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SURFACE A N D INTERFACE ANALYSIS, VOL. 24, 163-172 (1996)
Spectrum Synthesis Based on Non-linear Addition?
T. A. El Bakush and M. M. El Gomati*
Department of Electronics, University of York, Heslington, York YO1 5DD, UK
One of the proposed approaches in the literature for quantitative analysis in AES is the linear addition of elemental
spectra acquired in the direct energy mode (N(E) vs. E and E N(E) vs. E). Quantification is then achieved by
matching the shape of the added spectra to that of an unknown that was also collected under identical experimental
conditions. However, it is shown here that the linear combination of elemental spectra employed in this approach
has no real justification in theory. Any agreement with experiment found using this approach can therefore be of
doubtful value. To avoid uncertainty, non-linear addition formulae that take the matrix effects (of the substrate)
into consideration are developed. Results obtained with these formulae on AuCu alloys are described. The observed
success of the linear addition is explained in terms of more rigorous non-linear addition.
-
INTRODUCTION
Auger electron spectroscopy (AES) has been widely
used in many contexts since the introduction of electronic differentiation by Harris in the late 1960s. The
success of AES as a quantitative tool for surface
analysis lies primarily in the accuracy of the measurement of the Auger current. This has traditionally been
carried out by collecting spectra in the differential mode
and measuring the peak-to-peak height of the peaks of
interest. However, it emerged that the use of this mode
can lead to misleading or inaccurate results in some circumstances, due to changes in peak strengths and
shapes for the same elements in a different chemical
environment.’,’ Although the availability of computers
to record and process data, together with dispersive
analysers, has moved attention towards the use of the
direct mode, the differentiated spectra are still more
popular and widely used, simply because of the ease by
which the Auger intensity is measured from these
spectra. The difficulty that an analyst faces in using the
direct mode is the extraction of Auger current by the
measurement of the areas under the Auger peaks, since
this requires subtraction of the background upon which
the Auger peaks are superimposed. A number of models
have been developed for the background subtract i o q P 7 and the process is by no means considered an
easy task for a number of reasons: Auger peaks in the
low kinetic energy region can be superimposed on the
strong peak in the spectrum due to low-energy secondary electrons; Auger peaks of one element can be superimposed on a background that includes loss tails of
Auger peaks of other components; peaks due to different elements can themselves overlap. All of these problems can lead to a reduction in accuracy of the
evaluations of Auger intensities.
To avoid these difficulties an alternative method for
obtaining quantitative information was proposed by
* Author to whom correspondence should be addressed
t This paper is dedicated to Professor Martin Pruttan (University
of York, Department of Physics) on the occasion of his 60th birthday.
CCC 0142-242 1/96/030 163- 10
0 1996 by John Wiley & Sons, Ltd
Strausser et ~ l . ,namely
~
spectrum synthesis. This
involves collection of a spectrum, N(E), from the sample
of interest as well as spectra from samples of pure elements present in the sample, all under identical experimental conditions. The elemental spectra are then
rescaled and subtracted in turn from N ( E ) of the sample
of unknown composition, starting with the Auger peak
highest in energy. Each scaling factor is determined by
matching the height of the elemental spectrum to the
height of the corresponding peak in N(E) of the sample
of the unknown composition. A knowledge of the elemental scaling factors gives an estimate of the surface
composition of the elements present in the surface of the
sample. This approach has recently attracted more
attention and been applied to the E . N ( E ) spectra of
AuCu alloys by Ichimura et al.’ These authors considered the linear addition of elemental standard spectra
and compared these with the spectrum of the sample of
the unknown surface composition. However, neither
Strausser et al.’ nor Ichimura et al.’ have included
allowance for the influence of the matrix effects that are
known to affect the Auger spectra. Factor and target
factor analysis are also methods which use entire sections of a spectrum. By linear transformations of the
given data (unknowns and standards), estimates are
made of the surface composition. Again, matrix effects
are neglected in this approach.
