Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method
This paper presents research of the process for growing the crystals of semiconductor solid solutions Hg₁₋x₋y₋zAxByCzTe under conditions of a modified zone melting.
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2005
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| Cite this: | Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method / I.N. Gorbatyuk, V.V. Zhikharevich, S.E. Ostapov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 4. — С. 22-25. — Бібліогр.: 5 назв. — англ. |
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Gorbatyuk, I.N. Zhikharevich, V.V. Ostapov, S.E. 2017-06-14T16:15:27Z 2017-06-14T16:15:27Z 2005 Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method / I.N. Gorbatyuk, V.V. Zhikharevich, S.E. Ostapov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 4. — С. 22-25. — Бібліогр.: 5 назв. — англ. 1560-8034 PACS 74.62.Bf https://nasplib.isofts.kiev.ua/handle/123456789/121548 This paper presents research of the process for growing the crystals of semiconductor solid solutions Hg₁₋x₋y₋zAxByCzTe under conditions of a modified zone melting. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method Article published earlier |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method Gorbatyuk, I.N. Zhikharevich, V.V. Ostapov, S.E. |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method |
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investigation of growing the hg₁₋x₋y₋zaxbyczte solid solutions by modified zone melting method |
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Gorbatyuk, I.N. Zhikharevich, V.V. Ostapov, S.E. |
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Gorbatyuk, I.N. Zhikharevich, V.V. Ostapov, S.E. |
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2005 |
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English |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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This paper presents research of the process for growing the crystals of semiconductor solid solutions Hg₁₋x₋y₋zAxByCzTe under conditions of a modified zone melting.
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1560-8034 |
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https://nasplib.isofts.kiev.ua/handle/123456789/121548 |
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Investigation of growing the Hg₁₋x₋y₋zAxByCzTe solid solutions by modified zone melting method / I.N. Gorbatyuk, V.V. Zhikharevich, S.E. Ostapov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 4. — С. 22-25. — Бібліогр.: 5 назв. — англ. |
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AT gorbatyukin investigationofgrowingthehg1xyzaxbycztesolidsolutionsbymodifiedzonemeltingmethod AT zhikharevichvv investigationofgrowingthehg1xyzaxbycztesolidsolutionsbymodifiedzonemeltingmethod AT ostapovse investigationofgrowingthehg1xyzaxbycztesolidsolutionsbymodifiedzonemeltingmethod |
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2025-11-25T15:47:00Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 4. P. 22-25.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
22
PACS 74.62.Bf
Investigation of growing the Hg1−x−y−zAxByCzTe solid solutions
by a modified zone melting method
I.N. Gorbatyuk , V.V. Zhikharevich, S.E. Ostapov
Yuri Fed’kovich Chernivtsi National University, 2, Kotsyubinsky str.,
58012 Chernivtsi, Ukraine
Abstract. This paper presents research of the process for growing the crystals of
semiconductor solid solutions Hg1−x−y−zAxByCzTe under conditions of a modified zone
melting.
Keywords: multicomponent solid solution, crystal growth.
Manuscript received 04.08.05; accepted for publication 25.10.05.
Research of the process for zone melting of semicon-
ductor solid solutions of Hg1−x−y−zAxByCzTe type is
carried out in the works [1-3]. Contrary to [1], it is
shown in [2, 3] that the size of variable-composition
portions depends monotonically on the composition of
the source polycrystal, and for Hg1−хCdхTe it is
described by the empirical formula
Cs(z) = C0{1+b⋅exp(−(cz)2)}, (1)
where b = 1.512·10−2 + 0.22/x, c = 6.3·10−2 + 0.31/x
(x = 0.16 to 0.32), z is the distance from the ingot
beginning, х determines a crystal composition, Cs(z) and
C0 is the composition of ingot solid phase and the source
polycrystal, respectively. In the paper [2], the Pfann
equation is solved for zone melting, and it is shown that,
for Hg1−хCdхTe (x = 0.16 to 0.32), the best agreement
between calculated and experimental data is achieved by
the linear approximation of the introduced distribution
coefficient R(z) = Cs(z)/C0.
In the work [3], a dependence of the distribution
coefficient along the ingot length is derived, which is
described either by the nonmonotonical function with a
peak or by the monotonically increasing function
achieving the saturation when reaching the
homogeneous-composition portion.
