Carrier transport mechanisms in reverse biased InSb p-n junctions
Carrier transport mechanisms have been investigated in linearly graded InSb p-n junctions prepared using thermal diffusion of Cd into single crystal substrates of ntype conductivity. The investigations were focused on the reverse current as a function of bias voltage and temperature. The obtained ex...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2015
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| Цитувати: | Carrier transport mechanisms in reverse biased InSb p-n junctions / A.V. Sukach, V.V. Tetyorkin, A.I. Tkachuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 3. — С. 267-271. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859644869543198720 |
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| author | Sukach, A.V. Tetyorkin, V.V. Tkachuk, A.I. |
| author_facet | Sukach, A.V. Tetyorkin, V.V. Tkachuk, A.I. |
| citation_txt | Carrier transport mechanisms in reverse biased InSb p-n junctions / A.V. Sukach, V.V. Tetyorkin, A.I. Tkachuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 3. — С. 267-271. — Бібліогр.: 28 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Carrier transport mechanisms have been investigated in linearly graded InSb p-n junctions prepared using thermal diffusion of Cd into single crystal substrates of ntype conductivity. The investigations were focused on the reverse current as a function of bias voltage and temperature. The obtained experimental data show that local inhomogeneities in the depletion region are responsible for the excess tunneling current observed in the reverse biased junctions. The inhomogeneities have been attributed to dislocations, precipitates or other extended defects. A phenomenological model is proposed to explain experimental data.
|
| first_indexed | 2025-12-07T13:26:11Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 267-271.
doi: 10.15407/spqeo18.03.267
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
267
PACS 73.40.Kp, 73.40.Gk
Carrier transport mechanisms in reverse biased InSb p-n junctions
A.V. Sukach1, V.V. Tetyorkin1, A.I. Tkachuk2
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
2V. Vinnichenko Kirovograd State Pedagogical University, Kirovograd, Ukraine
Phone 38 (044) 525-1813, e-mail: teterkin@isp.kiev.ua
Abstract. Carrier transport mechanisms have been investigated in linearly graded InSb
p-n junctions prepared using thermal diffusion of Cd into single crystal substrates of n-
type conductivity. The investigations were focused on the reverse current as a function of
bias voltage and temperature. The obtained experimental data show that local inhomo-
geneities in the depletion region are responsible for the excess tunneling current observed
in the reverse biased junctions. The inhomogeneities have been attributed to dislocations,
precipitates or other extended defects. A phenomenological model is proposed to explain
experimental data.
Keywords: InSb, photodiode, inhomogeneous junction, tunnelling breakdown.
Manuscript received 12.03.15; revised version received 28.05.15; accepted for
publication 03.09.15; published online 30.09.15.
1. Introduction
Due to high structural perfection of InSb single crystals,
cooled photodiodes based on them are widely used for
detection of infrared radiation within the spectral range 3
to 5 µm [1-4]. Despite the fact that technology of InSb
photodiodes is improved over the last 40 years [5], a
number of problems remain valid [6, 7]. For instance, it
is known that IR photodiodes made of narrow-gap
semiconductors, including InSb photodiode, suffer from
excess leakage current at reverse bias, which can limit
their performance. Thus, understanding its nature is of
great importance. Experimental results published in
literature have contradictory character and suggestions
on the nature of the excess current mechanism and are
very different. For instance, it was explained by the
surface leakage [2] or by tunneling with participation of
extended defects (dislocations, precipitates) intersecting
the depletion region [8]. In p-n junctions produced by
ion implantation with Be or Mg, the interband tunneling
current was shown to be dominant at high reverse bias
voltages [5, 9, 10]. The breakdown voltage, UB, lies
within the range 3 to 5 V. Higher values of the break-
down voltage UB = 14…30 V associated with the
avalanche breakdown mechanism were observed in
diffused photodiodes [11, 12]. At last, in photodiodes
produced by molecular beam epitaxy the voltage of
avalanche gain was 4.5 V [13]. Thus, significant
difference in the breakdown voltage in photodiodes
produced by different methods, as well as the nature of
tunneling current in photodiodes with a rather wide
depletion region (approximately 0.5…1.0 µm at 77 K)
requires more thorough investigation, which was the
purpose of this study.
