NEGF analysis of InGaAs Schottky barrier double gate MOSFETs

Conference Paper (PDF Available) · January 2009with74 Reads
DOI: 10.1109/IEDM.2008.4796843 · Source: IEEE Xplore
Conference: Electron Devices Meeting, 2008. IEDM 2008. IEEE International
Abstract
A systematic study of InGaAs metallic source/drain Schottky barrier (SB) FET is conducted from a structural and material perspective by comparing it with InGaAs MOSFET and Si SBFET counterparts. The InGaAs SBFET exhibits a superior subthreshold swing compared to its Si counterpart due to its smaller transport mass. The contrary occurs at smaller channel length, demonstrating that InGaAs SBFETs are not as scalable. Since these devices exhibit different subthreshold and transconductance properties, their relative device advantage depends on the operating condition. We demonstrate that there is a window where the I<sub>ON</sub> of an InGaAs SBFET can outperform its InGaAs MOSFET and Si SBFET counterparts.

Figures

NEGF Analysis of InGaAs Schottky Barrier Double Gate MOSFETs
Himadri S. Pal, Tony Low and Mark S. Lundstrom
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
E-mail: hpal@purdue.edu
Abstract
A systematic study of InGaAs metallic source/drain Schottky
barrier (SB) FET is conducted from a structural and material
perspective by comparing it with InGaAs MOSFET and Si
SBFET counterparts. The InGaAs SBFET exhibits a superior
subthreshold swing compared to its Si counterpart due to its
smaller transport mass. The contrary occurs at smaller
channel length, demonstrating that InGaAs SBFETs are not
as scalable. Since these devices exhibit different subthreshold
and transconductance properties, their relative device
advantage depends on the operating condition. We
demonstrate that there is a window where the I
ON
of an
InGaAs SBFET can outperform its InGaAs MOSFET and Si
SBFET counterparts.
Introduction
III-V materials are currently being explored as possible
channel materials for nanoscale transistors due to their high
intrinsic mobility [1]. Due to lower solid solubility limits of
dopants in these materials, however, III-V MOSFETs with
doped source/drains (S/D) suffer from high series resistance,
which significantly degrades the on-current (I
ON
) [2,3].
Lower source doping also leads to transconductance
degradation at high gate bias, when the channel charge
density becomes comparable to that in the source [4]. Recent
Monte-Carlo studies also suggest that due to low doping, the
electrons at the source cannot reach thermal equilibrium and
hence cannot provide enough carriers to the channel with the
required forward momentum [5]. Metallic S/D Schottky
barrier MOSFETs (SBFETs) are being explored as an
alternative to effectively eliminate these issues.
In this paper, In
0.53
Ga
0.47
As is used as a
representative III-V channel material to compare SBFETs
with doped S/D III-V n-channel MOSFETs and also to
compare III-V and Si n-channel SBFETs. The subthreshold
swing, transconductance and on-current are compared for
various device dimensions and Schottky barrier energy.
Simulation Methodology
The non-equilibrium Greens function (NEGF) approach
within an effective mass treatment is employed in this paper
using the nanoMOS program [6]. The Schrödinger eqn. is
solved exactly along the confinement direction while
quantum ballistic NEGF is used along the transport direction,
in conjunction with self-consistent 2-D electrostatics. The
channel effective masses of thin film In
0.53
Ga
0.47
As are
interpolated from sp
3
d
5
s* tight-binding calculation of GaAs
and InAs effective masses [7]. Fig. 1 shows the extracted
quantization and transport mass (i.e. m
z
and m
x
) as a function
of film thicknesses, T
BODY
. The effective masses increase
with decreasing channel thickness, an already well-known
phenomenon attributed to bandstructure non-parabolicities of
-0.2 0.0 0.2 0.4
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
reverse bias
NEGF Modeling
Rext Ri
Vsd
Current (A/cm
-2
)
Voltage (V)
Experiment from
Q.T.Zhao et al, APL86
Fig. 2: Benchmarking of experimental NiSi/Si Schottky diode IV
characteristics [10] with NEGF Schottky model. Using a parasitic resistance
R
ext
= 0.3Ωcm
2
, metal bandwidth BW = 1.0eV, metal mass of m
M
= 0.5m
0
,
Schottky barrier height of Φ
SB
= 0.65eV and channel doping of N
D
=
1x10
16
cm
-3
, we obtain a best fit to the experimental curve in the forward
bias regime. The less satisfactory match in the reverse bias regime is due to
the full depletion approximation used in our Schottky diode model. Φ
SB
=
0.65eV is the commonly cited value for NiSi/Si [10].
