears to be analogous to a similar effect observed for silver films which arises from the coupling of the surface plasma oscillation mode to the radiation field through surface roughness.
With regard to the distinction between the ER effect produced by (i) a perturbation of the optical properties of a thin surface layer of the metal, and (ii) a small change of the real refractive index of the double layer, measurements at 41 = 45" are particu- larly useful. Owing to the symmetry between cl and Q3 in the linear-approximation relations for AR/R, the dielectric constant of the transition layer can be defined with reference to that of either semi-infinite bounding phase. For case (i) : (AR/R),, 4 5 ~ z
2(AR/R)s,450, regardless of the actual form of the field-induced shift of the optical constants. However, for case (ii) : (AR/R)p,450 = 0, whereas (AR/R)s,450 is small but non-zero. In the second case where n 2 z n 1 , the Brewster angle (or comple- mentary principal angle), cjhB = tan-l (n2/nl) , at which the reflectivity of the interface of two transparent phases vanishes for p-polarized radiation, is close to 45". These effects are, in fact, clearly shown in the computed curves in fig. 1 of Stedman's paper. Experimental ER spectra
(AE,) = (&- l)AN,/dN, (1)
of Ag and Au exhibit close agreement with case (i). J. D. E. McIntyre and D. M. Kolb, Symp. Faraday Soc., 1970,4. H. Ehrenreich, The OpticuZ Properties of Solids, ed. J. Tauc (Academic Press, New York, 1966), p. 106. J. D. E. McIntyre and D. M. Kolb, unpublished results. J. D. E. Mchtyre, paper presented at the Electrochem. SOC. Meeting (New York. 1969), abstr. no. 231.
According to the MA theory,l the ER effect for a free-electron metal is opposite in sign to that for metals such as Cu, Ag, Au and Pt, for which Re 8,> (cl - 1). Experimental evidence indicates the Drude theory is followed closely by liquid Hg for hcoG3 eV. The ER effect for Hg should provide a sensitive test of the validity of the MA theory, which predicts a sign reversal in the experimental ER spectrum near 5.0 eV. Also, this theory predicts an ER effect for Hg of opposite sign to that shown by Stedman in her fig. 1, when the refractive index 1.600 - 4.753‘ is used. These optical constants are both considerably higher than those predicted by Drude theory.
Dr. B. D. Cahan, Miss J. Horkans and Prof. E. Yeager (Case Western Reserve Uniuersity) (communicated) : We agree with McIntyre that a model explaining the electroreflectance behaviour of gold in terms of a modulation of the Fermi level of the metal is invalid. We identified this error in concept in the Hansen-Prostak theory in our paper and clearly did not use such in our explanation of the electromodulation. We therefore do not understand McIntyre’s association of our concept of the electro- modulation of surface states with the Hansen-Prostak model.
Perhaps a further discussion of the electromodulation phenomenon in gold would be appropriate at this point. The McIntyre-Aspnes (MA) theory seeks to explain this in terms of modulation of the electron density in the exponential tail of the free electron distribution at the surface. The dielectric constant B2 of the surface layer is assumed to differ from that of the bulk metal Eh3 due to the excess surface electronic charge on the electrode. This difference (A&) is postulated to be a result of changes in the free electron contribution & to the dielectric constant, which is calculated from the Drude-Zener theory. For an ensemble of free electrons in a conductor this is given by
8, = 1 - w;/(co2- iw/z).
Here cop( = (41Te2N/m*)3) is the plasma frequency and z( = oom*/Ne2) is the relaxa- tion time, with N the free electron concentration, m* the effective mass, and oo the d.c. conductivity of the metal. Thus, the free electron dielectric constant is approxi- mately linear with the carrier concentration (since the effect of the ico/z term is small in the wavelength region of interest), which leads to McIntyre’s eqn (1).
The Drude-Zener equation is based on a classical electron-gas model and considers the motion of individual electrons in the oscillating electric field of the optical waves. The electrons undergo periodic acceleration-deceleration due to this field and decelera- tion resulting from collisions with the ions. The concept of a tail for the free electron distribution extending into the potential energy wall at the limit of the metal phase, however, is purely quantum mechanical in origin. It is not obvious that the classical mechanical treatment of an oscillator is compatible with the quantum mechanical treatment upon which the existence of the tail in the electron distribution depends. We are forced to ask such questions as the following. What are the scattering ions in the tail of the free electron distribution? What is the physical significance of oo in this region, and why should it be invariant with the electron concentration in the tail?
