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Some considerations on the determination of optical properties of adsorbed films
Surface Science 56 (1976) 76-86 0 North-Holland Publishing Company
SOME CONSIDERATIONS ON THE DETERMINATION OPTICAL PROPERTIES OF ADSORBED FILMS
OF
Marjorie A. Barrett GCLTEPE Department
of Physical
Chemistry,
Bristol
University,
Bristol
8, England
A discussion is presented of the criteria involved in the choice of parameters where it is desired to extend either basically ellipsometric or reflectometric measurements to three parameter measurements for refractive index determination of very thin adsorbed films. It is shown that even three parameters often fail to give unique values of film optical properties, and that the requirements for accuracy are frequently extreme for any reasonable error limits in the determination. It is therefore advantageous to extend the measurements to a further angle of incidence, unless the equivalent is provided by measurements at several wavelengths. Although varying the angle of incidence in ellipsometry is of very little value, it is some help in three parameter measurements provided a proper choice of angles is made. As an example the anodic oxidation of Pt and adsorption of benzene on Pt is discussed. Cases where no solution is found for isotropic film models are presented. As these films can well be expected to be uniaxially anisotropic, a search was extended into this case, although by no means exhaustive. Solutions were found for all the examples, but in the benzene case alone, the solutions are plausible.
1. Introduction The realization has become fairly general recently that the measurement of two reflection parameters is not sufficient to determine the optical constants of a thin film. Several studies have been made in which the basic ellipsometric measurements of A and J/ have been augmented by those of SRIR of unpolarized light (denoted hereafter as &I/I). Studies that are essentially ellipsometric have tended to use this method, with the possibility of making simultaneous reflectometry measurements of all three quantities if a detector or beam splitter can be placed so as to interrupt the beam after reflection from the sample but prior to the final analyser, provided that the arrangement is such that the quarter wave plate precedes the reflecting surface. Alternatively, the reflectometry technique is necessarily augmented by measurement of A: there is little point in including $ measurements, as the equivalent information is recorded in (GR/R)p and (SR/R), measurements if the correct substrate constants have been assumed. The following is a discussion of the limits of accuracy from various considerations, first on the problem of the anodic oxidation of Pt, which has now been studied by several investigators, and second the case of benzene adsorption on Pt. 76
M.A.B. Giiltepe / Determiuatiwi
of optical properties ofadsorbed films
71
2. Experimental The experimental technique is basically the same as described earlier [l]. The electrolyte used was OSM H, SO,. The measurements used in the following discussion were made at the wavelength of 350 run unless otherwise stated. The (6R/R) quantities could be measured to 0.00015, and 6A to 0.01”. the main difficulty in the latter being that of calibration. The method of intensity recording at an off null setting of the polarizer was used. As an accurate calibration involves a knowledge of the departure from the ideal intensity-polarizer setting curve, resulting in finite intensity at the null setting, a complete calibration P versus intensity curve was obtained for two states of the Pt, one with adsorbed H and one in the state of oxidation after one minute at 1.34 V, then stepped down to 0.97 V versus 0.1 N cal. From these it was possible to interpolate the correct calibration for intermediate states with the accuracy warranted by the technique. Where in doubt, and to check the calibration, null offsets on both sides of null and at equal intensities were taken. This applied in particular to benzene adsorption. The results used for refractive index determinations for the benzene were all made during a single session to minimize any variation from day to day. A standard adsorption time was adopted of 5 min at a potential of 0.32 V in a solution of 5 X lops M benzene in 0.5M H,SO,. A check was first made in the pure H2S0, that all the reflection parameters were behaving as normal, and a calibration was made for determining A before the correct quantity of saturated benzene in water was added to make the desired concentration. This procedure was adopted to give minimum disturbance to the system to preserve the A calibration.
3. Results and their treatment The results for the anodic oxidation of Pt are summarized in fig. 1. For the purpose of giving an impression of the limitations of the measured parameters in the determination of refractive indices of the adsorbed film, it is useful to show the graphic solution. As the thickness parameter is unknown, it is simplest to eliminate this by treating only ratios of the measured quantities. The ratios determined give solutions in the form of a line or lines on the complex plane representing the optical constants of the film. Introducing the estimated error limits, these become areas. The overlap of the areas then gives slightly more than the total possible solutions; a correction may be made for the fact that any error in a parameter common to two ratios will be the same. The ratios (cYR/R)~/(FR/R), and (cSR/R)~/~A have been chosen in the present treatment. The results in this form are summarized in table 1. Areas on the complex plane in which any of the measured parameters change by the wrong sign can be eliminated at the outset. In the present case, these are shown in fig. 2 as shaded areas. The above mentioned lines, or more correctly strips, emanate
0
-0.01
0.1
0 -0.02
a - 0.1 Y)
la (r \ %
-0.2 -0.03
-0.3
-0,OL
0 2 5 5
-0.05
-0.01
- 0.03
0
0.5
1.u
POTENTIAL (V "so.1 N Cal )
Fig. 1. Values of the measured reflection 69” angle of incidence and 350 nm.
parameters
with potential
for Pt in OSM HzS04,
at
Fig. 2. Resume of the effect on the measurable reflection parameters of films of various optical constants forming on a metallic substrate at an angle of incidence = 69”) no = 1.354 and r22 = 1.45 - i2.94.
