Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures
The high-planar epitaxial layers of n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇ quaternary solid solutions, lattice matched with {111}BaF2 substrates, have been grown from bounded volume of supersaturated melt-solutions in the growth temperature region 773-873 K by the liquid phase epitaxy technique at a program...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2002
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irk-123456789-1195672017-06-08T03:02:28Z Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures Tkachuk, A.I. Tsarenko, O.N. Ryabets, S.I. The high-planar epitaxial layers of n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇ quaternary solid solutions, lattice matched with {111}BaF2 substrates, have been grown from bounded volume of supersaturated melt-solutions in the growth temperature region 773-873 K by the liquid phase epitaxy technique at a programmatic refrigeration rate of 0.1-0.2 K/min and a temperature reduction range of DT=5-10 K. The laboratory methodology of the production of Cu/δ-layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇ /In Schottky barrier structures by thermal vacuum deposition has been developed. The current- and farad-voltage characteristics of these structures have been measured at the 77 K, and the dependence of the diode electro-physical properties on the δ-layer width has been studied. 2002 Article Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures / A.I. Tkachuk, O.N. Tsarenko, S.I. Ryabets // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 51-57. — Бібліогр.: 20 назв. — англ. 1560-8034 PACS: 73.20.-r, 73.30.+y,73.40.Lq http://dspace.nbuv.gov.ua/handle/123456789/119567 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The high-planar epitaxial layers of n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇ quaternary solid solutions, lattice matched with {111}BaF2 substrates, have been grown from bounded volume of supersaturated melt-solutions in the growth temperature region 773-873 K by the liquid phase epitaxy technique at a programmatic refrigeration rate of 0.1-0.2 K/min and a temperature reduction range of DT=5-10 K. The laboratory methodology of the production of Cu/δ-layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇ /In Schottky barrier structures by thermal vacuum deposition has been developed. The current- and farad-voltage characteristics of these structures have been measured at the 77 K, and the dependence of the diode electro-physical properties on the δ-layer width has been studied. |
| format |
Article |
| author |
Tkachuk, A.I. Tsarenko, O.N. Ryabets, S.I. |
| spellingShingle |
Tkachuk, A.I. Tsarenko, O.N. Ryabets, S.I. Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Tkachuk, A.I. Tsarenko, O.N. Ryabets, S.I. |
| author_sort |
Tkachuk, A.I. |
| title |
Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures |
| title_short |
Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures |
| title_full |
Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures |
| title_fullStr |
Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures |
| title_full_unstemmed |
Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures |
| title_sort |
production and investigation of cu/thin intermediate tunnel-transparent dielectric oxide layer/n-pb₀.₉₃₅sn₀.₀₆₅te₀.₂₄₃se₀.₇₅₇/in schottky barrier structures |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2002 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119567 |
| citation_txt |
Production and investigation of Cu/thin intermediate tunnel-transparent dielectric oxide layer/n-Pb₀.₉₃₅Sn₀.₀₆₅Te₀.₂₄₃Se₀.₇₅₇/In Schottky barrier structures / A.I. Tkachuk, O.N. Tsarenko, S.I. Ryabets // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 51-57. — Бібліогр.: 20 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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51© 2002, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2002. V. 5, N 1. P. 51-57.
PACS: 73.20.-r, 73.30.+y,73.40.Lq
Production and investigation of Cu/thin intermediate
tunnel-transparent dielectric oxide layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier structures
A.I. Tkachuk, O.N. Tsarenko, S.I. Ryabets
Vynnychenko�s Kirovograd State Pedagogical University, 1 Shevchenko St., 25006 Kirovograd, Ukraine
Phone: +380 (522) 24 8901; fax: +380 (522) 24 8544; e-mail: atkachuk@kspu.kr.ua
Abstract. The high-planar epitaxial layers of n-Pb0.935Sn0.065Te0.243Se0.757 quaternary solid solutions,
lattice matched with {111}BaF2 substrates, have been grown from bounded volume of supersaturated
melt-solutions in the growth temperature region 773÷873 K by the liquid phase epitaxy technique at a
programmatic refrigeration rate of 0.1÷0.2 K/min and a temperature reduction range of ∆T=5÷10 K.