2. Samples and experimental methods
The investigated p-n junctions were produced by
diffusion of cadmium into monocrystalline substrates of
n-type conductivity with crystallographic orientation
(100) and average thickness close to 500 μm. The
concentration and mobility of electrons in the substrates
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 267-271.
doi: 10.15407/spqeo18.03.267
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
268
were of the order of 1.0·1015 cm−3 and 5.0·105 cm2/V·s at
77 K, respectively. The average density of dislocations
(the etching pits density) was less than 350 cm−2 [14].
The damaged layer was removed by chemical dynamic
polishing using the polishing etchant 2% Br2 + HBr. The
surface quality was controlled by an interference
microscope. The measured roughness at the surface after
polishing was close to 0.03 µm. Diffusion of dopant was
carried in a two-temperature furnace. The substrate and
source temperatures were 400 and 380 °C, respectively.
To prevent reevaporation of substrate components,
additionial amount of InSb and elemental Sb were
placed into a silica ampoule to ensure the saturation
vapor condition. The junction depth was determined by
measuring the sign of thermoEMF by using the probe
method during sequential chemical etching of the doped
surface layer. The mesa structures with the active area
1.4·10−2 cm2 and the junction depth close to 3 μm were
delineated. As determined by a differential Hall effect
[15], the average concentration of holes in the doped
layer was (7±1)·1018 cm−3 at 77 K. Ohmic contacts to p-
and n-type regions of the junctions were prepared using
In-Zn alloy and pure In, respectively. Formation of
ohmic contacts and purification of mesas has been
carried out in a hydrogen atmosphere at approximately
350 °C for 5 to 10 min. Thin polycrystalline films of
CdTe were used as passivation and protective layers due
to lattice parameters and thermal expansion coefficients
of CdTe and InSb agrees well. By using polycrystalline
CdTe, the density of interface states in the CdTe-InSb
heterojunction can be 3- to 4-fold reduced as compared
to the oxide-InSb interface [16]. The current-voltage and
high-frequency (1 MHz) capacitance-voltage characte-
ristics were measured as functions of the bias voltage
and temperature.
Fig. 1. Reverse I−U characteristics of diffused InSb p-n
junctions at temperatures, K: 77 (1), 89 (2), 120 (3), 138 (4),
156 (5).
3. Results and discussion
The measured capacitance-voltage characteristics are
linearized in C−3−U coordinates indicating formation of
linearly graded junctions. Typical values of the
concentration gradient a = 1.0·1019 cm−4 and the built-in
voltage Ubi = 190 mV were determined from the slope of
C−3−U straight lines and their intersection with the
voltage axis, respectively. The depletions region width,
W, was estimated as 1.3 µm at 77 K. The I−U charac-
teristics within the temperature range 77…160 K are
described by the formula:
( ) ( )
⎥
⎦
⎤
⎢
⎣
⎡
β
−
+⎥
⎦
⎤
⎢
⎣
⎡ −
=
KT
IRUe
I
E
IRUe
II ss expexp 02
0
01 , (1)
where E0 = 29 meV is the characteristic energy, 6.1=β −
ideality factor. The series resistance and built-in
potential determined from the I−U characteristics were
1.4 Ohm and 160 mV, respectively. The discrepancy in
experimental values of the built-in potential determined
by different methods is caused by the series resistance.
The rectification ratio at 77 K is reached 103 at voltages
±250 mV. The carrier transport mechanisms in diffused
InSb junctions at direct biases were analyzed in details
previously [8].
In order to clarify the impact of the surface leakage,
the I−U characteristics were investigated in a series of
junctions with a different ratio of the junction area A to
the perimeter length. It was concluded that in the
investigated junctions with rather large value of A the
measured current has bulk nature. Thus, in the below
analysis only bulk carrier transport mechanisms are
taken into account. Fig. 1 shows the reverse I−U
characteristics within the temperature range 77…156 K.
