Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique
Volume-gradient photovoltage and birefrigence caused by a difference of main mechanical stress components have been studied in the Ge-monocrystal with step-like distribution of the doping impurity concentration, N. The qualitative agreement between the function obtained by integration of the spatial...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
1999
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| Цитувати: | Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique / B.K. Serdega, Ye.F. Venger, Ye.V. Nikitenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 153-156. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1179562017-05-28T03:04:36Z Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique Serdega, B.K. Venger, Ye.F. Nikitenko, Ye.V. Volume-gradient photovoltage and birefrigence caused by a difference of main mechanical stress components have been studied in the Ge-monocrystal with step-like distribution of the doping impurity concentration, N. The qualitative agreement between the function obtained by integration of the spatial dependence of the anisotropy and of the coordinate dependence of the photovoltage was observed. Using this fact, the conclusion is made that the features of thermoelastic mechanical stress can be distribution of expressed by the dependence |σz - σy| ~ d²N/dz². Remove selected 1999 Article Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique / B.K. Serdega, Ye.F. Venger, Ye.V. Nikitenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 153-156. — Бібліогр.: 7 назв. — англ. 1560-8034 PACS 61.72 http://dspace.nbuv.gov.ua/handle/123456789/117956 535.3 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Volume-gradient photovoltage and birefrigence caused by a difference of main mechanical stress components have been studied in the Ge-monocrystal with step-like distribution of the doping impurity concentration, N. The qualitative agreement between the function obtained by integration of the spatial dependence of the anisotropy and of the coordinate dependence of the photovoltage was observed. Using this fact, the conclusion is made that the features of thermoelastic mechanical stress can be distribution of expressed by the dependence |σz - σy| ~ d²N/dz².
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Serdega, B.K. Venger, Ye.F. Nikitenko, Ye.V. |
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Serdega, B.K. Venger, Ye.F. Nikitenko, Ye.V. Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique Semiconductor Physics Quantum Electronics & Optoelectronics |
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Serdega, B.K. Venger, Ye.F. Nikitenko, Ye.V. |
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Serdega, B.K. |
| title |
Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique |
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Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique |
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Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique |
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Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique |
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Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique |
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thermoelasticity in ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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1999 |
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Thermoelasticity in Ge due to nonuniform distribution of doping impurity studied by light polarization modulation technique / B.K. Serdega, Ye.F. Venger, Ye.V. Nikitenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 153-156. — Бібліогр.: 7 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T13:04:14Z |
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| fulltext |
153© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 1. P. 153-156.
1. It is well-known that defects in the crystal lattice
lead to the appearance of local deformations. Also it is
known that the group of defects originated from doping
and background impurities, or some technological caus-
es, distributed nonuniformly in an ordered way, can re-
sult in the appearance of macroscopic deformations [1].
It means that the ordered nonuniformities which, in real
crystals, are created by the directed or uncontrolled dop-
ing, create a nonzero difference of main stress compo-
nents at distances much longer than the lattice parame-
ter. At the same time, a quantitative or, at least, a func-
tional connection between parameters of the spatial dis-
tribution of defect concentration and the magnitudes of
deformation-induced mechanical stresses remains to be
studied yet. To the best of our knowledge, the works as-
certaining the relation between distribution of residual
(intrinsic) mechanical stresses in a crystal and the char-
acteristics of nonuniformities of composition are absent.
The only exception is the work [2] where the distribution
of stress is studied for the particular case of the doping
impurity diffusion from the crystal surface in the z-axis
direction.
It can be supposed, extending the model of thermal
stresses caused by a temperature gradient [3], that the
mechanical stress, σ, occurring in the nonuniform con-
centration field (an analog of a temperature field) is pro-
portional to the magnitude d2N/dx2, where N is the dis-
tribution function of the defect (a doping impurity) con-
centration. Such an analogy can be based on a fact that
if the mean interatomic distance depends on the doping
impurity concentration (composition of the compound),
then its spatial variation is accompanied by the appear-
PACS 61.72, UDK 535.3
Thermoelasticity in Ge due to nonuniform distribution of
doping impurity studied by light polarization modulation
technique
B. K. Serdega, Ye. F. Venger, Ye. V. Nikitenko
Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv, 252028, Ukraine,
phone (044) 265 4020, e-mail: bshl@polarget.semicond.kiev.ua
Abstract. Volume-gradient photovoltage and birefrigence caused by a difference of main mechan-
ical stress components have been studied in the Ge-monocrystal with step-like distribution of the
doping impurity concentration, N. The qualitative agreement between the function obtained by
integration of the spatial dependence of the anisotropy and of the coordinate dependence of the
photovoltage was observed. Using this fact, the conclusion is made that the features of thermoelastic
mechanical stress can be distribution of expressed by the dependence |σ
z
- σ
y
| ~ d2N/dz2.