The laboratory methodology of the production of Cu/δ-layer/n-Pb0.935Sn0.065Te0.243Se0.757/In Schottky
barrier structures by thermal vacuum deposition has been developed. The current- and farad-voltage
characteristics of these structures have been measured at the 77 K, and the dependence of the diode
electro-physical properties on the δ-layer width has been studied.
Keywords: lead-tin chalcogenide; liquid phase epitaxy; Schottky barrier structures; intermediate oxide
layer.
Paper received 29.10.01; revised manuscript received 21.12.01; accepted for publication 05.03.02.
1. Introduction
The metal/lead-tin chalcogenide contacts with
Schottky barrier provide a convenient and relatively in-
expensive method to fabricate high-quality infrared
photodiodes for application in the wavelength region
8÷14 µm of the atmospheric window [1-3]. At the same
time, these barrier structures have been only partially
studied for the In (Pb, In-Ag)/p-Pb1-xSnxTe/Au [2-5],
Pb/p-Pb1-xSnxSe/Pt(Au) [6-9] and Pb/p-PbTe1-ySey/Pt [7,
10] junctions on the basis of epitaxial layers, which were
grown on {111}BaF2 and {111}Si (with CaF2-SrF2-BaF2
buffer layer) substrates by the molecular beam or hot wall
epitaxy. But the information about the production and
the properties of the Schottky diodes on the basis of
epitaxial layers of the Pb1-xSnxTe1-ySey quaternary solid
solutions, which were grown on BaF2 by the liquid phase
epitaxy technique, is absent. Furthermore, most of the
authors, when interpreting obtained electro-physical and
optical experimental characteristics of these barrier
structures, use only ideal Schottky barrier model and
disregard by the available thin intermediate tunnel-trans-
parent dielectric oxide layer (δ-layer). This layer is usu-
ally formed on the lead-tin chalcogenide surface during
chemical polishing or exposing to the ambient atmos-
phere prior to the vacuum deposition of the barrier metal.
However, practically, metal/lead-tin chalcogenide
Schottky barrier diodes with δ-layer have better charac-
teristics [11-13], moreover, the values of zero bias resist-
ance area product (R0A) and zero bias built-in potential
(ϕo
bi) increase with increase of δ-layer width [11,13]. The
absence of δ-layer may be reduced to the degradation of
the metal/lead-tin chalcogenide interface and deteriora-
tion of rectificational properties of the Schottky diode as
the result of chemical interaction between deposited bar-
rier metal and semiconductor material [5, 11, 12].
In accordance with [14], surfaces of the Pb1-xSnxTe
and Pb1-xSnxSe solid solutions oxidize at the atmospheric
pressure and room temperature rather quickly with for-
mation PbO, SnO2, TeO2, SeO2 oxides and acceptor sur-
face states. The composition and thickness of δ-layer de-
pend on the air exposition time, and it is known that tin
52 SQO, 5(1), 2002
A.I.Tkachuk et al.: Production and investigation of Cu/thin intermediate...
oxidize in the quickest way but lead � in the slowest [13,
14]. It should be taken into account at the analysis of
experimental data, while the surface state density de-
creases with increasing the δ-layer width and changing
its composition [11].
The main goal of this work was to search and develop
the laboratory methodology of the production of Cu/δ-
layer/n-Pb0.935Sn0.065 Te0.243Se0.757/In Schottky barrier
structures based high-quality epitaxial layers of n-
Pb0.935Sn0.065Te0.243Se0.757 quaternary solid solutions.
using industrial and original equipment for liquid phase
epitaxy and thermal vacuum deposition. Besides, we had
to study the dependence of electro-physical characteris-
tics of respective diodes on the δ-layer width.
1
2
3
4
5
Fig. 1 Schematic view of the Cu/δ-layer/n-Pb0.935Sn0.065Te0.243Se0.757/
In Schottky barrier structures:1 - {111}BaF2 substrate; 2 - epitaxial
layers of n-Pb0.935Sn0.065Te0.243Se0.757; 3 - ohmic In contact; 4 - rec-
tifying Cu contact; 5 - δ-layer.