They are satisfactorily approximated by a power
dependence I ~ Um. As seen, at temperatures T < 120 K
and reverse bias voltages U ≤ 0.2 V the sublinear I−U
dependences with the exponent m ≅ 0.8 are observed. At
higher temperatures (curves 4, 5), I−U characteristics
change significantly. At the bias voltages U ≤ 0.03 V,
the exponent m ≅ 0.7…0.8, whereas at 0.04 < U ≤ 0.2 V
the reverse current tends to saturation and the exponent
m equals approximately 0.3, which is typical for the
thermal generation mechanism of carrier transport in
homogeneous p-n junctions [1, 17]. With the reverse
bias increase, the current gradually increases. The
exponent m varies from 2 to 3 at U = 1…2 V up to
4.5…5.0 at higher biases, irrespective of temperature. In
the case of the voltage breakdown in a p-n junction is
determined at the current density equal to 1 A/cm2 [18],
in the investigated junctions the breakdown voltage UB is
decreased from 3 down to 1.8 V within the temperature
range 77…156 K, which clearly indicates realization of
tunnelling mechanism inherent to carrier transport [17].
The temperature dependences of the reverse current
measured at several fixed values of the bias voltage are
shown in Fig. 2 (curves 1-6). At relatively small biases
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 267-271.
doi: 10.15407/spqeo18.03.267
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
269
U ≤ 0.2 V and temperatures higher than 120 K, the
activation dependences are observed with the energy
close to 0.13 eV, indicating thermal generation of
carriers via deep defect states in the depletion region [1].
The presence of deep donor states with the activation
energy 132 ± 3 meV and density 1013 cm−3 has been
reported in [19]. In the authors opinion, these states were
not associated with technology of the starting material.
The lack of activation parts in I−U characteristics at the
biases U ≥ 0.5 V (curves 4-6) is attributed to contri-
bution of tunneling current component to the overall
current.
In the case when the reverse current dominates over
the interband tunneling, it is given by [17]:
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
−
π
=
heF
Em
E
FUAemI g
g 3
24
exp
4
2 2/3*
2/12
3*
, (2)
where F is the electric field in the junction, A − junction
area and other symbols have their usual meaning.
Obviously, the temperature dependence of the interband
tunneling current is determined mainly by the
dependence of Eg on temperature. Shown in Fig. 3 are
temperature dependences of the measured current plotted
in lgI−Eg
3/2 coordinates. The decrease in their slope at
higher biases may be caused by the increased
contribution of the interband tunneling current. At the
reverse bias U = 2 V, this current seems to be dominant.
By using the equation (2), one can estimate the
breakdown voltage for the homogeneous junction,
Fig. 4. As seen, there exist a large discrepancy between
experimental and calculated values of the breakdown
voltage (3 and 15 V, respectively). This means that
another model of tunneling current should be invoked to
interpret experimental data correctly.
6 7 8 9 10 11 12 13 14
10-6
10-5
10-4
10-3
10-2
I, A
6
5
4
3
2
1
103/T, K-1
Fig. 2. Temperature dependences of reverse current at bias
voltages, V: 0.01 (1), 0.05 (2), 0.2 (3), 0.5 (4), 1.0 (5), 2.0 (6).
In a number of published papers [20-26], various
models of the tunneling current in the reverse biased
diodes were developed. For instance, the interband
tunneling current associated with dislocations has been
analyzed in [20-22].
A model of the barrier width inhomogeneity has
been proposed in [23]. Due to fluctuation of dopant
concentration, the local thin barriers can dominate in the
overall transport of carriers. A model of trap-assisted
tunneling (TAT) current has been developed in [24, 25].
Based on this model experimental data were satis-
factorily explained in CdxHg1−xTe (x = 0.2…0.3) [25]
and InAs infrared photodiodes [26].
The excess tunneling current in the forward-biased
InAs photodiodes was satisfactorily explained in terms
of inhomogeneous junction that contains local areas with
a much higher concentration of defects [26]. The local
inhomogeneities may be related to dislocations or other
extended defects that release excess strains in semicon-
ductors. As known, dislocations can substantially affect
distribution of dopant impurities because they provide a
fast pathway to impurities as well as can segregate
impurities. Due to the last reason, the so-called Cottrell
atmospheres are formed around dislocations. Typical
values of their diameter are of the order of 0.5…2 µm
[2]. To explain the experimental data in Fig. 4, it was
assumed that the area of a local inhomogeneity should
correlate with the average diameter of Cottrell
atmosphere. Thus, the total area of inhomogeneities A1
should be proportional to the density of dislocation. At
the same time, it is obvious that the area A1 is much less
(several orders of magnitude) than the junction area A.
