I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
143–152
NOISE IN AUGER ELECTRON SPECTRA:
A SIGNAL-PROCESSING VIEW
[UM V AUGERJEVIH ELEKTRONSKIH SPEKTRIH – POGLED
Z VIDIKA OBDELAVE SIGNALOV
Igor Beli~
1
, Besnik Poniku
2
, Monika Jenko
1
1
Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
2
University of Karabuk, Faculty of Engineering, Biomedical Engineering, Kastamonu Yolu Demir Çelik Kampüsü, 78050 Kýlavuzlar
Köyü/Karabük Merkez/Karabük, Turkey
Prejem rokopisa – received: 2018-10-09; sprejem za objavo – accepted for publication: 2019-01-15
doi:10.17222/mit.2018.218
Auger electron (AE) spectroscopy is an important surface-analysis tool for conductive materials. However, the technique has a
serious drawback, i.e., the absence of automated spectra analyses. The goal of our research work, therefore, was to find a way
towards the automatic analysis of AE spectra, and in this paper we describe how the analysis of AE spectral noise is one of the
reasons preventing automatic analyses. Knowing the properties of noise is a key to knowing the true shape of the spectral
background, as well as the shape of the characteristic AE peaks. We are not interested in the properties of the noise in the sense
of how and what generates it, rather we want to discover what are its manifestations and consequences from the
signal-processing point of view. In the paper we give answers to several important noise-related (measured and simulated)
questions: Does the noise amplitude level vary with the kinetic energy? Is the measured noise "white noise"? Is the noise
temperature dependent? The answers to these questions also indicate how we can extract the AE spectral noise.
Keywords: Auger electron spectroscopy, noise, white noise, running average, Fourier transform, signal power
Augerjeva elektronska (AE) spektroskopija je pomembna tehnika za analizo povr{in prevodnih materialov. Analiza posnetih
spektrov ni avtomatizirana, kar predstavlja veliko slabost te analitske metode. Cilj na{ega raziskovalnega dela je najti pot do
avtomatizacije postopkov analize AE spektrov. Prispevek opisuje, kako na analizo AE spektrov vpliva {um, ki je eden od
razlogov, da analitska tehnika {e ni avtomatizirana. Poznavanje lastnosti spektrom prime{anega {uma je klju~ do poznavanja
dejanske oblike spektralnega ozadja in spektralnih vrhov. Ne zanimajo nas podrobnosti {uma v smislu njegovega nastanka,
zanimajo nas njegove lastnosti, ko je spekter `e izmerjen. Opazujemo ga s stali{~a obdelave signalov. Prispevek daje odgovore
na pomembna vpra{anja o {umu (merjenem in simuliranem), kot so: Ali se amplituda {uma spreminja s kineti~no energijo? Ali
spada izmerjen {um v kategorijo "belega {uma"? Ali je {um temperaturno odvisen? Odgovori na zastavljena vpra{anja
nakazujejo mo`nosti, kako se izogniti spektralnemu {umu.
Klju~ne besede: Augerjeva elektronska spektroskopija, {um, beli {um, teko~e povpre~enje, Fourierov transform, mo~ signala
1 INTRODUCTION
Today, Auger electron spectroscopy (AES) represents
one of the most important surface-analysis tools for sam-
ples of conductive material. AES allows the quantitative
analysis of surfaces with a 0.1 % sensitivity, elemental
detection (excluding H and He) with a spatial resolution
of better than 10 nm, as well as high-resolution depth
profiling. AES finds applicability in the areas of micro-
electronics, metallurgy and the analysis of thin films.
1
As
a result of its high surface sensitivity
2
and the ability to
focus the primary electron beam to a diameter of approx-
imately 10 nm,
3
using Auger electron spectroscopy it is
possible to characterize nanoscale surface features.
4–9
A very serious drawback of AES is the absence of
automated Auger electron (AE) spectra analysis. The
main reason that AE spectra analyses have not yet been
automated lies in the complexity and variability of the
spectrum.