This ambiguity of results and the appearance of new
experimental data caused a more detailed research of the
process for growing the mercury-containing semicon-
ductor solid solutions of the Hg1−x−y−zAxByCzTe type
under the modified zone melting.
Modification of the standard zone melting process
lies in the following:
• an ampoule with a synthesized polycrystal is located
at an angle to the horizon (the angle may vary within
30 to 45º).
• the ampoule is kept in permanent rotation around the
longitudinal axis, thus agitating components in the
melt zone.
The advantages of such modification are as follows.
When growing the ingot at an angle to the horizon, the
contact of liquid phase with polycrystalline ingot is
practically achieved over the entire ingot length. It
considerably reduces the influence of both gas interlayer
and non-uniform dissolution of polycrystal. The
agitation causes, firstly, the uniform dissolution of
polycrystal; secondly, the reduction of temperature non-
uniformity at a crystallization front, and, thirdly,
reduction of the diffusion layer thickness at the
crystallization front. It makes essential improvement
both in axial and radial homogeneity of the resulting
ingots. As shown in the experiments on drastic cooling
of a melted zone, this approach provides the practically
flat crystallization front, which is impossible to be
achieved by other methods [4].
And, finally, in all probability, control of melted
zone width will increase the yield of material of
homogeneous composition, i.e., the composition that
was planned when loading. A change in composition is
to be observed only for 1 – 2 lengths of melted zone at
the beginning of ingot and at its end, when the liquid
phase is no longer fed on polycrystal components. Need-
less to say, the length of variable-composition portions
depends on the length of melted zone. Thus, varying the
zone length, one can increase the yield of homogeneous-
composition material, thereby reducing its cost.
For modeling a variable-composition portion we
used two models. The first one [5] implies that
segregation coefficient K(z) (hereinafter we will use
exceptionally this term without introducing the
additional distribution coefficients) was considered to be
dependent on a liquid phase composition as follows:
K(z) = а·exp(−bСl(z)), where a, b are the fitting
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 4. P. 22-25.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
23
0.0 0.5 1.0 1.5 2.0 2.5
0.1
0.2
0.3
0.4
0.5
a)
1 - Hg0.685Cd0.315Te
2 - Hg
0.755
Cd
0.245
Te
3 - Hg
0.84
Cd
0.16
Te
4 - Hg
0.9
Mn
0.1
Te
4
3
2
1
0.0 0.5 1.0 1.5 2.0 2.5
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
b) 4
3
2
1
1 - Hg0.685Cd0.315Te
2 - Hg0.755Cd0.245Te
3 - Hg0.84Cd0.16Te
4 - Hg0.9Mn0.1Te
Fig. 1. Distributions of components along the ingot length in HgCdTe and HgMnTe crystals obtained by solving system (2) as
compared with the experimental data in the solid phase of ingots (а) and in the molten zone (b).
Table. Polynomial coefficients and the accuracy of
segregation coefficient calculation.
Se
gr
eg
at
io
n
co
ef
fic
ie
nt
ty
pe
Cu
rv
e
nu
m
be
r
(F
ig
.2
)
С0 ΔL K0 K1 K2 K3
1 0.315 0.054 1.687 0.007 −0.015 0.001
2 0.245 0.02 1.625 0.658 −0.118 0.007
3 0.16 0.016 1.898 0.505 −0.065 0.003 K(z)
4 0.1 0.019 1.63 0.647 0.001 −0.004
1 0.315 0.058 1.195 1.368 1.352 1.197
2 0.245 0.034 3.336 −6.428 −1.109 0.61
3 0.16 0.034 2.824 −3.951 –11.148 −1.421
K(Cl)
4 0.1 0.028 3.793 -20.761 −5.181 9.669
parameters. The algorithm of solution was as follows.
The system of equations was solved:
l·dСl(z) = (С0−K(z) Сl (z))dz,
K(z) = а·exp(−bСl(z)), (2)
where l is the molten zone length. There was the initial
condition for differential equation Сl(0) = С0. At the
same time, the component concentration in solid phase
was calculated as Сs(z)=Сl(z)К(z).