Taking this into account, the junction parameters
determined from C−U measurements refer to the homo-
geneous part of the junction. The same parameters (a, W
and F) for inhomogeneities can be determined from the
10-5
10-4
10-3
10-2
I,A
0.1150.1100.1050.100
4
3
2
1
Eg
3/2, eV3/2
Fig. 3. Reverse current as a function of temperature depen-
dence of the forbidden gap at bias voltages, V: 0.2 (1), 0.5 (2),
1 (3), 2 (4).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 267-271.
doi: 10.15407/spqeo18.03.267
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
270
Fig. 4. Experimental (dots) and calculated (solid lines) reverse
I−U characteristics at 77 K. The calculated curves refer to inter-
band tunneling current via homogeneous region (1), interband
tunneling current via local inhomogeneities (2), TAT current
via local inhomogeneities including thermal and tunnel tran-
sitions (3). Parameters used for calculation: a = 1.9·1019 cm−4,
me
∗= 0.014m0, mh
∗= 0.015m0, A1= 2·10−5 cm2, a1= 2.1·1021 cm−4,
Et = Eg /2, Nt = 1·1014 cm−3, τ1 = 10−9 s, ε = 17.
temperature dependences of the reverse current
measured at high biases, which are assumed to be caused
by interband tunneling with their participation. The
following values were found from the dependences
shown in Fig. 3 at the reverse voltage 2 V: F1 =
8.4·104 V/cm, W1 = 4.8·10−5 cm and a1 = 2.1·1021 cm−4.
These values are almost two orders of magnitude higher
than those in the homogeneous part of the junction.
From the fitting calculation (curve 2 in Fig. 4), the
effective area of inhomogeneities of the order of
10−5 cm2 was obtained. It must be pointed out that
the calculations were performed for the maximum
electric field F1 = 3(U + Ubi)/2W1, where W1 =
(12ε0ε(U + Ubi)/ea1)1/3 is the depletion region width.
Concerning InSb photodiodes, a model of
inhomogeneous junction has been successfully used for
explanation of direct I−U characteristics [8]. It is natural
to assume that the excess reverse current in the
investigated junctions is also related to inhomogeneities.
The TAT current is expressed as
1
11
11
−
νν
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+ω
+
+ω
=
ncNpcN
AeWNI
nccp
tTAT , (3)
where Nt is the density of traps participating in
tunneling, ωv Nv and ωc Nc denote rates of tunneling
transitions between the valence and conduction bands
and traps in the gap, cp p1 and cn n1 are thermal transition
rates [1].
The tunneling transition rates are given by
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ −
−
−
π
=ω
Fe
EEm
EEh
FMem
N tgh
tg
h
vv
h3
)(24
exp
)(
2/3
3
22
, (4)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
π
=ω
Fe
Em
Eh
FMemN ge
t
e
cc
h3
24
exp
2/3
3
22
, (5)
where Et is the trap energy measured from the
conduction band edge, M − matrix element for tunneling
transitions via traps [27]:
4/1
4/1
2
0
0
2 222
t
g
E
Em
m
M ⎟
⎠
⎞
⎜
⎝
⎛π
=
h
h , (6)
where m0 is the free electron mass. It should be pointed
out that this model has developed for homogeneous
distribution of traps in the depletion region. Because of
in InAs effective masses of electrons and light holes, me
and mh, are approximately equal, the tunneling proba-
bility reaches maximum for the midgap states Et = Eg /2,
for which ωv Nv = ωc Nc and (cp p1)−1 =(cn n1)−1 = τ. In the
calculations, the effective lifetime τ served as an
adjustable parameter. The used value of Nt correlates
well with the concentration of deep centers found in
[18, 28], but the generation lifetime is chosen to be one
order of magnitude less than that in homogeneous InSb
p-n junctions [1].
