Current transport mechanisms in metal – high-k dielectric – silicon structures
The mechanism of current transport in several high k -dielectric, including rare earth metal oxides (Gd₂O₃, Nd₂O₃), ternary compounds (LaLuO₃) and rare earth metal silicate (LaSiOx) thin films on silicon was studied using current-voltage ( I - V ) and conductance-frequency measurements at temper...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2012
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irk-123456789-1182832017-05-30T03:04:05Z Current transport mechanisms in metal – high-k dielectric – silicon structures Gomeniuk, Y.V. The mechanism of current transport in several high k -dielectric, including rare earth metal oxides (Gd₂O₃, Nd₂O₃), ternary compounds (LaLuO₃) and rare earth metal silicate (LaSiOx) thin films on silicon was studied using current-voltage ( I - V ) and conductance-frequency measurements at temperatures 100-300 K. It was shown that the current through the dielectric layer is controlled either by Pool-Frenkel mechanism of trap-assisted tunneling or by Mott’s variable range hopping conductance through the localized states near the Fermi level. From the results of measurements, the dynamic dielectric constant k of the material, energy positions and bulk concentrations of traps inside the dielectric layers were determined. 2012 Article Current transport mechanisms in metal – high-k dielectric – silicon structures / Y.V. Gomeniuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 2. — С. 139-146. — Бібліогр.: 35 назв. — англ. 1560-8034 PACS 73.20.-r http://dspace.nbuv.gov.ua/handle/123456789/118283 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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The mechanism of current transport in several high k -dielectric, including
rare earth metal oxides (Gd₂O₃, Nd₂O₃), ternary compounds (LaLuO₃) and rare earth
metal silicate (LaSiOx) thin films on silicon was studied using current-voltage ( I - V )
and conductance-frequency measurements at temperatures 100-300 K. It was
shown that the current through the dielectric layer is controlled either by Pool-Frenkel
mechanism of trap-assisted tunneling or by Mott’s variable range hopping conductance
through the localized states near the Fermi level. From the results of measurements, the
dynamic dielectric constant k of the material, energy positions and bulk concentrations of
traps inside the dielectric layers were determined. |
| format |
Article |
| author |
Gomeniuk, Y.V. |
| spellingShingle |
Gomeniuk, Y.V. Current transport mechanisms in metal – high-k dielectric – silicon structures Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Gomeniuk, Y.V. |
| author_sort |
Gomeniuk, Y.V. |
| title |
Current transport mechanisms in metal – high-k dielectric – silicon structures |
| title_short |
Current transport mechanisms in metal – high-k dielectric – silicon structures |
| title_full |
Current transport mechanisms in metal – high-k dielectric – silicon structures |
| title_fullStr |
Current transport mechanisms in metal – high-k dielectric – silicon structures |
| title_full_unstemmed |
Current transport mechanisms in metal – high-k dielectric – silicon structures |
| title_sort |
current transport mechanisms in metal – high-k dielectric – silicon structures |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118283 |
| citation_txt |
Current transport mechanisms in metal – high-k
dielectric – silicon structures / Y.V. Gomeniuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 2. — С. 139-146. — Бібліогр.: 35 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT gomeniukyv currenttransportmechanismsinmetalhighkdielectricsiliconstructures |
| first_indexed |
2025-07-08T13:40:30Z |
| last_indexed |
2025-07-08T13:40:30Z |
| _version_ |
1837086311195869184 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
139
PACS 73.20.-r
Current transport mechanisms in metal – high-k
dielectric – silicon structures
Y.V. Gomeniuk
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: yurigom@lab15.kiev.ua
Abstract. The mechanism of current transport in several high k -dielectric, including
rare earth metal oxides (Gd2O3, Nd2O3), ternary compounds (LaLuO3) and rare earth
metal silicate (LaSiOx) thin films on silicon was studied using current-voltage ( VI )
and conductance-frequency ( G ) measurements at temperatures 100-300 K. It was
shown that the current through the dielectric layer is controlled either by Pool-Frenkel
mechanism of trap-assisted tunneling or by Mott’s variable range hopping conductance
through the localized states near the Fermi level. From the results of measurements, the
dynamic dielectric constant k of the material, energy positions and bulk concentrations of
traps inside the dielectric layers were determined.
Keywords: high-k dielectric, dielectric-semiconductor interface.
Manuscript received 02.03.12; revised version received 12.03.12; accepted for
publication 27.03.12; published online 30.05.12.
1. Introduction
Further downscaling in micro- and nanoelectronics
motivates the search of a replacement gate dielectric
instead of conventional thermally grown silicon dioxide.
Reduction of SiO2 thickness below 1.5 nm is associated
with several critical drawbacks, the most important of
which is increased leakage current through the gate
oxide due to direct tunneling effects. In order to reduce
gate leakage while maintaining the gate capacitance,
dielectrics with higher dielectric constant than SiO2, the
so-called high k dielectrics, are being intensively
investigated now. The new materials must provide the
same or better control of semiconductor surface
properties than that for ultrathin SiO2 layers, with a
much lower level of leakage currents, due to suppression
of direct tunneling.
Among high-k dielectrics, epitaxial transition metal
and rare earth metal oxides have been considered as
perspective materials to replace silicon dioxide for future
CMOS technology because of their wide band gap and
large offsets between conductance and valence bands of
the dielectric and silicon. The complete and broad
reviews of future high k dielectrics for substitution of
silicon dioxide can be found in [1-4]. An ideal high k
gate dielectric must provide a low interface state density,
high band offsets at the interface with the semiconductor
and low leakage currents. The tunneling components of
the leakage current, such as direct tunneling and Fowler-
Nordheim tunneling currents, can be substantially
suppressed while using the thicker films. But there may
be also observed other types of leakage current in the
dielectric films, such as, trap-assisted currents in the case
when the dielectric contains deep traps in the bulk, or the
currents through grain boundaries in the case of
polycrystalline film. The crystallization temperature of
the silicon oxide exceeds 1000 °C, so that the dielectric
film remains amorphous after the high-temperature
technological steps of the integrated circuit fabrication
cycle. This is not the case for many high k dielectrics
with the crystallization temperature of about 400 °C.
Crystallization of the amorphous film deteriorates its
dielectric quality due to an increased leakage current
through the grain boundaries.
This problem can be solved, at least partially, by
the use of epitaxially grown single-crystalline thin layers
of rare earth oxide dielectric instead of the amorphous
films [5]. But even with the perfect crystalline quality of
the dielectric layer and abrupt oxide/silicon interface, the
achievement of low leakage currents in high k -silicon
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
140
systems is a problem, because the rare-earth oxides, as
most types of the high k dielectrics, are ionic
compounds with relatively weak chemical bonds
between ions, and are known to contain a high
concentration of oxygen vacancies [1]. These intrinsic
defects produce the local energy levels in the band gap,
being a reason of relatively high leakage currents.
Another possible mechanism of the leakage currents
through the high k dielectric layer is phonon-assisted
tunneling, since in higher dielectric constant metal
oxides the density of soft optical phonons is high
because of ionic bonds [2].
