- Email: [email protected]
Fitting the inelastic tail below experimentally observed Auger peaks
895
Surface Science 152/153 (1985) 895-901 North-Holland, Amsterdam
FI’ITING THE INELASTIC TAIL BELOW EXPERIMENTALLY OBSERVED AUGER PEAKS D.C. PEACOCK Department of Physics, University of York, Heslington, York YOl SOD, UK Received
27 March
1984; accepted
for publication
24 April 1984
A new iterative procedure enabling the extraction of Auger and associated loss peaks from the secondary electron spectrum N(E) is described and demonstrated. Sections of N(E) away from Auger and loss features are approximated by a cascade of the form AEmm where m is predicted to be unity. For a wide range of elements, experimental values of nr above an Auger peak in energy are found to be less than the theoretical value. After subtraction of the cascade, the step-like feature found beneath the Auger peak and arising from inelastically scattered Auger electrons is calculated. Unlike methods described previously, the procedure described here has the advantage that the fitted tail is forced to closely follow the spectrum below the Auger and loss features in energy. The ratio of the stripped peak area to the increase in background associated with the peak is calculated for the samples used in this study and the prospects of using this ratio for non-destructive depth profiling are discussed.
1. Introduction Two processing stages are necessary before peak areas in the secondary electron spectrum, N(E), can be integrated to give signals proportional to Auger currents. (a) The background, B(E), arising from the cascade of inelastic scattering events in the sample must be subtracted. By extending the analysis due to Wolff [l], Sickafus [2] derived an approximation to this background of the form B,(E)
= AIE-m’,
(1)
where m, is constant for regions of N(E) away from Auger and loss features. This power law was obtained by assuming that: electrons were incident normally upon a planar surface of homogeneous material, the ionization cross-section was of the Bethe form (E-’ log E), and the electron-electron interactions could be described by S-wave scattering. This last assumption should limit the validity of eq. (1) to energies below ca. 100 eV. Nevertheless, power law behaviour has been observed experimentally at energies up to 1000 eV and for various angles of incidence [2]. The present work shows that for 0039-6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
896
D.C. Peacock
/ Fittmg the inelastic tail
primary energies in excess of 15 keV, eq. (1) is a good approximation up to 2000 eV for a wide range of materials although experimentally measured values of m, differ from the theoretical value of unity. Because it has some physical basis, background removal using a least-squares fit of eq. (1) is preferable to the use of more general fitting methods (e.g. ref. [3]) and failure of an experimental spectrum to obey eq. (1) provides a sensitive diagnostic of instrument malfunction [4]. (b) After subtraction of B,(E) from N(E), allowance must be made for the contribution arising from Auger electrons which have undergone energy loss before or during escape from the surface. These electrons give rise to a cascade of the form of eq. (1) at energies below E, which is between 0.3 and 0.5 of the Auger energy. Removal of this contribution requires deconvolution of the instrument-specimen response function, M(E) [5,6], and an economical technique which approximates to this has been suggested recently [7]. This, and other techniques, use a spectrum collected with the primary energy near to the Auger energy of interest in approximating M(E) although this is not always convenient. Moreover, if high spatial resolution is required, limitations in the performance of the electron column may prevent the collection of a pair of spectra with the appropriate primary energies from the same small surface area and with the same spot size. A way round this problem is to subtract from the stripped data a “step” of the form [S] S(E)=$/FIN,(E’)
E
dE’,
where N,(E) is the Auger current at energy E and E, the threshold above which NA( E) = 0. Although eq. (2) is only an approximation to the desired deconvolution it can still be used in quantitative analysis provided that it is applied in a consistent manner to both the specimen of interest and the corresponding elemental standard spectra. The problem of consistently choosing suitable values of m2 is addressed in this paper.
