Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation
The analysis of photo-thermo-acoustic transformation in materials with the modified properties of a surface layer has been made in this work. Formation of a photoacoustic response in a layered structure of the type “implanted layer + crystalline Si substrate” as a result of its irradiation by one...
Gespeichert in:
| Datum: | 2011 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
|
| Schriftenreihe: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/117708 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation / R. Burbelo, M. Isaiev, A. Kuzmich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 167-169. — Бібліогр.: 4 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-117708 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1177082017-05-27T03:05:47Z Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation Burbelo, R. Isaiev, M. Kuzmich, A. The analysis of photo-thermo-acoustic transformation in materials with the modified properties of a surface layer has been made in this work. Formation of a photoacoustic response in a layered structure of the type “implanted layer + crystalline Si substrate” as a result of its irradiation by one laser pulse with duration of 20 ns is analyzed. 2011 Article Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation / R. Burbelo, M. Isaiev, A. Kuzmich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 167-169. — Бібліогр.: 4 назв. — англ. 1560-8034 PACS 78.20.nb, 81.70.Cv http://dspace.nbuv.gov.ua/handle/123456789/117708 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The analysis of photo-thermo-acoustic transformation in materials with the
modified properties of a surface layer has been made in this work. Formation of a photoacoustic
response in a layered structure of the type “implanted layer + crystalline Si
substrate” as a result of its irradiation by one laser pulse with duration of 20 ns is
analyzed. |
| format |
Article |
| author |
Burbelo, R. Isaiev, M. Kuzmich, A. |
| spellingShingle |
Burbelo, R. Isaiev, M. Kuzmich, A. Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Burbelo, R. Isaiev, M. Kuzmich, A. |
| author_sort |
Burbelo, R. |
| title |
Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation |
| title_short |
Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation |
| title_full |
Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation |
| title_fullStr |
Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation |
| title_full_unstemmed |
Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation |
| title_sort |
photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117708 |
| citation_txt |
Photo-thermo-acoustic analysis of heterogeneous semiconductor structures under pulse laser irradiation / R. Burbelo, M. Isaiev, A. Kuzmich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 167-169. — Бібліогр.: 4 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT burbelor photothermoacousticanalysisofheterogeneoussemiconductorstructuresunderpulselaserirradiation AT isaievm photothermoacousticanalysisofheterogeneoussemiconductorstructuresunderpulselaserirradiation AT kuzmicha photothermoacousticanalysisofheterogeneoussemiconductorstructuresunderpulselaserirradiation |
| first_indexed |
2025-07-08T12:40:08Z |
| last_indexed |
2025-07-08T12:40:08Z |
| _version_ |
1837082514269667328 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 167-169.
PACS 78.20.nb, 81.70.Cv
Photo-thermo-acoustic analysis of heterogeneous semiconductor
structures under pulse laser irradiation
R. Burbelo1, M. Isaiev2, A. Kuzmich3
Taras Shevchenko Kyiv National University, Physics Department,
64, Volodymyrs’ka str., 01601 Kyiv, Ukraine
E-mail: rmb@univ.kiev.ua1, isaev@univ.kiev.ua2, kuzmich@univ.kiev.ua3
Abstract. The analysis of photo-thermo-acoustic transformation in materials with the
modified properties of a surface layer has been made in this work. Formation of a photo-
acoustic response in a layered structure of the type “implanted layer + crystalline Si
substrate” as a result of its irradiation by one laser pulse with duration of 20 ns is
analyzed.
Keywords: photo-acoustics, heterogeneous structure.
Manuscript received 01.10.10; accepted for publication 16.03.11; published online 30.06.11.
1. Introduction
The basis of modern materials science is materials
inhomogeneous in their structure, in which the region of
modification is characterized by the size of nano- and
submicron scales. These issues include the structure that
in accord with technological needs has significant
changes in properties of a subsurface layer, such as
epitaxial and porous layers, ranges of doping in
semiconductor structures and others.
Clearly, in practice the study of structures with
regions of heterogeneity of such magnitude by photo-
acoustic (PA) methods using the sources of radiation
with the intensity modulated by the harmonic law is
quite complicated task. For example, during irradiation
of silicon with the frequency close to 30 MHz the length
of thermal diffusion (the main parameter of resolution in
the PA measurements) possesses the value
approximately 1 µm.
