Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes
A new method to analyze reverse characteristics of a 4H-SiC Schottky barrier diode has been presented in this paper. The model incorporates both the current induced by the tunneling of carriers through the Schottky barrier and that induced by the thermionic emission of carriers across the metal–semi...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| Zitieren: | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes / A. Latreche // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 1. — С. 19-25. — Бібліогр.: 33 назв. — англ. |
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| citation_txt | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes / A. Latreche // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 1. — С. 19-25. — Бібліогр.: 33 назв. — англ. |
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| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | A new method to analyze reverse characteristics of a 4H-SiC Schottky barrier diode has been presented in this paper. The model incorporates both the current induced by the tunneling of carriers through the Schottky barrier and that induced by the thermionic emission of carriers across the metal–semiconductor interface. The treatment includes the effect of image force, lowering both the thermionic emission and electron tunneling processes. This analysis allowed us to separate and identify the thermionic emission and tunneling components of the total current. The experimental reverse transition voltage between thermionic emission and tunneling process can be determined from the intersection of the two components by using two models: bias dependence and no bias dependence of barrier height. For high temperatures, the experimental reverse transition voltage increases with increasing temperature and decreases with increasing the doping concentration as predicted by Latreche’s model.
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| first_indexed | 2026-03-23T18:51:37Z |
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2019. V. 22, N 1. P. 19-25.
© 2019, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
19
Semiconductor physics
Combination of thermionic emission and tunneling mechanisms
to analyze the leakage current in 4H-SiC Schottky barrier diodes
A. Latreche
Département des sciences de la matière, Université de Bordj Bou Arreridj, Algeria
*
E-mail: hlat26@yahoo.fr
Abstract. A new method to analyze reverse characteristics of 4H-SiC Schottky barrier
diode has been presented in this paper. The model incorporates both the current induced by
the tunneling of carriers through the Schottky barrier and that induced by the thermionic
emission of carriers across the metal–semiconductor interface. The treatment includes the
effect of image force lowering both the thermionic emission and electron tunneling
processes. This analysis allowed us to separate and identify the thermionic emission and
tunneling components of the total current. The experimental reverse transition voltage
between thermionic emission and tunneling process can be determined from the intersection
of the two components by using two models; bias dependence and no bias dependence of
barrier height. For high temperatures, the experimental reverse transition voltage increases
with increasing the temperature and decreases with increasing the doping concentration as
predicted by Latreche’s model.
Keywords: reverse transition voltage, thermionic emission, tunneling current, SiC Schottky
diode, image force barrier lowering.
doi: doi: https://doi.org/10.15407/spqeo22.01.19
PACS 85.30.De, 85.30.Kk, 85.30.Mn
Manuscript received 20.12.18; revised version received 01.02.19; accepted for publication
20.02.19; published online 30.03.19.
1. Introduction
The wide bandgap semiconductor silicon carbide (4H-
SiC) is attractive in a wide range of application fields,
namely: high-power, high-temperature and high-
frequency electronic devices because of its excellent
material properties. The SiC material properties that
make it suitable to replace silicon in high power devices
include wider band gap, large breakdown fields, high
thermal conductivity and acceptable bulk mobility [1-4].
In the recent years, Schottky barrier diode (SBD) based
on 4H-SiC has been studied regarding its fast switching
capability and transport mechanisms. Under the reverse-
bias condition, the dominant mechanisms by which
carrier transport occurs in Schottky barriers are
thermionic emission and carrier tunneling through the
potential barrier [5]. Both models were used separately to
analyze the experimental reverse leakage current of SiC
and other wide-gap SBDs. Combined and not combined
with barrier lowering model, some authors [6-11]
described the reverse leakage current using the general
model [12] of the tunneling current. At the same time,
the others [13-18] used the thermionic field emission
(TFE) developed by Padovani–Stratton [19] also with
and without the effect of the image force barrier
lowering. However, some researchers [20-22] used
thermionic emission model in combination with the
barrier lowering one to describe the experimental reverse
characteristics data. In fact, the total current through SBD
is the sum of both these mechanisms: thermionic
emission and tunneling process [9, 23]. In his more
recent theoretical work, Latreche [24] showed the
importance of taking into account the both mechanisms
for analysis of reverse leakage current of 4H-SiC SBDs.
