- Email: [email protected]
A general procedure for extracting quantitative depth information from take-off-angle-resolved XPS and AES
__ __ B
-H CL
ELSEVIER
surface science Applied Surface Science lOO/lOl
(1996) 41-46
A general procedure for extracting quantitative depth information from take-off-angle-resolved XPS and AES Werner H. Gries Research Center FE, Received
Deutsche Telekom, 64295 Dannstadt,
15 August 1995; accepted
13 November
Germany
1995
Abstract An evaluation procedure is described for determination of the ultra-shallow depth composition of technological surfaces from angle-resolved intensity measurements of X-ray photoelectrons and Auger electrons which overcomes major deficiencies of several other procedures. Essentially, experimental data are compared to generalized model calculations such that the procedure is fully interactive at all stages of evaluation and that complete transparency of data treatment is maintained. The use of intensity self-ratios allows data to be ranked according to significance and quality and a realistic error analysis to be made. The use of supplementary information about the specimen and its treatment is encouraged to compensate for the inherent insufficiency of (all) angle-resolved data for surface reconstruction. The procedure can serve as a source of input data for the testing of less transparent procedures.
1. Introduction Take-off-angle-resolved measurements of signal intensity allow a non-invasive investigation of shallow and ultra-shallow depth distributions of the constituents of a solid. Ultra-shallow depth distributions ( < 10 nm) have been investigated for many years by angle-resolved X-ray photoelectron spectrometry (AR/XPS) and angle-resolved Auger electron spectrometry (AR/AES). In most procedures proposed to date for depth profile reconstruction from these AR signal measurements, use is made of inverse Laplace transformation or ‘iterative layerwise modelling’. Refs. [l-5] provide examples thereof, but also show these procedures to often lead to mathematically unstable solutions. Moreover, the computerized versions (if obtainable) are not transparent and their general reliability 0169-4332/96/$15.00 Copyright PII SO169-4332(96)00253-X
is unproven. Arguments are advanced here which put this reliability in doubt, and an alternative procedure is described which overcomes the main problems of these other procedures. One of the major points of criticism derives from the fact that angle-resolved signal intensity data alone are insufficient for a unique reconstruction of the depth distribution of analyte. This important fact has been pointed out already in 198 1 [6], when an equation was published linking the signal intensity to the moments of the depth distribution of an analyte. By means of this equation the first algebraic moment of any depth distribution (i.e. the centroid depth) was shown to be of overriding importance and the higher central moments (variance, skewness, kurtosis, etc.) to be of rapidly decreasing significance. In other words, the angle-resolved intensity data carry primarily information about the centroid depth and (particu-
0 1996 Elsevier Science B.V. All rights reserved.
42
W.H. Grirs/Applied
Sqtbce
larly if the data are laden with a significant experimental error) little or no information about the shape of the depth distribution. Hence, the angle-resolved intensity data alone practically never suffice for a unique reconstruction of the depth distribution of analyte, and (at least) the shape of the depth distribution is required as an additional input quantity. In Ref. [6] this was demonstrated for angle-resolved measurements by X-ray fluorescence spectrometry on ion-implanted analyte. There, it has also been emphasized that the information value of AR data depends on both the signal attenuation and the centroid depth. In other words, AR data from constituents at different depth are of different significance and quality. These findings hold for angle-resolved measurements of any kind. In the case of AR/XPS and AR/AES the situation is aggravated by the fact that the signal (consisting of characteristic electrons) may undergo diffraction as well as refraction. The latter is of significance only for low-energy electrons at very oblique angles of take-off. The former occurs in crystalline and partially crystalline materials, when it leads to significant local distortions of the otherwise smooth signal vs. take-off-angle relationship. Such distortions are revealed only if the signal intensity is recorded at small intervals over a wide angular range [7] and can certainly make a major contribution to differences in significance and quality of AR data (XPS and AES) from different surface constituents. The author’s particular points of criticism concerning the above-mentioned procedures are that: of the AR data for 1. the inherent insufficiency depth profiling and the causes thereof are not sufficiently emphasized; 2. the fact remains hidden that if in-process data treatment is applied, this amounts to coxing the data to yield a definite depth profile, depending on how the data are treated (the treatment known as regularization consists essentially of a smoothing of the data [14] and is supplemented by the application of constraints): 3. AR data of different levels of significance and quality are treated as input data of equal rank; 4. data of different significance and quality are mingled in the computation; and 5. the uncertainty of the attenuation lengths used is largely ignored.
