Surf. Interface Anal. 29, 403â406 (2000). RAPID COMMUNICATION. The Thickogram: a method for easy film thickness measurement in XPS. Peter J Cumpson*.
SURFACE AND INTERFACE ANALYSIS Surf. Interface Anal. 29, 403–406 (2000)
RAPID COMMUNICATION
The Thickogram: a method for easy film thickness measurement in XPS Peter J Cumpson* Centre for Materials Measurement and Technology, NPL, Teddington TW11 0LW, UK
SPONSOR REFEREE: Dr P. C. Zalm Philips Centre for Manufacturing Technology, Eindhoven, The Netherlands
We describe a simple graphical method for measuring film thickness by XPS, which we call a Thickogram. This method can be used even when the film and substrate peaks have very different kinetic energies and incorporates the effects of elastic scattering within the recommended range of take-off angles. The Thickogram may also be useful when measuring film thickness by AES, though this is less commonly required than in XPS. Copyright 2000 John Wiley & Sons, Ltd.
INTRODUCTION Measurement of the thickness of a surface film1 is a common requirement in XPS, and sometimes in AES too. New XPS instruments from at least three different manufacturers are designed to make film thickness measurements more quickly and easily than in the past, but there remains the problem of converting peak intensity measurements into a film thickness. A very popular method for measuring the thickness of oxide films by XPS was developed by Hill et al.2 Io /so t D cos ln 1 C .1/ Is /ss where t is the film thickness, is the attenuation length of the cation or metal photoelectrons in the film, is the emission angle (measured with respect to the surface normal, so that normal emission represents D 0), Io and Is are the measured peak intensities from film and substrate, respectively, and so and ss are their sensitivity factors. The equation for this popular method has four very useful features for routine film thickness measurement: (1) Thin, uniform surface contamination overlaying the film to be measured is unimportant here. Quite often one has contamination from atmospheric organic layers covering the film that one wants to measure. (2) Unknown instrumental factors, common to both the substrate and oxide signals, cancel. (3) The equation for film thickness is very simple, involving only a single logarithm, giving one a good overview of the sensitivity of the film thickness measurement to errors, and how to optimize the quality of a measurement by selecting the best inputs. (4) By using information from both the substrate and the oxide, the method even works well in the limit of large * Correspondence to: P. J. Cumpson, Centre for Materials Measurement and Technology, NPL, Teddington TW11 0LW, UK. Contract/grant sponsor: UK Department of Trade and Industry. Copyright 2000 John Wiley & Sons, Ltd.
and small film thicknesses, where methods based on the film or substrate intensities on their own would have larger fractional uncertainties. Thin oxide layers on Al and Si are of great technological importance3,4 and are ideal for Eqn (1). Chemical shifts and peak fitting allow the intensities of overlayer and substrate peaks to be measured,5 but these chemical shifts are sufficiently small that the signal electrons from oxide and substrate have very nearly the same energy and therefore almost identical attenuation lengths in the oxide. Therefore, this approach has been very successful in interlaboratory comparisons.6 These important advantages are balanced by one serious limitation of this popular method: the attenuation lengths of photoelectrons from the film and the substrate are assumed to be identical for electrons passing through the film. In practice this means that the two peaks measured must have almost identical kinetic energies. However, many studies require film thickness measurements from peaks widely separated in energy. In this case, the relevant equation is much more complex than Eqn (1) and is not so easy to solve. It would therefore be extremely useful to find a method of film thickness measurement that preserved as many as possible of the useful features of the popular method of Eqn (1), even for peaks that are well separated in energy.7 Figure 1 shows a new and straightforward nomogram solution, the details of which are described below. Recall that a nomogram8 is a plot designed to give a value (in our case, film thickness) that is dependent on two or more measurements (in our case, peak intensity ratio and peak energy ratio).
HOW TO USE THE THICKOGRAM Figure 1 shows an example of the usage of the Thickogram. Its purpose is to derive film thickness from data of the film and substrate intensities at one emission angle in the range 0 60° . Locate the point on the vertical Received Revised ; Accepted 5 April 2000
404
P. J. CUMPSON
Figure 1. Thickogram for film thickness measurement. This example shows a measurement using Mg K˛ radiation of the thickness of an evaporated carbon film (C 1s) on silicon dioxide (Si 2p). The ratio of kinetic energy of overlayer and substrate peaks is Eo /Es D 0.84. The intensity ratio (after dividing by the respective sensitivity factors) is 2.6, giving a straight line intersection with the thickness scale at the point labelled ‘C’, where t ¾ 1.4o cos , with a precision of about ¾1%. In this case D 45° and o D 2.07 nm from the CS2 equation,9 so that the film thickness is read from the thickness scale to be 2.1 nm with an estimated uncertainty of š10% arising from the uncertainty of inelastic mean free path (IMFP) calculations involved in the CS2 formula.