Further insight can be gained by consideration of the actual magnitudes of the relevant quantities. The free electron tail occupies a layer ~ 0 . 6 A thick.3 Even if the free electron concentration in the tail were as high as that in the bulk metal,
J. D. E. McIntyre and D. E. Aspnes, Bulf. Amer. Phys. Soc., 1970, 15, 366; in press. * E. G. Wilson and S. A. Rice, Optical Properties and Electronic Structure of Metals and Alloys,
ed. F. Abelh (North Holland, Amsterdam, 1966), p. 271. J. D. E. McIntyre, private communication.
GENERAL DISCUSSION 53 only -2 x 1014 electrons/cm2 of electrode surface could be accommodated in this region. (The actual number should be smaller.) Removal of all these electrons accounts for -30 pC/cm2 of charge. This is less than the charge required to change the potential across the double layer from the e.c.m. to + 1.0 V, which is of the order of 50 pC/cm2 (assuming an integral electronic capacitance of 50 pF/cm2). Thus, in order to account for the change in the charge on the metal surface, one must use more than just the electrons in the free electron tail. It follows that the effects of the applied electric field across the interior then extend into the metal phase beyond just the 0.6A tail of the $$* distribution function for the free electrons. If such is the case, this field should be felt by electrons not only in the 6s band but also in the 5d band and the 5d surface states.
The fact that the required change in number of electrons for a 1 V potential change is inconsistent with a reasonable value for the number of electrons available in the tail leads to unrealistic values of (At,) in McIntyre’s eqn (1). McIntyre and coworkers do not observe the inconsistency because their modulation (i.e., differential) technique involves a relatively small change in the number of electrons. Whatever model is used, however, must also be valid for d.c. (i.e., integral) techniques. When a 1 V potential change is considered? AN/N> 1, implying that ( 8 , ) is at least of the same magnitude as tf (which is even larger than &,). In view of this, any criticism of the size of the optical constant changes suggested in our paper is also applicable to the MA treatment. We do not share, however, McIntyre’s apparent reservations concerning gross changes in the optical constants at the electrode surface.
There are some experimental aspects of the electroreflectance of gold not accounted for by the theory of electromodulation of the free electron tail. We have done a calculation based on the MA theory and find that the calculated effect falls off much more rapidly than the observed AR/R at low energies. In addition, there is nothing presently incorporated in the theory to explain the change of the electroreflectance peak as a function of the mean potential of the electrode.
It is difficult to understand McIntyre’s interpretation of Ehrenreich (McIntyre’s ref. (6)) as indicating that the shape of the edge in the reflectivity at -2.3 eV is nut due primarily to interband transitions. This reference specifically states on p. 151 that such an edge shape is characteristic of a low-energy interband transition such as “ would typically correspond to Cu or Au near 2 eV ”. It is not the rapid variation in the free electron dielectric constant which determines the shape of the edge, but rather the detail in the contribution of the bound electronic states to the dielectric constant. P. 143 of the same reference states that “ It is this peak in [the real part of dielectric constant of the bound electrons, 6&p)] which is due to interband transi- tions, that is responsible for the characteristic colour of the noble metals.” Further, McIntyre’s statement that “ the real part of the free electron contribution . . . varies rapidly in this region ” seems to contradict fig. 9 of the same reference, from which it can be seen that the free electron contribution to the real part of the dielectric constant, &if), is a smooth function of the energy E of the photon and that deif)/dE near the edge is more than an order of magnitude smaller than it is at 1 eV. It would probably be more accurate to state that &if) has decreased sufficiently to allow the structure in &ib) to dominate in controlling the wavelength dependence of the reflectivity of this region.
While surface states are expected to contribute only a few percent to the total absolute reflectivity, they can give a contribution to the dielectric constant in the surface layer as great as that for any other bound or free electron in the wavelength regions where transitions involving these energy states are possible. A change in their concentration or energy levels can produce effects at least as large as the observed
electromodulation levels. These changes can be caused by interactions with the field at the interface or by a modification of their orbitals due to interactions with adsorbed species. Finally, the small dip in R in fig. 3 of our paper is probably due to a shift in baseline over the finite time necessary to obtain the digital data. The dip did not appear in other reflectivity data for similar samples. While it seems that some of the electroreflectance effect can be explained by a modulation of the free electron con- centration at the surface, it also appears that this alone cannot account for all of the features seen in the visible.
