Cadmium phosphide as a new material for infrared converters
Possible use of cadmium phosphide (Cd₃P₂) for infrared converter systems has been debated. The interband absorption coefficient calculations has been executed for single crystals of n-Cd₃P₂ and interpreted in the exact generalized Kildal band model. Relationship between the absorption coefficient an...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2006
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| Цитувати: | Cadmium phosphide as a new material for infrared converters / D. Stepanchikov, S. Shutov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 40-44. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1216322017-06-16T03:03:13Z Cadmium phosphide as a new material for infrared converters Stepanchikov, D. Shutov, S. Possible use of cadmium phosphide (Cd₃P₂) for infrared converter systems has been debated. The interband absorption coefficient calculations has been executed for single crystals of n-Cd₃P₂ and interpreted in the exact generalized Kildal band model. Relationship between the absorption coefficient and radiation temperature is presented. On the ground of our calculations, the theoretical temperature dependences of the maximum values of photovoltage and efficiency have been obtained. A common thermo-dynamical approach was applied in this case. The source of radiation was a black body. In our investigations, the barrier structure on metal-semiconductor basis with the Schottky layer has been considered. The operation temperature range for the Me–n-Cd₃P₂ converter has been found. 2006 Article Cadmium phosphide as a new material for infrared converters / D. Stepanchikov, S. Shutov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 40-44. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 71.20.-b, 71.18.+y http://dspace.nbuv.gov.ua/handle/123456789/121632 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Possible use of cadmium phosphide (Cd₃P₂) for infrared converter systems has been debated. The interband absorption coefficient calculations has been executed for single crystals of n-Cd₃P₂ and interpreted in the exact generalized Kildal band model. Relationship between the absorption coefficient and radiation temperature is presented. On the ground of our calculations, the theoretical temperature dependences of the maximum values of photovoltage and efficiency have been obtained. A common thermo-dynamical approach was applied in this case. The source of radiation was a black body. In our investigations, the barrier structure on metal-semiconductor basis with the Schottky layer has been considered. The operation temperature range for the Me–n-Cd₃P₂ converter has been found. |
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Stepanchikov, D. Shutov, S. |
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Stepanchikov, D. Shutov, S. Cadmium phosphide as a new material for infrared converters Semiconductor Physics Quantum Electronics & Optoelectronics |
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Stepanchikov, D. Shutov, S. |
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Stepanchikov, D. |
| title |
Cadmium phosphide as a new material for infrared converters |
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Cadmium phosphide as a new material for infrared converters |
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Cadmium phosphide as a new material for infrared converters |
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Cadmium phosphide as a new material for infrared converters |
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Cadmium phosphide as a new material for infrared converters |
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cadmium phosphide as a new material for infrared converters |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2006 |
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Cadmium phosphide as a new material for infrared converters / D. Stepanchikov, S. Shutov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 40-44. — Бібліогр.: 10 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT stepanchikovd cadmiumphosphideasanewmaterialforinfraredconverters AT shutovs cadmiumphosphideasanewmaterialforinfraredconverters |
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2025-07-08T20:15:11Z |
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1837111144321384448 |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 40-44.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
40
PACS 71.20.-b, 71.18.+y
Cadmium phosphide as a new material for infrared converters
D. Stepanchikov1, S. Shutov2
1Kherson National Technical University, Department of General and Applied Physics
24, Berislavskoye shosse, 73008 Kherson, Ukraine
E-mail: step_75@mail.ru; phone: +380(552) 326922
2V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: shutov_sv@mail.ru, phone/fax: +380(552) 515457
Abstract. Possible use of cadmium phosphide (Cd3P2) for infrared converter systems has
been debated. The interband absorption coefficient calculations has been executed for
single crystals of n-Cd3P2 and interpreted in the exact generalized Kildal band model.
Relationship between the absorption coefficient and radiation temperature is presented.
On the ground of our calculations, the theoretical temperature dependences of the
maximum values of photovoltage and efficiency have been obtained. A common thermo-
dynamical approach was applied in this case. The source of radiation was a black body.
In our investigations, the barrier structure on metal-semiconductor basis with the
Schottky layer has been considered. The operation temperature range for the Me–n-Cd3P2
converter has been found.
