Langmuir 1995,11, 963-968
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Interpretation of Spectroscopic Ellipsometry Data on Protein Layers on Gold Including Substrate-Layer Interactions Jan MArtensson and Hans h i n * Laboratory of Applied Physics, Department of Physics a n d Measurement Technology, Linkoping Institute of Technology, S-58183 Linkoping, Sweden Received September 26, 1994. I n Final Form: December 20, 1994@ Interface effects are often neglected when interpreting ellipsometric data on thin organic films on solid substrates. We find that on gold substrates such effects give rise to spurious absorption seen as a nonzero imaginary part of the optical response function of adsorbed protein layers. With spectroscopicellipsometry it is revealed that these effects are more pronounced in the visible part of the spectrum than in the ultraviolet part. We conclude that the standard three-phase model (ambient-layer-substrate) in general is insufficient for an accurate analysis of the layer properties. Large errors in the deduced refractive indices, film thicknesses, and surface concentrations may arise. A four-phase model for interpretation of spectroscopic ellipsometric data on protein layers on gold is proposed as an improvement. In this model the interaction between the adsorbed layer and the gold substrate is included and modeled in effective medium approximations. The physical mechanism behind the interaction is suggested to be depletion of electronsfrom a small zone in the gold substrate, close to its surface. By using this new model, a considerable improvement is obtained and the spectra obtained are free from the unphysical absorption in the visible part of the photon energy spectrum. The time development of the interaction between the protein layer and the gold substrate leads to a suggestion of a two-state adsorption model for protein adsorption. The studies in this report are limited to layers of ferritin and albumin, but we think that the results are applicable to other protein layers as well.
Introduction When studying adsorption of macromolecules, ellipsometry is a powerful tool for measuring adsorption kinetics and isotherms. With spectroscopic ellipsometry, it is also possible to determine optical spectra of thin films in situ at solifliquid interfaces.' However, ellipsometry is a n indirect method based on measurements of polarization changes upon reflection. It is therefore necessary to interpret these polarization changes using a n optical model representing the surface under study. In a n ellipsometric measurement only two quantities (I)and A) are obtained at each wavelength. Therefore, even in the simple three-phase model (ambient-film-substrate), the evaluation problem is underdetermined, as one generally has to work with three unknowns, the thickness (d)of the film and its complex refractive index (N = n ki). There exists several methods to get around this. A straight forward strategy is to assume the layer to be transparent (k = 0) in some part of the photon energy range used. This is often a valid assumption for the protein layers ofinterest in this study. Thus in principle it should be possible to determined and n in the range of transparency. However, it is not always possibel to use this strategy. Small experimental errors, a model mismatch, or correlation between d and n sometimes make it necessary to assume a value of n beforehand and then have d as the only unknown. This holds especially for very thin layers. Another, more sophisticated, strategy is to calucate a complex-valued thickness, assuming a real N = n Oi or, alternatively, to calcuate a complex N assuming a realvalued thickness. The imaginary parts obtained may be small, as often found on silicon, for example, and are often used in the analysis as a measure of the accuracy. The origin of these imaginary parts can either be the use of a too simple optical model or experimental errors. In
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@Abstractpublished in Advance ACS Abstracts, February 15,
1995. (1)Arwin, H.; MBrtensson,J.;Lundstrom, 1.Appl.Phys.Comm. 1992, 11, 41.