In this study, the author proposes a combined model to
analyze the leakage current of 4H-SiC Schottky diodes,
which takes into account in a common framework these
two main sources of leakage current present in Schottky
diodes, namely, the current caused by thermionic
emission and that caused by the tunneling of carriers
through the Schottky barrier. Both these models are
combined with the barrier lowering model. This new
method will allow us to separate the two components of
the total current; hence, we can experimentally determine
the reverse transition voltages between these two
contributing mechanisms and, then, we compare them
with those calculated using the Latreche model [24].
SPQEO, 2019. V. 22, N 1. P. 19-25.
Latreche A. Combination of thermionic emission and tunneling mechanisms …
20
2. Theory and modeling
Thermionic emission over the potential barrier and
carrier tunneling through potential barrier are two
dominant mechanisms by which the carrier transport
occurs in Schottky barriers [5]. The total current density
flowing through the Schottky potential barrier, which
consists of both thermionic emission and tunneling, can
be conveniently expressed according to the Tsu–Esaki
formalism as [7, 9, 12, 23]
( )
( )
( ) x
xR
x
xTun dE
TkEqVq
TkEq
ET
k
TA
J
−−ς−+
−ς−+
= ∫
∞∗
B
B
0B exp1
exp1
ln
(1)
where A
*
is the effective Richardson constant, T –
temperature, kB – Boltzmann constant, ζ denotes the
difference between the equilibrium Fermi level and
conduction bands, and T(Ex) is the tunneling probability
calculated using the WKB approximation:
( ) ( )
−−= ∫
∗
dxExU
m
ET
x
x
xxWKB
2
1
21
2
)(
2
2exp
h
. (2)
Here, x1 and x2 are the two turning points. The WKB
approximation could reasonably predict tunneling current
through the Schottky barrier with and without the effect
of lowering the image barrier [25]. When the effect of
lowering the force barrier is taken into account, the
potential energy of the Schottky barrier U(x) measured
from the bottom edge of the conduction band in the bulk
of the semiconductor is [9, 26]:
( ) ( )
x
q
xD
Nq
xU
SS
D
πε
−−
ε
=
162
2
2
2
, (3)
where εS is the semiconductor permittivity, ND – doping
density, D – depletion width dependent on reverse bias
voltage VR.
In the current expression (1), both these
mechanisms of the conduction carriers flow in SBD are
included: thermionic emission occurs for energy higher
than the maximum of the potential Schottky barrier
(Ex > Umax), and the tunneling process occurs for the
lower energy range (Ex < Umax) [9, 23]:
ThermTunTot JJJ += , (4)
where the reverse tunneling current density is given by
[7, 9, 12, 23]
( )
( )
( ) x
xR
x
U
xTun dE
TkEqVq
TkEq
ET
k
TA
J
−−ς−+
−ς−+
= ∫
∗
B
B
0B exp1
exp1
ln
max
(5)
and the thermionic emission current density with
including the image force decrease is expressed by [9,
23]:
( )
( )
( )
.