In our previous work we found that the shapes of
measured AE spectra are, in general, composed of three
principal components: the characteristic Auger electron
peaks, the background, and the noise,
10
as shown in
Figure 1.
Our main goal was to find a way towards the
automatic analysis of AE spectra. Since noise is one of
the primary reasons for the absence of automatic
analyses, it is necessary to understand the properties of
the noise. For quite some time, the physics of the
emergence of noise has been known and well docu-
mented.
11
It is known, for example, that the AE spectra
noise is a Poisson noise (Shot noise). However, in our
work we are not interested in understanding the
principles of how the noise is being produced. Our view
is turned in a completely different direction. Once the
AE spectrum is recorded, we take it as the signal that is
to be analysed with a very clear focus in mind being how
to remove it from the signal.
The present paper describes an analysis of the pro-
perties of AE spectral noise from the signal-processing
point of view. We are directly interested in what are the
Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152 143
UDK 544.171.7:543.428.2:536.94 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 53(1)143(2019)
*Corresponding author e-mail:
igor.belic@imt.si

manifestations and consequences of noise that is added
to the spectra. In this regard several questions were
addressed:
1. Does the amplitude of the noise vary with the kinetic
energy of the AE spectra?
2. What is the Fourier spectral composition of the noise
– does the measured noise fall into the category of
"white noise"?
3. Is the noise temperature dependent? (In materials
science adsorption and segregation experiments are
often conducted,
12–19
which may involve either
heating the sample in situ or fracturing the previously
aged sample while cooling it in situ by indirect
contact with liquid nitrogen.)
In order to develop reasonably reliable software for
the analysis of AE spectra, a large number of spectra are
required. Furthermore, to be able to assess the quality of
the developed analysis software, the exact composition
of the analysed spectra must be a-priori known. This
condition can only be met with simulation software that
generates virtual AE spectra. Then, only with a thorough
knowledge of the behaviour of the analysis software can
it be safely used on real AE spectra.
Since a simulator of AE spectra has already been
developed and described in our previous work,
20,21
and
since the generation of the simulated spectra takes
considerably less time than measuring spectra with the
instrument, the answers to the following simulation-
related questions were also of great interest:
S1 Can the noise produced by the AE spectra simulator
be compared to the measured noise?
S2 What are the differences between the measured and
simulated noise?
S3 Can the simulated noise adequately represent the
measured noise or should the AE spectra simulator be
appropriately tuned in order to give a better
representation of the measured noise?
To answer these questions, 247 AE spectra from
spring-steel samples and NiTi shape-memory alloy
samples were recorded and analysed. To allow a direct
comparison of the results, the same number of AE
spectra was simulated and analysed.
2 METHODOLOGY
In order to study the properties of the AE spectra,
including the noise, several data-analysis tools were
used. Our starting hypothesis was that the noise is close
to so-called white noise. Therefore, a set of tools was
selected that enables us to test the properties of the noise.
First, the noise must be separated from the background.
For this purpose a running-average algorithm was used.
Since, by definition, the white noise must have a zero
mean value, the criterion of optimality for the running-
average algorithm is set to produce the extracted noise
with mean values as close as possible to zero. Once the
noise is extracted, a discrete Fourier transformation is
used to calculate the complex-valued composition of the
noise in the frequency domain. The Fourier transform of
the noise is used to calculate the noise power spectral
density needed to further prove the properties of the
white noise. Finally, the auto-correlation of the noise was
calculated, proving the randomness of the noise. What
follows is a very brief summary of the tools that were
used.
2.1 White noise
The term white noise refers to a statistical description
of the signals and the signal sources. White noise is a
random signal with a flat (constant) power spectral den-
sity. In its discrete form it is a data sequence containing
equal power within any frequency band of a fixed width.
