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Background calculation for X-ray photoelectron spectra analysis
Journal
of Electron
Elsevier
Science
327
Spectroscopy and Related Phenomena, 59 (1992) 327-340
Publishers
B.V.,
Amsterdam
Background calculation spectra analysis
for X-ray photoelectron
A. Jouaiti, A. Mosser, M. Romeo and S. Shindol I.P.C.M.S, Pascal,
Groupe Surfaces-Interfaces, U.M. 380046, Universiti Louis Pasteur, 4 rue Blaise
F 67070 Strasbourg (France)
(First received
29 July 1991; in final form 4 March
1992)
Abstract We develop a fitting method for the background calculation of XPS spectra in order to determine the line shape and peak intensity of the primary emission. We compare the spectra theoretically and experimentally, using various methods based on the multiple inelastic scattering theory. We determine the inelastic background parameter, i.e. the ratio of the elastic peak area to the height of inelastic background, with which we compare the results of theoretical calculations. We investigate the contribution of surface excitations to the background formation using angle-resolved X-ray photoelectron spectra.
INTRODUCTION
Auger electron spectroscopy (AES) and X-ray ghotoelectron spectroscopy (XPS) are widely used techniques in the analysis of the surface properties of solids [l].By irradiation with photons or by bombardment with electrons or ions, electrons are excited in the solid, and the emitted electrons carry information on the physical and chemical properties of the solid. During the transport of the electrons from the point of excitation to the surface, the electron energy distribution is distorted due to inelastic scattering events. The accurate removal of the background contribution to a spectrum is a process that must be carried out with care because, except in the case of the trivial removal of a horizontal background, it may involve distortion of the data when applied incorrectly [2]. Any background removal will alter absolute peak intensities and will cause problems in
Correspondence too:A. Mosser, I.P.C.M.S., Groupe Surfaces-Interfaces, site Louis Pasteur, 4 rue Blaise Pascal, F 67070 Strasbourg, France. 1Permanent address: Tokyo Gakugei University, Tokyo 184, Japan.
036%2048/92/$05.00
0
1992 Elsevier
Science
Publishers
B.V.
U.M.
380046, Univer-
All rights reserved.
328
A. Jouaiti et al./J. Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
quantitation. At present there is no sure way of removing a background and the whole process remains controversial. The most common method of background subtraction, often called the Shirley method [3], considers the background due to inelastically scattered electrons. It assumes the background at a given energy to be proportional to the integrated photoelectron intensity of higher kinetic energy. However, Shirley did not make clear the physical meaning of his method. Many authors 14-111 have proposed other methods for subtracting the background; for example, by describing the inelastic scattering of electrons using the dielectric function [7,8]. In the present work we developed a fitting method in order to determine the line shape and peak intensity of the primary emission and also the contribution of the background intensity. The inelastic background parameter, i.e. the ratio of the elastic peak area to the height of inelastic background, was determined and compared with the theoretical calculations. We investigated the contribution of surface excitations to the background formation using angle-resolved X-ray photoelectron spectra. THEORY
An observed electron current J(E), where E is the electron kinetic energy, is composed of a zero-loss (elastic) part J”‘(E), and a background (inelastic) part P”l(E) J(E)
=
J”‘(E)
+ CPl(E)
(1)
The true spectrum at the localized point of emission appears in the elastic represents the distortion of the spectrum part Je’, and the inelastic part JineL due to the inelastic scattering of emitted electrons. The primary direction of emitted electrons will change due to phonon (pseudo-elastic) scatterings; the effect of this on the background intensity has been considered theoretically by several authors [4,6,9,10]. In the present paper we assume a straight-line motion of the emitted electrons. X-ray excited photoelectrons are created at localized sources, which are distributed in solids as given by g(R). The primary energy spectrum at the point of the electron emission is written as fO(E). The observed spectrum is the superposition of each individual emission J(E)
=
JJG(E -
E’, R)g(R) f O(E’) dE’ dR
(2)
where G(E,R) is a propagator which satisfies the transport equation dG dR=-
j K(E’ -
and K(E)
is the loss function
E)G(E,R)
dE’ + I K(E
-
E’)G(E’,R)
dE’
and represents the probability
that the
A. Jouaiti et al./J. Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
329
electron loses energy E per unit path length. This equation is solved and gives Landau’s formula [4]
WC@
syrn exp(-
=
RX(s) -
isE) &
(4)
where Z(s)
=
Jr K(E)(l
-
exp(isE)) dE = R(O) -
R(s)
(5)
and R(s) is the Fourier transform of K(E). The electron current J(E) can, in principle, be calculated when the depth distribution of the emitters g(R) is given and when details of the loss function K(E) are known. In order to obtain the elastic line shape J”‘(E) of eqn. (1) from the experimentally observed spectrum J(E), two methods can be considered. The first one is called the “inversion method” and has been developed by Tougaard and co-workers [4,5,7,8,11], i.e.