This paper presents the results of current-voltage
( VI ), current-temperature ( TI ) and a.c.
conductance-frequency ( G measurements for
several high k dielectrics, including rare earth metal
oxides (Gd2O3 and Nd2O3), ternary compounds
(LaLuO3) and silicate (LaSiOx) films, epitaxially grown
on silicon substrates.
2. Experimental
The single-crystalline Gd and Nd oxide films were
grown in an integrated multichamber ultrahigh vacuum
system using solid source molecular beam epitaxy
(MBE), which allows better control of
semiconductor/dielectric interface properties and can
avoid a low dielectric constant interfacial layer. The
details of deposition of metal oxide dielectric films can
be found elsewhere [6]. Prior to Pt metal dot deposition,
the structures were annealed in forming gas for 10 min at
450 or 500 °C to decrease the charge instability in the
dielectrics. Three structures were studied: Pt-Gd2O3-
pSi(111) annealed at 500 °C (hereafter denoted as #1),
Pt-Gd2O3-pSi(100) annealed at 450 °C (#2), and Pt-
Nd2O3-pSi(111) annealed at 450 °C (#4). The
thicknesses of the oxide layers were equal to 6.7 nm
(#1), 7.5 nm (#2) and 10 nm (#4), the dielectric constant
k of deposited oxide films was within the range from
11.2 to 11.9.
The dielectric layers in the Pt-LaLuO3-pSi(100)
MOS structures were deposited by molecular beam
deposition (MBD). Evaporation of La and Lu in O2 was
performed at a substrate temperature of 450 °C. Two
structures were studied with the nominal physical
thicknesses of the dielectric layer (LaLuO3) of tox = 6.5
and 20 nm. The samples were exposed to forming gas
annealing at 400 °C for 10 min (10% H2). Pt gates were
prepared by e-gun evaporation through a shadow mask.
The dielectric layers of the NiSi-LaSiOx-pSi(100)
MOS structures were deposited onto n- and p-type
silicon substrates by electron beam evaporation from
La2O3 pellets [7]. The structures were studied with the
nominal physical thicknesses of the dielectric layer
(LaSiOx) of tox = 10 and 7.5 nm. Circular NiSi electrodes
have been fabricated by full silicidation and reactive ion
etching [8]. The samples received no post-metallization
annealing treatment.
The films were characterized by conductance vs.
frequency measurements within the temperature range
120 to 320 K using an Agilent 4284A LCR meter.
Current-voltage and current-temperature dependences
were measured with Keithley 6485 picoammeter.
3. Results and discussion
3.1. Comparative analysis of a.c. and d.c. conductance
in rare-earth oxides Gd2O3 and Nd2O3
Let us consider first the G dependences measured in
the structures with Gd2O3 and Nd2O3 dielectrics. Fig. 1
shows the dependences of a.c. conductivity at different
temperatures for Pt-Gd2O3-pSi(111) structure annealed
at 500 °C (#1). The presented curves were measured at
small forward bias ( V1.0 at the metal electrode). At
low frequencies the conductivity is frequency
independent and at high frequencies the conductivity
obeys the power law relationship, so that the equation
for the frequency dependence of the conductivity can be
written as σ(ω) = σ0 + Aωs, where σ0 represents low-
frequency, or d.c. conductivity. Such behavior of the a.c.
transport is observed in a broad range of materials,
including amorphous semiconductors, ionic conductors
and heavily doped compensated semiconductors, and is
commonly treated either as a dielectric relaxation in
solids [9, 10] or as a variable-range hopping (VRH)
conductance through the random network of hopping
sites [11]. The critical exponent s in most cases is
slightly less than or close to unity. The temperature
dependence of conductivity at the low-frequency (d.c.) is
much more pronounced than at high-frequency, which is
also a mark of the hopping process and can be
theoretically explained in frames of free-energy barrier
model for disordered solids [12].
Rare-earth oxides are known to be good ionic
conductors [13]. Ionic conductance takes place via the
oxygen vacancies, and although it is usually observed at
high temperatures, we can not rule out this mechanism
of carrier transport. Theoretical consideration of ionic
transport in solids with account of the effect of
relaxation of ionic surrounding [14] gives the following
equation for a.c. conductivity: σ(ω) = σ0[1 + (ω/ωc)
2], so
that at frequencies exceeding some ωc the conductance is
proportional to the square of the frequency. Our results
show that the critical exponent s in the power law
approximation of the frequency dependence of
conductivity at high frequencies is higher than unity (see
Fig. 1), which can not be explained in the frames of
dielectric relaxation or hopping conductance theories.
One of possible explanations is that the ionic conduction
contributes into the observed a.c. conductance at high
frequencies. It should also be mentioned, that the
presence of grain boundaries in polycrystalline material
can enhance the ionic conductance by several orders of
magnitude [15] which is confirmed by the theoretical
calculations predicting that oxygen vacancies tend to
precipitate at grain boundaries [16].
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
141
Fig. 1. Dependences of a.c. conductivity on frequency at
various temperatures.
Taking into account the above arguments, we
consider the a.c. conductance in the studied systems to
be mainly related with the processes within oxide bulk
and not at the interface. Fig. 2 shows the dependences of
a.c. conductivity on frequency for all the samples. The
most remarkable feature is that the structure Pt-Gd2O3-
pSi(111) annealed at 500 °C shows the lowest a.c.
current at low frequencies. These measurements were
supplemented with the measurements of the temperature
dependences of d.c. forward current carried out at the
same small forward bias V1.0 . Fig. 3 shows the
temperature dependences of d.c. current plotted in
Mott’s coordinates log(σT1/2) vs. 41T . The current
appears to obey the Mott’s 41T law that corresponds to
the VRH conductance via the localized states at the
Fermi level.
The Mott model predicts the following dependence
of the conductivity for the variable-range hopping
process [11]:
)/exp()/()( 4/12/1
0 TBTT , (1)
1000 10000 100000 1000000
10-10
10-9
10-8
10-7
Gd2O3-Si(111), 500C
Gd2O3-Si(100), 450C
Nd2O3-Si(111), 450C
,
S
/c
m
F, Hz
200K
V=-0.1V
Fig. 2. Dependences of a.c. conductivity vs. frequency for
three samples.