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ellipsometric studies with visible light on thin organic films on gold substrates, the analysis often results in such effects with k-values different from zero. This is found whether the ambient is or liquid.' Spectroscopic ellipsometry reveals that on gold the effect occurs only in a limited photon energy range, typically below 2.5 eV. In this report this problem is addressed by assuming it to be a n effect of a model mismatch. We present ellipsometric results on protein monolayers or submonolayers measured in situ on gold substrates in buffer. Our aim is to develop procedures for interpretation of spectroscopic ellipsometry data to determine the complex refractive index and thickness of such layers. Due to the complexity in the interaction between protein layers and a solid surface we found it necessary to develop available optical models further. In this report, the emphasis is therefore on methodology and we believe that our findings have general applicability on many different types of organic films on gold and possibly also on other metal surfaces. More detailed studies of layers of selected proteins will be published elsewhere. Our results should be of general interest to those working with ellipsometric studies of thin organic films on metal surfaces, for example in areas like biomaterials, biosensors, fouling, and surface cleaning. The outline of this report is as follows: First we show that, when using a simple one-layer model, apparent absorption is found in the optical properties of protein layers, which on good grounds can be assumed to be transparent. With a two-layer model we can interpret ellipsometric data to avoid such apparent absorption. Then we improve the model by allowing it to be different at different photon energies. Finally we give two examples of refractive index spectra of protein layers and conclude (2) Arwin, H. Appl. Spectrosc. 1986,40, 313.
(3)Elliot, D.; Hamnett, A.; Lettingbon, 0. C.; Hill, H. A. 0.;Walton, N. J. J . Electroanal Chem. 1986.202. 303. (4) Porter, M. D.; Bright, T. B.; h l a r a , D. L.; Chidsey, C. E. D. J . Am. Chem. SOC.1987,109, 3559.
0 1995 American Chemical Society
Mhrtensson and Arwin
964 Langmuir, Vol. 11, No. 3, 1995 a
that ellipsometric thickness determination of thin layers on gold are most accurately done in the ultraviolet region.
I'"""'""""'""'"''''l
Experimental Section
0.4
Materials. Substrates were made by sequential vacuum deposition of chromium (10-50 A) and gold (2500 A) onto glass
slides. Chicken egg albumin(ovalbumin)was standard material of grade V (Sigma, USA). The ferritin (Fluka Chemie AG, Switzerland)had been recrystallized three times. Stock solutions were made by dissolvingthe proteins in 0.02 M phosphate buffer, pH 7.3, containing0.15 M NaCl (PBS). All experiments in this investigation were done at a protein concentrationof 1mg/mL. Ellipsometric Measurements. The measurements were carried out at room temperature with a rotating analyzer spectroscopic ellip~ometer,~ operated in the photon energy range 1.5-4.5 eV (825-275 nm) with an angle of incidence of 68".Our ellipsometric spectra consist of measurements taken at 256 equidistant photon energies. The kinetic measurements were done at 2 eV (620 nm). All ellipsometric measurements were made in situ in PBS in a quartz cuvette of 5 mL volume. Procedures. A typical experiment was carried out as follows: immediately before a substratewas used, it was washed in a mixture of HzO,HzOz, and NH40H (ratio 5:l:l) at 80 "C during 5 min, followed by rinsing in Millipore-filtered water. The substrate was then mounted in the buffer-filled cuvette, without drying to make sure that it was still clean when the measurement started. A reference spectrum was taken on the clean substrate. Thereafter a kinetic measurement was started and an appropriateamount ofa protein stock solution was added to give a cuvette concentration of 1 mg/mL. The kinetics were continuously recorded, and after some time the protein solution was exchanged with buffer by means of dilution. Then a second spectrum was taken, and in experiments in which long-term effects were studied, additional spectra were measured later.
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27A Albumin,
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( 5 ) Aspnes, D. E.; Studna, A. A. Appl. Optics 1976,14, 220.
(6)Azzam, R. M. A.; Bashara, N. M.EllipsometryandPo1arizedLight; North-Holland: 1987.