J”‘(E)
=
J(E)
where F’(E)
F’(E)
=
- 1; F’(E’ - E)J(E’)
dE’
(6a)
can be represented using g(R) and K(E)
{Tm P’(s)episE &
where
F’(s)
e-R'o)Rg(R)
=
d-R
In this method, the elastic spectrum of the primary emission P’(E) can be determined by direct substitution of the experimental spectrum in J(E) of eqns. (6), i.e. by subtraction of the calculated background from the experimental spectrum. This method requires that the energy-loss function K(E), the determination of which is still problematic both theoretically and experimentally, is precisely known. Moreover, the effect of surface excitation cannot be described by eqns. (6). Therefore we investigated an alternative method for calculating the background, called the “fitting method”. In this method we first assume that the shape of the elastic emission J”‘(E), which in our case is given by the Doniach-Sunjic (DS) [12] theory, is known a priori_ This quantity is inserted in the following formula, which is mathematically equivalent to eqns. (6) J(E)
=
J”‘(E)
+ Is+ F(E
- E’)P1(E’)
dE’
(7a)
330
A. Jouaiti et al./J. Electron S’C~FOSG. R&at. Phenom. 59 (1992) 327-340
where F(E) is given by
s-%, F(s)eeisE &
F(E) =
(7b)
where
I: e
F(s) =
- (40)-&@)Rg(JQ dR _ 1
I,” e -K’O’Rg(B)dR
(7c)
i
Then, the calculated spectrum J(E) is compared with the experimental one. The parameters a and y of the DS theory and the parameter of the energyloss function are self-consistently determined to give the best fit with the calculation and experiment. This is done by minimization of a merit function, which in our case is a x2 test. In order to determine the various parameters, this method needs more computation time in comparison with the inversion method. However, as the true K(E) cannot be known in almost all cases, our fitting method (eqns. (7)) has an advantage for the actual XPS analysis. Now, let us restrict ourselves, in the present article, to the case where the X-ray excited electrons are emitted from semi-infinite homogeneous sources, which represents a typical XPS experiment from a single element. In this case, the distribution of the emitter g(R) is g(R) = goB(R) where B(R) is the step function and R = 0 represents the surface position. Substituting this into eqns. (2) and (7), the elastic and inelastic parts of the electron current are given by
and p”‘(E)
=
md
O” I--OD R(0)
- R(s)
J”‘(s) exp( - iEs) &
respectively. The inelastic mean free path of electrons 1 is represented by 1 = l/(R(O)). It can be seen from eqn. (8) that the inelastic mean free path represents the escape distance of the elastic electrons. Shirley
background
Now, let us derive a simple analytic expression for the background signal represented by F(E) of eqn. (7). Let us first assume that multiple inelastic scatterings during the transport of the emitted electrons before arriving to the surface are dominant. In this case, we may expand R(s) in eqn. (9)
A. Jouaiti
et al.]J. Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
331
around s = 0, then JineL(E) N [ym -
s$)
J”‘(s) exp(-isE)
&
=
-:, lrm J”(E’)
dE’ (10)
where D is given by D
=
J‘,”EK(E) dE = AS I,” K(E) dE
(11)
and S is the stopping power of the solids, defined as S
=
jorn EK(E)
dE
02)
Equation (10) is identical to Shirley’s [3] formula, which is commonly used for XPS line-shape analysis. It should be remarked that Shirley’s formula can be applied only to the semi-infinite homogeneous solids. Note that the D value defined by the above formula gives the ratio of the total intensity of the elastic electrons to the height of the background far from the elastic peak, i.e. D=
s
mmJ.‘(E’)
dE’
(13)
Jinel(E )
It has been shown experimentally 151that the D value (hereaRer called the “inelastic background parameter”) defined by eqn. (13) is nearly independent of the electron kinetic energy, the metal and the line shapes. This can be derived theoretically from eqn. (11) by considering that the mean free path A_is nearly proportional to the electron kinetic energy and the stopping power S is inversely proportional to the kinetic energy. Therefore, the D value is approximately constant with respect to kinetic energy. In order to derive Shirley’s formula in eqn. (lo), we used the “large energy loss” approximation which is valid in the spectral region where the energy loss is larger than the D value. For the experimental determination of the XPS line shape, the-“small energy loss” region is more important because the elastic line shape J”’ can be determined by subtraction of the background in this region. Tougaard and coworkers [4-111 proposed the inversion method (eqn. (6)) for background subtraction, which in the case of the homogeneous infinite emitters becomes sin”‘(E)
=
J; AK(E’ -
E)J(E’)
dE’
(14)
However, this method is very sensitive to the choice of the loss function K(E). Conversely, in our fitting method (eqns. (7)), the multiple scattering effect spreads out the structure of the loss function. This can be confirmed
A. Jouaiti et al./J. Electron
332
Spectrosc.
Relat. Phenom.
59 (1992) 327-340
when we improve the approximation in eqn. (10)by P”‘(E)
m K(s)P(s) i‘ -a sR(0)
N
1 =Do
E ;2.
E-E’
i0
I
exp( - i&3) &
U5d
dE”J”‘(E’)
K(E”)
dE’
(15b)
Although this improvement is not valid in the small-energy-loss region, we quantitatively see that any structures in the loss function K(E) will be spread out over the background due to the integration in eqn. (14).For this reason some simplified analytic functions representing the global characteristics can be applied instead of the real energy-loss function K(E). When we choose an exponential decreasing function for K(E) K(E)
=
K, exp( --ET)
(16)
we reconfirm Shirley’s formula (eqn. (10))by its substitution in eqn. (9). Tougaard-Sigmund
background
The energy-loss function of eqn. (16)does not represent a true tendency of the loss function, the value of which becomes zero at the zero value of the lost energy E = 0.For metals, the loss function is proportional to the lost-energy value when it is small, it then goes through a maximum and decreases for high lost energy. Therefore, we chose the model function defined by K(E)
=
K,E
exp(-
Ez)
(17)
By substitution in eqn. (9) this model yields the inelastic electron current
P”(E)
= i
I_“, [l
- exp (-
4(E - E’) D
>IP(E’) dE’
(18)
This model energy loss function (eqn. (17)) and eqn. (18) were obtained by Tougaard and Sigmund [4]. In the present experimental analysis we compared the XPS line shapes and the background parameters D by using the two background formulae: Shirley’s formula (eqn. (10)) and Tougaard and Sigmund’s (TS) model (eqn. (18)). Calculation
of
the background
parameter
D
From eqn. (ll), the background parameter D may be calculated by multiplying the two quantities the mean free path R and the stopping power S. However, there is a more direct method of calculating D when using the TS model (eqn. (17)). We describe the loss function K(E) using the dielectric