axis on the left, corresponding to the measured ratio of peak intensities from overlayer, Io , and substrate, Is (each being divided by its sensitivity factor, so and ss , respectively). This is point ‘A’ in Fig. 1. Next locate the point in the curved logarithmic grid at the lower right, point ‘B’, corresponding to this same intensity ratio and the ratio of the kinetic energy of the overlayer peak to the substrate peak, Eo /Es . A straight line drawn between these points intersects the curved thickness scale at point ‘C’, the value of the film thickness, in units of o cos , where is the angle of emission with respect to the surface normal. The attenuation length of photoelectrons in the overlayer, o , may be obtained from measurements of films of known thickness, or from a predictive equation such as CS2.9 Note that the deepest section of the curved thickness scale is shown dashed, to indicate that films of this thickness are difficult to measure in practice, given typical XPS backgrounds. The Thickogram is applicable to a wide range of kinetic energy above ¾500 eV for any film thickness measurable by XPS and for any emission angle up to ¾60° .9 Emission angles close to 45° will lead to the most accurate results because they minimize errors due to elastic scattering9 and surface roughness.10 – 12 Figure 2 shows a blank Thickogram for those who wish to photocopy and use it. Provided that the low kinetic energy and grazing emission r´egimes are avoided, Fig. 2 is applicable to the great majority of film thickness measurements. We have found it particularly useful in experimental planning, when judging the film thicknesses that can be measured to a given accuracy using a particular emission angle and analytical line. For instance, it is clear that errors will be worst for low Is , high Es values. The Thickogram preserves the third and fourth features of Eqn (1) listed above, but sadly not the first and second, although the second is straightforward to achieve by intensity calibration of your spectrometer or by correct determination of the sensitivity factors. Surf. Interface Anal. 29, 403–406 (2000)
HOW THE THICKOGRAM WAS DERIVED We show elsewhere9 that, allowing for elastic scattering, exponential attenuation by the overlayer film is a good approximation for 0 60° , so to within a common proportionality constant we have Is /ss D exp. t/s cos /
.2/
and Io /so D 1
exp. t/o cos /
.3/
where o and s are the attenuation lengths of photoelectrons within the overlayer that originated in the overlayer and the substrate, respectively. This can be combined and rearranged to give 1 Io /so o t ln 2 ln Is /ss s 2 o cos t .4/ D ln sinh 2o cos The right-hand side of Eqn (4) is plotted as the thickness scale in Fig. 2. The term linear in t on the left-hand side gives rise to the straight line intersection of this thickness scale. The peak kinetic energies are easily available from the spectra, so that it is more convenient to use the ratio of these energies rather than the ratio of the attenuation lengths of substrate and overlayer electrons in the overlayer. We do this by making use of the following approximation, which is good for E ½ 100 eV for low atomic number overlayers, and good above ¾500 eV for overlayers of all atomic numbers13,14 0.75 o Eo D .5/ s Es Copyright 2000 John Wiley & Sons, Ltd.
FILM THICKNESS IN XPS
405
Figure 2. Thickogram suitable for photocopying.
This equation fixes the ratio of attenuation lengths for photoelectrons of two different energies within one material, the overlayer material. This ratio is usually more accurate than either of the attenuation lengths themselves, because by using only their ratio we do not need to take the material dependence of the attenuation length into account. Equation (5) is basically the power law dependence of attenuation length on kinetic energy of a type first proposed by Wagner. Thus, the Thickogram is a geometric solution of the equation # " 0.75 1 Io /so Eo t ln 2 ln Is /ss Es 2 o cos t .6/ D ln sinh 2o cos
Sensitivity factors
Why the Thickogram appears independent of chemical composition
CORRECTION FOR ORGANIC CONTAMINATION
The material dependence of the attenuation length is an important factor when expressing the thickness of a layer in length units such as angstroms or nanometres. However, this does not alter the Thickogram because the material dependence only becomes important when estimating the value of o to convert the thickness t from units of o cos to units of angstroms or nanometres. Recall that o and s both represent attenuation lengths in the overlayer, but for photoelectrons originating from overlayer and substrate, respectively. Therefore, only the energy ratio, and not the material dependence of the attenuation length, must be reflected in the logarithmic grid of the Thickogram.
As we have seen, Eqn (1) assumes that the kinetic energies of signal electrons from overlayer and substrate are the same. If this is the case then any contamination on top of the overlayer will attenuate both signals equally, and will have no effect on the overlayer thickness that we calculate. Such contamination is common in specimens exposed to the laboratory atmosphere for more than a few minutes before analysis. Of course, very thick contamination will make the peak intensity ratios difficult to measure accurately, but in principle the effect of surface contamination cancels, and one need not consider the thickness of contamination when applying Eqn (1).