The term is also used to describe a signal whose samples
are regarded as a sequence of uncorrelated random
variables with zero mean and finite variance.
22,23
White
noise is a general category that can be further divided
into somewhat narrower classes having a flat, Gaussian,
Poisson (Shot) or any other distribution of data samples
(e.g., representing amplitudes).
2.2 Running average
The running-average process is used to separate the
AE spectral noise from the background. It is a method
where a series of consequent averages of data subsets
(averaging windows) is calculated. It is a data-filtering
method referred to as a finite-impulse response filter.
24
We begin with a functiony=f (x) where both x and y
are a discrete set of data points and the function is
defined within the closed interval [x
min
,x
max
]. The width
of the window is denoted by w (an odd integer!). In
addition, the value w
\2
is defined, representing the integer
quotient for the division of w by 2. Therefore, the
definition
ww =+ 21
2
()
\
(1)
holds true.
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
144 Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152
Figure 1: AE spectrum from NiTi shape-memory alloy. AE spectra
are, in general, composed of three principal components: the charac-
teristic Auger electron peaks, the background, and the noise

The running-average function is defined as
Rx
w
fx
xxw
xw
() ( ) =
=−
+
∑
1
2
2
s
s \
\
(2)
The function R(x) is defined on the closed interval
[x
min
+w
\2
,x
max
–w
\2
], which is the subset of the interval
on which the original data reside.
The width w (number of data points forming the
window) of the averaging window controls the
smoothness of the gathered running-average function.
The wider the window, the smoother the running-average
function becomes. Since the running average is used to
filter out the fluctuations caused by the noise, it would be
appropriate to widen the window as much as possible.
On the other hand, the process also affects the original
function that is already distorted by the noise. The
selection of the averaging window’s width is therefore a
trade-off situation between the noise suppression and the
degradation of the original function. For each problem
the width of the optimal averaging window should be
determined, where the optimality criterion is to produce
extracted noise with a mean value closest to zero.
2.3 Fourier transformation for non-periodic functions
A physical process can be described either in the time
domain using the values of some quantity f as a function
of time f(t) or else in the frequency domain where the
process is specified by giving its amplitude F as a func-
tion of the frequency  , i.e., F( ), with -( <  < (.Itis
useful to think of f(t) and F( ) as being two different
representations of the same function.
It is important to note that originally the principle of
a Fourier analysis operates in the time and frequency
domains.
25
This is, however, just a matter of interpreta-
tion. In many cases a Fourier analysis is used for image
processing, where the time and frequency domains are
replaced by the length and spatial frequency. In the case
of AES the E(energy) and 1/E spaces are observed.
The definitive Fourier-transform equations are:
Fw fte t
ft Fwe
it
it
() ()
() ( )
=
=
−∞
∞
−∞
∞
∫
∫
   d
d
1
2π
(3)
2.3.1 Discrete Fourier transform
When the Fourier transform of a function is estimated
from a finite number of samples, the discrete Fourier
transform replaces the continuous form
25
. In such cases
we have N equidistant (D = t
k+1
– t
k
) sampled values
ff t
kk
≡ () ,tk
k
≡Δ , k = 0,1,2, ..., N–1
With N numbers of input, it is possible to produce no
more than N independent numbers of output. Instead of
estimating the Fourier transform F( ) for all the values
of  in the range – C
to  C
we only have estimates for
discrete values
f
n
N
n
≡
Δ
, n
NN
=−
22
,...,
The discrete Fourier transform replaces the integral
by the discrete sum
Fw fte t
fe fe
it
it
k
N ikn
N
k
() ( )
n
kk
n
nk
d =≈
≈=
−∞
∞
=
−
=
∫
∑
  ΔΔ
0
1
0
1 N−
∑
(4)
The inverse discrete Fourier transform is therefore
fk
N
Fe
ikn
N
k
N
() =
=
−
∑
1
2
0
1
π
n
2.4 Power spectral density
Parseval’s theorem
Pf ttF ≡=
−∞
∞
−∞
∞
∫∫
() ( )
2 2
dd  (5)
establishes the total power P in the time and frequency
domains.