A. Jouaiti et d/J.
Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
333
function e as K(fio)
=
1
r&E
Jkma’ 1 Im kin
(19)
k
where E is the kinetic energy of excited electrons, k,, = 2(2m~?3)“~/h and k,, = (~z/ZE)~‘~ w. Now, let us apply the two sum rules, the “oscillator strength sum rule” and “perfect screening sum rule”, for the dielectric function, which are written 113) as
s
%lax
w
0
Im
-’ 4k,
dw
=
;a:
(204
0)
and W-X I0
-’ dw E(JZ,a)
=_;
respectively, where
cw and Z,, is the effective number of electrons per atom contributing to the inelastic scatterings and is a function of the maximum transferred energy hU,,. If co_, = co, Z,, should be equal to the atomic number of the solid. According to the TS model (eqn. (17)), the result of the integrations in eqns. (20) becomes
Wb) The background parameter D is therefore given by D
=
f = fi(ttw,)
(23)
Although the numerical factor in eqn. (23), i.e. 3, depends on the choice of the model function of eqn. (17) for K(E), the calculated D value in eqn. (23), i.e. D M wo, represents the physical aspect of the D value which is the mean energy loss value in the single inelastic scattering. When we choose Z,, as the number of valence electrons per atom, we obtain D = 50.7, 41.8 and 42.8 eV for copper, silver and gold, respectively, where Z,, = 11 for these three metals. These values are close to those calculated by Tougaard [14], even though we used a special model for the energy-loss function. EXPERIMENTAL
XPS spectra were recorded using a Cameca-Riber Nanoscan-50 apparatus
334
A.
Jouaiti
et al&T. Electron
Spectrosc.
Relat.
Phenom.
59 (1992)
327-340
equipped with a twin Al/Mg Ka source and a MAC 2 analyser, which was set at 1 eV energy resolution. The analyser was calibrated before recording the spectra and no further energy calibration was done. All measurements were done in the same configuration of the X-ray source, the sample and the analyser positions. The photoelectron current was integrated over variable angles ranging from O” to 7’5Owith respect to the normal direction of the sample. The XPS lines were decomposed using a curve-fitting procedure based on Doniach-Sunjic (DS) 1121 theory. This procedure includes (1) the simulation of the photoelectron line (f’(E) of eqn. (2)) by an asymmetrical Lorentzian curve (Doniach-Sunjic lineshape [12]) characterized by the asymmetry parameter a and the line width y; (2) the simulation of the background due to inelastic scatterings; (3) the experimental analyser resolution simulated by a Gaussian curve; and (4) the X-ray-source broadening approximated by four Lorentzian curves corresponding to Ka, , Ka,, Ka, and Ka, lines. The fitting of our experimental spectrum with a DS line shape was performed using the Simplex search method [15]. The first iteration is composed of the following elementary steps: (i) the DS line is generated using an initial good guess of the parameters N and y; (2) the background energy distribution is calculated from the latter function using any of the proposed energy-loss distributions F(E) and an initial value for the inelastic background parameter D; (3) the sum of the previous distributions with the source and the experimental analyser resolution functions is convoluted - these convolutions are done by fast Fourier convolution (multiplication of the Fourier transformations of the functions to be convoluted, and inverse Fourier transformation of the resulting function); and (4) at this step a merit function (x2 test) is computed and a new set of parameters is generated using the Simplex search method. For subsequent iterations steps (1)to (4)are repeated with the new parameter set until the minimum of the merit function is reached. Figure 1 shows the result of fitting the Au4f,,, and Au4f,,, peaks using a Shirley background. The fit agreement is 98.31% (the normalized value of the merit function (100%) means that the calculated and experimental spectra are exactly the same). Similarly, Fig. 2 shows the result of fitting the same lines using a TS background. The fit agreement (98.49%) is of the same order as before, even though the shapes of the backgrounds are quite different. The y, a, peak area and D value obtained with the two methods are compared in Table 1. It can be seen that the a values obtained with the TS method are higher than those obtained with the Shirley method. The areas of the elastic peak differ only a little between the two methods. By comparing the peak areas in Figs. 1 and 2, it may be expected that the D value
335
A. Jouaiti et al./J. Electron Spectrosc. Relut. Phenom. 53 (1992) 327-340
UA
l-
-.
-.c-_-_
-_
--__.-.__
_---
100 Binding
eV
Energy
Fig. 1. The fitting of the Au4f,,2 and Au4f,,, peaks using the Shirley background method.
obtained with the TS model should be larger than that obtained with Shirley’s model, because the D value is obtained as the ratio of the peak area to the height of the inelastic background. However, due to the mismatch of our fit with the experimental spectrum, which may be due to the limitation of the DS line and the model energy-loss function, the D values obtained with the two methods are nearly the same. Because the detailed structure of the energy-loss function is spread out over the observed spectrum, the parameter characterizing the global shape of the energy-loss function does not strongly depend on the chosen model in our experimental condition. However, from the physical point of view, the TS model obviously has an advantage in that the shape of the energy loss function is more properly simulated by this model than by Shirley’s method.
A. Jouaiti et al.]J. Ekctron
Spectrosc.
337
59 (1992)327-340
ReZat. Phenom.
TABLE 1 Comparison of the experimental DS parameter (Y, 01),peak areas and D values obtained with the two background subtraction models (Shirley and TS) Parameter
Kinetic energy (eV) Y Geak area (%) l3 (eV)
Shirley background
TS background
Au4f,,,
Au4f,,,
Au4f,,z
Au4f,,,
1402.91
1399.24
1402.93
1399.25
0.13 0 56.6
0.12 0 43.3
0.12 0.03 55.9
0.16 0.02 44 26.2
28
where the kinetic energy dependence through Z,, is negligibly small. In addition, the D value does not depend on the nature of the metal, with both backgrounds being as would be expected theoretically. This may be due to the dielectric function of the metals analysed being similar. In the case of semiconductors or insulators, a more realistic model must be used for the loss function. Quantitatively, the calculated D values are larger than the
P
0 0
cab
x”
X
8”
Au
iP
xx
5%
m
0
Fig. 3. Plot of the determined background parameters (D values) as a function of the electron kinetic energy for different peaks obtained on several homogeneous metals (gold, silver, copper and platinum).