Keywords: cadmium phosphide, interband absorption, infrared converter.
Manuscript received 29.06.06; accepted for publication 23.10.06.
1. Introduction
In recent years, perceptible interest has been focused on
the two phosphorus compounds belonging to the
crystalline class V
2
II
3 BA : Zn3P2 and Cd3P2. It is caused by
their excellent prospects for optoelectronic applications.
For instance, cadmium phosphide is well known as the
infrared laser active medium. Besides, it may be
considered as an infrared converter or sensor due to the
suitable bandgap: gE = 0.53 eV.
The exceptionally complicated crystal structures
and the large unit cells are characteristic for the V
2
II
3 BA
compounds. For example, both crystals may have a
primitive tetragonal lattice with the unit cell consisting
of 16 P atoms and 24 metallic atoms. Their space group
is 15
4hD . Thereto, presence of the structural vacancies is
natural for these crystalline lattices. Each metallic atom
(cadmium, for instance) is in tetrahedral coordination
with four phosphorus atoms as with own nearest
neighbors, while a phosphorus atom is surrounded by
metallic atoms located only at six of the eight corners of
the coordination cube so that two vacant sites are placed
at the diagonally opposed corners of this cube [1].
Cadmium phosphide always possessed and
possesses hitherto only the n-type conductivity. Typical
concentrations of carriers for as-grown samples are
1017…1018 cm−3. The Fermi level is located somewhat
above the bottom of the conduction band. As a result,
cadmium phosphide is a degenerate n-type semi-
conductor.
In this paper, the authors examined such converter
parameters as the maximum values of the photovoltage
and efficiency in dependence on the radiation
temperature. These evaluations need the accurate
calculations of the absorption coefficient. This
coefficient ought to be computing here for Cd3P2 within
the recent generalization of the Kildal band model [2-4].
2. Band structure
The dispersion law (Hamiltonian) for V
2
II
3 BA
compounds has the following form within the model [2],
if to apply the spherical system of coordinates ( ϕθ ,,k ):
.0sin)()(
))cos)(sin)(()()((
22
3
2
22
2
2
1
2
=−
−+−Γ
θε
θεθεε
fPk
ffPk
(1)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 40-44.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
41
There ( ) ( ) ( ) ( )εεεε 321 ,,, fffΓ are the known
polynomials for the carrier energy and some material
parameters. There are no polynomials among them,
which exceed the fourth power.
The material parameters of this model are the
following five. At first, PEg ,, Δ are three well-known
Kane’s parameters [3] (i.e., the energy gap, the spin-
splitting parameter and the matrix element of the
momentum). Further, δ is the parameter of the
tetragonal crystal field [4], and d is the extra field
parameter describing the absence of the symmetry center
[2]. This additional is equal to zero, if the crystal has a
symmetry center. Finally, η is the scalar factor taking
into account the deformation of the lattice [2]. The
energy is measured from the heavy holes band top. Since
Eq. (1) does not contain the spherical angle ϕ , the
surfaces of equal energies are rotation surfaces around
the crystal main axis that is also the polar axis.
Obviously that Eq. (1) has the simple
decomposition into product of two factors. Both factors
should be even identical, if the crystal has a centre of
symmetry (herewith 0=d and 0)(3 =εf ). Since it is
valid for above mentioned space group 15
4hD , thus these
four solutions of Eq. (1) indeed were found (as
functions ( )θε ,k ) under this condition. In Fig. 1, the
curves in accord with these solutions are plotted for the
conduction band (c), heavy holes (v1), light holes (v2)
and spin-orbit splitting (v3) bands.
3. Interband absorption coefficient
Fig. 1 illustrates the band structure of Cd3P2 with the set
of the material parameters given in Section 2. All band
extremes are located at Г point ( 0=k ). The direct
interband transitions are most probable in this case for
the photon energy gEh ≥ν . Fig. 1 shows six possible
direct interband transitions labelled A, B, C, D, G and H.
The realization of transitions А, В and C causes the
generation of free carriers, which can participate in
initiating the converter photocurrent.