2. Experimental methods and data analysis The spectra used in this study were collected using a computer controlled scanning Auger microscope [9] incorporating a field emission column and a concentric hemispherical electron energy analyser (CHA) [lo]. With the exception of La, which was evaporated in situ, the specimens were cleaned by Ar ion bombardment. Each surface was accurately positioned in the CHA field of view as described elsewhere [4]. Primary energies in the range 16-18 keV and electron beam currents of 2-20 nA were used. The spectra were processed using a digital computer. Each was corrected to compensate for the experimentally determined analyser transmission function
D. C. Peacock / Fitting the inelastic tail
897
[4]. Eq. (1) was fitted to the region above each group of Auger peaks and was then subtracted from N(E). Energy ranges for fitting were identified from linear regions in a plot of log N(E) versus log E. The inelastic tail beneath each group of peaks was calculated iteratively using an expression based on eq. (2) such that the n th approximation was given by dE’,
S,(E)=A,E-m’/6T[N(E’)-B(E’)-S,,_,(E’)] E
subject
(3)
to the constraints
N(E)-B(E)-&(E)=0
(4)
for E = E, and E = E,. The initial approximation was S,,(E) = 0 for all E. A suitable value of E, was found by examination of log N(E) versus log E but the choice was not critical because if too low an initial value was chosen it effectively increased during subsequent iterations. For all the spectra used in this study, eq. (3) converged after five iterations such that subsequent iterations changed the resulting peak areas by less than 3% (fig. 1). The value of m2 was found, after subtraction of the first background B,(E), by fitting a power law
100ms
P LMM
per
point.
5
scans.
Beam
In
current-4nA
MNN
:_‘.‘:
...
r
.x
._;
S4(E) +(E
Fig. 1. Processing of a spectrum from an InP surface shown after subtraction of a power law background B,(E). As S(E) is refined the gradient at E, is more closely matched to that of the background B2( E) which itself forms the background for subtraction from the P Auger peak visible on the left.
898
D. C. Peacock / Fittrng the inelastic tail
to the data [N(E) - B,(E)] for E < E,. This is a new feature method and, strictly, requires that N(E)=AE-“=A,E-“I+A,E-“‘~
for
E
of the present
(5)
This equality is only approximate because in general m, # m2. For example, the In MNN peaks gave m, = 0.85 and m2 = 2.22. Nevertheless, over the range 100 to 400 eV the spectrum obeyed eq. (5) to better than 5%. The foregoing procedure for step remove differs from that proposed by Sickafus [8] which entailed finding S(E) of eq. (2) such that the baseline width (E, - E,) was minimised. However, the method described here has the practical advantage that subtraction of S(E) removes the cascade background from beneath peaks of energy less than E,. Hence, if processing is started with the peak of highest energy in N(E) the above method provides an efficient means of isolating each group of Auger features in turn. Nevertheless, although the above method gives reproducible results in quantitative composition analysis, it should be stressed that the method takes no account of the characteristic loss structure in M(E) and is therefore unsuitable for detailed lineshape analysis.
3. Results and discussion The reproducibility of experimental values of m, was ascertained from a series of five spectra collected from the same sample under identical conditions except that the specimen was deliberately displaced and then repositioned before acquisition of each spectrum. The scatter in values of m, (for the same energy region in each spectrum) was less than + 5%. Values of m, were measured for a wide range of elemental specimens by fitting eq. (1) to a 100 eV wide background region above each Auger peak (fig. 2). In general, the lower the energy of the fitted region the nearer is the value of m, to unity. This is in accord with the fact that the theoretical value m, = 1 was predicted for low energy regions of N(E) but the reason for the fall in m, with increasing energy is not understood. The data of fig. 2 were obtained with an angle of incidence (6) of 45’ while the theory leading to eq. (1) assumed normal incidence. It has been shown elsewhere that values of m, exhibit a rather weak and apparently unsystematic dependence upon 8 [2,4]. For example, for the region above the In MNN peaks obtained from InP, m, tends to increase towards unity as normal incidence is approached (fig. 3a). However, for Ag the value of m, increases with 8 (fig. 3b) and is furthest from unity for normal incidence. This is clearly at variance with the simple theory. The step removal procedure of eq. (3) was applied to each of the spectra collected. Fig. 1, for example, was part of a study of the effect of ion bombardment upon the P : In concentration ratio for InP surfaces [ll]. After subtraction of S,(E), the integrated data were used in determinations of
D.C. Peacock / Fitting the inelastic tail
899
1.2 ml 1.0
0.8
0.6
0.4
400
0
600
1200 RUGER
PERK
1600 ENERGY
2000 (eV)
Fig. 2. Values of m, for elemental specimens obtained by fitting eq. (1) to regions of spectra an Auger peak in energy plotted against the energy of the peak.