- 2
Prof. E. Yeager (Cleveland) (communicated) : Further evidence to support the view that the surface electronic properties are a major consideration in accounting for the change of specular reflectivity with potential is to be found in experiments involving the change of reflectivity with the deposition of monolayers of foreign metal ions on surfaces such as gold. In our laboratory Takamura, Takamura and I I have examined monolayers of foreign metal atoms such as lead and cadmium de- posited on gold from perchloric acid solution. The electrodeposition of monolayers of such metals occurs at potentials much less cathodic than those for the bulk metal.
I 1 - I)
I I I I I
I I I I 1 I
0 800 1600 potential (mV) (S.C.E.)
FIG. 1.-Relative change in (reflectivity, potential) and (current, potential) curves for gold in the presence of Pb2+ ions. Electrolyte 5 x lod4 M Pb2++0.2 M HC1O4 ; potential sweep rate, 105 mV/s ;
wavelength, 5200 A.
Fig. 1 shows the (reflectivity, potential) curves at two different wavelengths and the simultaneously recorded linear sweep voltammetry curve. At 7500 di, the reflectance of the gold is decreased by the monolayer of Pb while at 5200A, the reflectance is increased. The latter wavelength is close to that for the adsorption edge for gold
T. Takamura, K. Takamura, W. Nippe and E. Yeager, J . Electrochem. Soc., 1970, 117, 626.
(= 5500 A) associated with the 5d-6s interband transition. Oxide formation is also evident in these reflectance curves at potentials more anodic than 0.90 V (S.C.E.).
These reflectance curves were obtained using a multiple reflectance cell with - 19 reflections. This is far too many reflections for quantitative studies of either the absolute reflectance changes or the wavelength dependence of even the relative changes because of errors introduced by scattering as described in our paper. It is planned to establish the wavelength dependence for monolayers of various metals on gold using a single reflection technique in the near future.*
Dr. James McIntyre (Bell Telephone Laboratories) (communicated) : The response of Cahan, Horkans and Yeager (CHY) to my previous comments concerning their paper indicates a need for some further discussion of physical models for the electro- reflectance effect of metals. The CHY model is certainly different in concept from that of Hansen and Prostak (HP). The intent of my preceding comments was to point out that it is not necessary to postulate a gross distortion of the optical constants of the surface layer to account for the primary features of the observed electro- reflectance (ER) spectra of metals. For small modulating voltages, these features seem to be well-explained in terms of the most characteristic feature of metals-the free-electron plasma, without invocation of surface-state effects. Secondly, the fact that ER spectra of the noble metals are uniquely one-signed, even for metals such as Ag which exhibit a pronounced minimum in R, cannot be explained in terms of an edge-shift model. We must seek a model which accounts for the features of these spectra over the complete energy range.
Both the CHY and HP models have one feature in common-a modulation of the interband component t b of the metallic dielectric constant by the applied electric field. In the HP model, Fermi-level modulation produced by anodic polarization of the electrode causes the absorption edge of the 5d-+6s (Fermi surface) interband transition in Au to shift to longer wavelengths. In the edge region, the absorption coefficient a and Im &b are raised while Re gb undergoes both positive and negative excursions. Similarly, for the free-electron contribution, Re tf (large and negative) is shifted positively, while Im tf (small and positive) decreases. In the CHY model, modulation of the 5d surface state energies by the applied field shifts the components of &b in the same sense as that produced by Fermi-level modulation. In both models, the interband effects are reversed for transitions from the Fermi surface to vacant bands at higher energy.
Both of the above models differ significantly in this respect from that of McIntyre and Aspnes (MA). The latter model assumes to a f is t approximation that &b is not modulated by the applied field. This assumption is based on the facts (cf. Friedel l) that d-states have small orbits compared to sp-valence states of comparable energy, are localized and not strongly perturbed by the lattice potential, and are ineffective in screening the nuclear charge within the atom.