2. Experimental procedure
The epitaxial layers of n-Pb0.935Sn0.065Te0.243 Se0.757
quaternary solid solutions, lattice matched with
{111}BaF2 substrates, were grown from bounded vol-
ume of (Pb1-vSnv)1-w (Te1-uSeu)w melt-solutions in the
growth temperature region 773÷873 K by the liquid phase
epitaxy (LPE) technique at the programmatic refrigera-
tion of the growth solution. The LPE processes were per-
formed in a vertical reactor, placed into a furnace with a
resistive heater, in the flow of hydrogen purified by a
palladium filter. A special blacklead crucible and cylin-
drical rotating cassette were used for the LPE growth of
high-planar n-Pb0.935Sn0.065Te0.243Se0.757 epitaxial lay-
ers. The BaF2 dielectric substrates were obtained by the
spalling of Bridgman monocrystals in the direction of
the {111} crystallographic plane and dynamic-chemical
polishing of their surfaces in the 10% aqueous solution of
HNO3. These substrates had the form of washer with 20
mm in diameter and 2÷5 mm in thickness. Their surface
dislocation densities were Nd=(4÷8)×104 cm-2.
{111}BaF2 substrates were laid on the vertical rotating
blacklead cassette in pairs with 1÷2 mm clearance. The
(Pb1-vSnv)1-w(Te1-uSeu)w melt-solutions were prepared
from elemental lead, tin, tellurium and selenium of high-
est purity grade. Sn, Se and chalcogenide contents in the
liquid phase were varied within the ranges 0.073≤v≤0.078,
0.403≤u≤0.420 and 0.01≤w≤0.04 atomic fractions,
respectively. After the melt-solution was homogenized in
blacklead crucible during 2 hours at the temperature 2÷3 K
higher than the liquidus ones, the epitaxy growth was
initiated 1÷2 K below the liquidus temperature by filling
of the melt-solution on the substrates through the slot of
cassette. The range of the temperature reduction was
∆T=5÷10 K at a programmatic refrigeration rate of
0.1÷0.2 K per minute. The melt-solution was removed
from the growth surface by centrifugation.
The obtained Pb0.935Sn0.065Te0.243Se0.757 epitaxial
layers had the thickness of h=3÷7 mm, surface disloca-
tion density Nd<105 cm-2, n-type conduction, band gap
energy Eg=0.124 eV, electron concentration
n=(2.2÷2.7)×1017 cm-3 and Hall mobility
µ=(8.3÷9.1)×103 cm2V-1s-1 at 77 K.
Ohmic and rectifying contacts to the n-
Pb
0.935
Sn
0.065
Te
0.243
Se
0.757
epitaxial layers were obtained by
the thermal deposition of indium and copper in the
vacuum of about 10-5÷10-6 Torr through the system of
stainless-steel masks at a rate of about 500 Å per minute
and 1800 Å per minute, respectively. The In contacts
had a large area of about 50.2 mm2 and the thickness of
about 3000 Å. Prior to the deposition of In contacts, the
epitaxial layers were vacuum annealed at 423 K for about
1800 seconds to desorb a surface oxide layer. After the
deposition of In contacts and before to the deposition of
Cu contacts, the thin intermediate tunnel-transparent di-
electric oxide layers on the epitaxial layer surfaces were
formed by the forced oxidation at 473 K during 10÷1200
sec. The obtained Cu rectifying contacts had the thick-
ness of about 2000÷3000 Å and an active area A of about
2.25 mm2. In Fig. 1 a schematic view of Cu/δ-layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier structures
are shown. For electrical measurements, the thin copper
wires with diameter of about 0.1 mm were mounted to the
ohmic and rectifying contacts with the help of solder
52%In + 47% Sn + 1% Ag. The current-voltage charac-
ter i s t ics (CVC) of the Cu/δ - layer /n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier struc-
tures were measured at the direct current and 77 K. The
farad-voltage characteristics (FVC) were measured by
the bridge method at the frequency f=1MHz and 77 K.
-6
-4
-2
0
2
4
6
8
10
-0.8 -0.6 -0.4 -0.2 0.2
I, mA
U, V
Fig. 2 CVC of the Cu/δ-layer/n-Pb0.935Sn0.065Te0.243Se0.757 /In
Schottky barrier structures at 77 K (♦ - structure ¹1; ▲ - struc-
ture ¹2; g - structure ¹3; • - structure ¹4).