Keywords: double refraction, polarization, modulation, photovoltage, anisotropy, thermal stress.
Paper received 27.01.99; revised manuscript received 08.04.99; accepted for publication 19.04.99.
B. K. Serdega et al.: Thermoelasticity in Ge due to nonuniform distribution ...
154 SQO, 2(1), 1999
ance of the uncompensated deformation component. If
this is the case, then, taking into account the macroscop-
ic scale of nonuniformities, it appears to be possible to
study their spatial distribution using one of known tech-
niques. This is the aim of the present study.
Its idea consists in the following. In a sample of a
semiconductor crystal with a step-like coordinate depen-
dence of the electrically active doping impurity the re-
spective distribution of the volume-gradient photovolt-
age is measured [4] and compared with the experimen-
tally found coordinate dependence of the value of the
main component (Fig. 1). If the assumption is valid that
the dependence of the stress in the nonunformity region
has the form σ ∼ d2N/dz2, then the function obtained by
the double integration of the function σ(z) (Fig. 1c), and
the integral of the volume-gradient photovoltage Å(z)
(Fig. 1b) should coincide with the function N(z) (Fig. 1a).
2. Presently, various experimental methods are used
for measurements of stressed-deflected mode of aniso-
tropic solids: tensometry using the test structures, holo-
graphic interferometry, optopolarization method in a
wide range of electromagnetic waves [1]. Among all these
methods the most informative and having the highest
detection ability is the method based on measurement of
double refraction with modulation of electromagnetic ra-
diation [5]. This is related to the fact that the polariza-
tion mode representing the spatial characteristic of the
wave is described by a set of parameters, i. e., by compo-
nents of Maxwell-Jones or Stokes vectors [5]. Therefore,
in contrast to modulations of other physical magnitudes
dealing with one parameter only, the polarization mod-
ulation can be considered as the two-dimensional influ-
ence on the wave. It is this fact that provides high infor-
mation ability of methods and set-up based on the po-
larization modulation. Besides, the method possessing
the advantages of principles of differential spectrosco-
py, provides higher detective ability in respect to the mag-
nitude of anisotropy of dielectric properties.
It is also worth noting that the macroscopic size of
above mentioned nonuniformities makes it possible to
apply optopolarization techniques for investigation of
their properties. We mean here their spatial resolution
ability, when the diameter of the probing beam is less
than the characteristic size of nonuniformity, which al-
lows to reliably identify the features of the spatial distri-
bution of nonuniformities.
3. Since the expected regularity of the voltage depen-
dence on the characteristic of the defect distribution may
be of a general character, any semiconductor material
can be used for its experimental determination. Here,
however, several facts should be taken into account. First
of all, the volume-gradient photovoltage should neces-
sarily reflect the actual characteristic of the nonunifor-
mity. To ensure this, the next hierarchy of dimensions
should be chosen: d < L < l, where d is the diameter of
the probing light beam; L is the diffusion length of elec-
tron-hole pairs; l is the size of the nonuniformity in the
direction of measurements. It is essential that parame-
ters of nonuniformity are stable in the direction normal
to the crystal surface, at least, at a distance of the minor-
ity carrier diffusion length.
In view of the above mentioned and some other cir-
cumstances, a Ge single crystal seems to be the most ap-
propriate material to represent the discussed model. For
this purpose the single crystalline ingot was grown using
Czochralski method with in-situ formation of p+-p -junc-
tion by addition into the melt metal In as a dopant. The
junction region, 1 mm thick, was situated between ap-
proximately uniform, in respect to their resistivity, parts
of the ingot with resistivities of 3 and 0.5 Ω×cm. The
sample was cut from the ingot in the form of a bar with
dimensions l
z
×l
y
×l
x
= 10×4×1 mm, so that the gradient of
nonuniformity was directed along their longest side and
the p+-p - junction was situated near the middle of the
sample perpendicular to the largest side of the sample.