In this paper an analysis of spectrum synthesis is presented, including the derivation of some algebraic
expressions which take into account the effect of the
matrix corrections. The expressions are tested on AuCu
alloys of different compositions and compared with the
linear approach.
THE SPECTRAL BACKGROUND
The distribution of the emitted electrons which give rise
to the spectral background in an Auger spectrum has
conventionally been divided into two main components: one due to secondary electrons; the other due
to the primary electrons that have suffered inelastic
Receiued 19 July 1995
Accepted 3 November 1995
T. A. EL BAKUSH AND M. M. EL GOMATI
164
1
0
Energy Eo
Figure 1. Schematic of the background in AES, showing the two
main components: the secondary electron cascade and that due to
rediffused primaries.
losses as they travel through the material, termed backscattered electron^^.^ (see Fig. 1). The secondary electron component dominates the background at low
kinetic energy and, according to S i ~ k a f u s ,its
~ . ~shape is
independent of beam energy E , and angle of incidence
8,. However, the magnitude of the secondary electron
yield does increase as E , decreases or 8 , increases. This
is because the escape depth of the secondary electrons is
only a few nanometres in comparison to the range of
the incident electrons, which can be of the order of
microns (for primary beam energies > 10 keV), and so a
decrease in 8, or an increase in E , tends to generate
secondaries at greater depths than a few n a n o m e t r e ~ . ~ . ~
In contrast, as the beam energy is reduced or 8,
increases, more of these secondaries are produced
within the escape depth of secondary electron^.^-^.'^
On the other hand, the backscattered component
dominates the background at high energies and its
shape does change with E , and O 0 , i.e. it becomes flatter
as E , or 8, is increased. Bishop’ has carried out an
extensive study by considering the fraction of incident
electrons that are backscattered, q, as a function of the
atomic number and beam energy. He found that q
increases with the atomic number of the target material,
but observed very little dependence on the beam energy.
The increase in q with atomic number has been
explained in terms of elastic scattering cross-section,
which increases with atomic number. This causes q to
rise with atomic number, with the net effect that the
primary electrons travel shorter distances in heavy elements and hence the probability of being backscattered
is higher than in lighter elements.’ Similar results were
also reported by Darlington.”
Methods of modelling the background have been
discussed in the literature. Briefly, for a 2.0 keV primary
electron beam and electron kinetic energy < 1000 eV,
S i c k a f ~ s showed
~.~
that the background (further away
from the signal peaks) can be represented by the function AE-”, where E is the electron energy and A and m
are constants. In his study of secondary electron emission, he demonstrated that the direct N ( E ) spectrum,
when plotted on a log-log scale, exhibits linear regions
between characteristic peaks up to 1000 eV-the range
below which the secondary electron component was
expected to dominate. Moreover, Peacock and
Durandi3 showed that, for a primary energy of more
than 15 keV, the Sickafus function can be fully extended
up to 2000 eV. These authors have also interpreted the
deviation from the Sickafus function above 2000 eV to
be due to the contribution of the backscattered to the
spectral background, which becomes more significant
than that of the secondary electron component. Furthermore, Matthew et al.14 (1991) investigated Sickafus’s equation using Monte Carlo simulations to model
the background of Cu and Au, and obtained a reasonable agreement with standard spectra.I6 The applicability of this power law form has been examined
experimentally by Greenwood et al. for 32 elements (see
Ref. 24).
In summary, a great deal is known about the background of pure solids. The question of whether the elemental spectra can be used to represent the spectral
background of multi-component materials is the subject
of the following sections.
ANALYSIS
To avoid the difficulty of separating the peaks from the
background, Strausser et aL8 and Ichimura et aL9 used
linear addition of elemental spectra as a method to
obtain the spectrum of an unknown sample and hence
to estimate the surface composition. Ichimura et aL9
applied this approach to AuCu alloy E . N ( E ) spectra
collected with a 10 keV primary beam energy and considered only that part of the background between 100
and 1000 eV. Strausser et aL8 were the first to propose
linear addition of elemental spectra for the interpretation of N ( E ) spectra of alloys in which peaks of the constituent elements overlap.