M.A.B. Ciiltepe /Determination
of optical properties ofadsorbedfilms
79
Table 1 Summary of results for oxide formation and benzene adsorption on Pt in 0.5 M HzS04, at wavelength 350 nm; ail potentials are referred to 0.1 N cal
Film substance
Angle of incidence Meg)
R oxide 0.45-0.65 v (by sfope)
69
3.67 + 5
57
2.70+
Pt oxide
69
3.1
* 10
57
2.8
f 10
Pt oxide 0.1-1.0 v (by slope)
69
2,65 + 4
57
2.39 f
Benzene on Pt
69
5.0 * 15
57
5.09 t 20
0.024
+ 20
5
0.0235 + 9
al: 6.5 v
against 0.3 v
0.0265 t 11
5 0.012
Lk50
from points of intersection of the demarcation lines. The points representing the refractive indices of the substrate and the ambient phase are clearly two such points, and will be, regardless of the angle of incidence. Further points of intersection come into play that vary with angle of incidence_ Arising out of a study of these, some general remarks can be made about the choice of parameters for the purpose of refractive index determination.
4. Choice of measured parameters In the choice of parameters to measure, consideration must be taken of fi) magnitude of the change with the film formation, (2) the sensitivity of this magnitude to the value of nfti (which would amount to the spacing of contour lines of ratios on a diagram of the refractive index as in fig. 3) and finally (3) in terms of a graphical solution, the angle of Intersection with the other chosen quantities and the uniqueness of the solution. These are now considered separately, (1) The quantity (GRJRjP shows maximum sensitivity to growth of moderately absorbing films around 55” to 60” angle of incidence, while (&R/R), approaches its maximum sensitivity at 0”. In determining @R/R),, because of the close adherence to the approximation given by McIntyre [21 (showing that this quantity is proportional to the cosine of the angle of incidence) measurements may be restricted to the
80
M.A.B. Giiltepe /Determination
of optical properties of adsorbed films
k
1
0
1
3
2
Fig. 3. Possible n values for Pt oxide formed ing slopes of the reflection parameters. (-) 69”; (- * -) (sR/R)p/(GR/R)s, 57”.
"
L
5
6
from 0.7 to 1 V versus 0.1 N calomel electrode. (SR/R)p/6A, 69”; (- - -) (CiR/R+,!(GR/R),,
us-
lowest angle obtainable. (In order to gain maximum effectiveness of measurements, it is necessary to work outside the limits of applicability of his other approximations.) Measurements of (&R/R), were made at 57” in the present case, and calculated for 69”. The enhanced sensitivity of (6R/R)p at 57” over that at 69” on oxide did not result in any greater accuracy in practice, since the limit of accuracy appeared to come from a lack of reproducibility rather than sensitivity. The maximum sensitivity for A tends to be between 60” and 80”. The sensitivity of $ is decidedly the poorest of all measurable quantities. Changes are small for nearly all types of film normally encountered.
1
/,
0
,P 1
2
Fig. 4. As fig. 3 for oxide formed
3
"
L
5
from 0.45 to 0.65 V using slopes of reflection
6
parameters
M.A.B. Giiltepa /Determination
81
of optical properties of adsorbed films
k
-1
3
2
Fig. 5. As fig. 3 for oxide formed
at 0.65
n
V by difference
L
5
6
from the reflection parameters at 0.3 V.
(2) Considerable advantage can be gained by working at high angles of incidence in singling out possible values of nfh. At 45”, the ratio of the two reflectivity changes is almost everywhere 2, but this ratio becomes increasingly effective as the angle of incidence is increased. The difference between 57” and 69” for the oxide example is shown in figs. 3,4 and 5 where the ratios for both angles are given the same percentage error limits. Further advantage would be expected at higher angles of incidence, were it not for the increased experimental difficulty, loss of sensitivity, and increased requirement for accuracy of angle of incidence. Angles of incidence appreciably above 45” have a particular value in distinguishing between an absorbing and a transparent layer of refractive index above that of the ambient phase, in that the combination of positive (FR/R)p along with negative (6R/R), and 6A is almost unique for this condition. Similarly for the alternative set of measurements, 6 $ is positive, and SZ/I very small but positive. (3) The two ratios obtainable at the single angle of incidence of 69” cross at an extremely small angle: this is true of the regions below and to the right of nSubstrate on the diagram, whether the ratios are of the two reflectivities and (sR/R),/sA or s$/sA and sZ/Z)/sA. In addition, there are frequently two intersections denoting solutions. There is a small area where the one ratio line originates from nsubstrate while the other from ng, forming a more acceptible intersection, but even in this case the two continue towards high real n lying nearly parallel, and eventually re-crossing. This is the case illustrated in fig. 3, where there is another intersection at ‘I*-~,,= = 10.28 - i 2.4. It is necessary to augment the measurements, either with other angles of incidence, or other wavelengths. When measurements lead to solutions under the above conditions, it seems to lend confidence to the applicability of the model adopted, as many measured values would lead to no solution whatever, e.g. the case illustrated in fig. 4, and also for adsorbed
82
M.A.B. Giiltepe /Determination
of optical properties of adsorbed films
benzene. To some extent at least, this confidence later.