above
surface composition which agreed, to within the experimental errors of observation, with results given by measurement of peak-to-peak heights in differential spectra. Finally, the ratio R of the integrated stripped peak area to the height of the
1.0
-
0.6
-
0.6
/ -
A /
/ ‘/ 160 R
0.4
(eV)
140
-
ia0 0
10
20
30 ANGLE
OF
40 50 JNCIDErZCE
60 70 (degrees)
E0
Fig. 3. The angular dependence of m 1 for (a) an InP spectrum (470-570 eV) and (b) an Ag spectrum (400-500 ev). Values of R for the spectra used in (b) are shown in (c).
900
D. C. Peacock
/ Fitting the inelastic tail
“step” (h( ER) of fig. 1) was calculated for each spectrum studied. An analogous ratio has been suggested for non-destructive depth profiling in X-ray photoelectron spectroscopy (XPS) [12]. In the current work, for Auger electron spectroscopy (AES), h was measured at various energies E,. However R was defined, values for elemental specimens exhibited a scatter of over k 30% about the mean value (R = 300 eV if ER was defined as one third the Auger energy). This scatter is greater than expected from the level of statistical fluctuations in the spectra and probably arises because it is difficult to choose ER consistently for a range of spectra which exhibit very different behaviour below Auger peaks in energy. Therefore, in AES, unlike XPS, the measured values of R were not independent of peak energy or specimen material. Furthermore, R depended upon 0 (fig. 3c) and would be unreliable if used for rough surfaces. Compared with R, m2 for the Ag spectra varied only slightly (+ 6%) for angles 13between 0” and 73”. Although values of m2 found for the elemental samples of fig. 1 varied by -t 20% about the mean value of 2.14, the values found when an element was present in only the top few monolayers of a specimen (e.g. C or 0 contamination on a metal surface) were significantly different and near zero. This finding is consistent with the descriptive model due to Sickafus [2] who observed that in such cases the gradient of log N(E) versus log E was the same above and below the peak in energy whereas for elements present below the top few surface layers the gradient is greater below the peak than above. It is concluded that measurement of m, is more promising than use of the ratio R for probing the depth distribution of an element in AES.
Acknowledgements I am grateful to the SERC (UK) for financial support and would like to thank M. Prutton, M.M. El Gomati and C. Walker for many helpful discussions and the part they played in collecting some of the spectra used in this work.
References [l] [2] [3] [4] [5]
P.A. Wolff, Phys. Rev. 95 (1954) 56. E.N. Sickafus, Phys. Rev. B16 (1977) 1436, 1448. R. Hesse, U. Littmark and P. Staib, Appl. Phys. 11 (1976) 233. D.C. Peacock, R. Roberts and M. Prutton, Vacuum 34 (1984) 497. D.E. Ramaker, J.S. Murday and N.H. Turner, J. Electron Spectrosc. (1979) 45. [6] E.N. Sickafus and C. Kukla, Phys. Rev. B19 (1979) 4056. [7] M.C. Burrell and N.R. Armstrong, Appl. Surface Sci. 17 (1983) 53.
Related
Phenomena
17
D. C. Peacock
[8] [9] [lo] (111 [12]
/ Fitting the inelastic tail
E.N. Sickafus, Surface Sci. 100 (1980) 529. M. Prutton, R. Browning, M.M. El Gomati and D.C. Peacock, R. Browning, J. Phys. E (Sci. Instr.) 14 (1981) 58. D.C. Peacock, Vacuum 33 (1983) 601. S. Tougaard and A. Ignatiev, Surface Sci. 129 (1983) 355.