However, from the point of view of the matrix
effects” in AES, linear addition has no physical justification in theory due to the influence of the material
dependence of the backscattering, the atomic density
and the inelastic mean free path, a fact which has not
been addressed or justified by either Strausser et a/.* or
Ichimura et aL9 The influence of these factors is investigated as described below.
If an electron beam interacts with the surface of an
alloy which consists of elements 1 and 2, then the collected signal of interest (i.e. the Auger electron current),
S , , from the alloy is related to the physical parameter
by
S , = k l , A, N , R,
(1)
and A, and N , , respectively, for an alloy can be determined by”
N , = ( N , - N2)x
where N i is given by
+ N2
(34
N , = (iooop,~ ~ ~ ~ ) ~ ( I q - 3(3b)
A number of formulae have been reported for calculating the inelastic mean free path (IMFP)’8*’9. The
expression due to Tanuma et al.” is used here since this
SPECTRUM SYNTHESIS BASED O N NON-LINEAR ADDITION
is known to give a good account of the atomic number
Z and energy dependence for many materials. These
authors used experimental optical data and a theoretical dielectric function to calculate IMFPs for 31
materials in the energy range 50-2000 eV. The calculated IMFPs were then fitted to the Bethe" equation
for inelastic scattering. The resulting expression has the
form
+
+
+
B = -2.25 x l o p 2 0.944(Ei E i ) 7.39
p i , y = 0.191 P - O . ~ , C = 1.97 - 0.91,
D = 53.4 - 20.8 U , U = (Nav,piW - ' ) and E , =
2 8 . 8 p i~w;
~ 110.50.
~ ~ ~
The backscattering factor, R , , can be determined by
one of the two approaches:22by calculating elemental
factors R , and R , by one of the equations available in
the literature, e.g. the expression due to S h i m i ~ u , ' ~
which has the form
where
x
+ (0.462 0.777 Z 0 . 3 0 ) U - 0 . 3 2
+ (1.15 Z0.,O - 1.05)
Ri = 1
(2),(3) and (5) into Eqn. (1) and simplify to obtain
s, =
+ C(R1 - R,/R,) + ( N , - N,/N2)lx
+ W l - R,/R,XN, - N , / N , ) l x 2 }
{ ( A 2 - A1)X + A,}
klo 1 2 11N2 R2{1
(7)
Equation 7 indicates that the signal, S , , is related to the
atomic fraction x in a non-linear fashion and hence
there is a requirement for an expression which can nonlinearly add elemental spectra. Multiplying out the
brackets in Eqn. (7) gives
s
R,
= ( R , - R2)x
+ R2
(8)
+ All
- A&
N , R , 1, A,
= kl,
+ klo
22
(84
k l , A,A,N, R ,
-
AIR2 N , - k l , 1, 11 R , N ,
(6b)
and
c
= kIoA2A1R1N1
-
k I ~ A ~ R1
1 ~ N ~
- klo 1, I11NlR2
+ k l , A, N2 R2 1,
(8~)
Similarly, the signals from the standards are given by
S,
=
Sl
AINl = kIOR1
kloA,.NIRl
(9)
+ z,
(6)
Z , is then used in Eqn. (4) to yield the backscattering
factor of the alloy. A comparison of the approaches for
calculating R , is given in Fig. 2, which shows a discrepancy of 2% between the two procedures.
First, derivation of an expression for S,, with R ,
being given by Eqn. (9,is considered. Substitute Eqns.