Copyright 2000 John Wiley & Sons, Ltd.
The sensitivity factors correspond to the intensities that one would measure from pure specimens of the overlayer and substrate materials, respectively, given exactly the same instrumental conditions and primary beam. If you have pure specimens available, the most precise approach may be to measure these sensitivity factors under the same instrumental conditions as the film thickness measurement. If not, then of course reference tables may be used. If tables are used, take care when dealing with compounds that a sensitivity factor for the measured analytical peak in that compound is used. This will in general differ from that of the pure element, due to its smaller atomic fraction in the compound and often a difference in attenuation length too.
Surf. Interface Anal. 29, 403–406 (2000)
406
P. J. CUMPSON
We are not so fortunate when applying the Thickogram to specimens with contamination on top of the film. Unless Eo /Es D 1 we will have a shift in relative intensity according to the ratio of attenuation of the film and substrate peaks by the contamination. In these cases, we must:
IMFP data on 14 organics15 are almost identical and hence one can expect that the attenuation lengths are likely to be similar. Consequently, the correction will be very insensitive to the specific chemical nature of the contamination.
(1) Establish the thickness of the contamination. A useful way to do this is to tilt the specimen until the substrate peak intensity is negligible compared to that of the film or contamination (after dividing by sensitivity factors). Typically this is achieveable without exceeding an emission angle of about D 60° or D 70° (beyond which elastic scattering effects can cause significant errors). Then use a Thickogram to measure the thickness of the organic contamination film in units of attenuation length, D D t/C1s , treating the film below it as the substrate. (2) Returning to measurements of film and substrate intensity recorded closer to normal emission, correct these for the attenuation of the contamination layer, cc obtaining contamination-corrected values Icc o and Is 0.75 Icc .7/ o D Io exp D.EC1s /Eo /
CONCLUSIONS
and
0.75 Icc s D Is exp D.EC1s /Es /
.8/
cc (3) Input Icc o and Is into a new Thickogram to give the film thickness required.
This contamination-correction procedure will work well for the typical contamination thicknesses, with D ¾ 0.2–0.3 arising from temporary air exposure in the laboratory. It becomes increasingly inaccurate for very thick contamination, where D ½ 1. Tanuma, Powell and Penn
We have described an easy-to-use nomogram for film thickness measurement, which we call a Thickogram, with the following properties: (1) It is quick and easy to use. (2) It can be used with peaks well separated in energy. (3) It is thus more widely applicable than the well-known oxide/metal peak measurement method of Eqn (1). (4) It allows greater flexibility, e.g. consistency checks can be performed using two sets of peaks to check a thickness measurement. (5) It is advisable, but not essential, to use analytical peaks fairly close in kinetic energy. (6) The equation equivalent to the Thickogram, Eqn (6), may be easily solved within a computer spreadsheet, speeding the calculation in cases where many measurements are to be made. (7) A simple correction for hydrocarbon contamination has been described. Acknowledgements Thanks are due to Dr M. P. Seah and Professor P. C. Zalm for many useful comments and discussions, and to Dr M. P. Seah for the suggestion of the name ‘Thickogram.’ This work was conducted under the Valid Analytical Measurement (VAM) programme of the UK Department of Trade and Industry.
REFERENCES 1. Fadley CS et al., J. Electron Spectrosc. 1974; 4: 93. 2. Hill JM et al., Chem. Phys. Lett. 1976; 44: 225. 3. Gunter PLJ, de Jong AM, Niemantsverdriet JW, Rheiter HJH. Surf. Interface Anal. 1992; 19: 161. 4. Mitchell DF et al., Surf. Interface Anal. 1994; 21: 44. 5. Fulghum JE et al., J. Electron Spectrosc. 1992; 60: 117. 6. Marcus P, Hinnen C, Olefjord I. Surf. Interface Anal. 1993; 20: 923. 7. Leavitt PK. Surf. Interface Anal. 1992; 18: 387. 8. Lewis AS. Nomography. Wiley: New York, 1959.
Surf. Interface Anal. 29, 403–406 (2000)
9. Cumpson PJ, Seah MP. Surf. Interface Anal. 1997; 25: 430. 10. Gunter PLJ, Gijzeman OLJ, Niemantsverdriet JW. Appl. Surf. Sci. 1997; 115: 342. 11. Zalm PC. Surf. Interface Anal. 1998; 26: 352. 12. Fulghum JE, Linton RW. Surf. Interface Anal. 1988; 13: 186. 13. Cumpson PJ. Surf. Interface Anal. 1997; 25: 447. 14. Jablonski A, Powell CJ. J. Vac. Sci. Technol. A 1997; 15: 2095. 15. Tanuma S, Powell CJ, Penn DR. Surf. Interface Anal. 1993; 21: 165.
Copyright 2000 John Wiley & Sons, Ltd.