25
The total power P is the same, whether it is
calculated in the time domain or in the frequency
domain. Usually, it is important to know the amount of
power contained in the frequency interval between  and  +d  . The function describing such power inter-
vals is referred to as the power spectral density.
Although the complex Fourier spectrum spans the
–( <  < ( space, when dealing with power, it is conve-
nient to operate on the one-sided interval 0 < (
only. In such cases the one-sided power spectral density
of the function f is defined as
PFF
f
22
() () ()  ≡+− 0 < (
When the function f(t) is real (as is true in our case),
then both terms are equal, resulting in
PF
f
2
() ()  ≡2 (6)
The concept of the power spectral density is import-
ant for an assessment of the noise’s spectral properties.
2.5 Correlation function
A correlation function is a measure of the similarity
for two data sequences. It is commonly used to search a
data sequence for a known feature.
16
The correlation
provides a useful indicator of similarity as a function of a
lag in time, space, or any other quantity.
The cross-correlation C(f, g)of two real functions f(t)
and g(t) is defined by:
Cfg ft gtt (,) ( )() =+
−∞
∞
∫
 d (7)
The correlation is a function of the time lag  .F o r
real discrete functions, the cross-correlation is defined
as:
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152 145

Cfg fmngm
m
(,) ( )() =+
=−∞
∞
∑ (8)
The special case of the correlation is an auto-corre-
lation, which is the cross-correlation of a data sequence
with itself.
3 EXPERIMENTAL PART
3.1 Measurements
Two types of materials were used in this investiga-
tion. In total, 247 AE spectra from both types of samples
were recorded.
One set of samples consisted of spring steel provided
by the [tore Steel Company, which was used for measur-
ing AE spectra while analysing for non-metallic inclu-
sions present in these samples. Two specimens were
taken from the bulk material, both with dimensions of
(10 × 10 × 4) mm. First, the samples were cut from the
bulk material by abrasive wet cutting. Afterwards, the
samples were subjected to plane grinding and then fine
grinding. Then, they were polished, first with diamond
polishing and then oxide polishing. Oxide polishing
produces a finer surface, which is necessary for Auger
electron spectroscopy. Finally, the samples were cleaned
with ultrasound to remove any impurities that may have
been introduced onto the surface during the preparation.
The composition of these spring-steel samples (ex-
cluding iron) is given in Table 1. The primary electron
beam used for probing these samples was of 10-keV
energy, 10-nA intensity, and 10-nm beam diameter.
Table 1: The elemental composition of spring-steel samples used in
obtaining the measured AE spectra
Elements Atomic %
C 0.47
Si 0.15
Mn 0.7
P 0.035
S 0.035
Cr 0.9
V 0.1
The other set of samples consisted of NiTi shape-me-
mory alloy. This material was a commercial Ni 50.74 %
(x/%), Ti alloy with the composition according to ASTM
2063-05. It was in sheet form with the following
dimensions: 0.5±0.05 mm thick, 100±1.5 mm wide, and
300±3 mm long. It was produced by Baoji Seabird Metal
Material Co., Ltd., in the flat annealed condition. The
sheet was cut into flat samples of 10 mm in diameter
using a water jet. The samples were prepared according
to Struers instructions with SiC #paper 220, rough
polished by MD-largo, 9-μm diamond paste and oxide
polished using Struers MD-Chem, OPS (90 mL OPS +
10 mL H
2
O
2
); with a polishing time of 10 min.
To address question no. 3, a sample of NiTi alloy was
mounted into the experimental device developed at the
institute for studying the equilibrium surface segregation
of residual impurities and alloying elements in situ in an
ultra-high-vacuum environment in the analysing cham-
ber of a Microlab 310-F spectrometer. The linear heating
method (LHM) in the temperature range from 200°C to
800 °C was applied, and the temperature was measured
using a K-type thermocouple.