0.24 0.25 0.26 0.27 0.28 0.29
-8
-7
-6
-5
-4
-3
Gd2O3-Si(111), 500C
Gd2O3-Si(100), 450C
Nd2O3-Si(111), 450C
Lo
g(
IT
1/
2 ),
A
K
1/
2
1/T1/4, K-1/4
V=-0.1 V
Fig. 3. Temperature dependences of the forward current for
three structures plotted in Mott’s coordinates.
where σ0 is a temperature independent factor,
4/1
FB
3
0 )(
ENk
BB , B0 – factor ranging from 1.66 to
2.5, 1 – localization length of electron, kB –
Boltzmann’s constant, N(EF) – the bulk concentration of
the localized states at the Fermi level. From the slope B
of the ln(σT1/2) vs. 41T dependence, one can determine
the bulk concentration of the localized states near the
Fermi level as follows:
B
4
3
4
0F)(
kB
BEN
. (2)
The hopping conductivity through the states at the
Fermi level can be additionally described by the
following expression [17]:
,)/exp()2exp(
)(6/1)(
B
F
22
TkWR
ENRqT ph
(3)
where R is the hopping distance, νph is the phonon
frequency, W is the activation energy of the hopping,
and q is the electron charge. In Mott’s model, the
hopping activation energy is given by the equation [11]:
)(4
3
F
3 ENR
W
, (4)
where the hopping distance
4/1
B)(2
3
TkEN
R
F
.
Assuming the localization radius of the electron
wavefunction cm10 71 and B0 = 2 [18], from the
slope B of the characteristics log(σT1/2) vs. 41T
presented in Fig. 3 and using Eq. (2) we determine the
density of states at the Fermi level N(EF). The values of
bulk density of states N(EF) and of hopping activation
energy W for three measured samples are presented in
Table. The physical origin of the states being the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
142
hopping sites inside the dielectric layer is still discussed,
but most often the deep levels in the high k materials
are associated with oxygen vacancies and interstitials
randomly distributed in the dielectric film [1, 13, 19].
The role of oxygen related defects as carrier traps in
high k dielectrics HfO2 and ZrO2 is discussed in [20-
22]. Theoretical calculations of energy positions of trap
levels associated with various charge states of oxygen
vacancies for different high k dielectrics are presented
in [23, 24].
Finally, we have plotted the low-frequency a.c.
conductance σ0(T) in Arrhenius coordinates to check the
activation energy. Fig. 4 shows the respective
dependences for all the samples. As we have already
mentioned, the measurements were carried out at the
small forward bias Vg = V1.0 . At such low biases, the
probability of Fowler-Nordheim tunneling through the
triangular barrier or of thermally assisted tunneling of
Pool-Frenkel type is negligible. So, the derived values
are not related to the valence band offset at the interface.
We may suggest that the apparent activation energy is
related either to activation of holes from semiconductor
to the trap levels in the oxide band gap or to phonon-
induced excitation of carriers during VRH process inside
the dielectric. The values of activation energies Ea
derived from the temperature dependences of low-
frequency a.c. currents are presented in Table. The
lowest value of the activation energy Ea was found for
the Gd2O3 film grown on the Si(100) substrate (sample
#2). This sample also shows the lowest density of
interface states [25].
Table. Bulk trap concentration, hopping activation energy
and activation energy from low-frequency a.c. conductance
for Gd2O3 and Nd2O3 dielectrics.
Sample # N(EF)
[eV–1cm–3]
W (Mott)
[meV]
Ea (σ0(T))
[meV]
1 2.1×1017 107 138
2 1.8×1019 37 33
4 7.8×1019 30 126
0.004 0.006 0.008
-23
-22
-21
-20
-19
-18 Gd2O3-Si(111), 500C
Gd2O3-Si(100), 450C
Nd2O3-Si(111), 450C
Ea=126 meV
ln
,
S
/c
m
1/T, K-1
Ea=138 meV
Ea=33 meV
Fig. 4. Arrhenius plot of the low-frequency a.c. conductivity
for three samples.
Taking into account that the applied forward bias
during the measurement of temperature dependences is
low (Vg = V1.0 ) and assuming that the current is due
to the transport of holes, the energy levels corresponding
to the bulk defect centers in the dielectric should be
situated near the Fermi level, which is common for
dielectric and silicon. At room temperature for p-type
silicon doped with impurity concentration 316 cm105 ,
the Fermi level is situated at 0.13 eV above the Si
valence band [26]. The valence band offset at the
Gd2O3/Si interface lies in the range from 2.3 to 2.78 eV
[3, 27, 28] in dependence on methods of measurement
and at Nd2O3/Si interface is equal to 2.7 eV [29]. Thus,
in Gd2O3 location of the deep levels takes place at 2.5 to
3.0 eV above the valence band edge, and in Nd2O3 the
deep levels are situated at 2.9 eV above the valence band
edge. Therefore, we can suggest that the current occurs
via the transport of holes, which enter the interface
levels and then tunnel to the trap levels in the dielectric,
with the following VRH conductance process through
the random network of localized states in the band gap.
It can be seen from Table that there exists a quite
satisfactory correlation of activation energies calculated
from a.c. conductance and d.c. current-temperature
dependences for samples #1 and #2. Sample #4 with
Nd2O3 oxide dielectric shows much lower hopping
activation energy as compared to the activation energy
obtained from the temperature dependence of low-
frequency a.c. conductivity. This sample is also
characterized by much higher concentrations of interface
states in the silicon band gap. The reason for this
behavior may be the fact that the high concentration of
bulk interface states is involved into a recharging
process when the sample is tested in a.c. mode. Their
contribution to the total a.c. conductance has the
activation energy that may differ from that in d.c.
measurements.
3.2. Transport mechanisms in ternary dielectric
compound LaLuO3
LaLuO3 is an attractive candidate as a gate dielectric
material because of its low hygroscopicity, high thermal
stability, high optical bandgap (~5.6 eV) and high k-
value close to 30 [30]. VI characteristics measured
on the Pt/LaLuO3/p-Si(100) MOS structures have
revealed an apparent dependence of the leakage currents
on temperature for all the range of reverse and low
(|Vg|<1 V) forward biases indicating the thermally-
activated charge transport mechanism. For the forward
voltage absolute value of about 1 V the temperature
dependence of the current vanishes and at higher
forward biases it becomes metallic, so that the current
decreases with increasing the temperature. Because the
behavior of the temperature dependence of VI
characteristics appeared to be different at forward and
reverse biases, we analyzed them separately.
Figs 5a and 5b shows the current-voltage
dependences for the samples with thicknesses of the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
143
dielectric layers 20 and 6.5 nm, respectively, plotted in
Poole-Frenkel coordinates (ln(J/V) vs. V1/2). The sections
where the plots can be approximated by a straight line
indicate that the forward-bias current is governed by
Poole-Frenkel mechanism for trap-assisted thermally
activated transport through the potential barriers lowered
by the electric field. This is also confirmed by the
current-temperature dependence plotted in Arrhenius
coordinates (Fig. 5b, inset).