is not justified,
as will be shown
5. Problems peculiar to Pt There are a few problems concerning the analysis of optical data when it comes to Pt: among these are the variability of the refractive index of Pt, how to correct for double layer charging, and how to treat the variation with potential of reflection parameters at constant anodic film thickness. In addition to the poor agreement between the various determinations of optical constants of Pt, the observation has been recorded by Chao et al. [3], and confirmed by several others, that the constants drift in the course of anodic-cathodic treatment. This introduces an uncertainty into the results unless a determination is made together with the other measurements. The second problem originates from the uncertainty of how to treat the change of reflection coefficients observed across the essentially film-free conditions of double layer potentials. The refractive index determinations have in general been made by comparing the reflection parameter measurements to the equivalent measurements at a condition deemed to be the nearest possible to a film-free condition (in this case a measurement taken in the double layer potential region) Without extrapolation to the more anodic potentials, these values are not valid, strictly speaking. The suggestion has been made by Conway et al. [4] that the appropriate correction, where a partially-covered surface is involved, should be proportional to the atomic sites remaining free. (That work was not concerned with the determination of optical properties.) Because of the uncertainties involved, the procedure was adopted earlier [l ] and 6A with potential, with the object of miniof using slopes of (&R/R&(6R/R), mizing this error without making any assumptions, although it is not thereby eliminated. The present treatment differs only in the separate handling of the oxide formed at low and higher potentials. The more usual method gives determinations relating to the average of the entire oxide film, while the latter related only to the oxide being formed in the potential range under consideration. The latter is therefore only valid if the process can be considered as the addition of oxide, rather than conversion of previously formed material, which is a problem mainly concerning the higher potential oxide. The above procedure, applied to the lower potential oxide, yields no solution whatever of an isotropic film refractive index (fig. 4). If the more usual procedure is used of relating every reflectivity and A value to one in the double layer region, the data are shifted sufficiently to yield a solution. This might be taken as evidence that the latter procedure is correct, but only by rejecting the possibility that the film is anisotropic. It was considered more reasonable to investigate the low potential oxide for uniaxial anisotropy. The final uncertainty involves a change observed in the reflection coefficients with
M.A.B. Giiltepe /Determination
of optical properties
of adsorbed films
83
potential, where the oxide is known from coulometric measurements to remain constant. It can best be observed at high potentials, well away from the region that is prone to form some reversible oxide, and after sufficient time has elapsed so that oxide growth has virtually ceased. This has been discussed briefly in an earlier note [5]. It is also discernable in potential sweep measurements of optical parameters [6, 71, although it is then more difficult to disentangle the effect from one of residual oxide growth prevailing after the cathodic branch commences. In a discussion of the phenomenon by Conway [7], the observed increase of A on the cathodic branch was attributed to residual growth. The negative (GR/R)p/F V was considered as most likely a manifestation of double layer charging on the oxide layer, as in their experiments it had approximately the same value as in the double layer region. Probably as a result of using a lower angle of incidence, the difference in character was overlooked. At 69”, this quantity is positive in the double layer region, but negative at these higher potentials. Thus both the (6R/R)p/8 V and &A/??V reverse sign from those observed in the double layer region. A further difference from the double layer changes is that the latter decrease progressively to zero on decreasing the wavelength from 350 to 300 nm, while the former does not. (This observation refers to the reflectivity, and has not been tested for A.) Ord et al. [8] have observed a field dependence of the refractive index of anodic films of tantalum, niobium and tungsten, such that the refractive index decreases with increase of field. It was thought that possibly there could be a similar process applying to these thin films. As it happens, the results imply the opposite. trend in the optical constants: an increase in both n and k. Conversely, if one assumes that the entire effect should be eliminated from the quantities used in the determination, the resultant is a displacement of the area of possible solutions by about 0.1 in both IZand k. It may be significant that this treatment gives a better triple intersection of the three ratios when errors are disregarded. A similar trend is observed in the two procedures used by Horkans et al. [6], one of which makes most of this correction experimentally by dropping the potential to the lowest possible before reduction.
6. Anisotropy With thin oxides, and adsorbed films in general, it is reasonable to expect uniaxial anisotropy, with the axis vertical to the surface. In view of this, the first extension of analysis for film optical constants was to investigate uniaxial anisotropic transparent properties, which again can be represented on a two dimensional diagram, and then extend this by introducing absorption. In fig. 6 the signs of the reflection parameter changes are summarized for the transparent case and for a case in which one value of optical absorption normal to the surface is introduced. In the case of transparent films, the fact that all three measured parameters for the examples under discussion here are negative limits considerably the possibilities on the plane. Only areas
84
M.A.B.
Giiltepe
/Determination
of‘ optical properties
3
of’adsorbcd
films
3 -
?
1
2 " ,ang
A 1
3 Ik=Ol
n t3nt
(k=O)
3
Fig. 6. Diagrams representing uniaxial anisotropic film constants; transparent indices and an example introducing absorption; normal and tangential refer to the plane of the surface. Resume of the sign of changes of reflection parameters at angle of incidence 69”. Area A in the transparent diagram is compatible with the 69” data for oxide formed at 0.7 to 1 V versus 0.1 N cal.
ntang FGg. 7. Possible anisotropic benzene.