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Interpretation Procedures and Optical Models Ellipsometry. An ellipsometer measures the change in state of polarization for reflected polarized light. The measured quantity is the complex reflectance ratio, e = tan q eAi,where )I and A are the so-called ellipsometric angles. In a rotating analyzer ellipsometer, e is determined in the form of tan q and cos A from the phase and amplitude of the photomultiplet ~ i g n a l .In ~ this study the purpose is to characterize thin protein films, and then the complex refractive index, N , = n, k,i, ofthe substrate must be known. This is achieved by measuring Q on the clean gold substrate, mounted in buffer in the cuvette, before protein adsorption. N , can then be calculated by analytical inversion in the two-phase model (ambientsubstrateX6 The thickness and the optical properties of a subsequently adsorbed protein layer are then obtained by interpretation with a suitable optical model as described below. We describe the optical properties of the film with a complex refractive index, N = n ki, or alternatively with a complex dielectric function, c = €1 EZi. These two quantities are related through E = W . The Three-phaseModel. By usingNs and e measured on a substrate with an adsorbed protein film as input data, N and d of the protein layer can be obtained in the three-phase model (ambient-film-substrate). The calculations are done by numerical inversion of the Fresnel equations using a Newton-Raphson algorithm. First the thickness of the protein layer is determined in a photon energy region (normally 3-4 eV), where the protein can be assumed to be transparent (k = 0), leaving only n and d as unknowns. Figure l a shows a typical dielectric function spectrum and the real part of the refractive index of a protein layer, here albumin, evaluated with this procedure. Observe, however, that €2 * 0 below 3 eV shows
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Figure 1. (a)Dielectricfunction ( 6 = €1 czi) and the real part, n,of the complexrefractiveindex of a layer of albumin,evaluated
from ellipsometric data in the three-phase model using a thickness of 27 A. (b) Imaginary part of the dielectric function of a ferritin layer in an experiment where the adsorption was interrupted after 12 min by exchangingthe ferritin solution in the cuvette to clean buffer. The actual time (after rinse) of measurement and the layer thickness are shown at each curve. that this procedure cannot be used due to a model mismatch, as will be further discussed below. A different procedure has to be used for ferritin because it has absorption for all energies above 2 eV and below 3 eV, thus the three-phase model is insufficient, as for albumin. This is seen in the €2 spectra in Figure lb. Thus if the three-phase model is applied there is no photon energy (on gold) for which we can assume 12 = 0 for ferritin. To obtain the thickness of a ferritin layer the strategy is to solve the complex refractive index for different thicknesses, followed by a calculation of the absorption coefficient, a = 4nkI1, for each thickness. The thickness that gives an absorption coefficient spectrum that agrees with the corresponding spectrum (above2.5 eV) offerritin measured in solution with a spectrophotometer is then chosen as the correct one. The Four-PhaseModel. As shown above, the threephase model is not always sufficient. When it is extended with another layer, the four-phase model is obtained, shown in Figure 2a. In this model, the calculations are done by using the scattering matrix formalism for multilayer.6 When adding a second layer, three more parameters are introduced (the thickness and complex refractive index of the layer). We therefore have a total of six unknowns for the two layers. However, it is only possible to determine two of them from the ellipsometric data, and A, so the other four have to be determined independently. The actual procedure used in this inves-
Langmuir, Vol. 11, No. 3, 1995 965
Ellipsometry Data for Protein on Gold Ambient
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Photon energv Figure 2. (a) The four-phase model including an effective medium layer (EMA) for modeling of interface effects as described in the text. (b) Improved four-phasemodel in which the thickness of the EMA layer depends on the photon energy.
tigation, as well as the improved four-phase model shown in Figure 2b, is described in the next section. In the work presented in this report, we use the layer closest to the substrate to model an interface between a gold substrate and a protein film by using the Bruggeman effective-medium approximation In this approximation, the effective dielectric function, eeff=N&.,of a two component layer is found from
Ferritin on gold
97.5
where Ea and Eb are the dielectric functions of the materials in the layer, here assumed to be those of gold and protein, respectively. U a and Ub are the corresponding volume fractions (ua Ub = 1).