With regard to the use of the Drude relation
although this expression was originally derived on a classical basis, it also results
* This work has been supported by the U.S. Office of Naval Research. J. Friedel, Physics ofMetaZs, ed. J. M. Ziman, (Cambridge University Press, Cambridge, 1969), chap. 8, p. 340.
from quantum mechanical treatments of the one-electron model. 1-3 Secondly, the concept of a tail on the free-electron distribution at the surface is not uniquely quantum-mechanical. Consider the simple jellium model for a metal in which the positive charge of individual metal ions is replaced by a semi-infinite uniform dis- tribution of positive charge of density No, against which the free-electron assembly moves. The steepness with which the free electron density N falls from its uniform interior value No to zero outside the surface is determined by the kinetic energy of the electrons and the potential energy field in which they move. The gradual decrease in electron density at the surface gives rise to a negative surface dipole at the point of zero charge. Electrons exhibit wavelike behaviour, and a task of quantum mechanics (cf. Lang and Kohn is to calculate the exact form of the free-electron distribution at the surface in order that surface energies, work functions and electro- reflectance effects can be evaluated theoretically. With regard to the electron scatter- ing mechanism, the mean free path of an electron on the Fermi surface of a metal such as Au is -3 x 10' A. Electrons in the tail will be scattered by the positive ions of the host lattice with a characteristic relaxation time 2 ~ 2 . 5 x 10-14 s. The classical Lorentz-Sommerfeld relation, z = rn*ao/Ne2, is commonly employed to estimate the magnitude of z. In reality, z varies slowly with frequency, but at visible u.-v. wavelengths, w % l/z, so that little error results from use of this relation in eqn (1).
For the number of electrons in the tail, for intuitive purposes we can approximate the electron density distribution in this region by the sum of two terms (applicable inside (z>O) and outside ( z G 0 ) of the uniform positive charge distribution, respectively)
(2) where ZTF is the Thomas-Fermi screening length, and I, is the screening-length in the solution phase. Significantly, ZTF = vF/, /3~, , where vF is the velocity of an electron on the Fermi surface and w, is the plasma frequency. Then if Is% ITF, the number of electrons per unit surface area in the tail region (-2.3 Ztf,<z,<2.3 ZTF) is ca. 2.3 ZTFNO. For a metal such as Au, No = 5.9 x e ~ r n - ~ , 2.,+0.6 A and ntail= 81 pCcm-2. In their reply to my previous comments, CHY discuss a model in which all electrons must be stripped from this tail in order to charge the double layer from the P.Z.C. to + 1.0 V. Such a model seems physically unrealistic, however. An applied field will simply cause the tail to shift as a whole relative to the plane z = 0 as electrons flow to, or from, the external supply. This shift will be accom- panied by a distortion which shortens or lengthens the tail. The exact form of the electron density distribution at a charged metal surface is not known. In the simple MA model, however, it is not necessary to know the tail shape since for d<;Z it is possible to define an equivalent intermediate phase with sharp boundaries and uniform optical constants, which yields the same reflectance properties as the transition layer at the interface.' To first order, the quantity AR/R is independent of d. At the point of zero charge, therefore, the substrate is approximated as a single phase with uniform optical properties. This is analogous to the assumptions commonly made in measurements of the optical constants of metals by ellipsometry.
While the views of CHY concerning the electron density distribution at the surface are not in accord with our concepts, we concur that the electric field does penetrate
C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963), chap 6, p. 99. H. Ehrenreich, The Optical Properties of Solids, ed. J. Tauc (Academic Press, New York, 1966), p. 106.. M. Cardona, Modulation Spectroscopy (Academic Press, New York, 1969), chap. 2, p. 9. C. Herring, Metal Interfaces (American Society for Metals, Cleveland, 1952), p. 1. N. D. Lang and W. Kohn, Phys. Rev. B, 1970,1,4555.
N(z) = N o P - 3 exp (- z/4,)3 + (No/2) exp (z/Zs),
slightly into the metal surface and is felt by the ion cores of the metal atoms in the first layer. The effective field is strongly attenuated by the conduction electrons, however, and since d-orbitals in noble metals are not easily deformable (as evidenced by the low compressibility and high cohesive energy of these metals), it is reasonable to assume that the local value of tf in the surface region is modulated much more strongly than &.