II values for benzene
(k=Ol
adsorbed
on Pt in 0.5 hl H2SO4 + 5 X 10~’
M
M.A.B. Giiltepe /Determination
of optical properties of adsorbed fLlms
85
in which the tangential refractive index exceeds that normal to the surface are left as possibilities, (H,,,, < ntang ). This could well be expected to apply to adsorbed benzene, in virtue of the fact that it is known to adsorb with the ring lying parallel to the surface. In fact, no transparent solution exists for benzene, nor for the low potential oxide. On the other hand, the high potential oxide results satisfy also a long strip of this plane, marked A in the figure, but this is not considered a particularly reasonable value for the film. Likewise, the introduction of absorption normal to the surface, k,,,, = 0.2 or less produces areas of possible solutions, characterised by the fact that the real part of nnon,, is less than 1.36, which seems an unlikely value. The results of the search for possible solutions for adsorbed benzene with absorption normal to the surface are summarized in fig. 7. The search is far from exhaustive, but at least has yielded some plausible values for this adsorbed film.
7. Conclusion Examination of the data and analysis shows that extending measurements to three parameters greatly improves the possibility of assigning isotropic optical constants to a film, but this in general still leaves ambiguity and requires high accuracy in measurements for reasonable accuracy in the results. If measurements are extended to a further angle of incidence, further progress can be made, unlike the general experience in ellipsometry. Unless all three parameters are automatically recorded, a good distribution of measurements between two angles of incidence is to measure (6R/R), only at the lowest angle of incidence, 6A at the highest, and (6R/R& at both. It is of considerable value of examine a graphical analysis using the loci of possible refractive indices from ratios of the above quantities, taking into account the probable errors of measurement. Uncertainties involved in the transformation of the measurements into the appropriate form can have serious consequences for the determinations. For Pt in sulphuric acid, the necessity of extrapolating the double layer charging effect, and another electromodulation effect found at higher potentials to intermediate potentials brings uncertainty into the determinations for oxide films. This uncertainty cannot be resolved with the present state of knowledge. It is unrealistic to assume that monolayer or sub-monolayer films are necessarily isotropic. The analysis procedure can be extended to include uniaxial anisotropy with no great difficulty. This approach is found to yield reasonable values for benzene adsorbed on Pt, compatible with the known orientation of the benzene rings lying flat on the metal surface held by chemisorption bonds; no isotropic film model could explain the data. Possible values were also found for the constants for anodic oxide on Pt in two potential ranges, but a much more extended search would be advisable.
86
M.A.B. Giiltepe /Determination
of optical properties of adsorbed films
References and R. Parsons, Symp. Faraday Sot. 4 (1970) 72. and D.E. Aspnes, Surface Sci. 24 (1971) 417. A. Tadjeddine, Bull. Sot. Chim. France 7 (1971) 2466. (31 F. Chao, M. Costaand and L.H. Laliberte, J. Electrochem. Sot. 121 (1974) 141 B.E. Conway, H. Angerstein-Kozlowska 1596. 151 M.A. Barrett and R. Parsons, J. Electroanal. Chem. 42 (1973) Appl. 1. 161 J. Horkans, B.D. Cahan and E. Yeager, Surface Sci. 46 (1974) 1. J.C.S. Faraday I69 (1973) 1090. I71 B.E. Conway and S. Gottesfeld, Sot. 119 (1972) 439. [81 J.L. Ord, M.A. Hopper and W.P. Wang, J. Electrochem.
Ill
M.A. Barrett
PI J.D.E. McIntyre
Critique B.D. Cahan: You mentioned the obvious desirability of using three parameters. From what I understand of your description, you start off measuring three parameters and then reduce to two by taking a ratio. What happens when you try to do a solution on the simultaneous set of all three. M.A.B. Giiltepe: Eliminating thickness is a way of simplifying the matter. All the possible solutions will come forth from crossing of these two lines and one can angle back and find out what the thickness was. Otherwise you generate more lines and you look for triple or quadruple intersections if you have three or four parameters for every possible thickness. Its a very much more complicated problem. T. Smith: Usually if you don’t take into consideration roughness effects, even very small roughness, you sometimes cannot find solutions for your data without using extinction coefficients up to three or four, which are ridiculous for oxide films. That is, if roughness is ignored, the difference must be accounted for by absorption. I assume the data you were interpreting was the experimental data. In the areas where your solution bands crossed there were extremely high values for an oxide. Would you care to comment on that? M.A.B. Gtlltepe: I definitely agree that roughness has to be taken into consideration. S. Gottesfeld: May I point out that the insensitivity of the ratio of the differential reflectance parameters of the film is a general and expected phenomena for thin absorbing films on metalic substrates. It was shown in a paper by McIntyre and Aspnes in 1971. M.A.B. Giiltepe: Well, the ratio of reflectivities in this example turned out slightly better than the other ratio taking the reflectivity through delta, if you look at the width of the bands at 69” not at 57”. At low angles its hopeless. J.L. Ord: I’d like to add a technical note on roughness with platinum. If you carry out the Kolbe reaction on the surface as your final pre-treatment on flatness is perhaps the best way to smooth and stabilize surface roughness in the system. It’s something I wish I had published when I last published on platinum.