The results of calculations are shown in Fig. 1 for
HgCdTe of several compositions and HgMnTe.
As can be seen from the figure, the system of equa-
tions (2) provides an adequate description of experimental
data obtained after the completion of the ingot growing
(solid phase – Fig. 1а)). Really, at the distance of 1.5–2
zone lengths the curves flatten out, which corresponds to
central ingot portion of constant composition. The
behavior of curves calculated for the melt is similar, but
their composition values are naturally lower.
Essentially, the second model is as followings. The
segregation coefficient, like to that in the first model,
was considered to be dependent on the liquid phase
composition, however, this dependence was shown as a
power series of the type: ++= 110)( CKKCK l
3
13
2
12 CKCK ++ . The functional dependence К(z) was
also restricted by the third-power polynomial:
3'
3
2'
2
'
1
'
0)( zKzKzKKzK +++= . The third polynomial
power was chosen from considerations that this
polynomial describes both the monotonically increasing
functions and the functions with the peak found in the
work [3]. The polynomial coefficients were chosen from
the best fit of theoretical calculations to the experimental
data. For this purpose, we used the successive appro-
ximation method, each step of it calculating the value
( )∑
=
−=Δ
n
i
isi zCCL
1
theor
s
exp , (3)
where n is the number of experimental points, zi is the
distance from the ingot beginning exp
siC are experimental
values of component concentration in the solid phase,
)(theor
is zC are the calculated values of the component
concentration at the same experimental points. Then the
search for minimum ΔL value was started for each curve,
upon achieving which the iteration process was stopped.
The results of calculations by this method are shown
in Fig. 2.
Polynomial coefficients K(Cl) and K(z), as well as the
values of ΔL, obtained as a result of calculations, are
represented in Table. As can be seen from the figure and
the table, this method offers a good precision.
Theoretical curves show a good fit to the experimental
data along the whole length of variable-composition
portion. The segregation coefficient is described by
monotonic curves, reaching the saturation when
achieving the constant-composition portion. The value
of the segregation coefficients for studied ingots varies
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 4. P. 22-25.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
24
0,0 0,5 1,0 1,5 2,0 2,5 3,0
0,1
0,2
0,3
0,4
0,5
0,6
a)
1 - Hg0.685Cd0.315Te
2 - Hg0.755Cd0.245Te
3 - Hg0.84Cd0.16Te
4 - Hg
0.9
Mn
0.1
Te
C S
z/l
4
3
2
1
0,0 0,5 1,0 1,5 2,0 2,5 3,0
0,04
0,08
0,12
0,16
0,20
0,24
0,28
0,32
b)
1 - Hg
0.685
Cd
0.315
Te
2 - Hg0.755Cd0.245Te
3 - Hg0.84Cd0.16Te
4 - Hg0.9Mn0.1Te
C l
z/l
4
3
2
1
Fig. 2. Comparison of theoretical calculations to experimental data for three crystals of HgCdTe (curves 1-3) and one of HgMnTe
(curve 4): composition distributions in the solid phase (а) and in the molten zone (b).
0,0 0,4 0,8 1,2 1,6 2,0 2,4 2,8 3,2
0,1
0,2
0,3
0,4
0,5
0,6
a)
1 - Hg0.685Cd0.315Te
2 - Hg0.755Cd0.245Te
3 - Hg0.84Cd0.16Te
4 - Hg
0.9
Mn
0.1
Te
5 - Hg0.836Cd0.14Mn0.014Zn0.01Te
5
4
3
2
1
E
g,
e
V
z/l
0,0 0,5 1,0 1,5 2,0 2,5 3,0
1,6
1,8
2,0
2,2
2,4
2,6
2,8
3,0
3,2
3,4
3,6
3,8
4,0
b)1 - Hg0.685Cd0.315Te
2 - Hg0.755Cd0.245Te
3 - Hg0.84Cd0.16Te
4 - Hg0.9Mn0.1Te
5 - Hg
0.836
Cd
0.14
Mn
0.014
Zn
0.01
Te
K
z/l
4
3
5
2
1
Fig. 3. Component distribution for multicomponent solid solutions of Hg1−x−y−zAxByCzTe type in the solid solution (а), as well as
the segregation coefficient distribution (b).
from 1.5 to 3.2. Thereof, it can be concluded that with
the decreasing component concentration in the source
polycrystal the segregation coefficient is increased. It
reaches a peak in HgMnTe and varies from 1.7 to 3.2.