Initially, the sample was heated to 200 °C and the
surface was cleaned by argon-ion sputtering to remove
the adsorbed impurities. The sample was kept at this
temperature for 30 min and then AES measurements
were made. We continued this procedure up to 800 °C
where the temperature was linearly increased by 30 °C
every 30 min and the AES analyses were made. The
primary beam energy was 10 keV at a current of 10 nA.
The Microlab 310-F that was used to record the AE
spectra from all the samples is equipped with a Schottky
field-emission source that provides a stable electron
beam in the accelerating voltage range from 0.5 keV to
25 keV. The electron analyser is of the double-focusing
spherical-sector type with an electrostatic input lens and
can provide an energy resolution between 0.02 % and
2 %. The spectrometer has five sequential channeltrons
(electron detectors), each of which detects 2.5 % of the
pass energy. Spectra are mostly acquired with a constant
retard ratio (CRR) of 4, which provides an energy
resolution that is 0.5 % of the pass energy.
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
146 Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152
Figure 2: Auger electron spectra measured at points A1 and A2 on a
NiTi shape-memory alloy sample while the temperature was increased
from 200 to 800 °C in 30 °C increments

The AES spectra were acquired using Avantage v
3.41 data acquisition. The data-processing software was
supplied by Thermo Scientific. CasaXPS software was
used for the detailed data processing.
The measurements for investigating the effect of the
sample temperature on the noise content in the AE
spectra were conducted at two locations on the NiTi
sample. The number of spectra measured at each point
was 21, with the first spectra being measured at 200 °C,
and with the last ones being measured at 800 °C. The
overlaid and offset spectra from this set of measurements
are presented in Figure 2.
3.2 Simulation
The AES simulator
12
was used to generate data sets
containing only noise within the amplitude limits as
detected in the measured spectra. This step only equates
the maximum amplitudes of the simulated noise to that
of the measured noise, but the pseudo-randomness of the
generator, which is its inherent property, needs to be
investigated as the findings are related to the measured
noise. To allow a direct comparison with the measured
spectra the number of generated noise sequences was
247. Since the files contain only generated noise, without
the background, noise-extraction procedures were not
required.
4 RESULTS AND DISCUSSION
To investigate the AE spectral noise it is first
necessary to identify the regions of the AE spectra that
are not populated by spectral peaks. If possible, these
regions should be large enough to allow an analysis and
a comparison between the different AE spectra. The
selection of the sample material was such that the
high-energy portions of the measured spectra contained
no spectral peaks (Figure 3). In the case of the spectra
recorded from the NiTi samples, the portion of the
spectrum from 875 eV to 1650 eV satisfied this condi-
tion, whereas in the case of the spectra recorded from the
spring-steel samples the portion of the spectrum from
999 eV to 1630 eV was chosen.
To separate the noise from the background, the
optimal window width running-average algorithm was
used (Equations 1, 2). It must be mentioned that the
result of the running-average process is highly dependent
on the choice of the used window width (Figure 4). If a
small window width is used, the background resulting
from the running average follows the noise more closely,
as indicated by the two lowest lines in Figure 4, where
the running average was obtained by using window
widths of 3 and 9. The background is due to the small
averaging window width, which is still quite populated
by noise and the level of the extracted noise is far too
low. Using wider window widths the background
becomes smoother and the level of the extracted noise
becomes higher. The red line in Figure 4 indicates the
running average (background) obtained by using a
window width of 21. It was noted that when using win-
dow widths greater than 21 the RMS (Root Mean
Square) of the extracted noise does not become much
higher (Figure 5). In the experiments where the optimal
window width was searched for, the minimal window
width was limited to 21 points.