338
A. Jouaiti et d/J.
Electron S’pectrosc. Relat. Phenont. 59 (1992) 327-340
experimentally obtained values. This may be due to some other contribution to the background formation, e.g. surface excitations (see next section). BACKGROUND
CAUSED
BY SURFACE
EXCITATION
As seen in the previous section, our theory does not fully explain our experimental results, i.e. the calculated D value does not agree quantitatively with the experimenta values. This may be explained by surface excitation, which was not taken into account in our theory. Qualitatively speaking, electrons leaving the surface are also inelastically scattered because of the surface plasmon excitation. This effect may reduce the elastic contribution (peak area) of the spectrum and give a lower D value. By applying the well known theory of surface excitation [173, we can calculate the attenuation of the measured elastic intensity Je’ due to the surface plasmon excitation (24)
where J&k is the elastic intensity at the surface, v is the velocity of the elastic electrons, and 8 is the angle of emission measured with respect to the surface. Due to this additional attenuation of the elastic intensity, the experimental inelastic background parameter (the D value defined by eqn. (13)) is decreased by
(25) where D,,, represents the bulk D value defined by eqn. (11). Using this formula we predict that the D value depends on the emission angle of the electron when angle-resolved X-ray photoelectron spectra are measured. Figure 4 shows the angle-resolved X-ray photoemission spectra of the Au4f peaks recorded at 0 = 10Q, 35O and 60°. For this measurement we closed the analyser entrance with a shutter bored with a small hole (2 mm diameter). From this experiment it is obvious that the background increases when the emission angle decreases. The D values obtained from these spectra, using the TS model, are O(8. = loo) = 19.5, L)(e = 3!7’) = 39.5 and O(0 = 60°) = 45.5 eV. It can be shown that this experimental variation of the D value with respect to the &mission angle can be explained by eqn. (25). The D value due to the bulk excitation D,,, is determined from this experiment as Dbulk= 53 eV, which is relatively close to the calculated value (D = 42.8eV). It should be noted that in our theory we used the straight-path approximation, which neglects the effect of elastic scattering. Nevertheless, as the
A.
Jouaiti
et aL.jJ.
Electron
&WCtFOSC. Relat.
10
Phenom.
59 (1992)
327-340
339
Deg.
Fig. 4. Angle-resolved X-ray photoemission spectra of the Au4f,,, three different emission angles: 8 = 100, 0 = 35O and 8 = 600.
and Au4f,,,
peaks taken at
elastic scattering cross-section is independent of the emergence angle of electrons [4,6,9,10] it is not possible to explain the background variation in terms of this effect. However, coherent elastic-scattering effects, such as surface reflection and diffraction, may affect the intensity of elastic electrons J”’ and change the D values. But these phenomena are only important in the low-kineticenergy cases and can be ignored in the present experimental conditions. According to the above discussion, we may conclude that the surface plasmon excitation is very important in the formation of the ‘inelastic background and that this effect on the inelastic background parameter can be taken into account to a first approximation by using eqn. (25). CONCLUSIONS
AND
DISCUSSION
We have developed an inelastic-background calculation method, called the “fitting method”. Using this method we can determine the elastic line shape parameters of the primary emission (assuming a Doniach-Sunjic line shape) and the inelastic background parameter D. In addition, we have given a theoretical basis for the most common method, i.e. Shirley’s background subtraction method [3]. We have confirmed that the inelastic background parameter (D value) does not depend on the electron kinetic energy, to a first approximation. Moreover, we have theoretically and experimentally pointed out the importance for the XPS background formation of the surface plasmon excitations. It should be noted that our present
340
A. Jouaiti
et al.lJ.
Et?ectron Spectrosc.
Relut. Phenom.
59 (1992) 327-340
theory is not well suited for finite coverage layers. In future work we will extend the theory to finite-thickness cases, and apply it to metal adlayers on metallic substrates. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
M-P, Seah and D. Briggs, in D. Briggs and M.P. Seah (Eds.), Practical Surface Analysis, Wiley, New York, 1983. P.M.A. Sherwood, in D. Briggs and M.P. Seah (Eds.), Practical Surface Analysis, Wiley, New York, 1983. D.A. Shirley, Phys. Rev. B, 5( 1972) 4709. S. Tougaard and P. Sigmund, Phys. Rev. B, 25 (1982) 4452. S. Tougaard and A. Ignatiev, Surf. Sci., 129 (1983) 582. V.M. Dwyer and J.A.D. Matthew, Surf. Sci., 143 (1984) 57. S. Tougaard, Surf. Sci., 139 (1984) 208. S. Tougaard and B. Jorgensen, Surf. Sci., 143 (1984) 482. A.L. Tofterup, Surf. Sci., 167 (1986) 70. V.M. Dwyer and J.A.D. Matthew, Surf. Sci., 193 (1988) 534. S. Tougaard, Surf. Sci., 216 (1989) 343. S, Doniach and M. Sunjic, J. Phys. C, 3 (1970) 291. S. Tanuma, C.J. Powell and D.R. Penn, Surf. Interface Anal., 11 (1988) 577. S. Tougaard, J. Vat. Sci. Technol. A, 5 (1987) 1275. M. Romeo, P. Legare and J. Majerus, Surf. Interface Anal., submitted, 1992. S. Tougaard, J. Electron Spectrosc. Relat. Phenom., 52 (1990) 243. R. Kawai, N. Itoh and Y.H. Ohtsuki, Surf. Sci., 114 (1982) 137.