The standard mechanical and chemical treatment was
used to fabricate not only a mirror, but also a perfect
plane at the sample surface which is necessary for opto-
polarization measurements. Ohmic contacts at the sam-
ple end faces, created by tin welding, were used for con-
0
2
4
6
8
10
12
14
1 4 7 10 13 16 19 22
C
o
n
c
e
n
tr
a
ti
o
n
,
re
l.
u
n
.
-5
0
5
10
15
1 4 7 10 13 16 19 22P
h
o
to
-e
.m
.f
.,
r
e
l.
u
n
-1
0
1
0
1 4 7 10 13 16 19 22
Z - coordinate, arb. un.
M
e
c
h
a
n
ic
a
l
s
tr
e
s
s
,
re
l.
u
n
.
Fig. 1. Distributions of the doping impurity in the crystal (a),
of respective volume-gradient photo -e.m.f. (b) and of mechan-
ical stress (c).
a)
b)
c)
B. K. Serdega et al.: Thermoelasticity in Ge due to nonuniform distribution ...
155SQO, 2(1), 1999
nection to the measuring amplifier. The dependence of
the volume-gradient photovoltage on the coordinate of
the light beam at the sample surface was measured dur-
ing the sample displacement along the z axis by a con-
ventional technique using the synchronous phase detec-
tion.
Regarding the measurement of mechanical stress, in
our case the technique was needed which would provide
detection of its localization in the near-surface layer with
the thickness shorter than the minority carrier diffusion
length. As an effective technique of such type one can
chose the way used in measurements of double refrac-
tion in reflection [5]. This technique is based on the fact
(Fig. 2) that, at high values of an absorption index, the
reflection of light by a substance occurs in the layer thick-
ness of which is determined by the absorption length. If,
in this case, the reflection takes place normally to the
surface, then the polarization mode of the light changes
caused by anisotropy of dielectric properties induced by
the elastic deformation of the crystal (due to an external
force or a residual strain) by the magnitude related to
the difference of main stress components acting in the
plane z.
The polarization mode of reflected light was analy-
sed by the set-up consisting of the polarization modula-
tor and the linear polarizer, representing, in fact, the dy-
namic analyser. Since the orientation of optical indica-
trix of the sample is known a priori, because it is related
to the doping impurity gradient, this fact enabled one to
choose the linear polarization mode as an initial mode.
Its orientation, in respect to the gradient direction, was
set at the angle 450, and the modulator was tuned, by
adjusting the azimuthal position, for messuring the cir-
cular component of light. This component, measured by
the selective nanovoltmeter at a frequency of modulator,
appeared as a part of elliptically polarized, in the general
case, reflected light and served as a measure of the bere-
frigence magnitude, that is, of a deformation value.
As a source of light the He-Ne laser LG-126 was used,
the radiation of which at the wavelength 1.15 µm is pho-
toactive for Ge crystal, that is, effective for photovoltage
generation. The respective absorption coefficient at room
temperature, α, is of the order of 104 cm-1, and α-1< L,
which satisfies the condition of the experiment. The lat-
ter condition is necessary for reliable detlecting the char-
acter of nonuniformity in the photovoltage effect. The
laser beam was focused to the light spot with diameter
d ≈ 0.1 mm at the surface of the sample which could be
displaced in a controllable manner in respect to the beam
along the z axis. Each measurement was completed with
the sample returning to the strictly fixed initial position.
This allowed one to compare with each other the distri-
butions of the photoelectric and optical signals, which
were measured and recorded by plotter.
4. Results of measurements are presented in Fig. 3a,
where curves 1 and 2 represent the distributions of the
optical signal and of its integral, respectively. In Fig. 3b
the curve 2 from Fig. 3a is shown for comparison with
the photovoltage function. It can be seen that, differing
in details, the curves in Fig. 3b agree in main features, in
particular, in positions of maximums. It means that the
law σ
õ
-σ
ó
∼ d2N/dz2 is actually valid.
Really, the curve 1 in Fig. 3a is very similar, in its
shape, to the plot of voltage in Fig. 1c. At the same time,
it can be seen that the actual structure of p+-p -junction
is, nevertheless, different from the ideal one. So, the pho-
tovoltage function is asymmetrical in respect to the junc-
tion plane, which can be due to the fact that concentra-
tions, and, in turn, lifetimes at both sides of the junction
are strongly different. Besides, the junction itself is more
non-monotonic, than it is shown in Fig 1a. This is em-
phasized by a complicated form of the curve 1 in Fig. 3a,
representing the second derivative in respect to concen-
tration, a function which is more sensitive to nonunifor-
mities than the volume-gradient photovoltage represented
by the first derivative.