The voltage and temperature dependences of the
current density for the Poole-Frenkel emission
mechanism is described by the equation [26]:
bVa
Tk
q
VJ 2exp
B
, (5)
where b is the barrier height, q – elementary charge,
kB – Boltzmann’s constant, ox4 tkqa , k –
dielectric permittivity, tox – dielectric thickness. From
the slope S of the ln(J/V) vs. V1/2 dependence, one can
determine the dielectric permittivity k as follows:
ox
2 4 ta
q
k
, S
Tk
a
2
B . (6)
0.2 0.4 0.6 0.8 1.0 1.2
-12
-10
-8
-6
-4
-2
0 Pt-LaLuO
3
-pSi(100)
100
140
180
300
t
ox
= 20 nm
T, K =
ln
(J
/V
g)
,
A
/ V
cm
2
Vg
1/2, V1/2
a)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
3 4 5 6 7
-16
-14
-12
300
320
340
360
380
t
ox
= 6.5 nm
T, K =
Pt-LaLuO
3
-pSi(100)
ln
(J
/V
g
),
A
/ V
cm
2
Vg
1/2, V1/2
ln
(I
),
A
1/T, 10-3 1/K
b)
Fig. 5. Forward current for LaLuO3 film plotted in Poole-
Frenkel coordinates for the 20-nm (a) and 6.5-nm (b) thick
oxide layer (inset – I – T dependence in Arrhenius
coordinates).
This method gives us the values k = 16 and 20 for
the samples with tox = 6.5 and 20 nm, respectively. For
the thinner sample, we have taken for calculation the
initial parts of the VI curves (|Vg|<0.5 V), so that the
electric field in dielectric did not exceed 0.8 MV/cm.
Fig. 6 shows the temperature dependences of the
reverse current plotted in Mott’s coordinates ln(IT1/2) vs.
41T . The reverse-bias current for both samples
appeared to obey Mott’s 41T law for variable-range
hopping conduction. It can be seen that the dependences
are better fitted by Mott’s law for the sample with
tox = 20 nm than for that with tox = 6.5 nm. It could be
explained by higher contribution of bulk conductance as
compared to the more dominant interface-related
conductance mechanism for the thinner oxide sample.
From the slope of the Mott plots and using Eq. (2), we
can calculate the values of the bulk concentration of the
localized states at the Fermi level N(EF). For the thinner
sample N(EF) = 3116 cmeV107.4 at Vg = 1 V and
N(EF) = 3116 cmeV104.2 at Vg = 0.5 V, and for the
thicker one N(EF) = 3116 cmeV101.6 at Vg = 1 V and
N(EF) = 3116 cmeV105.4 at Vg = 0.5 V.
0.24 0.25 0.26 0.27 0.28
-25
-20
-15
-10
Vg, V
t
ox
= 20 nm
Pt-LaLuO
3
-pSi(100)
ln
(I
·T
1/
2
),
A
K
1
/2
T -1/4, K-1/4
0.5
1
2
5
a)
0.24 0.25 0.26 0.27 0.28
-30
-25
-20
-15
-10
Vg, V
0.5
1
Pt-LaLuO
3
-pSi(100)
t
ox
= 6.5 nm
ln
(I
·T
1
/2
),
A
K
1
/2
T -1/4, K-1/4
b)
Fig. 6. I-T dependences of the reverse current plotted in Mott’s
coordinates for the samples with tox = 20 nm (a) and tox =
6.5 nm (b).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
144
It should be noted that Pool-Frenkel emission as a
dominant mechanism of charge transport in high
dielectric constant thin films was reported in several
papers [31-34] for ZrO2, Eu2O3, Lu2O3 and HfLaSiON
dielectrics. At the same time, variable range hopping
conduction in these materials for the first time was
observed by our group.
3.3. Transport mechanisms in rare-earth silicate LaSiOx
Lanthanum silicate LaSiOx has a lower value of k than
La2O3 oxide, but it offers higher crystallization
temperature and lower hygroscopicity. Additionally, the
rare-earth metal silicate interface layer can be used as a
transition layer between high k dielectric and
semiconductor instead of SiOx, thus increasing the total
dielectric constant of a gate stack [35]. So, studies of
charge carrier transport mechanism in LaSiOx/Si
structures attract considerable interest.
Fig. 7a, b shows the I-V characteristics for 10-nm
thick lanthanum silicate layer on n- and p-Si substrates
measured within the temperature range 140 up to 300 K.
It can be seen that the forward current densities are
rather high. One should notice a different kind of
temperature dependence of the forward current for n-
and p-Si substrate. The reverse current densities differ
by several orders of magnitude for n- and p-type
substrates, which can be due to different offsets between
conduction and valence bands at the
semiconductor/insulator interface. The apparent
temperature dependence of the leakage currents is
observed for low (|Vg|<1 V) forward biases indicating the
thermally-activated charge transport mechanism.
Fig. 8 shows the forward branches of VI
dependences for the p-type sample with 7.5-nm LaSiOx
plotted in Poole-Frenkel coordinates (ln(J/V) vs. V1/2).
The sections where linear approximation is valid
indicate that the forward-bias current is determined by
the Poole-Frenkel mechanism for trap-assisted thermally
activated transport. This is also confirmed by the
Arrhenius plots of the current-temperature dependences
(Fig. 9). At a forward bias, the current inside dielectric is
mainly caused by transport of majority carriers, in our
case, of holes injected from the semiconductor. The
depth of hole traps in respect to the valence band edge
was calculated from the slopes of ln(J/V) vs. 1/kBT plots
and equals to b = 0.47 eV. The dynamic dielectric
permittivity kwas evaluated from the slopes of ln(J/V)
vs. V1/2 plots (Fig. 8) using Eq. (6) and gave the values
ranging from 16.3 to 16.8.
0.2 0.4 0.6 0.8 1.0
-18
-16
-14
-12
-10
-8
-6
-4
-2
t
ox
= 7.5 nm
NiSi / LaSiOx / p-Si
T, K
ln
(J
/V
g)
V
g
1/2, V1/2
180
260
300
Fig. 8. Forward current for the sample with 7.5-nm LaSiOx
layer plotted in Poole-Frenkel coordinates.
40 50 60 70 80 90
-24
-22
-20
-18
-16
-14
-12
-10
E
a
= 0.198 eV
E
a
= 0.031 eV
t
ox
= 7.5 nm
NiSi / LaSiOx / p-Si
ln
(I
)
1/k
B
T, eV-1
-0.2
-0.4
-0.8
V
g
, V
E
a
= 0.085 eV
Fig. 9. Forward current for the sample with 7.5-nm LaSiOx
layer plotted in Arrhenius coordinates for various Vg.
-5 -4 -3 -2 -1 0 1 2 3
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
300
260
180
140
NiSi / LaSiOx / n-Si
T, K
J,
A
/c
m
2
Vg, V
a)
-2 0 2 4 6 8 10
1E-12
1E-10
1E-8
1E-6
1E-4
0.01
1
300
260
220
180
T, K NiSi / LaSiOx / p-Si
J,
A
/c
m
2
Vg, V
b)
Fig. 7. J-V characteristics for (a) 10 nm LaSiOx/n-Si and (b)
10 nm LaSiOx/p-Si structures measured at various
temperatures.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
145
5. Conclusions
The mechanism of charge carrier transport through the
rare-earth metal oxide films Gd2O3 and Nd2O3 at a low
forward bias was found to be the Mott variable-range
hopping conductance through localized states near the
Fermi level. This mechanism also determines a.c.
conduction at frequencies above 100 kHz. From the
measurements of temperature dependences of forward
currents, the bulk concentrations of the deep levels in the
high k oxides were determined. These levels are most
probably related to the oxygen vacancies, the large
concentration of which is inherent to ionic metal oxides.