Science lOO/
101 (1996) -/i-Xi
In consequence we have (firstly) that the uncertainty on the proposed constituent distribution is unknown and is dominated by the most uncertain data. and (secondly) that the analyst remains unaware of the possible existence of another (as likely or even more likely) constituent distribution, which would emerge if only the constraints were modified, the input data were ranked according to significance and quality, and the uncertainty of the attenuation lengths were considered. These deficiencies are overcome by use of a generalized evaluation procedure for AR/XPS and AR/AES, which is based on the Cries-Wybenga moment equation derived in Ref. [ 1] (Eq. 13). As in Ref. [ 11, the data input consists of self-ratios of the AR signal intensities, i.e. the ratios of a given signal measured at different angles of take-off. Therefore, the evaluation procedure is also referred to as the self-ratio procedure. The use of self-ratios is of cardinal importance for ensuring that AR data for different components (at different depths) can be ranked according to significance and quality. Other strong points of the self-ratio procedure are that full transparency of data treatment is maintained throughout and that integration of supplementary information is possible at all stages. The self-ratio procedure is described below as it has been applied in particular to AR/XPS and AR/AES measurements on technological surfaces. Because of space limitations, the description has to remain sketchy, and is to be dealt with again in a forthcoming paper.
2. Self-ratio evaluation procedure for depth profiling by AR / XPS and AR / AES The following two situations are considered for the depth distribution of any analyte identified within the information depths of XPS and AES: the toplayer situation, i.e. the analyte extends to the surface, and the orler-layer situation, i.e. the analyte is completely buried and does not extend to the surface. For each of these situations the analyte configuration is varied from a delta layer to an effectively infinite layer in which the analyte is present either as a component or in pure form. In the over-layer situa-
W.H. Gries/Applied
Surjke
tion the analyte-containing layer is overlaid by a layer which merely attenuates the signal. Since the signal self-ratio is dominated by the centroid depth of the analyte profile, but remains practically unaffected by the kurtosis or higher distribution moments. it suffices if each of the two situations is further subdivided according to the following three types of analyte distribution (with strongly differing kurtosis values), viz. the rectangular type and two triangular types, one of the rising-ramp type and the other of the falling-ramp type. The combination of the three types of distributions with the two situations can be shown (in a forthcoming paper) to suffice for the evaluation of most surface structures within the information depths of XPS and AES. For each of the three types of depth distribution in each of the two situations mentioned above, the angle-resolved self-ratios Z(YZJ)/Z(90”) of the signal intensities Z(q) and Z(90”) are calculated as a function of the take-off angle, p, with the effective attenuation length, A, as parameter. The self-ratios are calculated by use of the Gries- Wybenga self-ratio
Rectangular
distribution
of analyte
Science 100/101
43
(1996141-46 Rectangular
distribution
of analyte
2.0 W) lW1
u 0
51 90
80
70
60
50
40
30
degrees Take-off angle,
Y
Fig. 2. As for Fig. 1, but for an over-layer situation instead of a top-layer situation (see text). The analyte-containing layer is efsectire& infinite.
equation from Ref. [6], in the general form given in Ref. [8]: Z(F,)/Z(V?) 1 + &T,( = Gexp[(
A, -A,)T]
i 1 + zA;T,( ?
90
80
70
60
50
40
30
degrees Take-off angle
,Y
Fig. I. The self ratio of X-ray photoelectron intensities as a function of the angle of take-off for the top-layer situation (see text), with the thickness of the top-layer as parameter in units of the effective attenuation length. A. The value of A is stepped in intervals of 0.1 A up to 1 A, 0.2 A up to 2 A, 0.5A up to 41, and 1 A up to 5A. The analyte distribution is rectangular.
- I)“,n!