With regard to the magnitude of (At), provided d<A, the incident light beam cannot distinguish whether the perturbation extends only over a charge sheet of infinitesimal thickness (corresponding to a delta-function in the charge density distribution) or whether the variation is more gradual, as in the MA tail model. Provided that AR/R is small, so that first-order theory is applicable, this will always be true. In principle, therefore, there is no reason why the MA theory cannot be scaled to large potential changes. In fact, the integral value of AR/R measured by CHY for a + 1 V potential change at 500 mp (close to the main peak in the ER spectrum) is -6.0 x (The polarization and angle of incidence of the light beam are not specified in their paper). Assuming normal incidence and an integral double layer capacity of 50 pF cm-2, the MA theory yields a value of -5.9 x at this wavelength. Such exact agreement is fortuitous in view of the approximations involved and the neglect of solution double-layer effects,2 but it is evident that the primary change in reflectivity can be attributed with some confidence to free-electron effects. Also, when such large potential changes are considered, the local value of 2, in the surface region must differ significantly from that in the bulk metal owing to the large excess or deficit of free electronic charge. Consideration of the screening action of the free-electron tail and the insensitivity of the incident light beam to its shape and length, indicates that the calculated values of (A&> are realistic. We agree with CHY that under such conditions, there are apparent large changes in the optical constants of the surface layer of the metal. This serves to re-emphasize the dangers involved in measuring optical constants of electrode substrate materials immersed in electrolyte solutions.
Scaling the MA theory to large potential changes, however, ignores the pro- nounced variations of double-layer structure with potential. More useful information about the optical and electronic properties of the metal-solution interface can be obtained by using modulation techniques under conditions such that the double- layer structure at a given bias potential is only slightly perturbed. If we can approxi- mate the uncharged metal as a single phase, then at normal incidence the differential ER effect at a potential E (measured from the P.z.c.) is given to first order by
(""> - R E - -- 8nnidIm( A <Afi)E+dE-<Afi)E) 81-23 (3)
This result is rigorous and independent of the origin of the optical modulation effect. If we assume as before that at a given bias potential, kf is modulated much more strongly by the field than Qb, then the differential ER effect is still primarily due to free electrons. However, if chemisorbed species alter the magnitude of kb in the interphase region, either through a strong interaction with the d orbitals in the surface atom layer of the metal or by introduction of new charge-transfer absorption processes (e.g., in adsorbed 0 or H regions), the effect will be much more complicated. These
J. D. E. McIntyre and D. E. Aspnes, Surface Sci., 1971,24,417. M. Stedman, Chem. Phys. Letters, 1968,2,457 ; Symp. Faraday Soc., 1970,4, OOO. J. D. E. McIntyre, paper presented at the Electrochemical Society Meeting, New York, May 1969 (Abstract no. 231).
effects will vary non-linearly with the bias potential, as will the double-layer capacity itself. It is these second-order effects which we presume to be responsible for the observed shifts in the ER spectra of the noble metals with bias p0tentia1.l'~ The details of these processes are not well understood, so that exact relations for their optical effects cannot yet be given. Conceptually, however, the form of their influence can be seen from eqn (3).
Extrinsic chemisorption surface states of the type discussed above are distinctly different in origin from the intrinsic Tamm states (due to lattice termination) discussed by CHY.3 Little or no experimental evidence has yet been found for intrinsic surface My original comment concerning the shape of the reflectivity edge was concerned with the question of whether one can attribute " excess absorp- tion " and assymmetrical broadening of the edge solely to intrinsic surface states as proposed by CHY in their original paper.3 As I noted previously, the edge shape
a
0
-a
8
-16
-24
-32
I I I 1 I I I I I
0.4
0.2
'0 1.0 2.0 3.0 4.0 5.0 6.0 tw [ev] 1
1 I I I I I I I I 2 3 4 5 6
[evl FIG. 1 .-Decomposition of experimental values ',* of the dielectric constant of Au into free and bound . ,, contributions: eexpt = &+b. -, &xpt = Eexpt-Z EeXpt; ---, &f = &>-k; ; . . . &, = 6i-k;.