The conduction via these defect levels in the band gap of
dielectric may be at the origin of the high leakage
currents observed in many high k materials.
The charge carrier transport and bulk density of
states was studied in MBD grown LaLuO3 oxide which
is considered as a perspective high k dielectrics for
micro- and nanoelectronics applications. It was shown
that the forward current through the dielectric is
controlled by the Poole-Frenkel mechanism of trap
assisted thermally activated transport. The mechanism of
the reverse current was found to be the variable-range
hopping conductance through localized states at the
Fermi level. The charge carrier transport through the
LaSiOx dielectric film was found to occur via Poole-
Frenkel mechanism.
Acknowledgements
This work has been partly funded by the National
Academy of Sciences of Ukraine in frames of the
Complex Program of Fundamental Research
“Nanosystems, nanomaterials and nanotechnologies”,
project No. H11/32/53 . Author is grateful to
M.C. Lemme, H.J. Osten, A. Laha, P.K. Hurley,
K. Cherkaoui, S. Monaghan, H.D.B. Gottlob, and
M. Schmidt for providing the samples for measurements,
and to V.S. Lysenko and A.N. Nazarov for useful
discussions and valuable comments.
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 2. P. 139-146.
PACS 73.20.-r
Current transport mechanisms in metal – high-k
dielectric – silicon structures
Y.V. Gomeniuk
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: yurigom@lab15.kiev.ua
Abstract. The mechanism of current transport in several high
k
-
-dielectric, including rare earth metal oxides (Gd2O3, Nd2O3), ternary compounds (LaLuO3) and rare earth metal silicate (LaSiOx) thin films on silicon was studied using current-voltage (
V
I
-
) and conductance-frequency (
w
-
G
) measurements at temperatures 100-300 K. It was shown that the current through the dielectric layer is controlled either by Pool-Frenkel mechanism of trap-assisted tunneling or by Mott’s variable range hopping conductance through the localized states near the Fermi level. From the results of measurements, the dynamic dielectric constant k of the material, energy positions and bulk concentrations of traps inside the dielectric layers were determined.
Keywords: high-k dielectric, dielectric-semiconductor interface.
Manuscript received 02.03.12; revised version received 12.03.12; accepted for publication 27.03.12; published online 30.05.12.
1. Introduction
Further downscaling in micro- and nanoelectronics motivates the search of a replacement gate dielectric instead of conventional thermally grown silicon dioxide. Reduction of SiO2 thickness below 1.5 nm is associated with several critical drawbacks, the most important of which is increased leakage current through the gate oxide due to direct tunneling effects. In order to reduce gate leakage while maintaining the gate capacitance, dielectrics with higher dielectric constant than SiO2, the so-called high
k
-
dielectrics, are being intensively investigated now. The new materials must provide the same or better control of semiconductor surface properties than that for ultrathin SiO2 layers, with a much lower level of leakage currents, due to suppression of direct tunneling.
Among high-k dielectrics, epitaxial transition metal and rare earth metal oxides have been considered as perspective materials to replace silicon dioxide for future CMOS technology because of their wide band gap and large offsets between conductance and valence bands of the dielectric and silicon. The complete and broad reviews of future high
k
-
dielectrics for substitution of silicon dioxide can be found in [1-4]. An ideal high
k
-
gate dielectric must provide a low interface state density, high band offsets at the interface with the semiconductor and low leakage currents. The tunneling components of the leakage current, such as direct tunneling and Fowler-Nordheim tunneling currents, can be substantially suppressed while using the thicker films. But there may be also observed other types of leakage current in the dielectric films, such as, trap-assisted currents in the case when the dielectric contains deep traps in the bulk, or the currents through grain boundaries in the case of polycrystalline film. The crystallization temperature of the silicon oxide exceeds 1000 °C, so that the dielectric film remains amorphous after the high-temperature technological steps of the integrated circuit fabrication cycle. This is not the case for many high
k
-
dielectrics with the crystallization temperature of about 400 °C. Crystallization of the amorphous film deteriorates its dielectric quality due to an increased leakage current through the grain boundaries.
This problem can be solved, at least partially, by the use of epitaxially grown single-crystalline thin layers of rare earth oxide dielectric instead of the amorphous films [5]. But even with the perfect crystalline quality of the dielectric layer and abrupt oxide/silicon interface, the achievement of low leakage currents in high
k
-
-silicon systems is a problem, because the rare-earth oxides, as most types of the high
k
-
dielectrics, are ionic compounds with relatively weak chemical bonds between ions, and are known to contain a high concentration of oxygen vacancies [1]. These intrinsic defects produce the local energy levels in the band gap, being a reason of relatively high leakage currents. Another possible mechanism of the leakage currents through the high
k
-
dielectric layer is phonon-assisted tunneling, since in higher dielectric constant metal oxides the density of soft optical phonons is high because of ionic bonds [2].
This paper presents the results of current-voltage (
V
I
-
), current-temperature (
T
I
-
) and a.c. conductance-frequency (
w
-
G
measurements for several high
k
-
dielectrics, including rare earth metal oxides (Gd2O3 and Nd2O3), ternary compounds (LaLuO3) and silicate (LaSiOx) films, epitaxially grown on silicon substrates.
2. Experimental
The single-crystalline Gd and Nd oxide films were grown in an integrated multichamber ultrahigh vacuum system using solid source molecular beam epitaxy (MBE), which allows better control of semiconductor/dielectric interface properties and can avoid a low dielectric constant interfacial layer. The details of deposition of metal oxide dielectric films can be found elsewhere [6]. Prior to Pt metal dot deposition, the structures were annealed in forming gas for 10 min at 450 or 500 °C to decrease the charge instability in the dielectrics. Three structures were studied: Pt-Gd2O3-pSi(111) annealed at 500 °C (hereafter denoted as #1), Pt-Gd2O3-pSi(100) annealed at 450 °C (#2), and Pt-Nd2O3-pSi(111) annealed at 450 °C (#4). The thicknesses of the oxide layers were equal to 6.7 nm (#1), 7.5 nm (#2) and 10 nm (#4), the dielectric constant k of deposited oxide films was within the range from 11.2 to 11.9.
The dielectric layers in the Pt-LaLuO3-pSi(100) MOS structures were deposited by molecular beam deposition (MBD). Evaporation of La and Lu in O2 was performed at a substrate temperature of 450 °C. Two structures were studied with the nominal physical thicknesses of the dielectric layer (LaLuO3) of tox = 6.5 and 20 nm. The samples were exposed to forming gas annealing at 400 °C for 10 min (10% H2). Pt gates were prepared by e-gun evaporation through a shadow mask.