of Electron
Elsevier
Science
327
Spectroscopy and Related Phenomena, 59 (1992) 327-340
Publishers
B.V.,
Amsterdam
Background calculation spectra analysis
for X-ray photoelectron
A. Jouaiti, A. Mosser, M. Romeo and S. Shindol I.P.C.M.S, Pascal,
Groupe Surfaces-Interfaces, U.M. 380046, Universiti Louis Pasteur, 4 rue Blaise
F 67070 Strasbourg (France)
(First received
29 July 1991; in final form 4 March
1992)
Abstract We develop a fitting method for the background calculation of XPS spectra in order to determine the line shape and peak intensity of the primary emission. We compare the spectra theoretically and experimentally, using various methods based on the multiple inelastic scattering theory. We determine the inelastic background parameter, i.e. the ratio of the elastic peak area to the height of inelastic background, with which we compare the results of theoretical calculations. We investigate the contribution of surface excitations to the background formation using angle-resolved X-ray photoelectron spectra.
INTRODUCTION
Auger electron spectroscopy (AES) and X-ray ghotoelectron spectroscopy (XPS) are widely used techniques in the analysis of the surface properties of solids [l].By irradiation with photons or by bombardment with electrons or ions, electrons are excited in the solid, and the emitted electrons carry information on the physical and chemical properties of the solid. During the transport of the electrons from the point of excitation to the surface, the electron energy distribution is distorted due to inelastic scattering events. The accurate removal of the background contribution to a spectrum is a process that must be carried out with care because, except in the case of the trivial removal of a horizontal background, it may involve distortion of the data when applied incorrectly [2]. Any background removal will alter absolute peak intensities and will cause problems in
Correspondence too:A. Mosser, I.P.C.M.S., Groupe Surfaces-Interfaces, site Louis Pasteur, 4 rue Blaise Pascal, F 67070 Strasbourg, France. 1Permanent address: Tokyo Gakugei University, Tokyo 184, Japan.
036%2048/92/$05.00
0
1992 Elsevier
Science
Publishers
B.V.
U.M.
380046, Univer-
All rights reserved.
328
A. Jouaiti et al./J. Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
quantitation. At present there is no sure way of removing a background and the whole process remains controversial. The most common method of background subtraction, often called the Shirley method [3], considers the background due to inelastically scattered electrons. It assumes the background at a given energy to be proportional to the integrated photoelectron intensity of higher kinetic energy. However, Shirley did not make clear the physical meaning of his method. Many authors 14-111 have proposed other methods for subtracting the background; for example, by describing the inelastic scattering of electrons using the dielectric function [7,8]. In the present work we developed a fitting method in order to determine the line shape and peak intensity of the primary emission and also the contribution of the background intensity. The inelastic background parameter, i.e. the ratio of the elastic peak area to the height of inelastic background, was determined and compared with the theoretical calculations. We investigated the contribution of surface excitations to the background formation using angle-resolved X-ray photoelectron spectra. THEORY
An observed electron current J(E), where E is the electron kinetic energy, is composed of a zero-loss (elastic) part J”‘(E), and a background (inelastic) part P”l(E) J(E)
=
J”‘(E)
+ CPl(E)
(1)
The true spectrum at the localized point of emission appears in the elastic represents the distortion of the spectrum part Je’, and the inelastic part JineL due to the inelastic scattering of emitted electrons. The primary direction of emitted electrons will change due to phonon (pseudo-elastic) scatterings; the effect of this on the background intensity has been considered theoretically by several authors [4,6,9,10]. In the present paper we assume a straight-line motion of the emitted electrons. X-ray excited photoelectrons are created at localized sources, which are distributed in solids as given by g(R). The primary energy spectrum at the point of the electron emission is written as fO(E). The observed spectrum is the superposition of each individual emission J(E)
=
JJG(E -
E’, R)g(R) f O(E’) dE’ dR
(2)
where G(E,R) is a propagator which satisfies the transport equation dG dR=-
j K(E’ -
and K(E)
is the loss function
E)G(E,R)
dE’ + I K(E
-
E’)G(E’,R)
dE’
and represents the probability
that the
A. Jouaiti et al./J. Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
329
electron loses energy E per unit path length. This equation is solved and gives Landau’s formula [4]
WC@
syrn exp(-
=
RX(s) -
isE) &
(4)
where Z(s)
=
Jr K(E)(l
-
exp(isE)) dE = R(O) -
R(s)
(5)
and R(s) is the Fourier transform of K(E). The electron current J(E) can, in principle, be calculated when the depth distribution of the emitters g(R) is given and when details of the loss function K(E) are known. In order to obtain the elastic line shape J”‘(E) of eqn. (1) from the experimentally observed spectrum J(E), two methods can be considered. The first one is called the “inversion method” and has been developed by Tougaard and co-workers [4,5,7,8,11], i.e.