SOME CONSIDERATIONS ON THE DETERMINATION OPTICAL PROPERTIES OF ADSORBED FILMS
OF
Marjorie A. Barrett GCLTEPE Department
of Physical
Chemistry,
Bristol
University,
Bristol
8, England
A discussion is presented of the criteria involved in the choice of parameters where it is desired to extend either basically ellipsometric or reflectometric measurements to three parameter measurements for refractive index determination of very thin adsorbed films. It is shown that even three parameters often fail to give unique values of film optical properties, and that the requirements for accuracy are frequently extreme for any reasonable error limits in the determination. It is therefore advantageous to extend the measurements to a further angle of incidence, unless the equivalent is provided by measurements at several wavelengths. Although varying the angle of incidence in ellipsometry is of very little value, it is some help in three parameter measurements provided a proper choice of angles is made. As an example the anodic oxidation of Pt and adsorption of benzene on Pt is discussed. Cases where no solution is found for isotropic film models are presented. As these films can well be expected to be uniaxially anisotropic, a search was extended into this case, although by no means exhaustive. Solutions were found for all the examples, but in the benzene case alone, the solutions are plausible.
1. Introduction The realization has become fairly general recently that the measurement of two reflection parameters is not sufficient to determine the optical constants of a thin film. Several studies have been made in which the basic ellipsometric measurements of A and J/ have been augmented by those of SRIR of unpolarized light (denoted hereafter as &I/I). Studies that are essentially ellipsometric have tended to use this method, with the possibility of making simultaneous reflectometry measurements of all three quantities if a detector or beam splitter can be placed so as to interrupt the beam after reflection from the sample but prior to the final analyser, provided that the arrangement is such that the quarter wave plate precedes the reflecting surface. Alternatively, the reflectometry technique is necessarily augmented by measurement of A: there is little point in including $ measurements, as the equivalent information is recorded in (GR/R)p and (SR/R), measurements if the correct substrate constants have been assumed. The following is a discussion of the limits of accuracy from various considerations, first on the problem of the anodic oxidation of Pt, which has now been studied by several investigators, and second the case of benzene adsorption on Pt. 76
M.A.B. Giiltepe / Determiuatiwi
of optical properties ofadsorbed films
71
2. Experimental The experimental technique is basically the same as described earlier [l]. The electrolyte used was OSM H, SO,. The measurements used in the following discussion were made at the wavelength of 350 run unless otherwise stated. The (6R/R) quantities could be measured to 0.00015, and 6A to 0.01”. the main difficulty in the latter being that of calibration. The method of intensity recording at an off null setting of the polarizer was used. As an accurate calibration involves a knowledge of the departure from the ideal intensity-polarizer setting curve, resulting in finite intensity at the null setting, a complete calibration P versus intensity curve was obtained for two states of the Pt, one with adsorbed H and one in the state of oxidation after one minute at 1.34 V, then stepped down to 0.97 V versus 0.1 N cal. From these it was possible to interpolate the correct calibration for intermediate states with the accuracy warranted by the technique. Where in doubt, and to check the calibration, null offsets on both sides of null and at equal intensities were taken. This applied in particular to benzene adsorption. The results used for refractive index determinations for the benzene were all made during a single session to minimize any variation from day to day. A standard adsorption time was adopted of 5 min at a potential of 0.32 V in a solution of 5 X lops M benzene in 0.5M H,SO,. A check was first made in the pure H2S0, that all the reflection parameters were behaving as normal, and a calibration was made for determining A before the correct quantity of saturated benzene in water was added to make the desired concentration. This procedure was adopted to give minimum disturbance to the system to preserve the A calibration.
3. Results and their treatment The results for the anodic oxidation of Pt are summarized in fig. 1. For the purpose of giving an impression of the limitations of the measured parameters in the determination of refractive indices of the adsorbed film, it is useful to show the graphic solution. As the thickness parameter is unknown, it is simplest to eliminate this by treating only ratios of the measured quantities. The ratios determined give solutions in the form of a line or lines on the complex plane representing the optical constants of the film. Introducing the estimated error limits, these become areas. The overlap of the areas then gives slightly more than the total possible solutions; a correction may be made for the fact that any error in a parameter common to two ratios will be the same. The ratios (cYR/R)~/(FR/R), and (cSR/R)~/~A have been chosen in the present treatment. The results in this form are summarized in table 1. Areas on the complex plane in which any of the measured parameters change by the wrong sign can be eliminated at the outset. In the present case, these are shown in fig. 2 as shaded areas. The above mentioned lines, or more correctly strips, emanate
0
-0.01
0.1
0 -0.02
a - 0.1 Y)
la (r \ %
-0.2 -0.03
-0.3
-0,OL
0 2 5 5
-0.05
-0.01
- 0.03
0
0.5
1.u
POTENTIAL (V "so.1 N Cal )
Fig. 1. Values of the measured reflection 69” angle of incidence and 350 nm.
parameters
with potential
for Pt in OSM HzS04,
at
Fig. 2. Resume of the effect on the measurable reflection parameters of films of various optical constants forming on a metallic substrate at an angle of incidence = 69”) no = 1.354 and r22 = 1.45 - i2.94.