The dielectric layers of the NiSi-LaSiOx-pSi(100) MOS structures were deposited onto n- and p-type silicon substrates by electron beam evaporation from La2O3 pellets [7]. The structures were studied with the nominal physical thicknesses of the dielectric layer (LaSiOx) of tox = 10 and 7.5 nm. Circular NiSi electrodes have been fabricated by full silicidation and reactive ion etching [8]. The samples received no post-metallization annealing treatment.
The films were characterized by conductance vs. frequency measurements within the temperature range 120 to 320 K using an Agilent 4284A LCR meter. Current-voltage and current-temperature dependences were measured with Keithley 6485 picoammeter.
3. Results and discussion
3.1. Comparative analysis of a.c. and d.c. conductance in rare-earth oxides Gd2O3 and Nd2O3
Let us consider first the
w
-
G
dependences measured in the structures with Gd2O3 and Nd2O3 dielectrics. Fig. 1 shows the dependences of a.c. conductivity at different temperatures for Pt-Gd2O3-pSi(111) structure annealed at 500 °C (#1). The presented curves were measured at small forward bias (
V
1
.
0
-
at the metal electrode). At low frequencies the conductivity is frequency independent and at high frequencies the conductivity obeys the power law relationship, so that the equation for the frequency dependence of the conductivity can be written as σ(ω) = σ0 + Aωs, where σ0 represents low-frequency, or d.c. conductivity. Such behavior of the a.c. transport is observed in a broad range of materials, including amorphous semiconductors, ionic conductors and heavily doped compensated semiconductors, and is commonly treated either as a dielectric relaxation in solids [9, 10] or as a variable-range hopping (VRH) conductance through the random network of hopping sites [11]. The critical exponent s in most cases is slightly less than or close to unity. The temperature dependence of conductivity at the low-frequency (d.c.) is much more pronounced than at high-frequency, which is also a mark of the hopping process and can be theoretically explained in frames of free-energy barrier model for disordered solids [12].
Rare-earth oxides are known to be good ionic conductors [13]. Ionic conductance takes place via the oxygen vacancies, and although it is usually observed at high temperatures, we can not rule out this mechanism of carrier transport. Theoretical consideration of ionic transport in solids with account of the effect of relaxation of ionic surrounding [14] gives the following equation for a.c. conductivity: σ(ω) = σ0[1 + (ω/ωc)2], so that at frequencies exceeding some ωc the conductance is proportional to the square of the frequency. Our results show that the critical exponent s in the power law approximation of the frequency dependence of conductivity at high frequencies is higher than unity (see Fig. 1), which can not be explained in the frames of dielectric relaxation or hopping conductance theories. One of possible explanations is that the ionic conduction contributes into the observed a.c. conductance at high frequencies. It should also be mentioned, that the presence of grain boundaries in polycrystalline material can enhance the ionic conductance by several orders of magnitude [15] which is confirmed by the theoretical calculations predicting that oxygen vacancies tend to precipitate at grain boundaries [16].
Fig. 1. Dependences of a.c. conductivity on frequency at various temperatures.
Taking into account the above arguments, we consider the a.c. conductance in the studied systems to be mainly related with the processes within oxide bulk and not at the interface. Fig. 2 shows the dependences of a.c. conductivity on frequency for all the samples. The most remarkable feature is that the structure Pt-Gd2O3-pSi(111) annealed at 500 °C shows the lowest a.c. current at low frequencies. These measurements were supplemented with the measurements of the temperature dependences of d.c. forward current carried out at the same small forward bias
V
1
.
0
-
. Fig. 3 shows the temperature dependences of d.c. current plotted in Mott’s coordinates log(σT1/2) vs. 4
1
-
T
. The current appears to obey the Mott’s
4
1
-
T
law that corresponds to the VRH conductance via the localized states at the Fermi level.
The Mott model predicts the following dependence of the conductivity for the variable-range hopping process [11]:
)
/
exp(
)
/
(
)
(
4
/
1
2
/
1
0
T
B
T
T
-
s
=
s
,
(1)
1000
10000
100000
1000000
10
-10
10
-9
10
-8
10
-7
Gd
2
O
3
-Si(111), 500C
Gd
2
O
3
-Si(100), 450C
Nd
2
O
3
-Si(111), 450C
s
, S/cm
F, Hz
200K
V=-0.1V
Fig. 2. Dependences of a.c. conductivity vs. frequency for three samples.
0.24
0.25
0.26
0.27
0.28
0.29
-8
-7
-6
-5
-4
-3
Gd
2
O
3
-Si(111), 500C
Gd
2
O
3
-Si(100), 450C
Nd
2
O
3
-Si(111), 450C
Log(
IT
1/2
)
, AK
1/2
1/T
1/4
,
K
-1
/
4
V=-0.1 V
Fig. 3. Temperature dependences of the forward current for three structures plotted in Mott’s coordinates.
where σ0 is a temperature independent factor,
4
/
1
F
B
3
0
)
(
÷
÷
ø
ö
ç
ç
è
æ
a
=
E
N
k
B
B
, B0 – factor ranging from 1.66 to 2.5,
1
-
a
– localization length of electron, kB – Boltzmann’s constant, N(EF) – the bulk concentration of the localized states at the Fermi level. From the slope B of the ln(σT1/2) vs. 4
1
-
T
dependence, one can determine the bulk concentration of the localized states near the Fermi level as follows:
B
4
3
4
0
F
)
(
k
B
B
E
N
×
a
=
.
(2)
The hopping conductivity through the states at the Fermi level can be additionally described by the following expression [17]:
,
)
/
exp(
)
2
exp(
)
(
6
/
1
)
(
B
F
2
2
T
k
W
R
E
N
R
q
T
ph
-
a
-
´
´
n
=
s
(3)
where R is the hopping distance, νph is the phonon frequency, W is the activation energy of the hopping, and q is the electron charge. In Mott’s model, the hopping activation energy is given by the equation [11]:
)
(
4
3
F
3
E
N
R
W
p
=
,
(4)
where the hopping distance
4
/
1
B
)
(
2
3
÷
÷
ø
ö
ç
ç
è
æ
pa
=
T
k
E
N
R
F
.
Assuming the localization radius of the electron wavefunction
cm
10
7
1
-
-
=
a
and B0 = 2 [18], from the slope B of the characteristics log(σT1/2) vs. 4
1
-
T
presented in Fig. 3 and using Eq. (2) we determine the density of states at the Fermi level N(EF). The values of bulk density of states N(EF) and of hopping activation energy W for three measured samples are presented in Table. The physical origin of the states being the hopping sites inside the dielectric layer is still discussed, but most often the deep levels in the high
k
-
materials are associated with oxygen vacancies and interstitials randomly distributed in the dielectric film [1, 13, 19]. The role of oxygen related defects as carrier traps in high
k
-
dielectrics HfO2 and ZrO2 is discussed in [20-22]. Theoretical calculations of energy positions of trap levels associated with various charge states of oxygen vacancies for different high
k
-
dielectrics are presented in [23, 24].