is determined by the combined contributions of and tb to the total dielectric constant of the metal, ern = &+ $. (Effects of bound electron surface states are included in tb). The relative importance of the individual terms is shown in fig. 1, which was calculated from the optical constants measured in this laboratory for a vacuum- evaporated Au film on a smooth quartz substrate. Here in the low-energy section
J. D. E. McIntyre, paper presented at the Electrochemical Society Meeting, New York, May 1969 (Abstract no. 231). T. Takamura, K.Takamura, W. Nippe and E. Yeager, J. Electrochem., Soc., 1970,117,626. B. Cahan, J. Horkans and €3. Yeager, Symp. Furduy SOC., 1970,3, 36. J. T. Law, Semiconductors, ed. N. B. Hannay, (Reinhold, New York, 1959), chap. 16, p. 675. D. E. Eastman, Phys. Rev. B, 1971,3,1769. J. D. E. McIntyre and D. M. Kolb, Symp. Furaday SOC., 1970,6,99.
of the edge (1.7-2.3 eV), the imaginary components of gf and Eb are small compared to their real parts. The normal incidence reflectivity (in vacuum),
thus depends primarily on the real components of 6,. Further, in this energy range, the variation in Re g b is much smaller than that in Re tf. The net effect of adding the approximately constant term, Re tb, to the rapidly varying term Re gf, is to increase Re k , rapidly from a large negative value to a value much closer to unity. As is evident from the above relation, the result is a rapid decrease in reflectivity (a pseudo- plasma edge) centred near 5500 A (2.35 eV), which accounts for the characteristic yellow colour of gold when viewed in reflection. Any small structural features in kb at longer wavelengths (e.g., those due to intrinsic surface states in the 5d band) will be strongly masked by the rapid fall in Re Ef towards - 00.
This analysis for Au differs in detail from that of Ehrenreich.l The sharpness of the derived peak near 2.5 eV in the plot of Re eb depends slightly on the method of analysis of the optical constant data and the value chosen for a,, but more critically on the accuracy of the measurements. The data shown in fig. 1 are in good agreement with recent measurements by Irani et aLY2 and earlier data of Schulz et aL39 However, even in the sharper structure in Ehrenreich's plots (cf. fig. 8 of ref. (3)), the variation in Re 6* is smaller by a factor of 5 than that in Re gf for Au in the energy region 1.7-2.5 eV. Our interpretation of the relative roles of Re 6, and Re gf in determining the edge shape of Au thus differs from that of CHY. Finally, although Im 6b vanishes outside frequency intervals where absorption occurs, Re &b
does not, since it corresponds to the sum of contributions from all polarizability mechanisms (other than intra-band) over the frequency range O,< cob co. Thus the value of Re g b at the edge is not solely due to the 5&6s interband transition. From the above analysis we conclude as before : (i) there is not a priori physical basis for expecting a symmetrical reflectivity edge with rounding solely due to thermal broadening of the Fermi distribution function; (ii) the rounding on the red side of the edge is primarily due to the free-electron behaviour of Au and not to " excess absorption " attributed to intrinsic surface states by CHY.
In the experimental ER spectrum of Au, a broadening of the low-energy side of the main peak at 2.5 eV is observed, as CHY point out. This is illustrated in fig. 2 where the experimental ER spectrum of Au measured in this laboratory using a rapid charge-injection technique, is plotted together with the spectrum calculated from the MA theory. While double-layer refractive index modulation can account for some of this broadening, its major source may be due to a surface plasma resonance. The conditions for this resonance to occur are that Re ern = E~ (where E~ is the dielectric constant of the transparent bounding phase) and that Im tm be small. Optical constant measurements on electrode substrate metals are generally made in air. Examination of fig. 1 shows that the first condition is satisfied by Au in air near 3.0 eV and again near 4.5 eV. In this energy region, however, Im &, is largely due to inter- band absorption processes and the surface plasma resonance is highly damped. As a result, the effects of this resonance do not appear in the measured optical constants of Au. When the bounding medium is an aqueous electrolyte, however, E~ z 1 8,
H. Ehrenreich, The OpticulProperties of Solids, ed. J. Tauc (Academic Press, New York, 1966), p. 106. ' G. B. Irani, T. Huen and F. Wooten, J. Opt. SOC. Amer., 1971,61,128.