J”‘(E)
=
J(E)
where F’(E)
F’(E)
=
- 1; F’(E’ - E)J(E’)
dE’
(6a)
can be represented using g(R) and K(E)
{Tm P’(s)episE &
where
F’(s)
e-R'o)Rg(R)
=
d-R
In this method, the elastic spectrum of the primary emission P’(E) can be determined by direct substitution of the experimental spectrum in J(E) of eqns. (6), i.e. by subtraction of the calculated background from the experimental spectrum. This method requires that the energy-loss function K(E), the determination of which is still problematic both theoretically and experimentally, is precisely known. Moreover, the effect of surface excitation cannot be described by eqns. (6). Therefore we investigated an alternative method for calculating the background, called the “fitting method”. In this method we first assume that the shape of the elastic emission J”‘(E), which in our case is given by the Doniach-Sunjic (DS) [12] theory, is known a priori_ This quantity is inserted in the following formula, which is mathematically equivalent to eqns. (6) J(E)
=
J”‘(E)
+ Is+ F(E
- E’)P1(E’)
dE’
(7a)
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A. Jouaiti et al./J. Electron S’C~FOSG. R&at. Phenom. 59 (1992) 327-340
where F(E) is given by
s-%, F(s)eeisE &
F(E) =
(7b)
where
I: e
F(s) =
- (40)-&@)Rg(JQ dR _ 1
I,” e -K’O’Rg(B)dR
(7c)
i
Then, the calculated spectrum J(E) is compared with the experimental one. The parameters a and y of the DS theory and the parameter of the energyloss function are self-consistently determined to give the best fit with the calculation and experiment. This is done by minimization of a merit function, which in our case is a x2 test. In order to determine the various parameters, this method needs more computation time in comparison with the inversion method. However, as the true K(E) cannot be known in almost all cases, our fitting method (eqns. (7)) has an advantage for the actual XPS analysis. Now, let us restrict ourselves, in the present article, to the case where the X-ray excited electrons are emitted from semi-infinite homogeneous sources, which represents a typical XPS experiment from a single element. In this case, the distribution of the emitter g(R) is g(R) = goB(R) where B(R) is the step function and R = 0 represents the surface position. Substituting this into eqns. (2) and (7), the elastic and inelastic parts of the electron current are given by
and p”‘(E)
=
md
O” I--OD R(0)
- R(s)
J”‘(s) exp( - iEs) &
respectively. The inelastic mean free path of electrons 1 is represented by 1 = l/(R(O)). It can be seen from eqn. (8) that the inelastic mean free path represents the escape distance of the elastic electrons. Shirley
background
Now, let us derive a simple analytic expression for the background signal represented by F(E) of eqn. (7). Let us first assume that multiple inelastic scatterings during the transport of the emitted electrons before arriving to the surface are dominant. In this case, we may expand R(s) in eqn. (9)
A. Jouaiti
et al.]J. Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
331
around s = 0, then JineL(E) N [ym -
s$)
J”‘(s) exp(-isE)
&
=
-:, lrm J”(E’)
dE’ (10)
where D is given by D
=
J‘,”EK(E) dE = AS I,” K(E) dE
(11)
and S is the stopping power of the solids, defined as S
=
jorn EK(E)
dE
02)
Equation (10) is identical to Shirley’s [3] formula, which is commonly used for XPS line-shape analysis. It should be remarked that Shirley’s formula can be applied only to the semi-infinite homogeneous solids. Note that the D value defined by the above formula gives the ratio of the total intensity of the elastic electrons to the height of the background far from the elastic peak, i.e. D=
s
mmJ.‘(E’)
dE’
(13)
Jinel(E )
It has been shown experimentally 151that the D value (hereaRer called the “inelastic background parameter”) defined by eqn. (13) is nearly independent of the electron kinetic energy, the metal and the line shapes. This can be derived theoretically from eqn. (11) by considering that the mean free path A_is nearly proportional to the electron kinetic energy and the stopping power S is inversely proportional to the kinetic energy. Therefore, the D value is approximately constant with respect to kinetic energy. In order to derive Shirley’s formula in eqn. (lo), we used the “large energy loss” approximation which is valid in the spectral region where the energy loss is larger than the D value. For the experimental determination of the XPS line shape, the-“small energy loss” region is more important because the elastic line shape J”’ can be determined by subtraction of the background in this region. Tougaard and coworkers [4-111 proposed the inversion method (eqn. (6)) for background subtraction, which in the case of the homogeneous infinite emitters becomes sin”‘(E)
=
J; AK(E’ -
E)J(E’)
dE’
(14)
However, this method is very sensitive to the choice of the loss function K(E). Conversely, in our fitting method (eqns. (7)), the multiple scattering effect spreads out the structure of the loss function. This can be confirmed
A. Jouaiti et al./J. Electron
332
Spectrosc.
Relat. Phenom.
59 (1992) 327-340
when we improve the approximation in eqn. (10)by P”‘(E)
m K(s)P(s) i‘ -a sR(0)
N
1 =Do
E ;2.
E-E’
i0
I
exp( - i&3) &
U5d
dE”J”‘(E’)
K(E”)
dE’
(15b)
Although this improvement is not valid in the small-energy-loss region, we quantitatively see that any structures in the loss function K(E) will be spread out over the background due to the integration in eqn. (14).For this reason some simplified analytic functions representing the global characteristics can be applied instead of the real energy-loss function K(E). When we choose an exponential decreasing function for K(E) K(E)
=
K, exp( --ET)
(16)
we reconfirm Shirley’s formula (eqn. (10))by its substitution in eqn. (9). Tougaard-Sigmund
background
The energy-loss function of eqn. (16)does not represent a true tendency of the loss function, the value of which becomes zero at the zero value of the lost energy E = 0.For metals, the loss function is proportional to the lost-energy value when it is small, it then goes through a maximum and decreases for high lost energy. Therefore, we chose the model function defined by K(E)
=
K,E
exp(-
Ez)
(17)
By substitution in eqn. (9) this model yields the inelastic electron current
P”(E)
= i
I_“, [l
- exp (-
4(E - E’) D
>IP(E’) dE’
(18)
This model energy loss function (eqn. (17)) and eqn. (18) were obtained by Tougaard and Sigmund [4]. In the present experimental analysis we compared the XPS line shapes and the background parameters D by using the two background formulae: Shirley’s formula (eqn. (10)) and Tougaard and Sigmund’s (TS) model (eqn. (18)). Calculation
of
the background
parameter
D
From eqn. (ll), the background parameter D may be calculated by multiplying the two quantities the mean free path R and the stopping power S. However, there is a more direct method of calculating D when using the TS model (eqn. (17)). We describe the loss function K(E) using the dielectric