M.A.B. Ciiltepe /Determination
of optical properties ofadsorbedfilms
79
Table 1 Summary of results for oxide formation and benzene adsorption on Pt in 0.5 M HzS04, at wavelength 350 nm; ail potentials are referred to 0.1 N cal
Film substance
Angle of incidence Meg)
R oxide 0.45-0.65 v (by sfope)
69
3.67 + 5
57
2.70+
Pt oxide
69
3.1
* 10
57
2.8
f 10
Pt oxide 0.1-1.0 v (by slope)
69
2,65 + 4
57
2.39 f
Benzene on Pt
69
5.0 * 15
57
5.09 t 20
0.024
+ 20
5
0.0235 + 9
al: 6.5 v
against 0.3 v
0.0265 t 11
5 0.012
Lk50
from points of intersection of the demarcation lines. The points representing the refractive indices of the substrate and the ambient phase are clearly two such points, and will be, regardless of the angle of incidence. Further points of intersection come into play that vary with angle of incidence_ Arising out of a study of these, some general remarks can be made about the choice of parameters for the purpose of refractive index determination.
4. Choice of measured parameters In the choice of parameters to measure, consideration must be taken of fi) magnitude of the change with the film formation, (2) the sensitivity of this magnitude to the value of nfti (which would amount to the spacing of contour lines of ratios on a diagram of the refractive index as in fig. 3) and finally (3) in terms of a graphical solution, the angle of Intersection with the other chosen quantities and the uniqueness of the solution. These are now considered separately, (1) The quantity (GRJRjP shows maximum sensitivity to growth of moderately absorbing films around 55” to 60” angle of incidence, while (&R/R), approaches its maximum sensitivity at 0”. In determining @R/R),, because of the close adherence to the approximation given by McIntyre [21 (showing that this quantity is proportional to the cosine of the angle of incidence) measurements may be restricted to the
80
M.A.B. Giiltepe /Determination
of optical properties of adsorbed films
k
1
0
1
3
2
Fig. 3. Possible n values for Pt oxide formed ing slopes of the reflection parameters. (-) 69”; (- * -) (sR/R)p/(GR/R)s, 57”.
"
L
5
6
from 0.7 to 1 V versus 0.1 N calomel electrode. (SR/R)p/6A, 69”; (- - -) (CiR/R+,!(GR/R),,
us-
lowest angle obtainable. (In order to gain maximum effectiveness of measurements, it is necessary to work outside the limits of applicability of his other approximations.) Measurements of (&R/R), were made at 57” in the present case, and calculated for 69”. The enhanced sensitivity of (6R/R)p at 57” over that at 69” on oxide did not result in any greater accuracy in practice, since the limit of accuracy appeared to come from a lack of reproducibility rather than sensitivity. The maximum sensitivity for A tends to be between 60” and 80”. The sensitivity of $ is decidedly the poorest of all measurable quantities. Changes are small for nearly all types of film normally encountered.
1
/,
0
,P 1
2
Fig. 4. As fig. 3 for oxide formed
3
"
L
5
from 0.45 to 0.65 V using slopes of reflection
6
parameters
M.A.B. Giiltepa /Determination
81
of optical properties of adsorbed films
k
-1
3
2
Fig. 5. As fig. 3 for oxide formed
at 0.65
n
V by difference
L
5
6
from the reflection parameters at 0.3 V.
(2) Considerable advantage can be gained by working at high angles of incidence in singling out possible values of nfh. At 45”, the ratio of the two reflectivity changes is almost everywhere 2, but this ratio becomes increasingly effective as the angle of incidence is increased. The difference between 57” and 69” for the oxide example is shown in figs. 3,4 and 5 where the ratios for both angles are given the same percentage error limits. Further advantage would be expected at higher angles of incidence, were it not for the increased experimental difficulty, loss of sensitivity, and increased requirement for accuracy of angle of incidence. Angles of incidence appreciably above 45” have a particular value in distinguishing between an absorbing and a transparent layer of refractive index above that of the ambient phase, in that the combination of positive (FR/R)p along with negative (6R/R), and 6A is almost unique for this condition. Similarly for the alternative set of measurements, 6 $ is positive, and SZ/I very small but positive. (3) The two ratios obtainable at the single angle of incidence of 69” cross at an extremely small angle: this is true of the regions below and to the right of nSubstrate on the diagram, whether the ratios are of the two reflectivities and (sR/R),/sA or s$/sA and sZ/Z)/sA. In addition, there are frequently two intersections denoting solutions. There is a small area where the one ratio line originates from nsubstrate while the other from ng, forming a more acceptible intersection, but even in this case the two continue towards high real n lying nearly parallel, and eventually re-crossing. This is the case illustrated in fig. 3, where there is another intersection at ‘I*-~,,= = 10.28 - i 2.4. It is necessary to augment the measurements, either with other angles of incidence, or other wavelengths. When measurements lead to solutions under the above conditions, it seems to lend confidence to the applicability of the model adopted, as many measured values would lead to no solution whatever, e.g. the case illustrated in fig. 4, and also for adsorbed
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benzene. To some extent at least, this confidence later.