L. G. Schulz, J. Opt. Soc. Amer., 1954,44, 357. L. G. Schulz and F. R. Tangherlini, J . Opt. SOC. Amer., 1954,44,362. H. E. Bennett, J. M. Bennett, E. J. Ashley and R. J. Motyka, Phys. Reu., 1968,165,755.
and the first resonance condition is satisfied near h co= 2.5 eV. Further, Im k, falls rapidly in this region as the energy is decreased. The conditions for surface plasma oscillations to occur thus appear to be satisfied. The height of the broad surface plasma peak in the spectrum of the dielectric loss function, Im 8; l, is critically dependent on the roughness of the reflecting surface. In Au, this peak will combine with the main loss peak at 2.55 eV, and will amplify this peak and broaden it on the low-energy side. For Ag, however, a small distinctly resolvable peak appears near
4.0 -
3.0 - w w
s I 2.0-
1
:
1.0 -
1.0 2 .o 3.0 4 .O 5.0 6.0 .ha [eYI
FIG. 2.-Electroreflectance spectra of Au in 1 M HClO, (Ar-saturated) at = 45". EH = 0.4 V. A Qm = + 1.91 pC cm-2 (r.m.s.) at 270 Hz. -, (AR/R),,t ; - - -, AR/R calc. from McIntyre-Aspnes theory. The dashed sections of the experimental curves indicate wavelength regions where
appreciable distortion may occur due to stray light effects.
3.2 eV in the experimental ER spectrum.l Analysis of dielectric constant data for Ag reveals that in air, the surface plasma resonance peak in the calculated loss function spectrum would occur near 3.6 eV and tend to be buried in the initial rise of the very large volume plasmon peak. (In the MA theory, the ER spectrum of metals is closely related to the loss function spectrum.l 9, Further, surface plasma resonance is a phenomenon exhibited by the free-electron plasma and is not associated with bound surface states. The simple MA free-electron model of metallic ER effects can be extended to take this resonance into account, Details of this calculation will be given elsewhere.
and experiment which is evident in fig. 2, provides convincing evidence of the essential validity of the first- order treatment of McIntyre and Aspnes. Future refinements to include specific
J. D. E. McIntyre, paper presented at the Electrochemical Society Meeting, New York, May 1969 (Abstract no. 231). J. D. E. McIntyre and D. E. Aspnes, Bull. Amer. Phys. SOC., 1970,15, 366.
effects of the electrical double layer, chemisorption surface states and surface plasmons will, we hope, enhance our ability to investigate in situ the detailed properties of the metal-electrolyte interface by means of electrochemical modulation spectroscopy.
Dr. B. D. Cahan, Miss J. Horkans and Prof. E. Yeager (Case Western Reserve University) (communicated) : In regard to McIntyre’s expansion of his previous com- ments, we would re-emphasize our position. It is imperative that any theory of modulation of the reflectivity by potential changes must apply to both integral and differential techniques. Recent measurements in this laboratory in which both techniques were used show good agreement between the two methods. Cahan, Horkans, and Yeager did not “ discuss a model in which all electrons must be stripped from the tail ”, but pointed out that this is a consequence of the MA theory when it is applied to integral changes.
We would make a related pointed regarding McIntyre’s eqn (2), which we prefer to write in the following form :
McIntyre’s choice of limits for the integration of this equation is difficult to understand. The integral was taken over a length of 4.6 ltf (= 2.76 A), which is much larger than the dimensions of the electron tail (= 0.6&. This gives too large a value of ntail because electrons from the bulk metal have also been included. A more meaningful calculation would be the evaluation of the change in the surface charge Antail with potential change across the interface within the basic mathematical framework used to derive the above equation.
The value of -6.0 x for AR/R for a 1 V change at 500 mp obtained by McIntyre from our paper was apparently taken from fig. 4. Unfortunately, there was a misprint in this figure in the original proof. The fact that the curve was obtained with 7 reflections was omitted and the ordinate was incorrectly labelled. It would seem more appropriate to have taken this value from our fig. 2, which shows R-l(aR/dE)A as a function of wavelength. Finally, McIntyre’s discussion of “ second order effects ”, such as interactions of liquid phase species with d orbitals, involve some of the kinds of effects we originally proposed to be responsible for the observed shifts in electroreflectivity spectra with potential.
Dr. J. D. E. McIntyre (Bell Laboratories) (communicated): In reply to CHY, it was pointed out explicitly in my previous comments that the MA theory should be equally applicable to both integral and differential techniques provided effects due to double-layer structure and specific adsorption are properly taken into account. Their is one further reservation concerning ER effects in metals which requires mention. For p-polarized radiation, (ARIA),, is strictly independent of d (to first order) only when (AS) 42%,, as can be verified by examination of the linear-approxi- mation relations. Otherwise the thickness of the transition layer must be included.