- l)“/n!
where G is a numerical factor which takes care of different geometries of measurement (and therefore differs for AR/XPS and AR/AES). A, and A2 are attenuation parameters depending on the attenuation lengths as well as the angles of incidence and take-off of the exciting and the excited radiations, T is the first moment and T, is the nth central moment of the depth distribution of the analyte. Because of space limitations, the reader must be referred to Ref. [8] for definitions and for a discussion of the above quantities. Sample curves of Z(?Z’)/Z(90”) vs. the take-off angle VJ for AR/XPS are shown in Fig. 1Fig. 2Fig. 3. These are the model calculations for AR/XPS that all experimental data are referenced to. ‘The
W. 17. Gries / Applied Surface Science 100 / 101
44
Rectangulardistribution ofanalyte
u 0
5.J. 90
60
70 Take&
60
50
40 30 degrees
angle,Y
Fig. 3. As for Fig. 2. The thickness (0.1 h) of the analyte-containing layer makes it a quasi-delta layer.
model curves for AR/AES are different, mainly because of a different geometric factor, G. The model calculations have to be carried out once only. The data can be stored digitally or in graphic form (e.g. on overlay transparencies). The task of the analyst is to find from the multitude of curves the ones which best fit his experimental data for a chosen analyte. This is readily done by visual inspection (e.g. by means of overlay transparencies), but can also be carried out by use of a suitable computer algorithm. The uncertainty margin is derived from the (vertical) spread of the experimental points within the given set of model curves (e.g. Figs. l-3). This search-and-select procedure is repeated for all analytes identified. After every analyte has been allocated one (or more> most likely depth distribution(s), the analyst has to decide on a most likely layer structure which accommodates the allocations in the order of significance and quality ranking (according to signal strength and the uncertainty margin), with due regard to all supplementary information on the specimen (such as its origin and history of treatment and exposure). Every proposal for a layer structure has to be measured against two criteria: (1) is the informa-
f I9961
41-46
tion at hand self-consistent, and (2) is the proposed structure plausible? The layer structure which best passes these tests is considered to be the most-probable one. At this stage, all depth information is still in units of effective attenuation length (EAL, h in Figs. l-3) and has to be converted to units of matter thickness (mass/area or atoms/area) or of geometric measure (nml. For this conversion, the EAL is required to be known in either unit (mass/area or nm) and for each material involved. If the EAL is to be expressed in units of nanometer, the density must also be known. Both, a definite EAL and a definite density, require a prior knowledge of composition, which, obviously, is not at hand. This dependence of physical units of EAL on the surface composition yet to be determined is a general peculiarity of any procedure for surface reconstruction from angle-resolved data and calls for the use of iterative procedures in which the composition and the EAL (and the density) are stepwise varied until a self-consistent sequence of surface layers emerges also after conversion. In practice, the problem of conversion is greatly simplified by the fact that the atomic number dependence of the EAL (in units of matter thickness) is generally much weaker than the centroid-depth dependence of the signal self-ratio, whence an approximate composition often suffices as input for prediction of the EAL involved. This approximate composition is obtained from the relative signal intensities and from the sequence of layers as derived before conversion. The type of depth information that can be obtained by use of the self-ratio procedure is shown in Fig. 4 [lo]. The figure depicts the proposed layered structure for a metallization film of titanium which was ion-bombarded by 1 keV Ar+ at a high partial pressure of water vapor. Atomic concentrations are not shown. Another (more complex) example of reconstruction of a technological surface by the selfratio procedure has been published in Ref. [9].
3. Discussion and conclusions The depth information in Fig. 4 pertains to rectangular analyte distributions. The use of triangular distributions leads to different widths and overlap-
W.H. Gries/Applied
Surface Science 100/101
4 nm N 0.1 7 nm C=O 0.3 0 nm (OHI' f 0.2
Carbon 0.35 nm * 0.05
Oxide 2.5 "m f 0.2
Ti (metallic)
2.3 nm Ti" f 0.2
\
0 - 0.2 nm Ti"
Fig. 4. Surface reconstruction in the form of a layered chemical constituent structure as obtained by means of the self-ratio procedure applied to angle-resolved intensity data of X-ray photoelectrons measured on a film of titanium which had been ionbombarded by 1 keV Ar’ at a high partial pressure of water vapor and then exposed to air. Argon (not shown) was found to be present to a depth of about 10 nm.