The work [5] gives the absorption coefficient ijK
for each transition from a band i to other band j as
follows:
ijijijij fM
mcn
e
K ρ
ωε
2
2
00
2π
= . (2)
Here ω is the photon frequency, 0ε is the electric
constant, 0m is the free electron mass, n is the refraction
index of Cd3P2 and c is the velocity of the light. ijM and
ijρ are the momentum matrix element and the joint
density of states between bands i and j, respectively.
Because Cd3P2 is an n-type degenerated material, the
factor ijf takes into account the distribution of
unoccupied states in the band j and the occupied ones in
the band i. The full photon energies νh in the
absorption processes of type A, B and C satisfy the
condition: νh >> Tk0 . Therefore, the realistic approach
may consider the lowest i-band as wholly filled.
Accordingly, just the statistics of unoccupied states of
the highest j-band remains to be taken into account.
Now, the factor ijf coincides with the Fermi-Dirac
distribution [6]:
1
0
Fexp11
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡ −
+−=
Tk
E
f j
ij
ε
. (3)
Here T is the temperature of materials, 0k is Boltz-
mann’s constant, jε is an energy level in the j-band.
Actually, the transitions between the valence bands D,
G, H (Fig. 1) will take place only after beginning of the
transitions A and B. The current calculations relate to
gg EEE 7.1≤≤ photon energy interval.
The momentum matrix element and the joint
density of states have been calculated by the method [5].
To be scrupulous, the total interband absorption
coefficient K must be determined by summing up all the
possible contributions:
HGDCBA KKKKKKK +++++= . (4)
Conversely, the part of contributions (primarily D,
G, H) may be omitted keeping a well approximation.
Although because the main contributions in absorption
are made by interband transitions (А, В, С), i.e., between
all the valence bands and conduction one. It looks
realistic for the investigated photon energy band at least.
4. Photovoltage and efficiency
Since the p-type samples of Cd3P2 are yet unattainable,
here just the barrier structure between metal and
semiconductor is considered. The following admissions
are accepted herewith: 1) the diode theory is equitable;
2) the space-charge region looks like the Schottky layer;
3) the tunnel effect is negligible.
The photovoltage may be calculated through the
account of the change in the surface potential on
irradiation [7]:
sssU φφ −= * . (5)
Here sφ is the surface potential in the absence of
irradiation. The magnitude gs E3
2=φ is in use further.
It corresponds to the maximum value of barrier for the
most of such systems on a uniform substrate [8].
The surface potential on irradiation *
sφ is available
from the Johnson equation [7]:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 40-44.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
42
( ) ( ) ( ) ( )( ) ( ) ( )
( ) ( ) 2expexp
1expexpexpexp
**
*2*2*
−+−
−−+−+−−−
=
−−
ss
ssssss
p
YY
YYYYYY λλ
δ , (6)
here TkeYTkeY ssss 0
**
0 ; φφ == are the
nondimensional potentials, 00 ppp Δ=δ and 0pΔ are
the hole injection degree and the excess hole
concentration, generated by the radiation, respectively.
The parameter λ is as follows: 00 np=λ . Let us
express the equilibrium carrier concentration through the
Fermi integrals [9]:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= ∗
Tk
E
F
h
Tk
mn e
0
F
2/1
2/3
2
0
0 2π4 , (7)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ +
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
= ∗
Tk
EE
F
h
Tk
mp g
h
0
F
2/1
2/3
2
0
0 2π4 , (8)
where 00 4.0,05.0 mmmm he == ∗∗ [5] are the effective
masses of electrons and holes, respectively, FE is the
Fermi energy computed from the bottom of the
conduction band.
The photon flux is decreased with the depth of a
sample as ( ) ( )zKNzN −= exp0 , whereas the velocity of
the electron-hole pair generation is
( ) ( )zKKNzddNzg −=−= exp/ 0 (here 0N is the
number of photons on the unit of the area per unit of
time). Therefore, the excess concentration on stationary
irradiation may be found by integration:
Fig. 1. Energy bands of Cd3P2 for Eg = 0.53 eV, Δ = 0.15 eV,
P = 6.7⋅10−10 eV m, δ = 0.023 eV, d = 0, η = 0.99, EF – Eg =
0.06 eV.