A. Jouaiti et d/J.
Electron Spectrosc. Relat. Phenom. 59 (1992) 327-340
333
function e as K(fio)
=
1
r&E
Jkma’ 1 Im kin
(19)
k
where E is the kinetic energy of excited electrons, k,, = 2(2m~?3)“~/h and k,, = (~z/ZE)~‘~ w. Now, let us apply the two sum rules, the “oscillator strength sum rule” and “perfect screening sum rule”, for the dielectric function, which are written 113) as
s
%lax
w
0
Im
-’ 4k,
dw
=
;a:
(204
0)
and W-X I0
-’ dw E(JZ,a)
=_;
respectively, where
cw and Z,, is the effective number of electrons per atom contributing to the inelastic scatterings and is a function of the maximum transferred energy hU,,. If co_, = co, Z,, should be equal to the atomic number of the solid. According to the TS model (eqn. (17)), the result of the integrations in eqns. (20) becomes
Wb) The background parameter D is therefore given by D
=
f = fi(ttw,)
(23)
Although the numerical factor in eqn. (23), i.e. 3, depends on the choice of the model function of eqn. (17) for K(E), the calculated D value in eqn. (23), i.e. D M wo, represents the physical aspect of the D value which is the mean energy loss value in the single inelastic scattering. When we choose Z,, as the number of valence electrons per atom, we obtain D = 50.7, 41.8 and 42.8 eV for copper, silver and gold, respectively, where Z,, = 11 for these three metals. These values are close to those calculated by Tougaard [14], even though we used a special model for the energy-loss function. EXPERIMENTAL
XPS spectra were recorded using a Cameca-Riber Nanoscan-50 apparatus
334
A.
Jouaiti
et al&T. Electron
Spectrosc.
Relat.
Phenom.
59 (1992)
327-340
equipped with a twin Al/Mg Ka source and a MAC 2 analyser, which was set at 1 eV energy resolution. The analyser was calibrated before recording the spectra and no further energy calibration was done. All measurements were done in the same configuration of the X-ray source, the sample and the analyser positions. The photoelectron current was integrated over variable angles ranging from O” to 7’5Owith respect to the normal direction of the sample. The XPS lines were decomposed using a curve-fitting procedure based on Doniach-Sunjic (DS) 1121 theory. This procedure includes (1) the simulation of the photoelectron line (f’(E) of eqn. (2)) by an asymmetrical Lorentzian curve (Doniach-Sunjic lineshape [12]) characterized by the asymmetry parameter a and the line width y; (2) the simulation of the background due to inelastic scatterings; (3) the experimental analyser resolution simulated by a Gaussian curve; and (4) the X-ray-source broadening approximated by four Lorentzian curves corresponding to Ka, , Ka,, Ka, and Ka, lines. The fitting of our experimental spectrum with a DS line shape was performed using the Simplex search method [15]. The first iteration is composed of the following elementary steps: (i) the DS line is generated using an initial good guess of the parameters N and y; (2) the background energy distribution is calculated from the latter function using any of the proposed energy-loss distributions F(E) and an initial value for the inelastic background parameter D; (3) the sum of the previous distributions with the source and the experimental analyser resolution functions is convoluted - these convolutions are done by fast Fourier convolution (multiplication of the Fourier transformations of the functions to be convoluted, and inverse Fourier transformation of the resulting function); and (4) at this step a merit function (x2 test) is computed and a new set of parameters is generated using the Simplex search method. For subsequent iterations steps (1)to (4)are repeated with the new parameter set until the minimum of the merit function is reached. Figure 1 shows the result of fitting the Au4f,,, and Au4f,,, peaks using a Shirley background. The fit agreement is 98.31% (the normalized value of the merit function (100%) means that the calculated and experimental spectra are exactly the same). Similarly, Fig. 2 shows the result of fitting the same lines using a TS background. The fit agreement (98.49%) is of the same order as before, even though the shapes of the backgrounds are quite different. The y, a, peak area and D value obtained with the two methods are compared in Table 1. It can be seen that the a values obtained with the TS method are higher than those obtained with the Shirley method. The areas of the elastic peak differ only a little between the two methods. By comparing the peak areas in Figs. 1 and 2, it may be expected that the D value
335
A. Jouaiti et al./J. Electron Spectrosc. Relut. Phenom. 53 (1992) 327-340
UA
l-
-.
-.c-_-_
-_
--__.-.__
_---
100 Binding
eV
Energy
Fig. 1. The fitting of the Au4f,,2 and Au4f,,, peaks using the Shirley background method.
obtained with the TS model should be larger than that obtained with Shirley’s model, because the D value is obtained as the ratio of the peak area to the height of the inelastic background. However, due to the mismatch of our fit with the experimental spectrum, which may be due to the limitation of the DS line and the model energy-loss function, the D values obtained with the two methods are nearly the same. Because the detailed structure of the energy-loss function is spread out over the observed spectrum, the parameter characterizing the global shape of the energy-loss function does not strongly depend on the chosen model in our experimental condition. However, from the physical point of view, the TS model obviously has an advantage in that the shape of the energy loss function is more properly simulated by this model than by Shirley’s method.
A. Jouaiti et al.]J. Ekctron
Spectrosc.
337
59 (1992)327-340
ReZat. Phenom.
TABLE 1 Comparison of the experimental DS parameter (Y, 01),peak areas and D values obtained with the two background subtraction models (Shirley and TS) Parameter
Kinetic energy (eV) Y Geak area (%) l3 (eV)
Shirley background
TS background
Au4f,,,
Au4f,,,
Au4f,,z
Au4f,,,
1402.91
1399.24
1402.93
1399.25
0.13 0 56.6
0.12 0 43.3
0.12 0.03 55.9
0.16 0.02 44 26.2
28
where the kinetic energy dependence through Z,, is negligibly small. In addition, the D value does not depend on the nature of the metal, with both backgrounds being as would be expected theoretically. This may be due to the dielectric function of the metals analysed being similar. In the case of semiconductors or insulators, a more realistic model must be used for the loss function. Quantitatively, the calculated D values are larger than the
P
0 0
cab
x”
X
8”
Au
iP
xx
5%
m
0
Fig. 3. Plot of the determined background parameters (D values) as a function of the electron kinetic energy for different peaks obtained on several homogeneous metals (gold, silver, copper and platinum).