A.I.Tkachuk et al.: Production and investigation of Cu/thin intermediate...
53SQO, 5(1), 2002
3. Results and discussions
For the forward voltage bias 0.02<U<0.16 V, the
experimental current-voltage curves of the Cu/δ-layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier structures
were good approximated by the expression:
[A], (1)
where ideality coefficient β and saturation curcurrent IS
ranged for the various structures within the limits from
1.8 to 3.1 and from 91 to 35 µA. The maximum value of
the zero bias resistance area product was about 10.6 Ωcm2.
Series resistance r, that is determined by the resistance of
the semiconductor quasi-neutral region, ohmic contact
resistance and spreading resistance, taken on a value
3.9÷6.3 Ω. In Fig. 2 shown are the typical CVC with the
example of four selected barrier structures with the dif-
ferent oxidation time t. Measured values of the R0A, r, IS
and β of these diodes were reduced in the Table with the
same numeration of structures as in Fig 2. The reverse
branches of the CVC did not saturate and had the view,
which is typical for the �soft breakdown� [12, 15].
( )
−=
âkT
IrUq
SII exp
Fig. 3 FVC of the Cu/δ-layer/n-Pb0.935Sn0.065Te0.243Se0.757 /In
Schottky barrier structures at 77 K (♦ - structure ¹1; ▲- struc-
ture ¹2; g - structure ¹3; • - structure ¹4).
−
−=− U
q
kT
BC bi
02 ϕββ [F-2], (2)
where coefficient B ranged within the limits from
1.31×1017 to 1.62×1017 C-2V-1, which may be explained
by different values of the product of ionized donor con-
centration into semiconductor dielectric permittivity for
various structures. In Fig. 3, the typical FVC on the ex-
ample of the same four selected barrier structures are
shown. For the determination of zero bias built-in
potentials from the relationship [12]:
Table1. Parameters of the Cu/δδδδδ-layer/n-Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier structures at 77 K.
For the reverse voltage biases �0.4<U<0 V, the ex-
perimental FVC plots of Cu/δ-layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier struc-
tures were good approximated by the expression:
q
kTU I
bi +=
β
ϕ 0 [V], (3)
the intercept voltages UI were obtained by extrapolation
of the line section of FVC plots onto the abscissa. Meas-
ured values of the B, UI, ϕo
bi and zero bias capacitance
(C0) for the four selected Cu/δ-layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier structures
are given in Table, too.
As the explanation of the obtained experimental re-
sults, we proposed a physical model of the Cu/δ-layer/n-
Pb1-xSnxTe1-ySey/In Schottky barrier structure. Con-
structing this model we proceeded on the assumptions
that: δ-layer is the tunnel-transparent for the electrons
and its influence reduce only to potential drop on it (∆ϕi);
surface state continuous distribution on the δ-layer/n-
Pb1-xSnxTe1-ySey interface is characterized by the elec-
trical neutrality level (ϕ0) � filling level of the surface
state band by electrons at the thermodynamic equilib-
rium between δ-layer and n-Pb1-xSnxTe1-ySey before the
deposition of copper and after the deposition of indium
contacts; after the deposition of copper, the surface states
on the δ-layer/n-Pb1-xSnxTe1-ySey interface interact well
with states in the metal conduction band at the expense of
tunneling, because of that the surface state filling is de-
termined by metal Fermi level (EFCu) and the surface
states become the acceptor surface states (the electrical
neutrality level in the state of the thermodynamic equilib-
rium is already placed below the semiconductor Fermi level
EFS); the energetic density of surface states DS [J-1m-2] is a
constant in the energy interval from ϕ0 to EFCu; the elec-
tric field strength in the δ-layer is a constant in the state
of the thermodynamic equilibrium (Ei
0(x)= const);
general charge in the barrier layer consists of the sum of
uniform completely ionized donor motionless
charge, free-electron charge (majority carrier) and free
hole charge (minority carrier). So, width, electric field
0.5
1
1.5
2
2.5
3
3.5
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1
¹ t, sec R0A, r, Ω IS, β C0, UI, V ϕo
bi, V δ, Å
Ωcm2 ×10-5A ×10-9F
1 180 2.9 3.9 9.2 1.8 6.69 0.092 0.058 199
2 370 4.7 6.3 7.1 2.2 4.53 0.137 0.069 268
3 690 7.5 5.7 5.5 2.7 3.41 0.203 0.082 431
4 1020 10.1 4.2 4.4 3.1 2.89 0.262 0.091 592
54 SQO, 5(1), 2002
A.I.Tkachuk et al.: Production and investigation of Cu/thin intermediate...