is not justified,
as will be shown
5. Problems peculiar to Pt There are a few problems concerning the analysis of optical data when it comes to Pt: among these are the variability of the refractive index of Pt, how to correct for double layer charging, and how to treat the variation with potential of reflection parameters at constant anodic film thickness. In addition to the poor agreement between the various determinations of optical constants of Pt, the observation has been recorded by Chao et al. [3], and confirmed by several others, that the constants drift in the course of anodic-cathodic treatment. This introduces an uncertainty into the results unless a determination is made together with the other measurements. The second problem originates from the uncertainty of how to treat the change of reflection coefficients observed across the essentially film-free conditions of double layer potentials. The refractive index determinations have in general been made by comparing the reflection parameter measurements to the equivalent measurements at a condition deemed to be the nearest possible to a film-free condition (in this case a measurement taken in the double layer potential region) Without extrapolation to the more anodic potentials, these values are not valid, strictly speaking. The suggestion has been made by Conway et al. [4] that the appropriate correction, where a partially-covered surface is involved, should be proportional to the atomic sites remaining free. (That work was not concerned with the determination of optical properties.) Because of the uncertainties involved, the procedure was adopted earlier [l ] and 6A with potential, with the object of miniof using slopes of (&R/R&(6R/R), mizing this error without making any assumptions, although it is not thereby eliminated. The present treatment differs only in the separate handling of the oxide formed at low and higher potentials. The more usual method gives determinations relating to the average of the entire oxide film, while the latter related only to the oxide being formed in the potential range under consideration. The latter is therefore only valid if the process can be considered as the addition of oxide, rather than conversion of previously formed material, which is a problem mainly concerning the higher potential oxide. The above procedure, applied to the lower potential oxide, yields no solution whatever of an isotropic film refractive index (fig. 4). If the more usual procedure is used of relating every reflectivity and A value to one in the double layer region, the data are shifted sufficiently to yield a solution. This might be taken as evidence that the latter procedure is correct, but only by rejecting the possibility that the film is anisotropic. It was considered more reasonable to investigate the low potential oxide for uniaxial anisotropy. The final uncertainty involves a change observed in the reflection coefficients with
M.A.B. Giiltepe /Determination
of optical properties
of adsorbed films
83
potential, where the oxide is known from coulometric measurements to remain constant. It can best be observed at high potentials, well away from the region that is prone to form some reversible oxide, and after sufficient time has elapsed so that oxide growth has virtually ceased. This has been discussed briefly in an earlier note [5]. It is also discernable in potential sweep measurements of optical parameters [6, 71, although it is then more difficult to disentangle the effect from one of residual oxide growth prevailing after the cathodic branch commences. In a discussion of the phenomenon by Conway [7], the observed increase of A on the cathodic branch was attributed to residual growth. The negative (GR/R)p/F V was considered as most likely a manifestation of double layer charging on the oxide layer, as in their experiments it had approximately the same value as in the double layer region. Probably as a result of using a lower angle of incidence, the difference in character was overlooked. At 69”, this quantity is positive in the double layer region, but negative at these higher potentials. Thus both the (6R/R)p/8 V and &A/??V reverse sign from those observed in the double layer region. A further difference from the double layer changes is that the latter decrease progressively to zero on decreasing the wavelength from 350 to 300 nm, while the former does not. (This observation refers to the reflectivity, and has not been tested for A.) Ord et al. [8] have observed a field dependence of the refractive index of anodic films of tantalum, niobium and tungsten, such that the refractive index decreases with increase of field. It was thought that possibly there could be a similar process applying to these thin films. As it happens, the results imply the opposite. trend in the optical constants: an increase in both n and k. Conversely, if one assumes that the entire effect should be eliminated from the quantities used in the determination, the resultant is a displacement of the area of possible solutions by about 0.1 in both IZand k. It may be significant that this treatment gives a better triple intersection of the three ratios when errors are disregarded. A similar trend is observed in the two procedures used by Horkans et al. [6], one of which makes most of this correction experimentally by dropping the potential to the lowest possible before reduction.
6. Anisotropy With thin oxides, and adsorbed films in general, it is reasonable to expect uniaxial anisotropy, with the axis vertical to the surface. In view of this, the first extension of analysis for film optical constants was to investigate uniaxial anisotropic transparent properties, which again can be represented on a two dimensional diagram, and then extend this by introducing absorption. In fig. 6 the signs of the reflection parameter changes are summarized for the transparent case and for a case in which one value of optical absorption normal to the surface is introduced. In the case of transparent films, the fact that all three measured parameters for the examples under discussion here are negative limits considerably the possibilities on the plane. Only areas
84
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/Determination
of‘ optical properties
3
of’adsorbcd
films
3 -
?
1
2 " ,ang
A 1
3 Ik=Ol
n t3nt
(k=O)
3
Fig. 6. Diagrams representing uniaxial anisotropic film constants; transparent indices and an example introducing absorption; normal and tangential refer to the plane of the surface. Resume of the sign of changes of reflection parameters at angle of incidence 69”. Area A in the transparent diagram is compatible with the 69” data for oxide formed at 0.7 to 1 V versus 0.1 N cal.
ntang FGg. 7. Possible anisotropic benzene.