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152 147
Figure 5: Level of extracted noise expressed in RMS (Root Mean
Square) as a function of the window width used for averaging
Figure 3: Extraction of the portion of the spectra containing no
characteristic peaks (NiTi shape-memory alloy)
Figure 4: Effect of the choice of window width on the resulting back-
ground

Figure 5 shows a plot of the level of noise extracted
through the running-average process. The level of noise
in this figure is expressed by the noise RMS as a func-
tion of the window width used for the averaging.
It is evident from Figure 5 that from a certain point
on, a further increase of the window width does not im-
prove the noise extraction very much. From the experi-
mental work with a number of AE spectra, the conclu-
sion was reached that the smallest window width used
for our study should be larger than 21 data points.
The complete process for separating the background
from the noise at the high-energy portion of the AE spec-
tra involves several steps. For each recorded spectrum
the optimal averaging window width is determined. The
optimal window width should ensure that the extracted
noise has a zero mean value, or that it is as close as
possible to it. Such a process of finding the optimal win-
dow width for performing the running average for one
data set is shown in Figure 6.
In this case a window width of 33 data points was
used, since from observing Figure 6 it is the one that
produces an extracted noise with an average closest to
zero. For the same file the resulting background is shown
in Figure 7, and the extracted noise is shown in Figure 8.
After extracting the noise, the Fourier analysis
follows, where both the real and imaginary parts are cal-
culated (Equations 3,4), as shown in Figure 9.
From both parts of the complex Fourier spectrum the
single-sided power spectrum is calculated, as illustrated
in Figure 10.
Finally, from the normalized power spectrum, the
power spectral density was calculated (Equations 5, 6),
as shown in Figure 11.
The normalization was performed since only the
shape of the power spectral density is of interest here.
The normalization process also enables a comparison
between the power spectral densities of spectral portions
with other files. As can be seen in Figure 11, the shape
of the power spectral density resembles that of white
noise.
22, 23
The same steps were performed for the rest of the
measured AE spectra. In order to get statistically relevant
results regarding the properties of the noise, the
following steps were carried out:
a) For all the files, the noise was normalized according
to the absolute maximum amplitude, and then the
cumulative noise was obtained by adding the
extracted and normalized noise at each data point for
all 247 cases;
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
148 Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152
Figure 9: Real (blue) and imaginary (red) parts obtained by
performing a Fourier transform on the extracted noise
Figure 7: Extracted background obtained through the running average
using a window width of 33
Figure 8: Extracted noise using a window width of 33 points for
performing the running average
Figure 6: Finding the optimal window width for the running average

b) The accumulated noise was assessed regarding the
amplitude vs. energy relationship;
c) The absolute amplitude distribution was calculated;
d) The Fourier transform of the accumulated noise was
calculated;
e) The power spectral density of the noise was cal-
culated.
The result of the noise-accumulation process is
presented in Figure 12.
From Figure 12 we can conclude that there is no
detectable pattern in the accumulated noise. The shape of
the accumulated noise is still very much the same as it
was for each individual sample. The noise amplitude
does not get statistically higher, or lower, while moving
over the energy scale. Had it been otherwise, due to the
accumulation process, the effect would have been
immediately detected.
The plot of the noise power spectral density (Figure
13), calculated from the Fourier transform of the
accumulated noise, shows that its properties are similar
to the one from a single spectrum, and it also reveals pro-
perties that are close to the concept of white noise.
This presumption of white noise is further supported
by performing a plot of the autocorrelation function
(Equations 7, 8) of the accumulated noise in which there
is a strong spike around the zero shift, whereas in the rest
of the shift axis there are no significant peaks. This form
of the plot of the autocorrelation function is a typical
property of white noise, i.e., there are no periodically
similar elements detected in the noise. The plot of the
autocorrelation function is presented in Figure 14.
To answer questions S1–S3 posed in the introductory
part, the same number (247) of AE spectra were simu-
lated in order to allow a direct comparison with the
results obtained from the measured AE spectra.