Finally, we have plotted the low-frequency a.c. conductance σ0(T) in Arrhenius coordinates to check the activation energy. Fig. 4 shows the respective dependences for all the samples. As we have already mentioned, the measurements were carried out at the small forward bias Vg = V
1
.
0
-
. At such low biases, the probability of Fowler-Nordheim tunneling through the triangular barrier or of thermally assisted tunneling of Pool-Frenkel type is negligible. So, the derived values are not related to the valence band offset at the interface. We may suggest that the apparent activation energy is related either to activation of holes from semiconductor to the trap levels in the oxide band gap or to phonon-induced excitation of carriers during VRH process inside the dielectric. The values of activation energies Ea derived from the temperature dependences of low-frequency a.c. currents are presented in Table. The lowest value of the activation energy Ea was found for the Gd2O3 film grown on the Si(100) substrate (sample #2). This sample also shows the lowest density of interface states [25].
Table. Bulk trap concentration, hopping activation energy and activation energy from low-frequency a.c. conductance for Gd2O3 and Nd2O3 dielectrics.
Sample #
N(EF)
[eV–1cm–3]
W (Mott)
[meV]
Ea (σ0(T))
[meV]
1
2.1×1017
107
138
2
1.8×1019
37
33
4
7.8×1019
30
126
0.004
0.006
0.008
-23
-22
-21
-20
-19
-18
Gd
2
O
3
-Si(111), 500C
Gd
2
O
3
-Si(100), 450C
Nd
2
O
3
-Si(111), 450C
E
a
=126 meV
ln
s
, S/cm
1/T, K
-1
E
a
=138 meV
E
a
=33 meV
Fig. 4. Arrhenius plot of the low-frequency a.c. conductivity for three samples.
Taking into account that the applied forward bias during the measurement of temperature dependences is low (Vg = V
1
.
0
-
) and assuming that the current is due to the transport of holes, the energy levels corresponding to the bulk defect centers in the dielectric should be situated near the Fermi level, which is common for dielectric and silicon. At room temperature for p-type silicon doped with impurity concentration
3
16
cm
10
5
-
´
, the Fermi level is situated at 0.13 eV above the Si valence band [26]. The valence band offset at the Gd2O3/Si interface lies in the range from 2.3 to 2.78 eV [3, 27, 28] in dependence on methods of measurement and at Nd2O3/Si interface is equal to 2.7 eV [29]. Thus, in Gd2O3 location of the deep levels takes place at 2.5 to 3.0 eV above the valence band edge, and in Nd2O3 the deep levels are situated at 2.9 eV above the valence band edge. Therefore, we can suggest that the current occurs via the transport of holes, which enter the interface levels and then tunnel to the trap levels in the dielectric, with the following VRH conductance process through the random network of localized states in the band gap.
It can be seen from Table that there exists a quite satisfactory correlation of activation energies calculated from a.c. conductance and d.c. current-temperature dependences for samples #1 and #2. Sample #4 with Nd2O3 oxide dielectric shows much lower hopping activation energy as compared to the activation energy obtained from the temperature dependence of low-frequency a.c. conductivity. This sample is also characterized by much higher concentrations of interface states in the silicon band gap. The reason for this behavior may be the fact that the high concentration of bulk interface states is involved into a recharging process when the sample is tested in a.c. mode. Their contribution to the total a.c. conductance has the activation energy that may differ from that in d.c. measurements.
3.2. Transport mechanisms in ternary dielectric compound LaLuO3
LaLuO3 is an attractive candidate as a gate dielectric material because of its low hygroscopicity, high thermal stability, high optical bandgap (~5.6 eV) and high k-value close to 30 [30].
V
I
-
characteristics measured on the Pt/LaLuO3/p-Si(100) MOS structures have revealed an apparent dependence of the leakage currents on temperature for all the range of reverse and low (|Vg|<1 V) forward biases indicating the thermally-activated charge transport mechanism. For the forward voltage absolute value of about 1 V the temperature dependence of the current vanishes and at higher forward biases it becomes metallic, so that the current decreases with increasing the temperature. Because the behavior of the temperature dependence of
V
I
-
characteristics appeared to be different at forward and reverse biases, we analyzed them separately.
Figs 5a and 5b shows the current-voltage dependences for the samples with thicknesses of the dielectric layers 20 and 6.5 nm, respectively, plotted in Poole-Frenkel coordinates (ln(J/V) vs. V1/2). The sections where the plots can be approximated by a straight line indicate that the forward-bias current is governed by Poole-Frenkel mechanism for trap-assisted thermally activated transport through the potential barriers lowered by the electric field. This is also confirmed by the current-temperature dependence plotted in Arrhenius coordinates (Fig. 5b, inset).
The voltage and temperature dependences of the current density for the Poole-Frenkel emission mechanism is described by the equation [26]:
(
)
ú
û
ù
ê
ë
é
f
-
µ
b
V
a
T
k
q
V
J
2
exp
B
,
(5)
where
b
f
is the barrier height, q – elementary charge, kB – Boltzmann’s constant,
ox
4
t
k
q
a
p
º
, k – dielectric permittivity, tox – dielectric thickness. From the slope S of the ln(J/V) vs. V1/2 dependence, one can determine the dielectric permittivity k as follows:
ox
2
4
t
a
q
k
p
=
,
S
T
k
a
2
B
º
.
(6)
0.2
0.4
0.6
0.8
1.0
1.2
-12
-10
-8
-6
-4
-2
0
Pt-LaLuO
3
-pSi(100)
100
140
180
300
t
ox
= 20 nm
T, K =
ln(
J
/
V
g
), A/ Vcm
2
V
g
1/2
, V
1/2
a)
EMBED Origin50.Graph 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
3
4
5
6
7
-16
-14
-12
300
320
340
360
380
t
ox
= 6.5 nm
T, K =
Pt-LaLuO
3
-pSi(100)
ln(
J
/
V
g
), A/ Vcm
2
V
g
1/2
, V
1/2
ln(I), A
1/T, 10
-3
1/K
b)
Fig. 5. Forward current for LaLuO3 film plotted in Poole-Frenkel coordinates for the 20-nm (a) and 6.5-nm (b) thick oxide layer (inset – I – T dependence in Arrhenius coordinates).
This method gives us the values k = 16 and 20 for the samples with tox = 6.5 and 20 nm, respectively. For the thinner sample, we have taken for calculation the initial parts of the
V
I
-
curves (|Vg|<0.5 V), so that the electric field in dielectric did not exceed 0.8 MV/cm.
Fig. 6 shows the temperature dependences of the reverse current plotted in Mott’s coordinates ln(IT1/2) vs. 4
1
-
T
. The reverse-bias current for both samples appeared to obey Mott’s 4
1
-
T
law for variable-range hopping conduction. It can be seen that the dependences are better fitted by Mott’s law for the sample with tox = 20 nm than for that with tox = 6.5 nm. It could be explained by higher contribution of bulk conductance as compared to the more dominant interface-related conductance mechanism for the thinner oxide sample. From the slope of the Mott plots and using Eq. (2), we can calculate the values of the bulk concentration of the localized states at the Fermi level N(EF). For the thinner sample N(EF) =
3
1
16
cm
eV
10
7
.