Fig. 1: Quantization and transport (i.e. m
z
and m
x
) effective masses o
f
In
0.53
Ga
0.47
As calculated based on a Vegard Law approximation of the
masses of InAs and GaAs. The masses of InAs and GaAs are extracte
d
from a sp
3
d
5
s* tight-
b
inding calculation of thin film as a function of film
thicknesses T
BODY
. The increase in effective masses with decreasin
g
T
BODY
is due to the well-known non-parabolicity effect [8, 9].
23456
0.05
0.10
0.15
0.20
0.25
Quantization Mass m
Z
In-plane Mass m
X,Y
Effective Mass (m
0
)
Body Thickness (nm)
InGaAs
Authorized licensed use limited to: Purdue University. Downloaded on July 17, 2009 at 16:33 from IEEE Xplore. Restrictions apply.
the III-V materials [8,9]. The effective masses for silicon are
assumed to remain constant at the bulk values for all the body
thicknesses considered here [9]. In this work, a finite
differencing NEGF scheme with a non-uniform mesh and
spatially dependent mass is developed for simulating
SBFETs. A finer mesh with a different effective mass is used
to describe the metal contacts. The choice of the metal
parameters, i.e. metal occupied bandwidth and metal effective
mass are unknown quantities, which are commonly extracted
by calibrating with experimental data on Schottky diode. Fig.
2 shows the excellent corroboration of our model with
experimental data on NiSi/Si Schottky diode [10]. We shall
use this set of metal parameters for our subsequent study in
this work.
Device Evaluation
Subthreshold swing (SS) and transconductance (g
M
) are two
important device metrics that characterize performance in the
subthreshold and overdrive regimes respectively. We conduct
a systematic study of an InGaAs SBFET, an InGaAs
MOSFET ((001)/[100] surface/transport orientation) and a Si
SBFET ((001)/[110]) with a double-gate (0.7nm EOT
insulator) device. We compare devices of channel lengths
L
G
=10, 20nm for a range of body thicknesses, 2nm < T
BODY
<
6nm. A Schottky barrier height Φ
SB
= 0.2, 0.4eV is used for
the SBFET simulations, and image force effects are ignored.
A source/drain doping of 1x10
19
/cm
3
and series resistance
R
SD
= 200, 500Ω-um are assumed for the InGaAs MOSFET.
The gate work-function is adjusted to maintain a constant off-
current (I
off
) of 1nA/µm for all the devices. As shown in Fig.
3a, the InGaAs MOSFET has a subthreshold swing SS
60mV/dec. The SBFETs exhibit a SS that decreases with
T
BODY
in an approximately linear fashion. This phenomenon
has been experimentally established [11]. The channel
electric field at the source – Schottky interface (E
S
) increases
linearly as a function of V
G
as depicted in Fig. 4a. Therefore,
the metric dE
S
/dV
G
is a measure of the efficiency of V
G
in
modulating E
S
, which essentially is a measure of SBFET
performance as a switch. Indeed, Fig. 4b shows that dE
S
/dV
G
improves with decreasing T
BODY
, suggesting better
electrostatics and therefore the better SS. The better SS for
the InGaAs SBFET compared to its Si channel counterpart in
Fig. 3a is due to its smaller transport mass, which makes the
I
ON
more sensitive to changes in E
S
. The SS for SBFETs
increases drastically compared to the MOSFET as L
G
is
scaled down to 10nm (Fig 3b), suggesting that SBFETs are
less scalable than MOSFETs in general [12]. Transport in the
Fig. 4: (a) Channel electric field at the source Schottky interface (E
S
) as
a
function of V
G
for InGaAs SBFET, Si SBFET with various T
BODY
for L
G
=
20nm. We consider Φ
SB
= 0.2eV. (b) Plot of dE
S
/dV
G
as a function o
f
T
BODY
for InGaAs SBFET and Si SBFET devices represented by dotted
and solid lines respectively. We consider cases with L
G
= 10, 20nm an
d
Φ
SB
= 0.2eV. Evidently, dE
S
/dV
G
increases with decreasing T
BODY
.
