In this paper, the solution of the problem of identification of thermal
properties of investigated multi-layer structure is presented. In order of
that, artificial neural network was used to find the set of thermal properties
for which the complex contrast characteric derived fits the best to the one
evaluated basing upon experimenatal data.Comment: Submitted on behalf of TIMA Editions
  (http://irevues.inist.fr/tima-editions

Duer, R.

Kosikowski, M.

Suszynski, Z.

English

arXiv

artificial neural network, thermal properties, invers problem, complex contrastIn this paper, the solution of the problem of identification of thermal properties of investigated multi-layer structure is presented. In order of that, artificial neural network was used to find the set of thermal properties for which the complex contrast characteric derived fits the best to the one evaluated basing upon experimenatal data

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 Nice, Côte d’Azur, France, 27-29 September 2006
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
THE APPLICATION OF ARTIFICIAL NEURAL NETWORK FOR
THE ASSESSMENT OF THERMAL PROPERTIES OF MULTILAYERED
SEMICONDUCTOR STRUCTURE
Zbigniew Suszyński 1, Mateusz Kosikowski 2, Radosław Duer 3
University of Technology Koszalin, Department of Electronics and Computer Science,
Śniadeckich 2, 75-453 Koszalin, Poland,
email: 1 zas@man.koszalin.pl , 2 kazuchiro@interia.pl, 3 rduer@man.koszalin.pl
ABSTRACT
This paper presents the method for determination of
thermal properties of multi-layered structure basing upon
experimental data acquired with the help of photo-
acoustic technique in harmonic modulation mode. The
method proposed is based upon the matching of
theoretical complex contrast characteristic of the
investigated object to the experimental contrast
characteristic realised by artificial neural network
1. INTRODUCTION
The non-destructive investigations of thermal
properties of solids are very important for the
semiconductor industry. Especially, in the case of high
power semiconductor devices, which are usually produced
as multli-layered planar structures, the quality of adhesion
between the layers is one of the most important factors of
reliability of such a device. The areas of weak adhesion
are characterised by high thermal impedance. Generally,
thermal properties of weak adhesion area are highly
diversified so it can be assumed that thermal non-
uniformity is present there [1]. The assessment of thermal
properties (such as diffusivity, effusivity, thickness of
layer) of such area is related to resolving the inverse
problem of deconvolution in order to estimate thermal
impedance of non-uniformity area. That was the
motivation for this contribution.
The method presented utilitizes Artificial Neural
Network (ANN) to resolve the inverse problem. In this
approach, well trained ANN identifies the set of thermal
properties for which the experimental complex contrast
characteristic (CTC) matches the best to the theoretical
CTC characteristic obtained from the model.
φ=0.3mm
 P = 1 [W]
 s
Si
Mo
 Eut Glass
 s
RrefΘ
Thremally
thick







Θ
Air
 d1
d2d3
d4
mmmmd 4.0;3.01 ∈
mmmmd 1.0;04.02 ∈
mmmmdd 44.0;34.021 ∈+
mpmd µ5;1.03 ∈
mmd 24 =
Fig.1. Profile of the experimental object.
2. THE EXPERIMENT
2.1. The object of investigation
The object investigated during photo-acoustic experiment
was typical high power thyristor structure. Three layers
can be distinguished in such a structure: silicon-eutectics-
molybdenum (Fig.1).
In the case of weak quality of adhesion the additional
layer of high thermal impedance can be formed in the
interface area between silicon and molybdenum. The
thermally thick piece of passivated glass was used as a
Zbigniew Suszyński, Mateusz Kosikowski, Radosław Duer3
The application of artificial neural network for the assessment of thermal properties ...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
reference object for calculations of complex contrast
characteristics.
2.2. The object of investigation
The experimental data were collected with the help of
photo-acoustic technique in harmonic excitations mode
with the standard measurement set-up [2]. The source of
energy excitation was modulated laser beam of power
about 1W. The frequencies of modulation were ranged
from 106Hz to 586Hz. The signal of temperature response
was acquired in both the amplitude and phase images [3].
The examples taken from the sequence of both the
amplitude and phase images are presented in Fig.2. This
figure also presents CTC images.
Am
pl
itu
de
Ph
a
se
CT
C
106 Hz 131 Hz 306Hz
Fig.2. Examples of amplitude, phase and CTC images of investigated object
For the purpose of proper analysis of thermal parameters
of the object basing upon the results of photo-acoustic
measurements it is mandatory to eliminate the influence of
linear distortions introduced by each element of the photo-
acoustic set-up. The best for that is the use of comparative
method of analysis – for example Complex Thermal
Contrast method [4, 5]. The mean value of temperature
response signal from both the area of non-uniformity and
the reference object were used further for determination of
complex contrast characteristics.
2.3. 1-D TLM model
1-D TLM model was used in order to derive the
theoretical complex contrast characteristics. The model
utilities the electro-thermal analogy for determination of
R
1
2 R
1
2 R
1
2
R
1
2 R
1
2 R
1
2
R
1
2 R
1
2 R
1
2
Zbigniew Suszyński, Mateusz Kosikowski, Radosław Duer3
The application of artificial neural network for the assessment of thermal properties ...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
temperature response. In this case, the investigated
structure is represented by four-terminal network
(Fig. 3) [5, 6].
)1(
ΘK
)2(
ΘK
)3(
ΘK )4(ΘK1Θ 2Θ 3Θ 4Θ 5Θ
Fig. 3. Four-terminal network model of 4-layer structure.


