4
-
-
´
at Vg = 1 V and N(EF) =
3
1
16
cm
eV
10
4
.
2
-
-
´
at Vg = 0.5 V, and for the thicker one N(EF) =
3
1
16
cm
eV
10
1
.
6
-
-
´
at Vg = 1 V and N(EF) =
3
1
16
cm
eV
10
5
.
4
-
-
´
at Vg = 0.5 V.
0.24
0.25
0.26
0.27
0.28
-25
-20
-15
-10
V
g
, V
t
ox
= 20 nm
Pt-LaLuO
3
-pSi(100)
ln(
I
·
T
1/2
), A K
1/2
T
-1/4
, K
-1/4
0.5
1
2
5
a
)
0.24
0.25
0.26
0.27
0.28
-30
-25
-20
-15
-10
V
g
, V
0.5
1
Pt-LaLuO
3
-pSi(100)
t
ox
= 6.5 nm
ln(
I
·
T
1/2
), A K
1/2
T
-1/4
, K
-1/4
b
)
Fig. 6. I-T dependences of the reverse current plotted in Mott’s coordinates for the samples with tox = 20 nm (a) and tox = 6.5 nm (b).
It should be noted that Pool-Frenkel emission as a dominant mechanism of charge transport in high dielectric constant thin films was reported in several papers [31-34] for ZrO2, Eu2O3, Lu2O3 and HfLaSiON dielectrics. At the same time, variable range hopping conduction in these materials for the first time was observed by our group.
3.3. Transport mechanisms in rare-earth silicate LaSiOx
Lanthanum silicate LaSiOx has a lower value of k than La2O3 oxide, but it offers higher crystallization temperature and lower hygroscopicity. Additionally, the rare-earth metal silicate interface layer can be used as a transition layer between high
k
-
dielectric and semiconductor instead of SiOx, thus increasing the total dielectric constant of a gate stack [35]. So, studies of charge carrier transport mechanism in LaSiOx/Si structures attract considerable interest.
Fig. 7a, b shows the I-V characteristics for 10-nm thick lanthanum silicate layer on n- and p-Si substrates measured within the temperature range 140 up to 300 K. It can be seen that the forward current densities are rather high. One should notice a different kind of temperature dependence of the forward current for n- and p-Si substrate. The reverse current densities differ by several orders of magnitude for n- and p-type substrates, which can be due to different offsets between conduction and valence bands at the semiconductor/insulator interface. The apparent temperature dependence of the leakage currents is observed for low (|Vg|<1 V) forward biases indicating the thermally-activated charge transport mechanism.
Fig. 8 shows the forward branches of
V
I
-
dependences for the p-type sample with 7.5-nm LaSiOx plotted in Poole-Frenkel coordinates (ln(J/V) vs. V1/2). The sections where linear approximation is valid indicate that the forward-bias current is determined by the Poole-Frenkel mechanism for trap-assisted thermally activated transport. This is also confirmed by the Arrhenius plots of the current-temperature dependences (Fig. 9). At a forward bias, the current inside dielectric is mainly caused by transport of majority carriers, in our case, of holes injected from the semiconductor. The depth of hole traps in respect to the valence band edge was calculated from the slopes of ln(J/V) vs. 1/kBT plots and equals to (b = 0.47 eV. The dynamic dielectric permittivity kwas evaluated from the slopes of ln(J/V) vs. V1/2 plots (Fig. 8) using Eq. (6) and gave the values ranging from 16.3 to 16.8.
-5
-4
-3
-2
-1
0
1
2
3
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
300
260
180
140
NiSi / LaSiO
x
/ n-Si
T, K
J
, A/cm
2
V
g
, V
a
)
0.2
0.4
0.6
0.8
1.0
-18
-16
-14
-12
-10
-8
-6
-4
-2
t
ox
= 7.5 nm
NiSi / LaSiO
x
/ p-Si
T, K
ln(
J
/
V
g
)
V
g
1/2
, V
1/2
180
260
300
Fig. 8. Forward current for the sample with 7.5-nm LaSiOx layer plotted in Poole-Frenkel coordinates.
40
50
60
70
80
90
-24
-22
-20
-18
-16
-14
-12
-10
E
a
= 0.198 eV
E
a
= 0.031 eV
t
ox
= 7.5 nm
NiSi / LaSiO
x
/ p-Si
ln(
I
)
1/
k
B
T
, eV
-1
-0.2
-0.4
-0.8
V
g
, V
E
a
= 0.085 eV
Fig. 9. Forward current for the sample with 7.5-nm LaSiOx layer plotted in Arrhenius coordinates for various Vg.
5. Conclusions
The mechanism of charge carrier transport through the rare-earth metal oxide films Gd2O3 and Nd2O3 at a low forward bias was found to be the Mott variable-range hopping conductance through localized states near the Fermi level. This mechanism also determines a.c. conduction at frequencies above 100 kHz. From the measurements of temperature dependences of forward currents, the bulk concentrations of the deep levels in the high
k
-
oxides were determined. These levels are most probably related to the oxygen vacancies, the large concentration of which is inherent to ionic metal oxides. The conduction via these defect levels in the band gap of dielectric may be at the origin of the high leakage currents observed in many highk
-
materials.
The charge carrier transport and bulk density of states was studied in MBD grown LaLuO3 oxide which is considered as a perspective high
k
-
dielectrics for micro- and nanoelectronics applications. It was shown that the forward current through the dielectric is controlled by the Poole-Frenkel mechanism of trap assisted thermally activated transport. The mechanism of the reverse current was found to be the variable-range hopping conductance through localized states at the Fermi level. The charge carrier transport through the LaSiOx dielectric film was found to occur via Poole-Frenkel mechanism.
Acknowledgements
This work has been partly funded by the National Academy of Sciences of Ukraine in frames of the Complex Program of Fundamental Research “Nanosystems, nanomaterials and nanotechnologies”, project No.
H
11
/
32
/
53
-
. Author is grateful to M.C. Lemme, H.J. Osten, A. Laha, P.K. Hurley, K. Cherkaoui, S. Monaghan, H.D.B. Gottlob, and M. Schmidt for providing the samples for measurements, and to V.S. Lysenko and A.N. Nazarov for useful discussions and valuable comments.
References
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� EMBED Origin50.Graph ���� EMBED Origin50.Graph ���
Fig. 7. J-V characteristics for (a) 10 nm LaSiOx/n-Si and (b) 10 nm LaSiOx/p-Si structures measured at various temperatures.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
139
-2
0
2
4
6
8
10
1E-12
1E-10
1E-8
1E-6
1E-4
0.01
1
300
260
220
180
T, K
NiSi / LaSiO
x
/ p-Si
J
, A/cm
2
V
g
, V
b
)
_1397914675.unknown
_1399633664.unknown
_1401358450.unknown
_1401362711.unknown
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_1397912423.unknown
_1397912510.unknown
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|