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Results and Analysis Figure 3 shows a representative time evolution in v-A for albumin and ferritin adsorbing from 1mg/mL solutions onto gold substrates. The total times of the experiments were 20 and 46 h for albumin and ferritin, respectively. Difference in molecular size accounts for the smaller total change in A and I,O for albumin than for ferritin. General features of the experiments were a n initial and fast decrease in A during the first 5 min, followed by a slower decrease in V . The near horizontal part, the first 5 min, of the ferritin curve can be explained by formation of a transparent layer if evaluated in the three-phase model. Any points below this curve can be shown to require the layer to be absorbing.8 Model simulations show for example that a decrease in A with constant A requires that the film has k = 0.01. The vertical part of the adsorption curve therefore corresponds to apparent film absorption, increasing with time. For albumin, these two processes, formation of a transparent film and growth of film absorption, were not so well separated in time as for ferritin. No initial increase in v is observed and A decreases with constant v during the first 5 min, which, according to the model simulations mentioned above, indicates an absorbing film. It can therefore be concluded that no part of the albumin curve can be described by a transparent layer. (7) Bruggeman, D. A. G. Ann. Phys. 1935,24, 636.
98.0
98.5 99.0 A [degrees]
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Figure 3. The course of v-A with time (shown in minutes), at a photon energy of 2 eV, for adsorption of (a) albumin and (b) ferritin, respectively.
The results of interpreting spectral data in the threephase model reveal that the films show apparent absorption, as can be seen in €2 below 2.5 eV in Figure 1. The apparent absorption in the film increased with time and its time evolution was different for different proteins. We attribute the source of this absorption to interactions between the protein molecules and the gold substrate. This conclusion is supported by Figure lb, which shows that the apparent €2 of a ferritin layer increased with time after adsorption, if evaluated in the three-phase model. Notice that no further adsorption of ferritin molecules took place after taking the first spectrum in Figure lb, as the ferritin solution in the cuvette was replaced by buffer. From Figures 1and 3 we conclude that the formation of protein layers on gold can not be described in simple threephase models and below we will concentrate on refinements of optical models for evaluation. Further analysis of the kinetics of ferritin adsorption will be presented elsewhere.8 However, an important result from the analysis of the kinetics is that the decrease in thickness with time seen in Figure l b is accompanied by an increase in refractive index of the ferritin film. This corresponds to a film densification. The molecules "come closer" to the gold surface with time and the possibilities for interaction increase. Obviously, the three-phase model is insufficient for describing our samples if we require the protein films to be transparent in the low-energy range. One refinement (8) MArtensson, J.; Arwin, H.; Nygren, H.; Lundstrom, I. J. Colloid Interface Sci. 1995, in press.
Mhrtensson and Arwin
966 Langmuir, Vol. 11, No. 3, 1995
is to add another layer, thus obtaining a four-phase model constituted of the ambient, a transparent top layer, an interface layer, and a gold substrate. The interface layer is an EMA layer, the optical properties of which are composed of those of the gold substrate and the top layer. An argument for introduction of such a n interface layer is that it would represent a rough interface between the substrate and the film. We have earlier shown that with such a layer it is possible to generate data which, if evaluated in the three-phase model, result in film optical properties with features similar to those shown in Figure la.' However, although the rough interface concept could be used to explain the shape of the spurious absorption, it was not sufficiently good to explain its magnitude in the refined analysis presented here. Instead we suggest that the interface layer represents a n electronicinteraction between the gold substrate and the protein layer. We use the Bruggeman EMA to model this interaction, even though the EMA model is microstructurally based. However, no other model with a reasonable low number ofparameters is available. It is important to bear in mind that the EMA parameters are only used formally in the analysis. The important parameter in the end is the actual refractive index of the interface layer. The parameters of the interface layer and the top layer can be obtained in a fitting procedure. In this procedure, the adjustable model parameters are the gold volume fraction (formal parameter, see above) ofthe intermediate layer, the thicknesses of the two layers, and the complex refractive index of the top layer. There seem to be too many unknowns, as we stated above, it is only possible to obtain values on two parameters from e. However, we make use of the spectral information. Basically, we use the photon energy range 1.5-2.5 eV to search for the parameters of the EMA layer and the energies above 3 eV to calculate the thickness of the top layer. The best-fit criterion used was that k = 0 as a n average over the whole energy range. By using the same data as for Figure l a , optical properties of the albumin layer evaluated in the four-phase model were obtained as shown in Figure 4a (dashed curves). The top layer thickness was determined to 150 A and the EMA layer thickness was 2.1 with a formal gold volume fraction of 0.3. Although the goal of having a transparent protein layer has been achieved by introducing an interface layer, the obtained protein layer thickness is far too large. 