+
−+
−+
−⋅=Θ
)4()3(
11
2)3(
12)3(
11
)2(
11
2)2(
12)2(
11
)1(
11
2)1(
12)1(
111
)(
)(
)(~
CZz
z
zz
z
zz
z
zP
 (1)
)sinh(
)cosh(
11 Γ
Γ
= CZz )sinh(
1
12 Γ
= CZz (2)
di ⋅+=Γ
α
ω
2
)1(
ωε 2
1)1(
S
iZC += (3)
nCfrontn WZP
)1(~
=Θ (4)
                                         2 ifor   
)( thick  thermallyif 1  ifor 
  )( thin  thermallyif  1  ifor 
sinh
cosh
sinh
1
sinh
cosh
1
sinh
cosh
1
1
1,1
1
1
1
2
1
1
1
1
1
≥
>>=
≤=

















+
Γ
Γ






Γ
−
Γ
Γ
Γ
Γ
=
+−+
−
+−
+−
+−
+−
+−
µ
µ
ε
α
d
d
W
inn
i
in
in
in
in
in
i (5)
Where:
1Θ - temperature of input of analyzed object [K], Γ - operator of propagation,
CZ - characteristic impedance [K/W], P
~
- stimulation power ω  - frequency [Hz],
ε  - thermal effusivity [ -1-20.5 KmWs ⋅⋅ ], α  - thermal diffusivity [ 12 −⋅ sm ],
d - thickness of layer [m], n – number of layers, i – number of particular layer.
Zbigniew Suszyński, Mateusz Kosikowski, Radosław Duer3
The application of artificial neural network for the assessment of thermal properties ...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
Temperature response at the surface of investigated object
is given by the equation (1). It is possible to transform the
equation (1) into more convenient form (4) using the
recursive coefficient Wi given by the equation (5)  [7].
The values of temperature obtained were used
for derivation of complex contrast characteristics.
Complex contrast is defined as difference between
normalized complex temperatures for both the
investigated and the reference objects. Thus, CTC
presents the changes of both amplitude and phase of
temperature disturbance [8].
INPUT (CTC  characteristics)
…
Fuzzy system
(preliminary data)
ANN
…
a)
OUTPUT (thermal parameters)
b)
Fig. 4. Examples of CTC theoretical characteristics (a). Structure of designed system (b).
Tab. 1. The effusivity and diffusivity values of particular layer of investigated object appointed by ANN. The thickness
ranges of each layer used for ANN training are shown in Fig.1.
Fig. 5. Example-results of pattern mach by ANN.
Area 1
(NNet result)
Area 1
(Real Value)
Area 2
(NNet result)
Area 2
(Real Value)
Sid 319µm 311µm 387 µm 396µm
Aird 4.8 µm 30.3 µm 0.1 nm 0
Eutε 18068 no data 15087 no datavar
u
ab
le
s
Eutα 8531 no data 8968 no data
Siε 14000 Airε 65 Moε 18800
Co
n
st
.
Siα 8e-5 Airα 2.14e-5 Moα 5.38e-5
Zbigniew Suszyński, Mateusz Kosikowski, Radosław Duer3
The application of artificial neural network for the assessment of thermal properties ...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
3. THE RESULTS OF THE ANALYSIS OF
THERMAL PROPERTIES
Fig.5 presents the comparison of CTC contrasts
characteristics obtained from the ANN and the CTC
contrasts characteristics values evaluated from
experimental data. The relevant sets of geometrical and
thermal parameters of particular layers of the object are
presented in Tab.1. Solid line represents the CTC
characteristics obtained from ANN and dots represents the
values of CTC characteristics determined upon
experimental data. The evaluated values of thickness of
the silicon and the air layer are respectively: 319µm and
4.8µm (for the area of non-uniformity Fig.2 – area 1).
These vales obtained for the uniform areas (Fig.2 – area
2) are as following: 387µm and 0.1nm.
For the purpose of verification of ANN
simulation, the results of destructive investigations were