The “ breathing ” action of the electron plasma was discussed in detail in my previous comments. The tail itself is never stripped but only shifted and distorted by the applied field. Since the arguments of CHY against the MA free electron model rest largely on the premise of an insufficiency of electrons in the tail region, some further discussion on this point may be helpful.
The choice of integration limits for eqn (2) in my previous comment is easily explained. Assuming Zs*ZTF, the limits z = -2.3 IT, and z = +2.3 ZTF simply correspond to the distances at which N(z) attains values of 0.1 No and 0.9 No,
respectively. This choice is analogous to common practice in specifying the rise-time of electronic circuitry. The more restrictive limits, z = -ZTF and z = ZTF, corre- sponding to the distances at which N(z) = 0.368 No and 0.632 No, would lead to ntail = No ZTF. For Au, this would yield a value for ntail = 3 . 5 ~ 1014 electrons cm-2 = 57 pC cm-2, which may be compared to the value of 2 x 1014 electrons cm-2 ( 3 0 ~ C c m - ~ ) given by CHY in their earlier comment. Such values under- estimate the number of electrons in the tail region. The cut-off limits for the integra- tion in my previous comments were chosen so as to include most of the electrons in the short-range exponential tail while excluding the long-range Friedel oscillation region. The integration does not include electrons in the bulk metal, but only those in the surface region which contribute to the surface dipole.
Concerning the dimensions of the tail region, it should be emphasized that 0.6A is the value of the Thomas-Fermi screening parameter for Au and not the tail length. For a metal such as Au, the Wigner-Seitz radius, rs = ($nNo)%, is 3.0 a.u. Examina- tion of the recent work of Lang and Kohn reveals that the electron density falls from 0.9 No to 0.1 No over a distance of 0.34 Fermi wavelengths (ca. 1.8 A) for such a metal, with an average screening parameter, 2=OO.65A. The tail in this case is shorter than that predicted by the approximate eqn (2) in my previous comments due to the Friedel oscillations in the density, but the screening lengths are in close agreement.
According to eqn (2), displacement of the whole electron density distribution by an amount ZTF relative to the rigid positive charge background, without any change in tail shape, would give Antailx 1.06 ZTF No in the region -2.3 ZTF<Z< 2.3 ZTF. For Au, this corresponds to a surface charge density change of 60 pC cm-2 and provides a rough estimate of the shifts to be expected when large fields are applied to an electrode. A more detailed consideration of the tail shape would require a self-consistent field treatment and hardly seems justified in view of the fact that the MA theory predicts that AR/R is directly proportional to the change in integral surface charge and is insensitive to the precise form of the electron density distribution. These points were also discussed at length in my previous comments.
The average value for R-l (AR/AE) at 500 nm reported by CHY in fig. 2 of their paper is ca. - 1 x V-l, and is greater by a factor of ca. 2 than that predicted by the MA theory. Since we do not have any information concerning the double-layer capacity, angle of incidence, polarization or electrode optical constants in their experiments a more detailed comparison with theory is not possible. The discrepancy is in the same sense as that illustrated in fig. 2 in my previous comments. One possible cause for this experimental peak height amplification was advanced previously. In my previous communication, the data in fig. 4 of CHY was specifically chosen to test the applicability of the MA theory to integral measurements of ARIR. Low-frequency measurements of R-l(AR/AE) are more susceptible to spurious adsorption kinetic effects and changes in double-layer capacity than are the rapid- charge-injection measurements of R-I(AR/AQ) shown in my fig. 2. These measure- ments are independent of surface-charge modulation frequency. Frequency-dependent effects are commonly observed, however, when the potential alone is modulated. AR/R is observed to decrease linearly as logfincreases. Previously reported measure- ments from this laboratory suggested that for potential regions in which no Faradaic reactions occur, this frequency dependence is associated with the dispersion of the double-layer capacity of the solid electrodes and the effects of uncompensated electro- lyte resistance in the potentiostatic control circuit.
The significant contributions of Yeager and his coworkers have greatly increased our understanding of the optical effects due to specific adsorption, and we have
endeavoured to acknowledge these specifically in our previous comments. Now that methods for determining the actual absorption spectra of monolayers of chemisorbed species are available, rapid progress should be made in elucidating the detailed features of the electronic interactions of these species with the metal surface.