150 is much larger than expected for an albumin monolayer. Multilayer formation is unlikely and studies on other substrates give thicknesses of the order of 20-30 A.2 However, in the four-phase model the apparent absorption can be removed efficiently, which is a strong argument for its validity. On the other hand, the three-phase model gives an excellent result in photon energy regions where no apparent absorption is observed. These findings lead us to the suggestion that the threephase model basically is sufficient in photon energy regions where no electronic protein-gold interaction can be observed. For energies where such interaction is seen, here below 2.5 eV, the four-phase model must be used. We therefore develop the four-phase model further. A basic assumption is that the interaction mainly affects near-surface states of the gold substrate, leaving the protein layer unaffected in the energy range used. Furthermore, the interaction is assumed to be restricted to the Drude region. This involves the free electrons and the 5d 6s transition around 2.5 eV. Therefore, the experimental photon energy range is divided into three regions: low (1.5-2.5 eV), intermediate (2.5-3.0 eV), and high energies (3.0-4.5 eV). The ranges were determined by manual inspection of each spectrum and found to vary
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Figure 4. (a)Optical properties of an albumin layer (the same as in Figure l a ) evaluated in the standard four-phase model with a thickness of 150 A (dashed curve),and in the modified four-phasemodel with a thickness of 27 A(so1idcurve). Details are given in the text. (b)Optical properties of a 95 A thick layer of ferritin evaluated in the modified four-phase model, from the same samples as in Figure l b (46 h curve).
only slightly between different proteins. We now use the four-phase model, including a n EMA layer, in the lowenergy range and the three-phase model in the high-energy range. The intermediate range was included to make the transition between the low and high ranges smooth. Figure 2b, shows the improved model. The thickness of the top (protein) layer was determined in the high-energy region, using the k = 0 criterion described in the interpretation section above. In the low-energy region the interface layer was modeled as a n EMA mixture of gold and protein. The real part of the refractive index, n, calculated in the three-phase model with the thickness as above, was used as a first approximation to the true n of the top layer. The parameters of the interface layer could now be calculated together with n of the protein layer, by searching for a solution for which the imaginary part of the top layer was a s small as possible. The actual procedure was to vary the parameters of the EMA layer and then, for each combination, calculate the complex refractive index of the top layer. By inspection of the k-spectra determined for the different parameter combinations, we selected the best parameter set to be that for which k averaged to zero in the largest energy range, i.e. the deviation of k from zero is within the noise level. The intermediate range was needed to make a smooth transition from the low-energy to the high-energy range. This was achieved by reducing the EMA layer thickness to zero in about five steps, each step being 0.05-0.1 eV. It was not meaningful to use smaller steps with the present data because the changes between the steps would then
Ellipsometry Data for Protein on Gold be smaller than the noise level. An alternative to tapering the thickness of the EMA layer would be to taper its refractive index toward that ofgold. This would probably be closer to the true situation but was not possible to do with our software. In Figure 4a, the solid curves show the spectrum of the same albumin layer as in Figure l a , but now evaluated in the improved four-phase model. The albumin layer is 27 A thick and the optimal interface layer is 2.1 A in the range 1.5-2.5 eV with a formal gold volume fraction of 0.3. Note that these are the same values as obtained in the standard four-phase model above. This illustrates that the low photon energies can be used to determine the interface layer and the higher energies to determine the top layer. In the intermediate region 2.5-3.0 eV the thickness of the interface layer decreases and above 3 eV it is zero. Figure 4b shows the optical properties of a 95 A thick ferritin layer evaluated with similar procedure in the improved four-phase model. The interface layer is 3.1 A in the range 1.5-2.45 eV and decreases between 2.45 and 2.7 eV. The formal volume fraction of gold is 0.19. Also here we can see a substantial improvement compared to the result in Figure l b (46 h curve).