pings of layers, but not to a different layer sequence. The possibility of tailing beyond the stated widths cannot be excluded, and is actually rather likely. The uncertainty margins given do not pertain to such tailing (which cannot be determined from AR data), but are derived from the uncertainty of allocation of the experimental data to a particular curve of the model calculations (here obtained by visual comparison with graphs of the type shown in Figs. l-3). Figs. l-3 show the uncertainty to increase rather drastically with depth beyond about 2h. These figures show also the difficulty of a singular allocation of a depth distribution to an experimental set of AR self-ratio data. This fact highlights the importance of additional input of supplementary information about the origin and history of the specimen. Only a combination of AR data with such supplementary information in a self-consistency-and-plausibility check leads to a most probable layered structure in the complex situation normally existing at technological surfaces.
(1996141-46
45
A rather obvious prerequisite for meaningful results is that the surface area where AR measurements are made is of sufficient smoothness. For the data in Fig. 4 this condition has been ascertained by means of atomic force microscopy. The depths and widths stated in Fig. 4 depend directly on the EAL values used for conversion from units of EAL to those of nanometer. The EAL were derived from inelastic mean free pathlengths (IMFPs), which (in turn) were calculated by means of a recently published [9] new universal predictive equation. Values of EAL can be derived from these IMFPs on the basis of an approach published in Ref. [l 11. The IMFP predictive equation in Ref. [9] is based on a set of IMFPs derived by Tanuma et al. [ 121 from optical data. Uncertainties of 30% on these optical-data-derived IMFPs are not uncommon. and a significant systematic error on these IMFPs can also not be ruled out at present [9]. Therefore, due to the uncertainties of the IMFPs, the depths and widths stated in Fig. 4 are in fact considerably more uncertain than indicated in the figure. In conclusion, technological surfaces can be reconstructed from angle-resolved XPS and AES intensity data by use of the self-ratio procedure. The reconstruction is in the form of a most probable layered structure. The self-ratio procedure provides all the information required for a detailed error analysis. Because of the complete transparency of the procedure, it can also be used as a source of input data for the testing of less transparent procedures (such as are mentioned in the introduction). (The author offers to make model data available for this purpose). The reliability of the self-ratio procedure rests, of course, on the reliability of the Gries-Wybenga self-ratio equation used for calculation of the model data (Figs. l-3). The reliability of the equation has repeatedly been confirmed in measurements on ionimplanted analytes as well as on thin films by means of AR X-ray fluorescence spectrometry and AR electron microbeam analysis [8,13].
Acknowledgements Susie Krell has kindly generated
the figures.
46
W.H. Cries/Applied
Surface Science lOO/ 101 (1996) 41-46
References [l] S. Hofmann, Analusis 9 (1981) 181. [2] T.H. Bussing and P.H. Holloway, J. Vat. Sci. Technol. A 3 (19851 1973. [3] L.B. HazeIl, IS. Brown and F. Freising, Surf. Interf. Anal. 8 (19861 25. [4] R.S. Yih and B.D. Ratner, J. Electron Spectrosc. Rel. Phen. 43 (1987) 61. [5] N.1. Nefedov and O.A. Baschenko, J. Electron Spectrosc. Rel. Phen. 47 (1988) 1. [6] W.H. Gries and F.T Wybenga, Surf. Interf. Anal. 3 (19811 251. [7] W.H. Gries, Surf. Interf. Anal. 17 (1991) 803.