-
Substituting relations (9) and (10) into Eqns @a), (8b)
and (8c), and then substituting these for a, b and c in
relation (8) and rearranging gives the form
s, =
S,A,
+ CS,
x
~ A R , l R 2 ) - 2 S z11 + SlA2(R,/RI)l
+ CSlA2 - s, ~
3.0
2.5
+ bx + cx2
= klo A 2 N2 AIR,
(4)
Alternatively, R , can be calculated via the mean atomic
number of the alloy, Z , , which in turn can be determined by
2, = ( Z , - Z,)X
a
[(A,
a
b
(5)
=-
where
-
for a primary electron beam incident at 30" to the
surface normal of the specimen. The backscattering
factor of an alloy is then found by adding R , and R ,
linearly according to
165
,
~
~
C(A2 - A1)X
1
/
~
2
~
-
+~ S21 M~ x2 2~
+All
(1 1
-
Now consider the case in which the backscattering
factor, R , , of the alloy is determined via the atomic
number, Z , . This simplifies Eqn. (7) to the form
2.0-
s, = ( k l , A,N1A2 R , .- k l , 1 2 N , AIR& + k l , 12 N , 1,
21.5-
(A2
- A,)x
+ 11
(12)
Substitution of relations (9) and (10) into Eqn. (12)
yields
(s, 3,s, -1,
-
R2
Rx
s, =
0
500
1000
1500
2000
Energy (eV)
Figure 2. Comparison of the backscattering equations
(A2
- A,)x
x
)
+ s, -Rx1 ,
+ A,
R2
(13)
Since the overall measured spectrum, SP, is the sum
of the Auger signal and the background, then SP is
~
2
/
~
T. A. EL BAKUSH AND M. M. EL GOMATI
166
7000
i
6000-
5000-
w^
q4000-
w
30002000-
500
1000
1500
Energy (eV)
2000
500
lo00
1500
Energy (eV)
2000
0
l
500
1000
m
1500
2000 m
Energy (eV)
Figure 3. Comparison of measured (solid line) and synthesized (dotted line) spectra for the Au,,,,Cu,,,,
carried out according to: (a) SSI; (b) SL; (c) SSII.
obtained by
SP
= S,
+ BG,
(14)
where the background signal, BG, , is given by13
BG,
= AE-"
+ BE4
(15)
The first term in Eqn. (15) describes the cascade of the
secondary electrons (i.e. the secondary electron component of the background) and the second term
describes the component due to the backscattered electrons.I3
Equations 11 and 13 indicate that the Auger signal is
not related to x by a simple linear relationship.
However, it has been postulated in the literature'.' that
the spectrum of the unknown can be obtained simply by
linear addition of the elemental standard spectra, i.e.
s, = ( S , - S,)x + s,
(16)
alloy where spectrum synthesis is
Comparison of Eqns (11) and (13) with Eqn. (16) shows
that the former reduce to the form of the latter if, and
only if, it is asumed that Liand Riare both the same in
the elements that constitute the binary alloy.
Ideally, Eqn. (14) should be used for adding elemental
spectra. However, there are considerable practical dificulties involved in using Eqn. (14) since this requires a
knowledge of the values of m i and q i for the pure elements and the unknown spectrum, and their dependence on x. This is problematic since m i and q i change
above and below each family of Auger peaks. The situation becomes more complex if more peaks are present
in the spectrum and is simplified by assuming that Eqns
(11) and (13) hold for both the Auger and the background signals. This is a valid approximation for the
secondary electrons since Auger electrons are themselves secondaries. The assumption made is also a reasonable approximation for the background due to the
backscattered electrons, since Batchelor et al.' report-
SPECTRUM SYNTHESIS BASED ON NON-LINEAR ADDITION
161
8000
7000-
:-i
6Ooo-
5000-
w^
r4000-
w
W
3ooo-
3000
2000-
'"1
10000
I
I
1
1
500
1000
1500
2000
lo00
1500
Energy (eV)
500
-1
2000
i
5000
/
"30001
"
I
1
I
\
500
loo0
1500
2Ooo
Energy (eV)
Figure 4. Comparison of measured (solid line) and synthesized (dotted line) spectra for the Auo.soCuo.soalloy where spectrum synthesis is
carried out according to: (a) SSI; (b) SL; (c) SSII.
ed that the backscattered electrons have a similar cosine
angular distribution to that of the Auger electrons.