strength and electric field potential of the barrier layer
of Cu/δ-layer/n-Pb1-xSnxTe1-ySey/In Schottky barrier
structure are assigned by expressions [15,16,18]:
2
1
002
)(
−−= dbi
D
S U
q
kT
qN
xL ϕεε
[m],
( )xL
qN
xE
S
D
S −−=
εε0
)(
( )2
02
)( xL
qN
x
S
d
S −=
εε
ϕ
[Vm-1], (4)
where q is the electronic charge; ND - ionized donor con-
centration; εS - relative static dielectric permittivity of
semiconductor; Ud � voltage drop on the barrier
layer; x � distance, which is counted off from δ-
layer/n-Pb1-xSnxTe1-ySey interface into the semicon-
ductor.
In Fig. 4 the qualitative energy-band diagrams of the
Cu/δ-layer/n-Pb1-xSnxTe1-ySey/In Schottky barrier struc-
ture are shown for the zero (a), forward (b) and reverse (c)
voltage biases, where: ÅCu
0, ÅS
00 (ÅS
0F, ÅS
0R) and ÅIn
0 -
zero level of the Cu, n-Pb1-xSnxTe1-ySey and In, respec-
tively; ÅCS
0 (ÅCS
F, ÅCS
R) � conduction band edge of the
semiconductor; ÅFCu and ÅFIn � Fermi level of the Cu
and In; ÅFS
0 and ÅFS
F(ÅFS
R) - Fermi level (at the zero
bias) and quasi-Fermi level (at the forward/reverse bias)
of the semiconductor lying µS [J] below the conduction
band edge; ÅVS
0 (ÅVS
F, ÅVS
R) � valance band edge of the
n-Pb1-xSnxTe1-ySey; ACu, AS and AIn � work function of
the Cu, semiconductor and In, respectively; χS � electron
affinity of the n-Pb1-xSnxTe1-ySey; Eg � band gap energy
of the semiconductor; Ud
F (Ud
R) � voltage drop on the
barrier layer; Ui
F (Ui
R) - voltage drop on the δ-layer;
ϕ0 - electrical neutrality level; q∆ϕ³
0 (q∆ϕ³
F, q∆ϕ³
R) �
potential drop on the δ-layer; qϕbi
0 (qϕbi
F, qϕbi
R) - built-
in potential; qϕb
0 (qϕb
F, qϕb
R) � barrier height; q∆ϕbi
0
(q∆ϕbi
F, q∆ϕbi
R) - built-in potential lowering due to im-
age forces; εi - relative static dielectric permittivity of the
δ-layer; δ − δ-layer width; L0 (LF, LR) - barrier layer
width; QSC
0 (QSC
F, QSC
R) - surface density of the barrier
layer charge; QSS
0 (QSS
F, QSS
R) - charge density of the
acceptor surface states; QCu
0 (QCu
F, QCu
R) - charge sur-
face density on the active surface of the Cu barrier contact.
The electrical neutrality condition of the Cu/δ-layer/
n-Pb1-xSnxTe1-ySey Schottky barrier contact at the zero
bias (Fig. 4, a) can be written [15, 16]:
0000 =++ SCSSCu QQQ [Cm-2], (5)
where
( )000
biSCu
i
Cu qAA
q
Q ϕ
δ
εε
−−−= [C m-2];
( )0
0
0
biSgSSS qEqDQ ϕµϕ −−−−= [C m-2]; (6)
Fig. 4 Qualitative energy-band diagrams of the Cu/δ-layer/n-
Pb1-xSnxTe1-ySey/In Schottky barrier structure for the zero (a),
forward (b) and reverse (c) voltage bias.
[V],
A.I.Tkachuk et al.: Production and investigation of Cu/thin intermediate...