exp1
exp1
ln
B
B
B
max
x
xR
x
U
xTherm dE
TkEqVq
TkEq
ET
k
TA
J
−−ς−+
−ς−+
= ∫
∞∗
(6)
When the effect of lowering the image force is
taken into account, by setting the tunneling probability
T(Ex) = 1 for the energies higher than the maximum of
the Schottky potential barrier and approximating the
Fermi–Dirac statistics with the Maxwell–Boltzmann one,
Eq. (6) of the thermionic emission current can be re-
written as [9, 23]
( )
−=
φ∆−φ−
∗ 1BB2 Tk
qV
Tk
q
Therm eeTAJ
bb
, (7)
where the image force decrease is given by [27]:
( )
41
32
3
8
επ
−ς−φ
=φ∆
S
RbD
b
VNq
. (8)
In order to predict the reverse transition voltage between
thermionic emission and tunneling process as a function
of temperature, doping concentration and barrier height
for 4H-SiC Schottky barrier diode, the analytical model
was proposed by Latreche [24]:
( ) ( ) ( ) ( )[ ]
[ ]
φ=>
+−
φ=≤≤
φ+φ+φ+φ
≈
−
b
D
b
D
bbbb
T
TT
N
TT
TT
N
TpThTgf
V
300for
10
8210.204.1301.137
300K50for
10
2
15
23
2
15
32
(9)
where the functions ( )bf φ , ( )bg φ , ( )bh φ and ( )bp φ are
given by
( )
( )
( ) ( )
( ) ( )
φ+−=φ
φ+=φ
φ−=φ
φ+−=φ
−
−
−
6
3
2
105.18836.114
1013.23124.11
548.113410.6
179.85027.39
bb
bb
bb
bb
p
h
g
f
(10)
To extract barrier height ( )bφ from the reverse I-V
characteristic, we propose two models. The first one
assumes that the barrier height bφ is bias-dependent due
to the presence of an interfacial layer and interface states
located at the contact between metal and semiconductor
SPQEO, 2019. V. 22, N 1. P. 19-25.
Latreche A. Combination of thermionic emission and tunneling mechanisms …
21
[28, 29]. In this case, the following equation can be
solved numerically by using the Newton method:
( ) ( ) ( ) ( )j
j
j
j
Thermj
j
Tunj
j
theor VJVJVJVJ exp=+= . (11)
Here, ( )j
j
VJexp is the reverse current density for
each bias voltage measurement, ( )j
j
Tun VJ and ( )j
j
Therm VJ
are the theoretical components of the current given by
Eqs (5) and (7), respectively.
The second model assumes that the effective barrier
height is independent of applied bias, and it can be
determined from the first model by calculating the
average value of the barrier height values calculated for
each bias voltage measurement.
3. Results and discussion
In order to apply our new method, we used the
experimental data on silicon carbide (4H-SiC) previously
published in the literature by several authors [13, 30, 31].
The wafers had an n-type epitaxial layer. The type of
diode, doping concentration ND and temperatures are
summarized in Table. The values of Richardson’s
constant and effective masses were taken as follows:
146 A·cm
–2
·K
–1
and m
*
= 0.2m0, respectively [32, 33].
Fig. 1 shows the extracted barrier height as a
function of the reverse bias for 4H-SiC Schottky barrier
diodes at various temperatures, when both these
mechanisms are combined. In the case of diode D1
(Fig. 1a), where the doping concentration is 7·10
15
cm
–3
,
the barrier height increases slightly with increasing the
reverse bias within the high temperatures range
373...473 K. However, in the case of these two low
temperatures 323 and 294 K, the barrier height increases
with increasing the reverse bias in particular for reverse
bias less than 380 V, whilst beyond this value the barrier
height increases slightly with increasing the reverse bias.
In the case of two diodes D2 and D3, where the
doping concentrations are 3·10
15
and 2·10
15
cm
–3
,
respectively, the barrier height decreases slightly for all
the temperatures for the high reverse bias (> 200 V for
D2 and > 100 V for D3), while for low temperatures the
barrier height is strongly decreased at low reverse bias.
For three these diodes, the barrier height decreases with
decreasing the temperature. We noted that for SiC SBDs
the Schottky barrier height strongly depends on the
reverse bias voltage, temperature and doping
concentration [10]. These dependences are caused by
combination of the effects of the interfacial layer and
interface states located at the contact interface between
metal and semiconductor [10].
Fig. 2 shows experimental and calculated reverse
current densities according to tunneling and thermionic
models for 4H-SiC Schottky diode D2 at various
temperatures by using the first model that assumes bias
dependence of barrier height (model 1). The calculated
reverse current densities are obtained using the
corresponding extracted barrier height which is plotted in
Fig. 1b. The intersection between the components of
thermionic emission and tunneling currents represents
Fig. 1. Schottky barrier height as a function of the reverse bias
voltage at various temperatures for 4H-SiC SBDs.