0.0 0.2 0.4 0.6
-0.5
0.0
0.5
1.0
1.5
2.0
Increasing
Body Thickness
Modulation of E
S
by V
G
dE
S
/dV
G
(/um)
InGaAs
SBFET
Surface Field at Interface E
S
(MV/m)
Gate Voltage (V)
Φ
,
SB
=0.2eV
23456
0.20
0.25
0.30
0.35
0.40
0.45
0.50
L
G
=10nm
Si
InGaAs
(b)
Body Thickness (nm)
L
G
=20nm
(a)
Fig. 3: (a) Subthreshold swing (SS) for InGaAs SBFET, Si SBFET an
InGaAs MOSFET versus T
BODY
for L
G
= 20nm. For the SBFET devices, we
consider Φ
SB
= 0.2 (dashed) and 0.4eV (solid). The InGaAs MOSFET has
a
series resistance R
SD
= 500Ω-um. (b) Same as (a) except for L
G
= 10nm.
23456
60
70
80
90
100
110
120
Si SBFET
InGaAs SBFET
Subthreshold Swing (mV/dec)
Body Thickness (nm)
InGaAs MOSFET
23456
60
80
100
120
140
160
180
200
(b) L
G
=10nm
Si SBFET
InGaAs
SBFET
Body Thickness (nm)
InGaAs MOSFET
(a) L
G
=20nm
Fig. 5 (Left): (a) I
ON
of the InGaAs SBFET and Si SBFET devices as
function of T
BODY
for L
G
= 20nm. We set Φ
SB
= 0.2eV. The dotted-line
considers the case where non-parabolicity effect is un-accounted for the
InGaAs SBFET (b) same as (a) except for effective Schottky barrie
r
height Φ
SB
= 0.2eV.
23456
0
100
200
300
400
500
600
700
neglecting
non-parabolicity
Si SBFET
InGaAs SBFET
Drain Current (uA/um)
Body Thickness (nm)
23456
300
400
500
600
700
800
900
1000
Si SBFET
InGaAs SBFET
(b) Φ
,
SB
=0.2eV
(a) Φ
SB
=0.2eV
Authorized licensed use limited to: Purdue University. Downloaded on July 17, 2009 at 16:33 from IEEE Xplore. Restrictions apply.
subthreshold region is dominated by thermionic emission at
this L
G
, and tunneling at the top of the barrier makes the SS
of InGaAs SBFET particularly worse.
Increasing Φ
SB
does little to degrade the SBFET’s
SS, but it degrades the I
ON
exponentially. Φ
SB
is usually set
by the composite material system rather than being a
‘tweakable’ design parameter. Nevertheless, the body
confinement energy (ε) results in an apparent increase of Φ
SB
.
This effect is especially strong for III-V materials due to the
smaller quantization mass than Si. Fig. 5a shows I
ON
as a
function of T
BODY
for InGaAs and Si SBFETs for Φ
SB
=
0.2eV. Instead of an improved I
ON
with decreasing T
BODY
as
in the case for Si, InGaAs exhibits an opposite phenomena
when a constant bulk m
Z
is assumed (dotted line). The
apparent increase of Φ
SB
due to body confinement effect
completely negates the benefit of improved SS with
decreasing T
BODY
. Accounting for the increase of m
Z
due to
non-parabolicity helps to retard the increase of ε and result in
an improved I
ON
with deceasing T
BODY
(Fig. 5a). In light of
this, we shall define an effective Schottky barrier height Φ
SB
= Φ
SB
+ ε to facilitate our subsequent analysis.