55SQO, 5(1), 2002
where
( ) ( )( )[ ]SgSCu EAA
q
µϕγγϕ −−−+−= 01 1
1
[V],
Si
i
Dq δεε
εε
γ
2
0
0
+
= ; [V].
In the case when the forward (reverse) voltage bias U
has been applied to the Cu/δ-layer/n-Pb1-xSnxTe1-ySey/In
Schottky barrier structure (Fig. 4,b,c), the electrical neu-
trality condition (2) can be rewritten:
[C m-2], (9)
where
( )22
0
2
0
Si
SD
Dq
qN
δεε
δεε
α
+
=
0=++ SCSSCu QQQ
( )qVqAA
q
Q biSCu
i
Cu −−−−= ϕ
δ
εε0
( )qVqEqDQ biSgSSS −−−−−= ϕµϕ0
2
1
02
−=
q
kT
qNQ biDSSC ϕεε
[C m-2];
[C m-2];
[C m-2]; (10)
dbibi U−= 0ϕϕ iii U−∆=∆ 0ϕϕ
ibb U+= 0ϕϕ bdi UUUU ++=
[V]; [V];
[V]; [V];
bid UUUUV −=+= [V]; Ub - voltage drop on the series
resistance r (Fig. 5).
From (9) and (10) we have:
2
1
1
2
1 2
−−+−−+= V
q
kT
Vbi ϕαααϕϕ [V];
2
1
1
2
1 2
−−+−++= V
q
kT
q
S
b ϕαα
µ
αϕϕ [V];
2
1
1
2
2
1
1
2
2
2
−+−
−
−−++=
q
kT
V
q
kT
VUd
ϕαα
ϕαα
[V], (11)
2
1
1
2
2
1
1
2
2
2
−−+−
−
−+=
V
q
kT
q
kT
Ui
ϕαα
ϕαα
[V];
( )
2
1
1
2
0
2
1
−−++
+−++−−−=∆
V
q
kT
EAA
q SgSCui
ϕαα
αµϕγϕ
[V].
So, from the Fig. 4 and expressions (11) it follows that
the barrier height of the Cu/δ-layer/n-Pb1-xSnxTe1-ySey/In
Schottky barrier structure (qϕb) depends on the applied
voltage bias and decreases with increase of the reverse
bias. It explains the absence of reverse branch saturation
of the experimental CVC (Fig. 2). Furthermore, the built-
in potential lowering due to image forces (∆ϕbi) can also
influence on the appearance of current-voltage curves.
R
r
R
C C
i
ss d
d
Fig. 5. Equivalent circuit of the Cu/δ-layer/n-Pb1-xSnxTe1-ySey/In
Schottky barrier structure: Ri - δ-layer resistance; Rd - differen-
tial resistance of the barrier layer; CSS - surface state capaci-
tance; Cd - differential capacitance of the barrier layer; r - series
resistance.
In accordance with [15-20], the barrier reduc-
tion can be calculated from the relationship for the
summation potential energy on the interface of δ-
layer/n-Pb1-xSnxTe1-ySey:
( ) ( ) ( )xqxqxq S
∗
∑ += ϕϕϕ [J], (12)
where [J] � potential en-
ergy of the image forces. Proceeding on the assumption
that qϕΣ(x) extremum places in the xmax<<L, then the
built-in potential lowering due to image forces can be written:
( ) ( )
( )x
q
xq
SiS
Si
εεεπε
εεϕ
+
−
=∗
0
2
16
(8)
[V],
[V], (7)
[V],
2
1
0
0
0 2
−=
q
kT
qNQ biDSSC ϕεε
From (5) and (6) we have:
2
1
1
2
1
0 2
−+−+=
q
kT
bi ϕαααϕϕ
2
1
1
2
1
0 2
−+−++=
q
kT
q
S
b ϕαα
µ
αϕϕ
( )
2
1
1
2
0
0
2
1
−++
+−++−−−=∆
q
kT
EAA
q SgSCui
ϕαα
αµϕγϕ
[C m-2].
56 SQO, 5(1), 2002
A.I.Tkachuk et al.: Production and investigation of Cu/thin intermediate...