901
Vacuum
32 (1982) 351.
Surface Science 152/153 (1985) 895-901 North-Holland, Amsterdam
FI’ITING THE INELASTIC TAIL BELOW EXPERIMENTALLY OBSERVED AUGER PEAKS D.C. PEACOCK Department of Physics, University of York, Heslington, York YOl SOD, UK Received
27 March
1984; accepted
for publication
24 April 1984
A new iterative procedure enabling the extraction of Auger and associated loss peaks from the secondary electron spectrum N(E) is described and demonstrated. Sections of N(E) away from Auger and loss features are approximated by a cascade of the form AEmm where m is predicted to be unity. For a wide range of elements, experimental values of nr above an Auger peak in energy are found to be less than the theoretical value. After subtraction of the cascade, the step-like feature found beneath the Auger peak and arising from inelastically scattered Auger electrons is calculated. Unlike methods described previously, the procedure described here has the advantage that the fitted tail is forced to closely follow the spectrum below the Auger and loss features in energy. The ratio of the stripped peak area to the increase in background associated with the peak is calculated for the samples used in this study and the prospects of using this ratio for non-destructive depth profiling are discussed.
1. Introduction Two processing stages are necessary before peak areas in the secondary electron spectrum, N(E), can be integrated to give signals proportional to Auger currents. (a) The background, B(E), arising from the cascade of inelastic scattering events in the sample must be subtracted. By extending the analysis due to Wolff [l], Sickafus [2] derived an approximation to this background of the form B,(E)
= AIE-m’,
(1)
where m, is constant for regions of N(E) away from Auger and loss features. This power law was obtained by assuming that: electrons were incident normally upon a planar surface of homogeneous material, the ionization cross-section was of the Bethe form (E-’ log E), and the electron-electron interactions could be described by S-wave scattering. This last assumption should limit the validity of eq. (1) to energies below ca. 100 eV. Nevertheless, power law behaviour has been observed experimentally at energies up to 1000 eV and for various angles of incidence [2]. The present work shows that for 0039-6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
896
D.C. Peacock
/ Fittmg the inelastic tail
primary energies in excess of 15 keV, eq. (1) is a good approximation up to 2000 eV for a wide range of materials although experimentally measured values of m, differ from the theoretical value of unity. Because it has some physical basis, background removal using a least-squares fit of eq. (1) is preferable to the use of more general fitting methods (e.g. ref. [3]) and failure of an experimental spectrum to obey eq. (1) provides a sensitive diagnostic of instrument malfunction [4]. (b) After subtraction of B,(E) from N(E), allowance must be made for the contribution arising from Auger electrons which have undergone energy loss before or during escape from the surface. These electrons give rise to a cascade of the form of eq. (1) at energies below E, which is between 0.3 and 0.5 of the Auger energy. Removal of this contribution requires deconvolution of the instrument-specimen response function, M(E) [5,6], and an economical technique which approximates to this has been suggested recently [7]. This, and other techniques, use a spectrum collected with the primary energy near to the Auger energy of interest in approximating M(E) although this is not always convenient. Moreover, if high spatial resolution is required, limitations in the performance of the electron column may prevent the collection of a pair of spectra with the appropriate primary energies from the same small surface area and with the same spot size. A way round this problem is to subtract from the stripped data a “step” of the form [S] S(E)=$/FIN,(E’)
E
dE’,
where N,(E) is the Auger current at energy E and E, the threshold above which NA( E) = 0. Although eq. (2) is only an approximation to the desired deconvolution it can still be used in quantitative analysis provided that it is applied in a consistent manner to both the specimen of interest and the corresponding elemental standard spectra. The problem of consistently choosing suitable values of m2 is addressed in this paper.