used. Those investigations were performed for the same
high power thyristor structure after photo-acoustic
experiment. The results of this kind of investigations are
presented in Tab.1 (Real Values). As it follows, the
thickness of silicon layer as well as the thickness of air
layer is in high convergence for the uniform area. The
zero value means that spacial resolution of destructive
investigation method was to low so it could not be
compared with the value of 0.1nm achieved for the ANN
method
Concerning the area of non-uniformity, both of
the geometrical parameters investigated are different from
each other. For the case of non-uniformity area it is
caused by the insensibility of the model for the air layer
thickness above 5µm so it was the biggest thickness of air
layer assumed during thermal modelling and training of
ANN.
4. CONCLUSIONS
The final results obtained are encouraging
concerning the fact that the convergence of experimental
characteristics to the ones obtained from ANN was good.
Differences can be caused by the use of 1D thermal
model. The limitations of 1D model in comparison to the
2D model can be significant. The solution for that can be
usage of 2D or 3D thermal models for the purpose of
ANN training. However, it will be related with extensive
increase of the independent variables as well as the
consumption of computer system resources. Nevertheless,
the method for thermal properties analysis presented
allows to utilise the advantages of CTC contrast method
and the quickness of artificial neural networks. The
solution of inverse problem given that way is insensible to
the disturbances of measurement data as well as
measurement errors. The trained ANN produces relevant
and precise enough results even with significantly wrong
value of experimental CTC characteristics for some
frequency, which can appear due to large error made
during the measurements for this frequency.
5. REFERENCES
[1] Z. Suszyński, R. Duer: Photoacoustic inspection of
thermal properties of layered structure with pulse
excitations, Microelectronics Reliability 45 (2005),
pp. 1910-1915,
[2] A. C. Tam: Applications of photoacoustic sensing
techniques, Rev. Mod. Phys., Vol. 58, 1986,
pp. 381-431.
[3] A. Rosencwaig, J. Opsal: Thermal wave imaging
with thermo-acoustic detection. IEEE Trans.
Ultrason. Freq. Contr., vol. UFFC-33, pp. 516-527,
1986.
[4] Z. Suszyński, R. Arsoba, P. Majchrzak: Thermal
Diagnostic of Power Thyristor. Proceedings of the
7th THERMINIC Workshop, Paris, France, 2001,
pp. 180-184.
[5] Z. Suszyński: Termofalowe metody badania
materiałów i przyrządów elektronicznych,
Wydawnictwo Uczelniane Politechniki
Koszalińskiej, 2001 (in Polish).
[6] D. de Cogan: Propagation analysis for thermal
modeling. IEEE Trans. On Comp., Pack. And
Manuf. Techn., A, 21, 3, pp.418.
[7] R. Arsoba: Badanie jakości termokompresji w
strukturach tyrystorowych metodami termofalowymi
dla pobudzeń zmiennych w czasie lub przestrzeni, ,
Wydawnictwo Uczelniane Politechniki
Koszalińskiej, 2005 (in Polish), p. 96-104.
[8] Z. Suszyński, P. Majchrzak: The idea of complex
temperature contrast images for thermal-waves
measurements, J. Phys. IV France 117, pp. 95-100.


The application of Artificial Neural Network for the assessment of thermal properties of multi-layer semiconductor structure

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