On the other hand, it is possible in principle to
investigate structures with characteristic sizes at the
submicron level, using for excitation of the PA signal by
short (about 10 ns) laser pulses.
This work presents a mathematical model of photo-
thermo-acoustic transformation in heterogeneous media.
Formation of an acoustic signal in a layered structure of
the type “implanted layer + crystalline Si substrate” as a
result of its irradiation by the laser pulse with duration
20 ns is analyzed on the base of the model proposed. The
case is described when layers of such structure differ
only by thermal parameters. The influence of value ratio
between the thermal parameters of structure layers on
formation of PA response is analyzed. It is shown that in
the case of strong absorption, the value of these ratios
influences significantly the PA signal even for
submicron size structures.
2. Evolution of temperature distribution in
inhomogeneous solids
Let’s consider the following non-stationary heat
equation
( ) ( ) ( ) zetg
c
RI
z
TzD
zt
T α−⋅⋅
ρ
α⋅−
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
∂
∂
=
∂
∂ 1 (1)
where g(t) describes the temporal distribution of the
incident light intensity. In the case of a single pulse,
g(t) = H(t) – H(t – τ), H(t) is the Heaviside function.
In all these calculations, we will take I =
1 MW/cm2, R = 0.37, τ = 20 ns, , c =
0.8 J/(g·K), ρ = 2.3 g/cm
-14 cm105 ⋅=α
3 as constants and will examine
only changes in the thermal diffusivity.
The following boundary conditions are more often
realized in practice:
• ( ) 0
0
=∂∂
=z
zT – absence of heat outflow from
the sample’s top surface into external environment;
• 0
max
==zzT – contact of the sample’s bottom
surface with the thermostat ( – thickness
of the sample);
m300max μ=z
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
167
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 167-169.
The initial conditions are as follows:
• 00 ==tT – the uniform distribution of the
temperature in the sample before irradiation (we will
accept that the initial temperature is zero without any
loss of generality: we will consider only growth over the
initial temperature).
For definiteness, the case when the thickness of
layer l lies within the limits of 0.5 to 1 µm (thickness of
the sample ) is considered. The value of
thermal diffusivity for the top layer is D
m300max μ=z
1 =0.09 cm2/s
and for crystal-substrate material is D2 = 0.94 cm2/s. The
value corresponds to a real situation [1], for example,
when surface of the monocrystalline Si plate is
processed (i.e., under modification). The time
dependence of surface temperature ( ) for different
thicknesses of the modified layer in this structure is
shown in Fig. 1. The solid line illustrates
( )tT ,0
( )tT ,0 for
homogeneous samples with D1 and D2. As one can see,
with increasing the layer thickness, surface temperature
increases, too (temperature at the heated end for a
homogeneous sample and that for the sample with a
modified surface layer are different in their magnitude
up to 80 K), and, as shown in [2, 3] (where more detail
evolution of temperature distribution is considered), the
region of thermal energy localization is reduced.
As seen from this figure, at the initial stage of
heating (when 1
2 Dlt < − thermal energy is
concentrated in the first layer) the time dependence of
surface temperature ( ) has the character similar to
that of the curve ( ) for a homogeneous sample
with the coefficient of thermal diffusivity D
( )tT ,0
( )tT ,0
1. As heat
diffuses into the second layer, the curve of time
dependence of surface temperature gradually gets a
shape of the curve for a homogeneous sample
with the coefficient of thermal diffusivity D
( )tT ,0
2, and in the
case 1
2 Dlt >> they have the same asymptote.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 1. Time dependence of the surface temperature for two-
layer structure with different values of the thickness of
modified layer.
3. Thermo-elastic displacements
To calculate the elastic displacements, we use the one-
dimensional thermo-elasticity equation [4]
z
T
z
uv
t
u
∂
∂
β=
∂
∂
−
∂
∂
2
2
2
2
2
, (2)
here u is the elastic displacement inside material (caused
by non-equilibrium temperature distribution); v – sound
velocity; β = αT (3λ + 2μ) / ρ; λ and μ – Lame
parameters; αT – coefficient of the lattice thermal
expansion.