Discussion The effects observed on gold are not limited to ferritin and albumin layers but are also observed for other proteins including lactoperoxidase, lysozym, and p-lactoglobulin. These results will be presented elsewhere. Spurious absorption in thin layers has also been reported by Elliot et al.3 Their measurements a t three wavelengths correspond well with our observations. They suggest that “the k-values have no physical significance but to serve to account for the inadequacies of the ellipsometric model.” In this they refer to Dignam et al.,9 who showed that a transparent anisotropic layer evaluated in a n isotropic three-phase model shows spurious absorption. However, Dignam et al. concluded that this absorption follows the absorption of the metal substrate. This is not true for our observations on gold. Elliot et al. also suggest that absorption occurs through charge transfer from molecular orbitals to the gold substrate, which is a model close to the one presented here. The spurious absorption is not only found for protein layers. A similar phenomenon is seen when measuring on alkyl thiol layers, though it is not described in terms of a complex-valued refractive index. Nuzzo et al.1° and Porter et aL4 as well as researchers in our laboratory calculate thicknesses of thiol layers by assuming a fxed n in the range 1.45-1.50. Neglectingk gives a discrepancy between the measured and the “real” t h i c k n e ~ s .Porter ~ et al. also suggest the same explanation as we want to stress here, namely that the adsorbed layer induces changes in the optical response of the gold substrate close to the surface. As seen in Figure 4, the modified four-phase model led to significant improvements compared to the three-phase model in Figure 1. Not only is the apparent absorption below 3 eV gone but also the increase in n toward lower energies has been removed. At first glance, the albumin spectrum evaluated in the standard four-phase model (Figure 4a, dashed line) seems to be the best one as the noise level is low and €2 is close to zero over the whole energy range. However, a low-noise level is a n intrinsic feature of the evaluation and cannot be used as a criterion (9) Dignam, M. J.;Moskovits, M.; Stobie, R. W. Trans. Faraday SOC. 1971,67,3306. (10)Nuzzo, R. G.;Fusco, F. A,; Allara, D. L. J . A m . Chem. SOC.1987, 109,2358.
Langmuir, Vol. 11, No. 3, 1995 967 for the best result. The general effect is that, with increasing thickness, n and el will decrease toward the values of the ambient (here buffer) and the curves will look smooth due to the lower values of n (or el). Some dimensional considerations may also be made. The ovalbumin molecule is approximately spherical with a diameter of 55 A.11 Thus the 150A thick layer in Figure 4a could be interpreted as a multilayer. However, the low value of n (1.35)indicates that such a layer would be sparse, and we think that a dilute multilayer is unlikely, as proteins generally do not form multilayers. We therefore believe that the albumin spectrum evaluated in the modified four-phase model is considerably more representative than those obtained in the three-phase or standard four-phase model. The assumption that the model is different at different photon energies originates from the observation that the apparent absorption coincides with the Drude region in gold.12 The implications of the modified four-phase model is that, in the Drude region below 2.5 eV, there is a zone just below the surface in which the optical properties of gold differ from the bulk. Above 2.5 eV this zone cannot be detected in our measurements and the gold substrate has the same optical properties all the way up to the abrupt gold-protein interface. A plausible explanation is that the near-surface free electrons are affected by the presence of the protein layer while the interband electrons above 2.5 are unaffected. Support for this is given by the findings that the interface layer can be modeled as a n EMA layer composed of gold and a dielectric material (here the protein). The dielectric portion can be as high as 81%(in the ferritin case) and the interface zone could then be regarded as a depletion region almost free from free electrons. The region close to the surface in which there are ion concentration gradients, the so called electric double layer, may also play a n important role. In fact, due to the adsorption of a protein layer, the double layer is removed (or at least moved further from the gold surface) and the electrostatic conditions change a t the interface. It has earlier been shown by Chao and Costal3that A and q are sensitive to the surface charge on gold. By applying different potentials the observed changes in A and q could be correlated to the surface charge. It was found that the interface layer was in the range 0-10 A and that it was much