[8] W.H. Gries, Mikrochim. Acta 107 (19921 117. [9] W.H. Cries. J. Vat. Sci. Technol. A 13 (19951 1304: Surf. Interf. Anal 24 (19961 38. [lo] W.H. Gries and S. Krell, presented at the 5th European Conf. on Applications of Surface and Interface Analysis. Catania. Italy. 1993. unpublished. [I 1] W.H. Gries and W.S.M. Werner, Surf. Interf. Anal. 16 (19901 149. [12] S. Tanuma, C.J. Powell and D.R. Penn, Surf. Interf. Anal. 11 (19881 577; 17 (1991) 919; 17 (1991) 929; 20 (19931 77; 21 (1994) 165. [13] W. Schmitt, J. Rothe. J. Hermes and W.H. Gries, J. Vat. Sci. Technol. A 12 (19941 2467. [14] P.J. Cumpson. J. Electron Spectrosc. Rel. Phen. 73 (19951
-H CL
ELSEVIER
surface science Applied Surface Science lOO/lOl
(1996) 41-46
A general procedure for extracting quantitative depth information from take-off-angle-resolved XPS and AES Werner H. Gries Research Center FE, Received
Deutsche Telekom, 64295 Dannstadt,
15 August 1995; accepted
13 November
Germany
1995
Abstract An evaluation procedure is described for determination of the ultra-shallow depth composition of technological surfaces from angle-resolved intensity measurements of X-ray photoelectrons and Auger electrons which overcomes major deficiencies of several other procedures. Essentially, experimental data are compared to generalized model calculations such that the procedure is fully interactive at all stages of evaluation and that complete transparency of data treatment is maintained. The use of intensity self-ratios allows data to be ranked according to significance and quality and a realistic error analysis to be made. The use of supplementary information about the specimen and its treatment is encouraged to compensate for the inherent insufficiency of (all) angle-resolved data for surface reconstruction. The procedure can serve as a source of input data for the testing of less transparent procedures.
1. Introduction Take-off-angle-resolved measurements of signal intensity allow a non-invasive investigation of shallow and ultra-shallow depth distributions of the constituents of a solid. Ultra-shallow depth distributions ( < 10 nm) have been investigated for many years by angle-resolved X-ray photoelectron spectrometry (AR/XPS) and angle-resolved Auger electron spectrometry (AR/AES). In most procedures proposed to date for depth profile reconstruction from these AR signal measurements, use is made of inverse Laplace transformation or ‘iterative layerwise modelling’. Refs. [l-5] provide examples thereof, but also show these procedures to often lead to mathematically unstable solutions. Moreover, the computerized versions (if obtainable) are not transparent and their general reliability 0169-4332/96/$15.00 Copyright PII SO169-4332(96)00253-X
is unproven. Arguments are advanced here which put this reliability in doubt, and an alternative procedure is described which overcomes the main problems of these other procedures. One of the major points of criticism derives from the fact that angle-resolved signal intensity data alone are insufficient for a unique reconstruction of the depth distribution of analyte. This important fact has been pointed out already in 198 1 [6], when an equation was published linking the signal intensity to the moments of the depth distribution of an analyte. By means of this equation the first algebraic moment of any depth distribution (i.e. the centroid depth) was shown to be of overriding importance and the higher central moments (variance, skewness, kurtosis, etc.) to be of rapidly decreasing significance. In other words, the angle-resolved intensity data carry primarily information about the centroid depth and (particu-
0 1996 Elsevier Science B.V. All rights reserved.
42
W.H. Grirs/Applied
Sqtbce
larly if the data are laden with a significant experimental error) little or no information about the shape of the depth distribution. Hence, the angle-resolved intensity data alone practically never suffice for a unique reconstruction of the depth distribution of analyte, and (at least) the shape of the depth distribution is required as an additional input quantity. In Ref. [6] this was demonstrated for angle-resolved measurements by X-ray fluorescence spectrometry on ion-implanted analyte. There, it has also been emphasized that the information value of AR data depends on both the signal attenuation and the centroid depth. In other words, AR data from constituents at different depth are of different significance and quality. These findings hold for angle-resolved measurements of any kind. In the case of AR/XPS and AR/AES the situation is aggravated by the fact that the signal (consisting of characteristic electrons) may undergo diffraction as well as refraction. The latter is of significance only for low-energy electrons at very oblique angles of take-off. The former occurs in crystalline and partially crystalline materials, when it leads to significant local distortions of the otherwise smooth signal vs. take-off-angle relationship. Such distortions are revealed only if the signal intensity is recorded at small intervals over a wide angular range [7] and can certainly make a major contribution to differences in significance and quality of AR data (XPS and AES) from different surface constituents. The author’s particular points of criticism concerning the above-mentioned procedures are that: of the AR data for 1. the inherent insufficiency depth profiling and the causes thereof are not sufficiently emphasized; 2. the fact remains hidden that if in-process data treatment is applied, this amounts to coxing the data to yield a definite depth profile, depending on how the data are treated (the treatment known as regularization consists essentially of a smoothing of the data [14] and is supplemented by the application of constraints): 3. AR data of different levels of significance and quality are treated as input data of equal rank; 4. data of different significance and quality are mingled in the computation; and 5. the uncertainty of the attenuation lengths used is largely ignored.