Fig. 5b shows the I
ON
as a function of T
BODY
for
InGaAs and Si SBFETs for Φ
SB
= 0.2eV. Based on this
comparison, InGaAs and Si SBFETs both exhibit similar I
ON
characteristics that increase with decreasing T
BODY
. The better
SS of the InGaAs SBFET than its Si counterpart is reflected
in its higher I
ON
. The transconductance (g
M
) for both Si and
InGaAs SBFETs are similar as depicted in Fig. 6a. The lower
density-of-states of InGaAs compared to Si could have
lowered the g
M
, but that is compensated by the lower
transport effective mass which facilitates tunneling in the
InGaAs. Fig. 6b shows the g
M
of the InGaAs MOSFET for
two different series resistances, showing that lowering the
parasitic series resistance is vital to improving the g
M
and I
ON
.
Lower source doping in the MOSFET causes source
exhaustion at high gate bias as the channel charge density
becomes comparable to that at the source (Fig. 7). This leads
to g
M
degradation in the InGaAs MOSFET, while g
M
for
SBFETs increases exponentially with increasing V
G
.
Saturation of g
M
for SBFET begins to occur only when the
channel potential forms a ‘sink’ for lateral confinement of
states (Fig. 8). The density-of-states demonstrates the
standing wave pattern formed by reflections at the source-to-
channel and the channel-to-drain Schottky barriers. The
standing wave pattern is a characteristic of the ballistic
transport simulations, and may diminish in the presence of
scattering. The peak g
M
for SBFETs improves with body
thickness scaling (Fig. 9a). InGaAs has a lower g
M
than Si at
Φ
SB
= 0.2eV due to lower density-of-states. However,
tunneling efficiency is more important at Φ
SB
= 0.4eV,
making the InGaAs g
M
comparable to that of Si. The g
M
of
InGaAs MOSFET is fairly independent of the body thickness
(Fig. 9b).
Finally, we conduct a systematic evaluation of the
InGaAs SBFET versus its InGaAs MOSFET and Si SBFET
Fig. 7: Position resolved conduction band diagram from off to on-state (V
G
= 0~0.5V) for a T
B
= 5nm and L
G
= 20nm InGaAs MOSFET. The lowes
t
plot shows the onset of source exhaustion [4, 5], where the top-of-the-
b
arrier is pushed close to the source conduction band edge. The source
cannot supply more charge if the gate voltage is further increased.
Fig. 8: Energy-position distribution of local density-of-states for InGaAs
SBFET at on-state, where g
M
b
egins to saturate due to formation of
a
channel ‘sink’ that causes source-to-drain confinement of states. The dotte
d
lines show the conduction band at off and on-state.
Fig. 6: (a) Transconductance (g
M
) of InGaAs SBFET and Si SBFET as
function of V
G
. We set L
G
= 20nm, T
BODY
= 2nm and Φ
SB
= 0.2, 0.4eV. (b)
Transconductance g
M
of InGaAs MOSFET as function of V
G
. We set L
G
=
20nm, T
BODY
= 2nm and consider parasitic contacts resistance R
P
= 500,
200
Ω-um. In contrast to SBFET, the MOSFET g
M
saturates shortly above
threshold, while the former increases exponentially. For all the
calculations, V
D
= 0.7V.
0.2 0.4 0.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
R
SD
=0.2kΩ
R
SD
=0.5kΩ
Φ
,
SB
=0.4eV
Φ
,
SB
=0.2eV
Si SBFET
InGaAs SBFET
Transconductance (mS/um)
Gate Voltage (V)
0.2 0.4 0.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
InGaAs MOSFET
(b)
(a)
Authorized licensed use limited to: Purdue University. Downloaded on July 17, 2009 at 16:33 from IEEE Xplore. Restrictions apply.