2. Experimental methods and data analysis The spectra used in this study were collected using a computer controlled scanning Auger microscope [9] incorporating a field emission column and a concentric hemispherical electron energy analyser (CHA) [lo]. With the exception of La, which was evaporated in situ, the specimens were cleaned by Ar ion bombardment. Each surface was accurately positioned in the CHA field of view as described elsewhere [4]. Primary energies in the range 16-18 keV and electron beam currents of 2-20 nA were used. The spectra were processed using a digital computer. Each was corrected to compensate for the experimentally determined analyser transmission function
D. C. Peacock / Fitting the inelastic tail
897
[4]. Eq. (1) was fitted to the region above each group of Auger peaks and was then subtracted from N(E). Energy ranges for fitting were identified from linear regions in a plot of log N(E) versus log E. The inelastic tail beneath each group of peaks was calculated iteratively using an expression based on eq. (2) such that the n th approximation was given by dE’,
S,(E)=A,E-m’/6T[N(E’)-B(E’)-S,,_,(E’)] E
subject
(3)
to the constraints
N(E)-B(E)-&(E)=0
(4)
for E = E, and E = E,. The initial approximation was S,,(E) = 0 for all E. A suitable value of E, was found by examination of log N(E) versus log E but the choice was not critical because if too low an initial value was chosen it effectively increased during subsequent iterations. For all the spectra used in this study, eq. (3) converged after five iterations such that subsequent iterations changed the resulting peak areas by less than 3% (fig. 1). The value of m2 was found, after subtraction of the first background B,(E), by fitting a power law
100ms
P LMM
per
point.
5
scans.
Beam
In
current-4nA
MNN
:_‘.‘:
...
r
.x
._;
S4(E) +(E
Fig. 1. Processing of a spectrum from an InP surface shown after subtraction of a power law background B,(E). As S(E) is refined the gradient at E, is more closely matched to that of the background B2( E) which itself forms the background for subtraction from the P Auger peak visible on the left.
898
D. C. Peacock / Fittrng the inelastic tail
to the data [N(E) - B,(E)] for E < E,. This is a new feature method and, strictly, requires that N(E)=AE-“=A,E-“I+A,E-“‘~
for
E
of the present
(5)
This equality is only approximate because in general m, # m2. For example, the In MNN peaks gave m, = 0.85 and m2 = 2.22. Nevertheless, over the range 100 to 400 eV the spectrum obeyed eq. (5) to better than 5%. The foregoing procedure for step remove differs from that proposed by Sickafus [8] which entailed finding S(E) of eq. (2) such that the baseline width (E, - E,) was minimised. However, the method described here has the practical advantage that subtraction of S(E) removes the cascade background from beneath peaks of energy less than E,. Hence, if processing is started with the peak of highest energy in N(E) the above method provides an efficient means of isolating each group of Auger features in turn. Nevertheless, although the above method gives reproducible results in quantitative composition analysis, it should be stressed that the method takes no account of the characteristic loss structure in M(E) and is therefore unsuitable for detailed lineshape analysis.
3. Results and discussion The reproducibility of experimental values of m, was ascertained from a series of five spectra collected from the same sample under identical conditions except that the specimen was deliberately displaced and then repositioned before acquisition of each spectrum. The scatter in values of m, (for the same energy region in each spectrum) was less than + 5%. Values of m, were measured for a wide range of elemental specimens by fitting eq. (1) to a 100 eV wide background region above each Auger peak (fig. 2). In general, the lower the energy of the fitted region the nearer is the value of m, to unity. This is in accord with the fact that the theoretical value m, = 1 was predicted for low energy regions of N(E) but the reason for the fall in m, with increasing energy is not understood. The data of fig. 2 were obtained with an angle of incidence (6) of 45’ while the theory leading to eq. (1) assumed normal incidence. It has been shown elsewhere that values of m, exhibit a rather weak and apparently unsystematic dependence upon 8 [2,4]. For example, for the region above the In MNN peaks obtained from InP, m, tends to increase towards unity as normal incidence is approached (fig. 3a). However, for Ag the value of m, increases with 8 (fig. 3b) and is furthest from unity for normal incidence. This is clearly at variance with the simple theory. The step removal procedure of eq. (3) was applied to each of the spectra collected. Fig. 1, for example, was part of a study of the effect of ion bombardment upon the P : In concentration ratio for InP surfaces [ll]. After subtraction of S,(E), the integrated data were used in determinations of
D.C. Peacock / Fitting the inelastic tail
899
1.2 ml 1.0
0.8
0.6
0.4
400
0
600
1200 RUGER
PERK
1600 ENERGY
2000 (eV)
Fig. 2. Values of m, for elemental specimens obtained by fitting eq. (1) to regions of spectra an Auger peak in energy plotted against the energy of the peak.