It should be noted that the amplitudes of measured
signals and calculated curves are presented in arbitrary
units. The matter is that the comparison in absolute units
and, therefore, in the same dimensionalities has sense only
for results of single integration of the photovoltage func-
tion and of double integration of the optical signal. How-
Fig. 2. The optical layout of the experiment (a) and conditions
of the sample illumination (b). LG-126 is the He-Ne laser, S �
the sample, PM is the photoelastic modulator of polarization,
P � the polarizer, PD � the Ge photodiode, AR is the anisotro-
pic reflector, Å~ � the strength of the electric field of the wave.
a)
b)
AR
LG -126
S
PM
P
PD
y
x
z
y
z
E∼
B. K. Serdega et al.: Thermoelasticity in Ge due to nonuniform distribution ...
156 SQO, 2(1), 1999
ever, in this case, the respective constants of integration,
one for the photovoltage and two constants for the pho-
toelasticity, must be known. For their determination ad-
ditional measurements are required, which do not pro-
vide new information for the problem solution. The main
conclusion drawn from Fig. 3b is that the inflection points
in the two-dimensional plot of the resistivity form a sur-
face (a plane in the particular case) dividing the regions
with different compositions and opposite signs of me-
chanical stress.
It is of interest to consider the obtained result in re-
spect to the paper [2]. The calculated there coordinate
dependencies of mechanical strain on the form of the dis-
tribution function of diffusing impurity have the form
(in the coordinates of Fig. 2): σ
x
∼ exp [(a - z)2 ⁄ 4Dt] � for
Gauss distribution and σ
x
∼ erfc[(a - y) ⁄ (4Dt)1/2] for the
distribution described by the complementary error func-
tion (here a is the thickness of the sample, D, t are the
coefficient of diffusion and diffusion time, respectively).
It should be noted that in both cases the distribution func-
tion of stress follows the impurity distribution function.
But just this should be expected, if we rely on the regu-
larity ascertained in this work, since the double differen-
b)
a)
-5
0
5
10
15
20
1 3 5 7 9 11 13 15 17 19 21 23
O
p
ti
c
a
l
s
ig
n
a
l,
i
n
te
g
ra
l,
r
e
l.
u
n
.
1
2
-5
0
5
10
15
20
1 3 5 7 9 11 13 15 17 19 21 23
Z- coordinate, arb. un.
P
h
o
to
-e
.m
.f
.,
i
n
te
g
ra
l,
r
e
l.
u
n
.
2
3 2
3
Fig. 3. Distributions, along the doping impurity gradient, of
the birefringence signal of double refraction (curve 1), its inte-
gral (curve 2) (a) and that of the photo-e.m.f. signal (curve 3)
compared to the curve 2 in the Fig. 1a (b).
tiation of exponential functions which were used to char-
acterize the diffusion, does not change their form. And,
finally, we should note that the established coordinate
dependence of the stress is a consequence of the Poisson
equation solution for the displacement u created by the
specific force f, i.e., by stress [7, p.242]: ∇2u = - f/τ, where
τ -1 is the coefficient of proportionality, the physical sense
of which in each specific case is determined by the re-
spective conditions.
Thus, it is found that the nonuniform concentration
field, in the same way as the nonuniform temperature
field, creates the internal mechanical stress in the solid
with a magnitude determined by the function of the spa-
tial distribution of composition. The question about spa-
tial limitations of applicability for this law is still open.
This is essential in the case when the macroscopic non-
uniformity with decreasing the characteristic size becomes
comparable to the interatomic distance, when the field
of lattice deformation is created by some discrete defect.
We can only suppose that within the magnitudes of de-
formations which obey the Hooke law, this regularity is
valid.
We did not discuss the features related to the impuri-
ty (defect) type, namely, to the difference in the coordi-
nation radii of the parent atom and of the defect. It is
clear that in the above law these features should be man-
ifested in the magnitudes and signs of coefficients of pro-
portionality in the presented relation, i.e., under other
equal conditions they should determine the quantitative
differences in the stress parameters.
And, finally, we note that the described experiments
could be made possible, to the great extent, due to the
application of the polarization modulation technique,
which allows to register the double refraction in reflec-
tion. Therefore, the opticopolarizational method can be
applied to the investigations of nontransparent substanc-
es, and hence, in a wide range of wavelengths.
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