Science lOO/
101 (1996) -/i-Xi
In consequence we have (firstly) that the uncertainty on the proposed constituent distribution is unknown and is dominated by the most uncertain data. and (secondly) that the analyst remains unaware of the possible existence of another (as likely or even more likely) constituent distribution, which would emerge if only the constraints were modified, the input data were ranked according to significance and quality, and the uncertainty of the attenuation lengths were considered. These deficiencies are overcome by use of a generalized evaluation procedure for AR/XPS and AR/AES, which is based on the Cries-Wybenga moment equation derived in Ref. [ 1] (Eq. 13). As in Ref. [ 11, the data input consists of self-ratios of the AR signal intensities, i.e. the ratios of a given signal measured at different angles of take-off. Therefore, the evaluation procedure is also referred to as the self-ratio procedure. The use of self-ratios is of cardinal importance for ensuring that AR data for different components (at different depths) can be ranked according to significance and quality. Other strong points of the self-ratio procedure are that full transparency of data treatment is maintained throughout and that integration of supplementary information is possible at all stages. The self-ratio procedure is described below as it has been applied in particular to AR/XPS and AR/AES measurements on technological surfaces. Because of space limitations, the description has to remain sketchy, and is to be dealt with again in a forthcoming paper.
2. Self-ratio evaluation procedure for depth profiling by AR / XPS and AR / AES The following two situations are considered for the depth distribution of any analyte identified within the information depths of XPS and AES: the toplayer situation, i.e. the analyte extends to the surface, and the orler-layer situation, i.e. the analyte is completely buried and does not extend to the surface. For each of these situations the analyte configuration is varied from a delta layer to an effectively infinite layer in which the analyte is present either as a component or in pure form. In the over-layer situa-
W.H. Gries/Applied
Surjke
tion the analyte-containing layer is overlaid by a layer which merely attenuates the signal. Since the signal self-ratio is dominated by the centroid depth of the analyte profile, but remains practically unaffected by the kurtosis or higher distribution moments. it suffices if each of the two situations is further subdivided according to the following three types of analyte distribution (with strongly differing kurtosis values), viz. the rectangular type and two triangular types, one of the rising-ramp type and the other of the falling-ramp type. The combination of the three types of distributions with the two situations can be shown (in a forthcoming paper) to suffice for the evaluation of most surface structures within the information depths of XPS and AES. For each of the three types of depth distribution in each of the two situations mentioned above, the angle-resolved self-ratios Z(YZJ)/Z(90”) of the signal intensities Z(q) and Z(90”) are calculated as a function of the take-off angle, p, with the effective attenuation length, A, as parameter. The self-ratios are calculated by use of the Gries- Wybenga self-ratio
Rectangular
distribution
of analyte
Science 100/101
43
(1996141-46 Rectangular
distribution
of analyte
2.0 W) lW1
u 0
51 90
80
70
60
50
40
30
degrees Take-off angle,
Y
Fig. 2. As for Fig. 1, but for an over-layer situation instead of a top-layer situation (see text). The analyte-containing layer is efsectire& infinite.
equation from Ref. [6], in the general form given in Ref. [8]: Z(F,)/Z(V?) 1 + &T,( = Gexp[(
A, -A,)T]
i 1 + zA;T,( ?
90
80
70
60
50
40
30
degrees Take-off angle
,Y
Fig. I. The self ratio of X-ray photoelectron intensities as a function of the angle of take-off for the top-layer situation (see text), with the thickness of the top-layer as parameter in units of the effective attenuation length. A. The value of A is stepped in intervals of 0.1 A up to 1 A, 0.2 A up to 2 A, 0.5A up to 41, and 1 A up to 5A. The analyte distribution is rectangular.
- I)“,n!