SPQEO, 2019. V. 22, N 1. P. 19-25.
Latreche A. Combination of thermionic emission and tunneling mechanisms …
22
the reverse transition voltage (VT) between both
corresponding mechanisms. The thermionic emission
component is seen to be dominant for low voltages up to
about VT, whereas the tunneling mechanism becomes
dominant for the biases higher than VT. Near the reverse
transition voltage, neither tunneling nor thermionic
emission accurately describes the conduction process,
because both these currents have the same order of
magnitude, and, therefore, both these mechanisms should
be combined together to analyze the reverse I-V
characteristics. In this model, where the barrier height is
extracted from each data (Ii-Vi), the total current that
presents the sum of two these components have the same
value as the experimental one. Fig. 3 shows comparison
of experimental reverse transition voltage with calculated
results obtained by using the Latreche model presented
by equations (9) and (10) for all diodes. It can be seen in
Fig. 3 that the experimental values of VT of this work
shows good agreement with the calculated values within
the whole temperature range for all the diodes. As
predicted by Latreche’s model (Eqs (9) and (10)), the
experimental reverse transition voltage decreases when
the doping concentration is increased, and also the
reverse transition voltage increases with increasing the
temperature in the high temperature range on the
parabolic shape, wharever the value of the barrier height.
At low temperatures, the Latreche model predicts a peak
that is absent in this study due to the high temperatures
used in the experiments. In this context, it may be noted
that for low temperatures the barrier height will decrease,
hence, the current will be small, difficult to measure, in
particular at lower reverse bias where probably the
transition between thermionic emission and tunneling
process may occur. In the case of diode D1, the reverse
transition voltage increases from 20.6 V at the
temperature 373 K to 30.5 V at the temperature 323 K.
Comparison between the barrier height
corresponding to the reverse transition voltage ( )Tb Vφ
extracted using model 1 (barrier height is bias-
dependent) and the effective barrier height effbφ is
shown in Fig. 4. It can be seen in this figure that ( )Tb Vφ
Fig. 2. Reverse J-U characteristics based on both thermionic
emission and tunneling process for 4H-SiC SBD; D2 for various
temperatures. Experimental data are also shown. The calculated
J-U characteristics are resulting, if using the extracted barrier
height plotted in Fig. 1b.
SPQEO, 2019. V. 22, N 1. P. 19-25.
Latreche A. Combination of thermionic emission and tunneling mechanisms …
23
Fig. 3. Experimental reverse transition voltage as a function of
temperature for 4H-SiC Schottky barrier diodes. Comparison
with the calculated reverse transition voltage by using
Latreche’s model (Eqs. (9) and (10)).
Fig. 4. Effective barrier height as a function of temperature for
4H-SiC SBDs. Comparison with the barrier height
corresponding to the reverse transition voltage ( )Tb Vφ .
is in good agreement with effbφ for high temperatures,
while this agreement becomes worse at low temperatures
due to the strong bias dependence of the barrier height at
low reverse bias for low temperatures, as we have shown
above. In the case of diode D2, ( )Tb Vφ is not shown in
Fig. 4 for low temperatures, because the I-V data are not
available at lower reverse biases where probably the
transition between thermionic emission and tunneling
process may occur (see Fig. 2a in Ref. [31]).
Fig. 5. Reverse J-U characteristics based on both the thermionic
emission and tunneling process for 4H-SiC SBD; D2 for various
temperatures. Experimental data are also shown. The calculated
J-U characteristics are resulting, if using the extracted effective
barrier height effbφ plotted in Fig. 4 (D2).
SPQEO, 2019. V. 22, N 1. P. 19-25.
Latreche A. Combination of thermionic emission and tunneling mechanisms …
24
Fig. 6. Experimental reverse transition voltages as functions of
temperature extracted by using bias dependence and no bias
dependence of barrier height models for SiC SBDs.