They showed that the ratio of the Auger yield to that of
the background (due to the backscattered electrons) for
different angles of incidence of the primary beam is con-
stant up to 60".This was found to be true for a number
of pure elements in the Periodic Table: copper, silicon
and tungsten. These conclusions were further substantiated by the results of Crone et aL41 These authors
show that for Au, Ag and C the energy and angle
Table 1. Estimated average surface composition using the three Eqns (ll), (13) and
(16) (SSI, SSII and SL)
Average estimated surface compositions
Alloy
Au,,,,Cu,,,,
Auo,,Cuo,,
Au,,,,Cu,,,
SSI
SL
26.1% Au (60.7%)
73.9% CU
52.3% Au (*1.7%)
47.7% CU
78.2% Au (*0.66%)
21.8% CU
26.1% Au (*0.6%)
73.9% CU
52.3% AU (*1.4%)
47.7% AU
78.2% Au (*0.6%)
21.8% CU
SSll
25.3% Au (*5.0%)
74.7% c u
53.2% Au (*4.8%)
46.8% CU
77.5% Au (*3.4%)
22.5YoCU
T. A. EL BAKUSH AND M. M. EL GOMATI
168
1000-
500
1000
1500
2000
500
lo00
1500
Energy (eV)
2000
Figure 5. Comparison of measured (solid line) and synthesized (dotted line) spectra for the Au,,,,Cu,
carried out according to: (a) SSI; (b) SL; (c) SSII.
dependencies of the peak heights and backgrounds are
very similar. Furthermore, Greenwood et aLZ4demonstrated that the secondary electron component of the
background can be expressed by the form
SEX = k N , I , E - "
(1 7)
Using this relation in an analogous manner to the derivation given above for S, (for homogeneous alloy), one
may derive a relationship for SEX of an alloy in terms of
the elemental background signals. In this way one
obtains
SEX =
[(E"-"'Iz - E " - m z I l ) ~+ E m - m z I 1 ]
(18)
(2, - IJX + 4
which is similar to Eqn. (13) and suggests also that the
background signals of the pure elements can only be
added linearly if I , = 1 , .
Equations ( l l ) , (13) and (16) will be referred to as SSI,
SSII and SL, respectively.
76
alloy where spectrum synthesis is
EXPERIMENTAL
T o test the applicability of the different expressions (i.e.
SSI and SSII), a family of AuCu alloys has been chosen
for the following reasons. Firstly, Cu and Au are known
to form solid solutions, i.e. they are completely miscible
in each other at all compositions. Secondly, as far as
AES is concerned, the surface compositions of these
alloys are found to be the same as the bulk, i.e. no preferential sputtering effects have been o b ~ e r v e d . ~ ~Ion
-~*
scattering spectroscopy (ISS), however, has revealed
that ion bombardment induces surface enrichment of
Au at the outermost atomic layer^.'^-^' The difference
between the results of AES and the ISS has been attributed to the following two mechanisms. The first is the
ion beam-induced enhanced surface segregation which
causes the Au atoms to segregate to the outermost atom
layer due to their low surface energy in comparison to
those of the Cu, which in turn leaves a depletion region
SPECTRUM SYNTHESIS BASED O N NON-LINEAR ADDITION
I:
,
I
,
,
-400
1
-300
L___r__
500
lo00
1500
Energy (eV)
169
2000
500
I
I
I
lo00
1500
2000
I
Enery (eV)
500
1000
1500
2000
Enery (eV)
Figure 6. Plots of the residual, i.e. the difference between measured and synthesized, spectra using SSll and
alloy; (c) for the Au,,,,Cu,,,,
alloy.
alloy; (b) for the Au,,,,Cu,,,
of Au atoms just beneath the enriched 0ne.30p31The
second is the difference in sampling depths of the signals
in AES and ISS. In the case of AES, the high-energy
Auger signals of Au and Cu are often used due to the
overlap of low-energy Auger signals. The average AES
information depth is -5-6 nm at least. On the other
hand, the signal in ISS reflects a concentration of atoms
in the topmost atomic layer of a specimen surface31 of
no more than 1 nm. However, in the present work it is
the spectral background and Auger electron signals
which are of concern and both of these eminate from
depths of more than those in ISS. It is therefore safe to
use these alloys to test a non-linear combination of
spectra.