The calculated TAT current through the local
inhomogeneities is shown in Fig. 4 (curves 2 and 3). In
the bias voltage range 0.8…2 V the calculated I−U de-
pendence satisfactorily coincides with experimental data.
At biases U < 0.7 V, thermal transitions are dominant
(curve 3), whereas within the range 0.7 < U < 2.0 V the
tunneling component of TAT current prevails. The
difference between the slope of calculated and measured
curves at U < 0.7 V may be caused by the dependence of
the generation time τ on electric field in the depletion
region or participation of several traps in the carrier
transport. At biases U ≥ 2.0 V, better coincidence of
experimental and calculated I−U characteristics is
observed for the interband tunneling current via local
inhomogeneities (curve 2). There is no need to prove
that in this case the voltage breakdown strongly depends
on availability of local inhomogeneities in the active
region of p-n junctions and their parameters such as
density and concentration gradient.
Thus, the excess tunneling current in the
investigated diffused InSb p-n junctions at temperatures
close to 77 K is explained by local inhomogeneities in
the depletion region. At a relatively small bias voltages
eU < 2Eg, thermal transitions via traps in the gap are
dominant. In the bias voltage range 3Eg ≤ eU ≤ 8Eg, the
TAT current is dominant and at high biases eU > 8Eg the
current is determined by the interband tunnelling.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 267-271.
doi: 10.15407/spqeo18.03.267
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
271
3. Conclusions
1. The carrier transport mechanisms are investigated
in the linearly graded p-n junctions prepared by
cadmium diffusion into n-InSb single crystal substrates.
Experimental results are satisfactorily explained within
the model of inhomogeneous p-n junction. The total dark
current consists of generation and tunneling components.
The excess tunneling current is caused by carrier
transport via local inhomogeneities.
2. Dispersion of breakdown voltages in InSb photo-
diodes prepared by different methods is mostly caused
by the interband tunneling current via local inhomo-
geneities.
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| id | nasplib_isofts_kiev_ua-123456789-121213 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T13:26:11Z |
| publishDate | 2015 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Sukach, A.V. Tetyorkin, V.V. Tkachuk, A.I. 2017-06-13T16:54:06Z 2017-06-13T16:54:06Z 2015 Carrier transport mechanisms in reverse biased InSb p-n junctions / A.V. Sukach, V.V. Tetyorkin, A.I. Tkachuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 3. — С. 267-271. — Бібліогр.: 28 назв. — англ. 1560-8034 DOI: 10.15407/spqeo18.03.267 PACS 73.40.Kp, 73.40.Gk https://nasplib.isofts.kiev.ua/handle/123456789/121213 Carrier transport mechanisms have been investigated in linearly graded InSb p-n junctions prepared using thermal diffusion of Cd into single crystal substrates of ntype conductivity. The investigations were focused on the reverse current as a function of bias voltage and temperature. The obtained experimental data show that local inhomogeneities in the depletion region are responsible for the excess tunneling current observed in the reverse biased junctions. The inhomogeneities have been attributed to dislocations, precipitates or other extended defects. A phenomenological model is proposed to explain experimental data. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Carrier transport mechanisms in reverse biased InSb p-n junctions Article published earlier |
| spellingShingle | Carrier transport mechanisms in reverse biased InSb p-n junctions Sukach, A.V. Tetyorkin, V.V. Tkachuk, A.I. |
| title | Carrier transport mechanisms in reverse biased InSb p-n junctions |
| title_full | Carrier transport mechanisms in reverse biased InSb p-n junctions |
| title_fullStr | Carrier transport mechanisms in reverse biased InSb p-n junctions |
| title_full_unstemmed | Carrier transport mechanisms in reverse biased InSb p-n junctions |
| title_short | Carrier transport mechanisms in reverse biased InSb p-n junctions |
| title_sort | carrier transport mechanisms in reverse biased insb p-n junctions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/121213 |
| work_keys_str_mv | AT sukachav carriertransportmechanismsinreversebiasedinsbpnjunctions AT tetyorkinvv carriertransportmechanismsinreversebiasedinsbpnjunctions AT tkachukai carriertransportmechanismsinreversebiasedinsbpnjunctions |