( )∫ −=Δ
2
1
exp0
ν
ν
ντ dzKKNp p . (9)
Let us suppose that the source of radiation is a
black body (so, the magnitude 0N is determined by
Planck’s formula). We consider the direct interband
transitions in the field of intrinsic absorption, while the
interband absorption is interpreted using the generalized
Kildal band model. Thus, the ideal filter is used. The
optical transmission spectrum for this filter is located in
[ ]hEhE gg 7.1, 21 == νν frequency band. The
interband radiative recombination is the main
mechanism of the carrier recombination of
semiconductor material. Therefore, the hole lifetime is
attainable through interband radiative recombination rate
(Shockley’s formula [9]):
ν
ν
ν
ν
ν
d
Tk
h
Kn
c
R v ∫
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
2
1 1exp
π8
0
22
2
, (10)
v
p R
p0=τ . (11)
Fig. 2. Total interband absorption coefficient of Cd3P2.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 40-44.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
43
Fig. 3. Theoretical dependences of the photovoltage (1) and
efficiency (2) vs the radiation temperature for Ме–n-Cd3P2
system (the temperature of material is 300 K).
Now it is possible to determine the surface
potential on irradiation and photovoltage of the space-
charge region, respectively, having solved Eq. (6)
relative to ∗
sφ . Fig. 3 shows these results (curve 1).
The general thermodynamical approach was used
to determine the maximum theoretical value of the
converter efficiency [8]:
c
vhm
E
NE
=η . (12)
Here ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−⎥
⎦
⎤
⎢
⎣
⎡
+−≈
e
TAk
TAk
eU
e
TAk
UeE s
sm
0
0
0 1ln is
the attainable energy as a result of the absorption of one
photon, if the barrier and external electric circuit had
been optimally coordinated (A is the index of ideality).
Let it be A = 1 in these calculations, because the
maximal efficiency is interesting in fact. ∫=
2
1
ν
ν
νdNN vh
is the total number of photons on the unit area per unit of
time in [ ]21;νν frequency band; ∫=
2
1
ν
ν
νν dNhEc is the
full surface density of the radiation.
Infrared radiation causes heating the material of
converter. This affects badly the converter output
characteristics. Present theoretical studies have also
shown that the temperature increase leads to detectable
decrease of the photovoltage and efficiency values (see
Fig. 4). Herewith the dependence of the bandgap value is
one of the negligible factors [10].
Fig. 4. Theoretical dependences of the photovoltage (1) and
efficiency (2) vs the temperature of semiconductor material for
Ме–n-Cd3P2 system (the radiation temperature is 2000 K).
Besides, the impurities and vacancies must interact
with each other much more intensively with temperature
increasing. Furthermore, the temperature increase can
vastly accelerate the aging process associated with the
slow “annealing” of non-equilibrium vacancies. Such
aging of the crystal results in lowering the Fermi level
and the electron concentration more than twice for Cd3P2
at the same time [10]. For these reasons, the preventive
measures of the converter heating will be rather
necessary for this material.
5. Conclusions
The main results of the present investigation are as
follows:
1. The set of the material parameters of Cd3P2
allows to more effectively use the converter for the
transformation of infrared radiation into the electricity
for the operating temperature range (1000…2500 К) of
the heat source.
2. The theoretical values of photovoltage and
efficiency of the Me–n-Cd3P2 Schottky diode are quite
comparable with those for well-known diodes based on
classical p-n junctions.
3. The reliable thermal protection of converter (in
the vicinity of the room temperature point) is rather
requisite because of numerous vacancies in the
crystalline structure of Cd3P2 and the aging phenomena.
These conclusions are quite preliminary, because,
firstly, they are based just on theoretical calculations.
Secondly, the complete and non-simplified theoretical
description of the metal-semiconductor contacts is a very
complex problem. For these reasons, the experimental
confirmation is necessary, too. That is why the final
decision about possibility to use cadmium phosphide for
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 40-44.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
44
infrared converters may be reliable only after practical
experiments. Nevertheless, the present results show
these experiments are undoubtedly perspective.
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