The minimum segregation coefficient can be found in
HgCdTe (х = 0.315), varying from 1.8 to 1.55 at the
constant-composition portion.
As is evident from the foregoing research, the
method proposed is in a good agreement with the
experimental and literary data, allowing us to use it for
other materials of the type under study.
This simple method can be used only to compare the
component distribution in three-component solid
solutions (HgCdTe, HgMnTe, HgZnTe, etc.). If the
number of components increases, as it occurs in the
multicomponent solid solutions, they cannot be
compared directly on the basis of composition. In this
case, the only possible way for comparison is
consideration from the viewpoint of the energy gap.
Therefore, to compare the submitted results with a
component distribution in a new five-component
semiconductor solid solution Hg1−x−y−zCdxMnyZnzTe, we
had to convert all the submitted experimental data by
using the energy gap approach.
For this case, the theoretical calculations were made
by the same method (minimization of the expression (3))
modified to calculate the energy gap. The calculation
results as compared with the experimental ones are
depicted in Fig. 3. As can be also seen, in this case, the
method proposed provides a good fit of theoretical
results to the experimental ones.
As seen, the component distribution in the new solid
solution Hg1−x−y−zAxByCzTe obeys the same regularities
as in the rest narrow-gap semiconductor solid solutions
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 4. P. 22-25.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
25
of HgCdTe type. As regards to the energy gap at the
homogeneous portion, this ingot is much the same as
Hg0.8Cd0.2Te and, obviously, Hg0.9Mn0.1Te. The
segregation coefficient of Hg1−x−y−zAxByCzTe is also
higher than unity and monotonously increases at the
initial ingot portion with subsequent reaching the
plateau. However, as can be seen from Fig. 3b, the
segregation coefficient of Hg1−x−y−zAxByCzTe is
practically identical to Hg0.755Cd0.245Te one, varying
from 1.175 to 2.75. In our opinion, this inconsistency is
attributable to the presence of Mn and Zn in
Hg1−x−y−zAxByCzTe crystal.
Based on the research performed, the following
conclusions can be made:
• growth of multicomponent semiconductor solid
solutions of Hg1−x−y−zAxByCzTe type is described by
the segregation coefficient higher than unity;
• presentation of the segregation coefficient as the
third-power polynomial ++= 110)( CKKCK l
3
13
2
12 CKCK ++ ( 3'
3
2'
2
'
1
'
0)( zKzKzKKzK +++= )
results in a good fit of theoretical results to the
experimental data;
• the calculated segregation coefficients for solid
solutions of Hg1−x−y−zAxByCzTe type monotonically
increase from 1.7 – 1.9 to 2.4 – 3.2 at the initial ingot
portion and become saturated on reaching the constant-
composition portion.
References
1. V.M. Yezhov, A.S. Tomson // Proc. of Moscow
Institute of Steel and Alloys N 106, p. 61-64 (1978)
(in Russian).
2. S.E. Ostapov, I.N. Gorbatyuk, A.I. Rarenko,
Research on process parameters for zone melting of
HgCdTe and HgMnTe crystals // Тheses of Report to
ІІІ all-union conference “Crystal Growth Modeling”,
Riga, March 12-16, 1990, vol. 3, p. 255-256.
3. О.А. Bodnaruk, I.N. Gorbatyuk, S.E. Ostapov et al.,
Research on the processes of growth and structural
perfection of cadmium-mercury and manganese-
mercury chalcogenides // Neorganicheskiye Mate-
rialy 31, N 10, p. 1347-1350 (1995) (in Russian).
4. О.А. Bodnaruk, I.N. Gorbatyuk, V.I. Kalenik et al.,
Crystalline structure and electrophysical parameters
of HgMnTe crystals // Ibid. 28, N 2, p. 335-339
(1992) (in Russian).
5. N.P. Gavaleshko, P.N. Gorley, V.A. Shenderovsky,
Narrow-gap semiconductors. Preparation and
physical properties. Naukova Dumka, Kiev (1978)
(in Russian).
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