- l)“/n!
where G is a numerical factor which takes care of different geometries of measurement (and therefore differs for AR/XPS and AR/AES). A, and A2 are attenuation parameters depending on the attenuation lengths as well as the angles of incidence and take-off of the exciting and the excited radiations, T is the first moment and T, is the nth central moment of the depth distribution of the analyte. Because of space limitations, the reader must be referred to Ref. [8] for definitions and for a discussion of the above quantities. Sample curves of Z(?Z’)/Z(90”) vs. the take-off angle VJ for AR/XPS are shown in Fig. 1Fig. 2Fig. 3. These are the model calculations for AR/XPS that all experimental data are referenced to. ‘The
W. 17. Gries / Applied Surface Science 100 / 101
44
Rectangulardistribution ofanalyte
u 0
5.J. 90
60
70 Take&
60
50
40 30 degrees
angle,Y
Fig. 3. As for Fig. 2. The thickness (0.1 h) of the analyte-containing layer makes it a quasi-delta layer.
model curves for AR/AES are different, mainly because of a different geometric factor, G. The model calculations have to be carried out once only. The data can be stored digitally or in graphic form (e.g. on overlay transparencies). The task of the analyst is to find from the multitude of curves the ones which best fit his experimental data for a chosen analyte. This is readily done by visual inspection (e.g. by means of overlay transparencies), but can also be carried out by use of a suitable computer algorithm. The uncertainty margin is derived from the (vertical) spread of the experimental points within the given set of model curves (e.g. Figs. l-3). This search-and-select procedure is repeated for all analytes identified. After every analyte has been allocated one (or more> most likely depth distribution(s), the analyst has to decide on a most likely layer structure which accommodates the allocations in the order of significance and quality ranking (according to signal strength and the uncertainty margin), with due regard to all supplementary information on the specimen (such as its origin and history of treatment and exposure). Every proposal for a layer structure has to be measured against two criteria: (1) is the informa-
f I9961
41-46
tion at hand self-consistent, and (2) is the proposed structure plausible? The layer structure which best passes these tests is considered to be the most-probable one. At this stage, all depth information is still in units of effective attenuation length (EAL, h in Figs. l-3) and has to be converted to units of matter thickness (mass/area or atoms/area) or of geometric measure (nml. For this conversion, the EAL is required to be known in either unit (mass/area or nm) and for each material involved. If the EAL is to be expressed in units of nanometer, the density must also be known. Both, a definite EAL and a definite density, require a prior knowledge of composition, which, obviously, is not at hand. This dependence of physical units of EAL on the surface composition yet to be determined is a general peculiarity of any procedure for surface reconstruction from angle-resolved data and calls for the use of iterative procedures in which the composition and the EAL (and the density) are stepwise varied until a self-consistent sequence of surface layers emerges also after conversion. In practice, the problem of conversion is greatly simplified by the fact that the atomic number dependence of the EAL (in units of matter thickness) is generally much weaker than the centroid-depth dependence of the signal self-ratio, whence an approximate composition often suffices as input for prediction of the EAL involved. This approximate composition is obtained from the relative signal intensities and from the sequence of layers as derived before conversion. The type of depth information that can be obtained by use of the self-ratio procedure is shown in Fig. 4 [lo]. The figure depicts the proposed layered structure for a metallization film of titanium which was ion-bombarded by 1 keV Ar+ at a high partial pressure of water vapor. Atomic concentrations are not shown. Another (more complex) example of reconstruction of a technological surface by the selfratio procedure has been published in Ref. [9].
3. Discussion and conclusions The depth information in Fig. 4 pertains to rectangular analyte distributions. The use of triangular distributions leads to different widths and overlap-
W.H. Gries/Applied
Surface Science 100/101
4 nm N 0.1 7 nm C=O 0.3 0 nm (OHI' f 0.2
Carbon 0.35 nm * 0.05
Oxide 2.5 "m f 0.2
Ti (metallic)
2.3 nm Ti" f 0.2
\
0 - 0.2 nm Ti"
Fig. 4. Surface reconstruction in the form of a layered chemical constituent structure as obtained by means of the self-ratio procedure applied to angle-resolved intensity data of X-ray photoelectrons measured on a film of titanium which had been ionbombarded by 1 keV Ar’ at a high partial pressure of water vapor and then exposed to air. Argon (not shown) was found to be present to a depth of about 10 nm.