above
surface composition which agreed, to within the experimental errors of observation, with results given by measurement of peak-to-peak heights in differential spectra. Finally, the ratio R of the integrated stripped peak area to the height of the
1.0
-
0.6
-
0.6
/ -
A /
/ ‘/ 160 R
0.4
(eV)
140
-
ia0 0
10
20
30 ANGLE
OF
40 50 JNCIDErZCE
60 70 (degrees)
E0
Fig. 3. The angular dependence of m 1 for (a) an InP spectrum (470-570 eV) and (b) an Ag spectrum (400-500 ev). Values of R for the spectra used in (b) are shown in (c).
900
D. C. Peacock
/ Fitting the inelastic tail
“step” (h( ER) of fig. 1) was calculated for each spectrum studied. An analogous ratio has been suggested for non-destructive depth profiling in X-ray photoelectron spectroscopy (XPS) [12]. In the current work, for Auger electron spectroscopy (AES), h was measured at various energies E,. However R was defined, values for elemental specimens exhibited a scatter of over k 30% about the mean value (R = 300 eV if ER was defined as one third the Auger energy). This scatter is greater than expected from the level of statistical fluctuations in the spectra and probably arises because it is difficult to choose ER consistently for a range of spectra which exhibit very different behaviour below Auger peaks in energy. Therefore, in AES, unlike XPS, the measured values of R were not independent of peak energy or specimen material. Furthermore, R depended upon 0 (fig. 3c) and would be unreliable if used for rough surfaces. Compared with R, m2 for the Ag spectra varied only slightly (+ 6%) for angles 13between 0” and 73”. Although values of m2 found for the elemental samples of fig. 1 varied by -t 20% about the mean value of 2.14, the values found when an element was present in only the top few monolayers of a specimen (e.g. C or 0 contamination on a metal surface) were significantly different and near zero. This finding is consistent with the descriptive model due to Sickafus [2] who observed that in such cases the gradient of log N(E) versus log E was the same above and below the peak in energy whereas for elements present below the top few surface layers the gradient is greater below the peak than above. It is concluded that measurement of m, is more promising than use of the ratio R for probing the depth distribution of an element in AES.
Acknowledgements I am grateful to the SERC (UK) for financial support and would like to thank M. Prutton, M.M. El Gomati and C. Walker for many helpful discussions and the part they played in collecting some of the spectra used in this work.
References [l] [2] [3] [4] [5]
P.A. Wolff, Phys. Rev. 95 (1954) 56. E.N. Sickafus, Phys. Rev. B16 (1977) 1436, 1448. R. Hesse, U. Littmark and P. Staib, Appl. Phys. 11 (1976) 233. D.C. Peacock, R. Roberts and M. Prutton, Vacuum 34 (1984) 497. D.E. Ramaker, J.S. Murday and N.H. Turner, J. Electron Spectrosc. (1979) 45. [6] E.N. Sickafus and C. Kukla, Phys. Rev. B19 (1979) 4056. [7] M.C. Burrell and N.R. Armstrong, Appl. Surface Sci. 17 (1983) 53.
Related
Phenomena
17
D. C. Peacock
[8] [9] [lo] (111 [12]
/ Fitting the inelastic tail
E.N. Sickafus, Surface Sci. 100 (1980) 529. M. Prutton, R. Browning, M.M. El Gomati and D.C. Peacock, R. Browning, J. Phys. E (Sci. Instr.) 14 (1981) 58. D.C. Peacock, Vacuum 33 (1983) 601. S. Tougaard and A. Ignatiev, Surface Sci. 129 (1983) 355.
901
Vacuum
32 (1982) 351.