After generating the required number of files
containing random noise, its analysis followed. Since the
files contain only generated noise without the back-
ground, all the steps that were carried out previously in
the measured spectra were carried out in this case as
well, with the exception of the separation of the back-
ground and the noise, which was not necessary. Figure
15 shows the accumulated noise from 247 simulated data
sets.
Following on from the Fourier transform and the
single-sided power spectrum of the noise in Figure 16,
the power spectral density of the accumulated noise from
the simulated data sets is calculated.
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152 149
Figure 12: Accumulated noise from the extracted and normalized
noises of the 247 data sets
Figure 10: Single-sided power spectrum of the extracted noise
Figure 13: Power spectral density of the accumulated noise
Figure 11: Power spectral density of the extracted noise

Figure 16 shows that the simulated noise displays the
characteristics of white noise as well. If we take a look at
the amplitude distribution of the measured noise and the
simulated noise (Figure 17), it is evident that the simu-
lated noise exhibits a more uniform amplitude distri-
bution. This results in a power spectral density for the
generated noise, as displayed in Figure 16, which is
closer to the ideal white noise than the measured one.
4.1 Noise and temperature dependence
The data of the AE spectra recorded for investigating
the effect of the sample temperature on the noise content
were additionally treated. Initially, the spectra were
transformed from the E×N(E) vs. KE (Energy × Number
of electrons as a function of energy vs. the Kinetic
energy of the electrons) to the N(E) vs. KE (Number of
electrons as a function of energy vs. the Kinetic energy
of the electrons) form of representation by dividing the
CPS (Counts per second) values by the KE values at each
data point (in our case the energy step size was 1 eV).
Figure 18 represents such a case for one spectrum.
This was performed based on the assumption that
along with the magnification of the signal for better peak
visibility, by multiplying the N(E) signal by the KE
values the noise also becomes magnified. On the other
hand, when moving from the E*N(E) vs. KE to the N(E)
vs. KE form of representation, the interval of interest
(875–1650 eV) approaches a horizontal line, as in Fig-
ure 18 (red). Not having any exact function to calculate
the real signal and relate the noise to, through this form
of representation it was possible to conduct the averaging
using a wider window.
The procedure was continued by finding the average
of the transformed signal by applying a moving average
for which a window of 21 data points was arbitrarily
chosen. Then the standard deviation from this averaged
signal was calculated for all of the 42 spectra (21 at point
A1 and 21 at point A2 on the sample), since the standard
deviation from the average was chosen to be used as a
representation of the noise content. The same procedure
was applied in all the spectra that were taken into
consideration in this study, and since the objective is just
a comparison of the noise levels of the spectra measured
at one point at different temperatures, we believe that
this form of approaching the problem is valid. Figure 19
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
150 Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152
Figure 17: Amplitude distribution of the measured noise (blue) and
the simulated noise (red)
Figure 15: Accumulated noise from the normalized noises of the 247
simulated data sets
Figure 16: Power spectral density of the accumulated noise from the
simulated data sets
Figure 14: Plot of the autocorrelation function of the accumulated
noise

presents the noise given as the peak-to-peak difference
and as a standard deviation for the 21 spectra measured
at point A1 and the 21 spectra measured at point A2 in
the interval 200–800 °C.
As can be seen from Figure 19, the values of the
standard deviation for the set of spectra measured at one
point on the sample are relatively constant, indicating
that the noise level in the AE spectra stayed almost the
same, even though they were measured in a temperature
interval 200–800 °C in steps of 30 °C.
5 CONCLUSIONS
The aim of this study was not to investigate in detail
all the contributions to the noise in the AE spectra and to
describe the theory behind each mechanism. Rather, it
was to better understand some of the properties of the
noise in the AE spectra that would be useful to us for
preparing the AE spectra for automated analyses.