Spectra from three Au,Cul - x alloys of different compositions (Au75%-Cu25Y0, AuSO%-Cu50%
and
Au25%-Cu75%) and from pure Cu and Au samples
have been collected using the acylindrical mirror
analyzer (CMA).28The samples were obtained from the
SL; (a) for the Au,,,,Cuo,,,
Japanese VAMAS working group who reported that
the purity of the specimens was better than 99.7%.32
A primary energy of 5.0 keV and a beam current of
-0.95 pA were used in collecting spectra from the Au
and Cu standards as well as the alloys. Prior to collection, the surfaces of all specimens were bombarded with
a 3.0 keV beam and 0.5 pA mmP 2 of Ar' ions for 60
min each to remove any contamination present on the
surface. In spite of this, some spectra still showed traces
of carbon, possibly due to the cracking of hydrocarbons, residual in the system, by the electron beam. The
spectra were then recorded in the energy range 1002300 eV with a 100 ms dwell time per energy channel
and with -10 V applied to a grid placed between the
exit slit aperture of the CMA and the electron detector.
The purpose of using a negatively biased grid is to minimize the internal scattering contribution to Auger
The spectra were all corrected for the
response function3' of the CMA.
T. A. EL BAKUSH AND M. M. EL GOMATI
170
I
0 '
(a'
RESULTS AND DISCUSSION
I
I
I
I
I
500
1000
1500
2000
I
Energy (eV)
30
25
f0
E
815.
9
mz
10
-
5-
0-
The surface compositions of the AuCu alloys estimated
via SSI, SL and SSII are shown in Table 1. In comparing the measured and the synthesized spectra, the chisquared criterion was used over different energy
intervals and the surface composition was determined
as the average of the evaluated best-fit values. Generally, the estimated surface compositions show satisfactory agreement with the nominal composition.
Moreover, it was found that the linear (SL) and nonlinear addition (SSI) of spectra yielded similar results in
all cases. The similarity is also reflected in the shape of
the spectra, shown in Figs 3(a,b), 4(a,b) and 5(a,b), where
it is evident that the synthesized spectrum matches reasonably the corresponding measured spectrum for all
alloys. However, there is a noticeable discrepancy of
-2% or less in the lower energy part of the spectra, i.e.
below 1000 eV, which is the same in the case of SSI and
SL. This agreement between the linear and non-linear
combinations indicates that the matrix effects are not
critical in the AuCu alloys, despite the large atomic
number difference ( Z = 29 for Cu and 79 for Au).
On the other hand, if the spectra synthesized using
SSII are compared with the corresponding measured
spectra from the alloys, some discrepancies can be seen
(Table 1). These discrepancies appear to be systematic
in terms of the Cu concentration in the alloys. Figures
3(c)-5(c) show a comparison of the synthesized and
measured spectra. From these, it is clear that the synthesized spectrum, obtained using SSII, is always higher
than the corresponding measured spectrum above
1100 eV. The trend is visible in all of the alloys and is
largest in the case of the Au,.,,Cu,,,, alloy. This was
not the case when the elemental Au and Cu spectra
were added according to SSI or SL. Furthermore, at
low energies (<lo00 eV) SSII gives more satisfactory
agreement between the synthesized and the measured
spectra than that obtained by either SSI or SL, as can
be seen from the residual plots shown in Fig. 6.
However, it should be noted that although the shapes of
the spectra generated via SSI and SSII do differ at low
and high energies, the surface compositions obtained
from the average of the best-fit values agree to within
the random errors of these spectra. For example, the
surface compositions of the Au,,,Cu,,, alloy obtained
using SSI and SSII are Au 52.3Yo-C~ 47.7% and Au
53.2Yo-C~ 46.8% respectively. The same trend is also
found for other alloys, as shown in Table 1.