II values for benzene
(k=Ol
adsorbed
on Pt in 0.5 hl H2SO4 + 5 X 10~’
M
M.A.B. Giiltepe /Determination
of optical properties of adsorbed fLlms
85
in which the tangential refractive index exceeds that normal to the surface are left as possibilities, (H,,,, < ntang ). This could well be expected to apply to adsorbed benzene, in virtue of the fact that it is known to adsorb with the ring lying parallel to the surface. In fact, no transparent solution exists for benzene, nor for the low potential oxide. On the other hand, the high potential oxide results satisfy also a long strip of this plane, marked A in the figure, but this is not considered a particularly reasonable value for the film. Likewise, the introduction of absorption normal to the surface, k,,,, = 0.2 or less produces areas of possible solutions, characterised by the fact that the real part of nnon,, is less than 1.36, which seems an unlikely value. The results of the search for possible solutions for adsorbed benzene with absorption normal to the surface are summarized in fig. 7. The search is far from exhaustive, but at least has yielded some plausible values for this adsorbed film.
7. Conclusion Examination of the data and analysis shows that extending measurements to three parameters greatly improves the possibility of assigning isotropic optical constants to a film, but this in general still leaves ambiguity and requires high accuracy in measurements for reasonable accuracy in the results. If measurements are extended to a further angle of incidence, further progress can be made, unlike the general experience in ellipsometry. Unless all three parameters are automatically recorded, a good distribution of measurements between two angles of incidence is to measure (6R/R), only at the lowest angle of incidence, 6A at the highest, and (6R/R& at both. It is of considerable value of examine a graphical analysis using the loci of possible refractive indices from ratios of the above quantities, taking into account the probable errors of measurement. Uncertainties involved in the transformation of the measurements into the appropriate form can have serious consequences for the determinations. For Pt in sulphuric acid, the necessity of extrapolating the double layer charging effect, and another electromodulation effect found at higher potentials to intermediate potentials brings uncertainty into the determinations for oxide films. This uncertainty cannot be resolved with the present state of knowledge. It is unrealistic to assume that monolayer or sub-monolayer films are necessarily isotropic. The analysis procedure can be extended to include uniaxial anisotropy with no great difficulty. This approach is found to yield reasonable values for benzene adsorbed on Pt, compatible with the known orientation of the benzene rings lying flat on the metal surface held by chemisorption bonds; no isotropic film model could explain the data. Possible values were also found for the constants for anodic oxide on Pt in two potential ranges, but a much more extended search would be advisable.
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References and R. Parsons, Symp. Faraday Sot. 4 (1970) 72. and D.E. Aspnes, Surface Sci. 24 (1971) 417. A. Tadjeddine, Bull. Sot. Chim. France 7 (1971) 2466. (31 F. Chao, M. Costaand and L.H. Laliberte, J. Electrochem. Sot. 121 (1974) 141 B.E. Conway, H. Angerstein-Kozlowska 1596. 151 M.A. Barrett and R. Parsons, J. Electroanal. Chem. 42 (1973) Appl. 1. 161 J. Horkans, B.D. Cahan and E. Yeager, Surface Sci. 46 (1974) 1. J.C.S. Faraday I69 (1973) 1090. I71 B.E. Conway and S. Gottesfeld, Sot. 119 (1972) 439. [81 J.L. Ord, M.A. Hopper and W.P. Wang, J. Electrochem.
Ill
M.A. Barrett
PI J.D.E. McIntyre
Critique B.D. Cahan: You mentioned the obvious desirability of using three parameters. From what I understand of your description, you start off measuring three parameters and then reduce to two by taking a ratio. What happens when you try to do a solution on the simultaneous set of all three. M.A.B. Giiltepe: Eliminating thickness is a way of simplifying the matter. All the possible solutions will come forth from crossing of these two lines and one can angle back and find out what the thickness was. Otherwise you generate more lines and you look for triple or quadruple intersections if you have three or four parameters for every possible thickness. Its a very much more complicated problem. T. Smith: Usually if you don’t take into consideration roughness effects, even very small roughness, you sometimes cannot find solutions for your data without using extinction coefficients up to three or four, which are ridiculous for oxide films. That is, if roughness is ignored, the difference must be accounted for by absorption. I assume the data you were interpreting was the experimental data. In the areas where your solution bands crossed there were extremely high values for an oxide. Would you care to comment on that? M.A.B. Gtlltepe: I definitely agree that roughness has to be taken into consideration. S. Gottesfeld: May I point out that the insensitivity of the ratio of the differential reflectance parameters of the film is a general and expected phenomena for thin absorbing films on metalic substrates. It was shown in a paper by McIntyre and Aspnes in 1971. M.A.B. Giiltepe: Well, the ratio of reflectivities in this example turned out slightly better than the other ratio taking the reflectivity through delta, if you look at the width of the bands at 69” not at 57”. At low angles its hopeless. J.L. Ord: I’d like to add a technical note on roughness with platinum. If you carry out the Kolbe reaction on the surface as your final pre-treatment on flatness is perhaps the best way to smooth and stabilize surface roughness in the system. It’s something I wish I had published when I last published on platinum.