Based on the results presented in this paper the
questions posed in the introduction can be answered as
follows:
1. Does the noise amplitude level vary with the kinetic
energy of the AE spectra? When observing the direct
form of the AE spectra the noise amplitude level does
not vary with the AE kinetic energy (Figure 12). This
is important because the same conclusions about the
noise (reached by analysing the higher-energy por-
tion of the spectra without spectral peaks) can be
safely extrapolated to other spectra regions.
2. What is the Fourier spectral constitution of noise –
does the measured noise come into the category of
"white noise"? The noise in the measured AE spectra
consists of basically all the frequencies (Figure 9).
The plot of the power spectral density (Figure 13)is
close enough to ideal white noise (in which case it
would be completely flat). The claim that the noise in
the measured AE spectra is close to ideal white noise
is further supported by the shape of the autocorrela-
tion function presented in Figure 15, where only one
strong peak at 0 shift is observed. From the signal-
processing point of view it is not important to what
sub-class (i.e., Shot) of white noise it actually be-
longs. The consequence of white noise is that it
cannot be successfully filtered out by any signal-pro-
cessing spectral method.
3. Is the noise temperature dependent? According to the
results presented in Figure 19, the conclusion is
reached that for the conditions in which the experi-
ments were carried out in this case, as the tempera-
ture of the sample increases from 200 °C to 800 °C
no significant change in the noise level of the AE
spectra can be observed. Therefore, as far as the noise
is concerned, the same procedures for the automatic
treatment of the AE spectra can be used for these
cases as well.
S1.Can the noise produced by the AE spectra simulator
be compared to the measured noise? The conclusion
is reached that the noise produced by the AE spectra
simulator can be compared to the noise in the
measured AE spectra (Figures 13 to 16). It is ob-
vious that the noise amplitude level does not change
with the AE kinetic energy and that the plot of the
power spectral density is close to that of ideal white
noise also for the noise from the simulated AE
spectra.
I. BELI^ et al.: NOISE IN AUGER ELECTRON SPECTRA: A SIGNAL-PROCESSING VIEW
Materiali in tehnologije / Materials and technology 53 (2019) 1, 143–152 151
Figure 19: Noise represented as the peak-to-peak difference and as
the standard deviation for the 21 Auger electron spectra measured at
point A1 and for the 21 spectra measured at point A2
Figure 18: Auger electron spectrum of NiTi alloy represented in E*N
(E) vs. kinetic energy (blue) and N (E)(red) vs. kinetic energy

S2.What are the differences between the measured and
simulated noise? Comparing Figure 13 and Figure
16 it is evident that the plot of the power spectral
density of the simulated noise comes slightly closer
to that of ideal white noise compared to the noise
from the measured AE spectra. This is a direct con-
sequence of the more uniform amplitude distribution
of the simulated noise compared to the measured one,
as shown in Figure 17.
S3.Can the simulated noise adequately represent the
measured noise or should the AE spectra simulator be
appropriately tuned in order to give a better represen-
tation of the measured noise? Based on the answers
to questions S1 and S2, it can be concluded that the
simulated noise does adequately represent the
measured noise. The fact that the simulated noise
shows some properties that come slightly closer to
the ideal white noise compared to the measured one
only serves better the intended purpose of using
simulated spectra for testing the noise-reduction
routines. This means that the simulated noise, being
more similar to white noise, is slightly harder to
remove than the measured noise; therefore, whatever
routine is developed that will be successful in re-
moving the simulated noise, will remove the
measured noise with even greater efficiency. There-
fore, no corrections are needed for the AE spectra
simulator in this regard.
The findings of the described research work on the
properties of AE spectral noise suggest a method for its
extraction.
Acknowledgement
Authors would like to acknowledge the financial
support provided by ARRS, The Slovenian Research
Agency, through the project groups P2-0132 Surface
Physics and Chemistry of Metallic Materials, and
P2-0056 Vacuum technique and materials for electronics.
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