less absorbing than the bulk. At E = 2.1 eV (600 nm) the refractive index of the interface layer was calculated to 0.20 0.56i, which should be compared with the bulk value for gold which is 0.28 3.223.in the study by Chao and Costa. The corresponding values in our study are 1.61 0.82i for a typical interface layer and 0.22 3.10i for gold. In Figures l a and 4a we can also see some features around 3.5 eV which coincide with interband transitions in gold. However, these features are too small, compared to the noise level, to be modeled. Frequently de Feijter’s formula14is used to calculate the amount of adsorbed material in terms of the mass per unit area, I‘+g/cm2). Mostly the noise level in r is much smaller than in d and n. A representative example is protein adsorption on silicon, where there is a high correlation between layer thickness and refractive index. r also shows less sensitivity t o experimental errors.15The disadvantage of using to represent the layer properties is that the optical and microstructural information
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(11) Tiselius, A.;Svensson, H. Trans. Faraday SOC.1940,36, 16. (12) Aspnes, D. E.;Kinsbron, E.; Bacon, D. D. Phys. Reu.B 1980,21, 3290. (13) Chao, F.; Costa, M. Surf. Sci. 1983,135, 497. (14) de Feijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17,1759. (15) Tiberg, F.; Landgren, M. Langmuir 1993,9,927.
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968 Langmuir, Vol. 11, No. 3, 1995 contained in n and d are lost. However, for thin layers on gold the applicability of de Feijter’s formula to calculate r is more unclear if n and d are determined in the visible part of the spectrum. For albumin there is a 25% difference in r when calculated a t 2 eV in the four-phase model (Figure 4a) compared to the three-phase model (Figure la). We believe that r obtained from the modified four-phase model data is closer to the real value of the amount adsorbed. With access to spectroscopic data, the following question also arises: a t which photon energy should r be calculated? In de Feijter’s formula the energydependent input data are the refractive index of the layer and the refractive index increment, dnldc, of the layer material. The latter is often determined with a refractometer, using white light, and is therefore a n average value. A general conclusion from our analysis is that a n interface zone develops during the adsorption process. For ferritin this development is considerably slower than the adsorption process itself. For albumin these two process have more similar time dependence. An interesting implication is, however, that the protein molecules adsorb in a two-step process. First they are adsorbed (trapped)in a precursor state with small or no electronic interaction with the gold surface. Then they are subsequently adsorbed on the surface in a second state with a more pronounced effect on the electronic properties of the metal substrate. The molecules are on average closer to the substrate in the second state, which also is indicated by the decrease in film thickness with time, as shown in Figure 1b. These phenomena will be further discussed in a forthcomingreport on ferritin adsorption.8 Here we want to point out that kinetic ellipsometric measurements
evaluated either in terms of d or r using the standard three-phase model may have large errors due to the fact that this model gradually changes to a four-phase model during the course of adsorption. The errors can be very large, up to 25%in r as reported above. An improvement can be obtained by doing measurements a t photon energies higher than 3 eV. Porter et al.4 advise measurement a t two wavelengths to make sure the single wavelength measurement is reliable. However, the accurate analysis of the adsorption of proteins on gold surfaces calls for a development of time-resolved spectroscopic ellipsometry.
Conclusions (1)The three-phase model is insufficient to model a protein layer on a gold substrate for photon energies below 2.5 eV and leads to errors in determination of layer thickness and refractive index. (2)A modified four-phase model is suggested. This model includes an electrondepleted interface zone a t the surface of the substrate. (3) The kinetics ofthe formation of the interface zone indicates that ferritin and possibly also other proteins adsorb in a two-state process. (4) The adsorption of proteins on gold is most accurately monitored by ellipsometry a t photon energies above 3 eV. For more detailed microstructural studies, the development of time-resolved spectroscopic ellipsometry should be encouraged.
Acknowledgment. The ferritin was gift from H&an Nygren (Goteborgs Universitet, Goteborg, Sweden). Financial support has been obtained from the Swedish National Board for Industrial and Technical Development. LA940764Q