2
1
1
2 21
1
−
−−+−== V
q
kT
dV
dUd ϕααα
β
β
ϕααα
β
1
12
1 2
1
1
2
/
−=
−−+==
−
V
q
kT
dV
dUi
(15)
and expression (14) at the V≥3kT/q can be rewritten:
=
kT
qV
II S β
exp
dSS CCC
111 +=
( )
δ
δεε Si
SS
DqA
C
2
0 +
=
L
A
C S
d
εε0=
( )
δγβ
βεε 10 −
= iA
C
( ) S
i
Dq
A
C 2
0
1
−
−
=
β
β
εε
δ
[A], (17)
that agrees well with the obtained experimental results.
Capacitance of the Cu/δ-layer/n-Pb1-xSnxTe1-ySey/In
Schottky barrier structure consists of two capacitances
(Fig. 5), which are connected in series [17-20]:
(18)
where
- surface state capacitance;
- differential capacitance of the barrier layer.
Finally combining (11), (16) and (18) we have:
[F]. (19)
This expression gives the possibility to obtain the rela-
tionship for the calculation of assessmentive value of
δ-layer width:
[m]. (20)
Calculated assessmentive values of δ-layer width
for the selected Cu/δ-layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier struc-
tures are reduced in Table.
Form the Fig. 2, Fig. 3 and Table, it is apparent
that the R0A, β, UI, ϕo
bi increase and IS, C0 de-
crease with the increasing δ-layer width. Further-
more, the current value I at one and the same volt-
age bias U decrease with the increasing δ-layer
width. It may be explaned by corresponding in-
crease of the δ-layer barrier and dependence of the
barrier height qϕb on the values of relative static
dielectric permittivity of the δ-layer, δ-layer width
and density of surface states (see expressions (8) and
(11)). Increasing of the zero bias built-in potential
with the increasing δ-layer width may be explained
by the decreasing density of surface states and in-
crease of the relative static dielectric permittivity
of the δ-layer due to the changing of its composition
increasing oxidation time (see expressions (8) and
(11)).
Conclusions
The high-planar epitaxial layers of n-
Pb0.935Sn0.065Te0.243Se0.757 quaternary solid solutions,
lattice matched with {111}BaF2 substrates, have been
grown from bounded volume of supersaturated melt-so-
lutions in the growth temperature region 773÷873 K by
the liquid phase epitaxy technique at a programmatic
refrigeration rate of 0.1÷0.2 K/min and a temperature
reduction range of ∆T=5÷10 K. The laboratory method-
ology of the production of Cu/δ-layer/n-
Pb0.935Sn0.065Te0.243Se0.757/In Schottky barrier structures
by thermal vacuum deposition has been developed. The
analysis of the dependence of the CVC and FVC on the δ-
layer width has shown that: 1) the values of zero bias
resistance area product, ideality coefficient, intercept
voltage, zero bias built-in potential increase and satura-
tion current, zero bias capacitance decrease with the in-
creasing of δ-layer width; 2) the barrier height depends
on the applied voltage bias; 3) the current value at the
one and the same voltage bias decreases with the increas-
ing of δ-layer width; 4) the reverse branches of the CVC
does not saturate.
,
(16)
4
1
33
0
2
32
8
−
+
−
=∆
q
kTNq
bi
S
D
iS
iS
bi ϕ
εεπεε
εε
ϕ [V]. (13)
Thus, ∆ϕbi depends on the ϕbi(V) and increase with
the increasing reverse bias, as shown in Fig. 4.
In the general case, the current through the Cu/δ-layer/
n-Pb1-xSnxTe1-ySey/In Schottky barrier structure can be
described by the expression [18-20]:
−−
=
kT
qV
kT
qV
II S /
expexp
ββ
[A], (14)
and can be determined by: charge carrier emission over
the barrier of depletion layer; charge carrier tunnelling
through the barrier of depletion layer; charge carrier
generation or recombination in the barrier layer; reso-
nance tunnelling of charge carrier through the localized
levels in the barrier layer; hole recombination and gen-
eration in the quasi-neutral region of semiconductor;
passage of charge carrier through the surface states;
charge carrier tunnelling through the barrier of δ-layer;
passage of charge carrier over the barrier of δ-layer. If
d(lnIS)/dV≈0, then ideality coefficients of CVC may be
calculated as:
A.I.Tkachuk et al.: Production and investigation of Cu/thin intermediate...
57SQO, 5(1), 2002
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