pings of layers, but not to a different layer sequence. The possibility of tailing beyond the stated widths cannot be excluded, and is actually rather likely. The uncertainty margins given do not pertain to such tailing (which cannot be determined from AR data), but are derived from the uncertainty of allocation of the experimental data to a particular curve of the model calculations (here obtained by visual comparison with graphs of the type shown in Figs. l-3). Figs. l-3 show the uncertainty to increase rather drastically with depth beyond about 2h. These figures show also the difficulty of a singular allocation of a depth distribution to an experimental set of AR self-ratio data. This fact highlights the importance of additional input of supplementary information about the origin and history of the specimen. Only a combination of AR data with such supplementary information in a self-consistency-and-plausibility check leads to a most probable layered structure in the complex situation normally existing at technological surfaces.
(1996141-46
45
A rather obvious prerequisite for meaningful results is that the surface area where AR measurements are made is of sufficient smoothness. For the data in Fig. 4 this condition has been ascertained by means of atomic force microscopy. The depths and widths stated in Fig. 4 depend directly on the EAL values used for conversion from units of EAL to those of nanometer. The EAL were derived from inelastic mean free pathlengths (IMFPs), which (in turn) were calculated by means of a recently published [9] new universal predictive equation. Values of EAL can be derived from these IMFPs on the basis of an approach published in Ref. [l 11. The IMFP predictive equation in Ref. [9] is based on a set of IMFPs derived by Tanuma et al. [ 121 from optical data. Uncertainties of 30% on these optical-data-derived IMFPs are not uncommon. and a significant systematic error on these IMFPs can also not be ruled out at present [9]. Therefore, due to the uncertainties of the IMFPs, the depths and widths stated in Fig. 4 are in fact considerably more uncertain than indicated in the figure. In conclusion, technological surfaces can be reconstructed from angle-resolved XPS and AES intensity data by use of the self-ratio procedure. The reconstruction is in the form of a most probable layered structure. The self-ratio procedure provides all the information required for a detailed error analysis. Because of the complete transparency of the procedure, it can also be used as a source of input data for the testing of less transparent procedures (such as are mentioned in the introduction). (The author offers to make model data available for this purpose). The reliability of the self-ratio procedure rests, of course, on the reliability of the Gries-Wybenga self-ratio equation used for calculation of the model data (Figs. l-3). The reliability of the equation has repeatedly been confirmed in measurements on ionimplanted analytes as well as on thin films by means of AR X-ray fluorescence spectrometry and AR electron microbeam analysis [8,13].
Acknowledgements Susie Krell has kindly generated
the figures.
46
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Surface Science lOO/ 101 (1996) 41-46
References [l] S. Hofmann, Analusis 9 (1981) 181. [2] T.H. Bussing and P.H. Holloway, J. Vat. Sci. Technol. A 3 (19851 1973. [3] L.B. HazeIl, IS. Brown and F. Freising, Surf. Interf. Anal. 8 (19861 25. [4] R.S. Yih and B.D. Ratner, J. Electron Spectrosc. Rel. Phen. 43 (1987) 61. [5] N.1. Nefedov and O.A. Baschenko, J. Electron Spectrosc. Rel. Phen. 47 (1988) 1. [6] W.H. Gries and F.T Wybenga, Surf. Interf. Anal. 3 (19811 251. [7] W.H. Gries, Surf. Interf. Anal. 17 (1991) 803.
[8] W.H. Gries, Mikrochim. Acta 107 (19921 117. [9] W.H. Cries. J. Vat. Sci. Technol. A 13 (19951 1304: Surf. Interf. Anal 24 (19961 38. [lo] W.H. Gries and S. Krell, presented at the 5th European Conf. on Applications of Surface and Interface Analysis. Catania. Italy. 1993. unpublished. [I 1] W.H. Gries and W.S.M. Werner, Surf. Interf. Anal. 16 (19901 149. [12] S. Tanuma, C.J. Powell and D.R. Penn, Surf. Interf. Anal. 11 (19881 577; 17 (1991) 919; 17 (1991) 929; 20 (19931 77; 21 (1994) 165. [13] W. Schmitt, J. Rothe. J. Hermes and W.H. Gries, J. Vat. Sci. Technol. A 12 (19941 2467. [14] P.J. Cumpson. J. Electron Spectrosc. Rel. Phen. 73 (19951