Shown in Fig. 4 are the experimental and calculated
reverse current densities according to tunneling and
thermionic models for 4H-SiC Schottky diode D2 at
various temperatures using the second model that
assumes no bias dependence of barrier height. As can be
seen from this figure, the total current is in good
agreement with experimental data, especially for higher
temperatures. The discrepancies between calculation and
experiment become large at low temperatures. This
observation was reported in several works in the
literature [6, 13, 14, 18] because the barrier height is
strongly dependent on the reverse bias (first model),
especially at lower temperatures. Thus, we can conclude
that the first model which assumes bias dependence is
more appropriate than the second one that assumes no
bias dependence for analysis of the reverse characteristics
of the 4H-SiC Schottky barrier diodes and other wide
bandgap SBDs.
The experimental reverse transition voltage between
the thermionic and tunneling currents for these two
models (bias and no bias dependence) are plotted in
Fig. 5. The values of the reverse transition voltage for
these two models have practically the same values over
all the temperature ranges for the diode D2. However, for
the diode D1 the agreement becomes worse at low
temperatures.
4. Conclusion
Our study has been based on the reverse current model
that incorporates in a unified way both the current due to
the thermionic emission of carriers across metal–
semiconductor interface and the tunneling current
through the potential barrier. By means of the analytical
method of the model, the different contributions to the
net current of the 4H-SiC Schottky barrier diode have
been identified from the I-V experimental data previously
published in the literature. The reverse transition voltage
(VT) between thermionic emission and tunneling currents
represents the value of the intersection of the both curves
I-V of the two components. Two models have been used
to analyze experimental data such as bias dependence
and no bias dependence of barrier height. It has been
shown that bias dependence of barrier height model is
more appropriate to describe leakage current of Schottky
barrier diode, in particular at low temperatures and low
reverse bias, because in these ranges the barrier height is
strongly dependent on temperature and reverse bias. The
experimental reverse transition voltage was found to
increase with decreasing the doping concentration and
increase with increasing temperatures as predicted by
Latreche’s model.
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Authors and CV
Abdelhakim Latreche is an assistant
professor of the Department Material
Sciences at Bordj Bou Arreridj
University, Algeria. His main
research interests include the
electrical characterization and
simulation of semiconductor devices,
in particulary, wide gap (SiC,
Ga2O3,…..) Schottky barrier diodes.
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| id | nasplib_isofts_kiev_ua-123456789-215432 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:51:37Z |
| publishDate | 2019 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Latreche, A. 2026-03-16T11:01:42Z 2019 Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes / A. Latreche // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 1. — С. 19-25. — Бібліогр.: 33 назв. — англ. 1560-8034 PACS: 85.30.De, 85.30.Kk, 85.30.Mn https://nasplib.isofts.kiev.ua/handle/123456789/215432 https://doi.org/10.15407/spqeo22.01.19 A new method to analyze reverse characteristics of a 4H-SiC Schottky barrier diode has been presented in this paper. The model incorporates both the current induced by the tunneling of carriers through the Schottky barrier and that induced by the thermionic emission of carriers across the metal–semiconductor interface. The treatment includes the effect of image force, lowering both the thermionic emission and electron tunneling processes. This analysis allowed us to separate and identify the thermionic emission and tunneling components of the total current. The experimental reverse transition voltage between thermionic emission and tunneling process can be determined from the intersection of the two components by using two models: bias dependence and no bias dependence of barrier height. For high temperatures, the experimental reverse transition voltage increases with increasing temperature and decreases with increasing the doping concentration as predicted by Latreche’s model. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Semiconductor physics Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes Article published earlier |
| spellingShingle | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes Latreche, A. Semiconductor physics |
| title | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes |
| title_full | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes |
| title_fullStr | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes |
| title_full_unstemmed | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes |
| title_short | Combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4H-SiC Schottky barrier diodes |
| title_sort | combination of thermionic emission and tunneling mechanisms to analyze the leakage current for 4h-sic schottky barrier diodes |
| topic | Semiconductor physics |
| topic_facet | Semiconductor physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215432 |
| work_keys_str_mv | AT latrechea combinationofthermionicemissionandtunnelingmechanismstoanalyzetheleakagecurrentfor4hsicschottkybarrierdiodes |