The reason for the observed discrepancy between the
synthesized spectra using SSII and measured spectra
may be envisaged from plots of the R,A2/R, and
R,A,/R2 terms in SSII [Fig. 7(a)]. These terms are
respectively referred to as Beta and Gamma in the
figure, which shows that the difference between the two
terms increases with energy and reaches 8.0% at high
energies. A plot of similar terms R,A1/R2 and R2A2/R1
in SSI, referred to as Beta2 and Gamma2 respectively, is
also given in Fig. 7(b). In this case, although the behaviour of the corresponding terms in SSII is the same,
their influence in SSI appear to be less effective due to
the presence of other terms in the equation which seem
to compensate for them.
I
500
I
1
1000
1500
Energy (eV)
1
2000
Figure 7. (a) A plot of the R,A,/R, and R,A,/R, terms in SSII.
(b) A plot of theR,A,/R, andR,A,/R, terms in SSI.
The surface composition was estimated by comparing
the spectrum of the unknown (M) with the synthesized
spectrum (SI) (Table 1) via an iteration process which
involved changing the value of x in SSI, SSII and SL
until the closest fit between the two spectra was found.
The criterion used for such a comparison was the chisquare test, which has the
where M i and SIi are the contents of the ith channel of
the unknown and the synthesized spectra, respectively.
The chi-squared test requires that the square of the sum
of the unknown ( M i ) and synthesized (SZi) spectra
becomes a minimum over the energy interval of interest.
The value of x (the surface concentration) that will
cause the spectrum calculated from the pure elements to
match the measured spectrum as closely as possible is
found by performing a non-linear least-squares
-
SPECTRUM SYNTHESIS BASED ON NON-LINEAR A D D I T I O N
CONCLUSIONS
The AES spectral background upon which the Auger
peaks are superimposed is usually considered a hindrance to quantitative analysis. However, as no exact
method exists for the removal of the background, its
elimination can introduce a significant element of uncertainty in the results. To alleviate this problem, a method
of estimating the alloy composition corresponding to an
unknown spectrum is described, which in fact utilizes
the spectral background, as opposed to peak height or
area, and so avoids the need for background removal
with its consequent loss of accuracy. The spectrum synthesis suggested here goes beyond the linear addition of
elemental spectra, which has no physical justification in
theory, and is based on two non-linear expressions
derived by the authors. The method has been applied to
AuCu alloys and yielded encouraging results which
agree well with the nominal composition. The good
agreement suggests that the technique could be a useful
tool for quantitative analysis in AES. The linear addition formula is not expected to hold generally for other
systems and the use of the non-linear addition might
give better agreement with experiment in such cases.
At this stage, it is dificult to draw any general conclusion about the applicability of the two derived
expressions, and the final assessment should be made by
further application to different systems, especially those
in which the elemental system constituents exhibit a
large difference in matrix effects (e.g. W,-,C, and
W, -,Six alloys). Also, some pure elements (which
include gases such as oxygen) cannot be studied using
AES except as chemical compounds. The use of spectrum synthesis might be useful in obtaining elemental
Auger spectra for such inaccessible materials. Furthermore, since AES analysis is usually carried out on a
sputtered surface, it would be interesting to test the
171
model on systems in which preferential sputtering effects
do exist. This may require the inclusion of the sputtering yield factors in the model, which could be cumbersome.
In summary, more work is needed to establish the
limitations of this technique, but it promises to be a
useful tool, at least for alloy systems in which no preferential sputtering effects are observed.
Acknowledgement
The authors would like to thank Professor M.Prutton of the Physics
Department for his valuable comments on the paper.
LIST OF SYMBOLS
k
= analysing
constant, which includes the ionization cross-section, escaping probability and the
response function and is assumed to be composition independent
I , = electron beam current
1, = inelastic mean free path of the alloy
li = elemental inelastic mean free path
N , = atomic density of the alloy
R, = backscattering factor of the alloy
Zi = atomic number
Ri = elemental backscattering factor
FT( = atomic weight
pi = bulk density
Navg= Avogadro's number
m i =constant
qi
=constant
E , = free electron plasmon energy
E, = bandgap energy
A
=constant
B
=constant
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