To solve the equation, let us use the following
boundary conditions – the bottom surface of the sample
is rigidly fixed and the top is free:
⎪
⎩
⎪
⎨
⎧
=
=
∂
∂
=
=
.0
0
max
0
zz
z
u
z
u
In accordance with the given boundary conditions,
the function ( )tzu , can be written as follows:
( ) ( ) ( )∑
∞
=
=
0
cos,
m
mm zatftzu ,
max
1
2 z
mam ⎟
⎠
⎞
⎜
⎝
⎛ π+
π
= . (3)
Putting (3) into the formula (2), taking into account
the boundary conditions to the heat equation (1) and the
linear independence of the basic functions ( )zamcos , we
can get the equation for the coefficients fm(t):
( ) ( ) ( )∑
∞
=
β−=+
0
22
2
2
d
d
n
nmnnmm
m ctbatfav
t
tf
, (4)
where
( ) ( ) ( ) zzatzT
z
tb n
z
n dcos,2 max
0max
⋅= ∫ ,
( ) ( )
( )
( )⎪
⎪
⎩
⎪⎪
⎨
⎧
∈+=+
π−
∈=+
π++=
=⋅= ∫
.,12,2
,2,
1
2
dcossin2 max
0max
Z
Z
ppnm
mn
ppnm
nm
zzaza
z
c m
z
nnm
Considering zero initial conditions
( ( ) ( ) 0000, =⇒= mfzu and
( ) ( ) 000/0, =′⇒=∂∂ mftzu ), we can obtain a solution
of the equation (3) in the form
( ) ( )( ) ( ssbtsva
a
ac
v
tf n
n
t
m
m
n
nmm dsin
0 0
⋅−
β
= ∑ ∫
∞
=
) ,
and, accordingly, for the elastic displacements
( )( ) ( ) ( .cosdsin
0 0 0
∑∑ ∫
∞
=
∞
=
×⋅−
β
=
m
mn
n
t
m
m
n
nm zassbtsva
a
ac
v
u )
168
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 167-169.
Fig. 2. Elastic displacements of top surface for the samples
with different values of the thermal diffusivity coefficient.
Fig. 3. Time dependence of elastic displacements for the top
surface of structures with different thicknesses of the modified
layer.
In Fig. 2, the time dependence of surface
displacements ( ) for homogeneous samples with
different values of the thermal diffusivity coefficients
are presented. Fig. 2 shows that the curve
( )tu ,0
( )tu ,0 has
oscillating character with frequencies corresponding to
resonance frequencies of the sample, i.e. the oscillating
nature of the curves in Fig. 2 is a consequence with
multiple reflection of sound waves in the system “top –
bottom boundary”. Fig. 2 shows that oscillation of the
function is non-stationary (amplitude and phase
shift depend on time), but reaches the stationary mode
with time.
( )tu ,0
In Fig. 3, the time dependence for surface
displacements in the structure with the modified
subsurface layer is presented. Thicknesses of the layer
correspond to the situation that we considered in the
item 2. Fig. 3 shows that, with increasing the thickness
of the modified layer, the amplitude of displacements
increases, which correlates with the time dependence of
surface temperature (Fig. 1). As one can see from Fig. 3,
after the end of laser pulse, material continues to expand,
which is caused by further redistribution of the sources
of thermo-elastic stresses (heat diffusion) and with the
mass inertia of the system.
4. Conclusions
In this work, the mathematical model of photo-thermo-
acoustic transformation in heterogeneous media is
presented. Being based on the proposed model,
formation of the acoustic signal in a layered structure of
the type “implanted layer + crystalline Si substrate” as a
result of its irradiation by the laser pulse with duration
20 ns is analyzed. The case when layers of this structure
differ only by thermal parameters has been described.
The influence of value ratio between the thermal
parameters of structure layers on formation of the photo-
acoustic response has been analyzed. It has been shown
that in the case of strong absorption, the value of these
ratios significantly influences the photo-acoustic signal
even for submicron size structures.
References
1. A. Okhotin, Thermal Conduction of Solids
(Handbook). Energoatomizdat, Moscow, 1984 (in
Russian).
2. R. Burbelo, M. Isaiev, A. Kuzmich, Evolution of
temperature distribution in implanted Si-based
structures: pulse mode of laser irradiation // Ukr. J.
Phys., 55 (3), p. 317-321 (2010).
3. R. Burbelo, M. Isaiev, A. Kuzmich, Photothermal
analysis of heterogeneous semiconductor structures
under pulse laser irradiation // Semiconductor
Physics, Quantum Electronics & Optoelectronics,
12(4), p. 403-405 (2009).
4. A. Kovalenko, Thermoelasticity. Vyshcha Shkola,
Kyiv, 1975 (in Russian).
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
169
|