338
A. Jouaiti et d/J.
Electron S’pectrosc. Relat. Phenont. 59 (1992) 327-340
experimentally obtained values. This may be due to some other contribution to the background formation, e.g. surface excitations (see next section). BACKGROUND
CAUSED
BY SURFACE
EXCITATION
As seen in the previous section, our theory does not fully explain our experimental results, i.e. the calculated D value does not agree quantitatively with the experimenta values. This may be explained by surface excitation, which was not taken into account in our theory. Qualitatively speaking, electrons leaving the surface are also inelastically scattered because of the surface plasmon excitation. This effect may reduce the elastic contribution (peak area) of the spectrum and give a lower D value. By applying the well known theory of surface excitation [173, we can calculate the attenuation of the measured elastic intensity Je’ due to the surface plasmon excitation (24)
where J&k is the elastic intensity at the surface, v is the velocity of the elastic electrons, and 8 is the angle of emission measured with respect to the surface. Due to this additional attenuation of the elastic intensity, the experimental inelastic background parameter (the D value defined by eqn. (13)) is decreased by
(25) where D,,, represents the bulk D value defined by eqn. (11). Using this formula we predict that the D value depends on the emission angle of the electron when angle-resolved X-ray photoelectron spectra are measured. Figure 4 shows the angle-resolved X-ray photoemission spectra of the Au4f peaks recorded at 0 = 10Q, 35O and 60°. For this measurement we closed the analyser entrance with a shutter bored with a small hole (2 mm diameter). From this experiment it is obvious that the background increases when the emission angle decreases. The D values obtained from these spectra, using the TS model, are O(8. = loo) = 19.5, L)(e = 3!7’) = 39.5 and O(0 = 60°) = 45.5 eV. It can be shown that this experimental variation of the D value with respect to the &mission angle can be explained by eqn. (25). The D value due to the bulk excitation D,,, is determined from this experiment as Dbulk= 53 eV, which is relatively close to the calculated value (D = 42.8eV). It should be noted that in our theory we used the straight-path approximation, which neglects the effect of elastic scattering. Nevertheless, as the
A.
Jouaiti
et aL.jJ.
Electron
&WCtFOSC. Relat.
10
Phenom.
59 (1992)
327-340
339
Deg.
Fig. 4. Angle-resolved X-ray photoemission spectra of the Au4f,,, three different emission angles: 8 = 100, 0 = 35O and 8 = 600.
and Au4f,,,
peaks taken at
elastic scattering cross-section is independent of the emergence angle of electrons [4,6,9,10] it is not possible to explain the background variation in terms of this effect. However, coherent elastic-scattering effects, such as surface reflection and diffraction, may affect the intensity of elastic electrons J”’ and change the D values. But these phenomena are only important in the low-kineticenergy cases and can be ignored in the present experimental conditions. According to the above discussion, we may conclude that the surface plasmon excitation is very important in the formation of the ‘inelastic background and that this effect on the inelastic background parameter can be taken into account to a first approximation by using eqn. (25). CONCLUSIONS
AND
DISCUSSION
We have developed an inelastic-background calculation method, called the “fitting method”. Using this method we can determine the elastic line shape parameters of the primary emission (assuming a Doniach-Sunjic line shape) and the inelastic background parameter D. In addition, we have given a theoretical basis for the most common method, i.e. Shirley’s background subtraction method [3]. We have confirmed that the inelastic background parameter (D value) does not depend on the electron kinetic energy, to a first approximation. Moreover, we have theoretically and experimentally pointed out the importance for the XPS background formation of the surface plasmon excitations. It should be noted that our present
340
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et al.lJ.
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theory is not well suited for finite coverage layers. In future work we will extend the theory to finite-thickness cases, and apply it to metal adlayers on metallic substrates. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
M-P, Seah and D. Briggs, in D. Briggs and M.P. Seah (Eds.), Practical Surface Analysis, Wiley, New York, 1983. P.M.A. Sherwood, in D. Briggs and M.P. Seah (Eds.), Practical Surface Analysis, Wiley, New York, 1983. D.A. Shirley, Phys. Rev. B, 5( 1972) 4709. S. Tougaard and P. Sigmund, Phys. Rev. B, 25 (1982) 4452. S. Tougaard and A. Ignatiev, Surf. Sci., 129 (1983) 582. V.M. Dwyer and J.A.D. Matthew, Surf. Sci., 143 (1984) 57. S. Tougaard, Surf. Sci., 139 (1984) 208. S. Tougaard and B. Jorgensen, Surf. Sci., 143 (1984) 482. A.L. Tofterup, Surf. Sci., 167 (1986) 70. V.M. Dwyer and J.A.D. Matthew, Surf. Sci., 193 (1988) 534. S. Tougaard, Surf. Sci., 216 (1989) 343. S, Doniach and M. Sunjic, J. Phys. C, 3 (1970) 291. S. Tanuma, C.J. Powell and D.R. Penn, Surf. Interface Anal., 11 (1988) 577. S. Tougaard, J. Vat. Sci. Technol. A, 5 (1987) 1275. M. Romeo, P. Legare and J. Majerus, Surf. Interface Anal., submitted, 1992. S. Tougaard, J. Electron Spectrosc. Relat. Phenom., 52 (1990) 243. R. Kawai, N. Itoh and Y.H. Ohtsuki, Surf. Sci., 114 (1982) 137.