Fig. 10: Color intensity plot of the percentage difference in the on-state
current of InGaAs SBFET and MOSFET for a T
B
= 3nm and L
G
= 20nm
device, where a series resistance of R
SD
= 500 and 200Ωum for MOSFET
is employed for (a) and (b) respectively. The SBFET uses a
Φ
SB
= 0.2eV.
They are plotted as function of on-state supply voltages and off-state
current. The dotted line indicates the boundary where the current for both
devices are the same. (c) Similar comparison of InGaAs SBFET and Si
SBFET on-current.
counterparts. Due to their different device properties (i.e. SS
and g
M
) their I
ON
should be evaluated over the device
specification space stipulated by I
OFF
and V
DD
. Fig. 10a
compares the I
ON
of an InGaAs SBFET with an InGaAs
MOSFET while Fig. 10c compares the I
ON
of an InGaAs
SBFET with a Si SBFET. From Fig. 10a and 10c, we see that
the I
ON
of an InGaAs SBFET can outperform its InGaAs
MOSFET as a high performance device, and its Si SBFET
counterpart in the low power region. Fig 10b shows that
InGaAs MOSFET will perform better than the SBFET if the
R
SD
is low.
Conclusion
InGaAs SBFETs are compared with InGaAs doped
source/drain MOSFETs and Si SBFETs using quantum
ballistic NEGF simulations to evaluate their subthreshold and
gate overdrive characteristics. We find that the increase in
Φ
SB
as a result of the strong body quantization effect is
detrimental to its I
ON
. Bandstructure non-parabolicity in III-V
materials helps to retard the increasing body quantization
energy with decreasing T
BODY
. The InGaAs SBFET exhibits
better SS than its Si counterpart due to its smaller transport
mass. Compared with its MOSFET counterpart, it exhibits an
exponentially increasing g
M
with V
G
. We find that SBFETs
are less scalable than MOSFETs when the channel length is
decreased from 20nm to 10nm. The SBFET performance is
strongly influenced by the Schottky barrier height, while the
parasitic series resistance limits the I
ON
of MOSFET. We
demonstrate that in the I
OFF
vs. V
DD
space, one can find a
window in which the I
ON
of InGaAs SBFET should
outperform its InGaAs MOSFET and Si SBFET counterpart.
Acknowledgements
This work was supported by the MARCO Focus Center on
Materials, Structures, and Devices. Computational support
was provided by the NSF Network for Computational
Nanotechnology (NCN).
References
[1] D-H. Kim and J. A. del Alamo, IEDM Tech. Dig., pp 629-632, 2007.
[2] Y. Xuan, Y. Q. Wu, and P. D. Ye, Elec. Dev. Let., 29, pp. 294-296,
2008.
[3] M. Passlack et al., IEDM Tech. Dig., pp 621-624, 2007.
[4] N. Neophytos et al., in press, IEEE TED, 2008.
[5] M. V. Fischetti et al., IEDM Tech. Dig., pp 109-112, 2007.
[6] Z. Ren, R. Venugopal, S. Goasguen, S. Datta, and M. S. Lundstrom,
IEEE Trans. Elec. Dev., 50, pp. 1914-1925, 2003.
[7] T. B. Boykin, G. Klimeck, R. C. Bowen, and F. Oyafuso, Phys. Rev. B,
66, 125207, 2002.
[8] Z. G. Zhu et al., IEDM Tech. Dig., pp 807-810, 2006.
[9] K. D. Cantley et al., IEDM Tech. Dig., pp 113-116, 2007.
[10] Q. T. Zhao et al., Appl. Phys. Let., 86, 062108, 2005.
[11] J. Knoch, M. Zhang, S. Mantl, and J. Appenzeller, IEEE Trans. Elec.
Dev., 53, pp. 1669-1674, 2006.
[12] M. Shin, IEEE Trans. Elec. Dev., 55, pp. 737-742, 2008.
Fig. 9: (a) Peak transconductance vs. Body thickness of InGaAs and Si
SBFET for
Φ
SB
= 0.2, 0.4eV and L
G
= 20nm. (b) Similar plot for InGaAs
MOSFET with Rsd = 200, 500
Ω-um.
23456
0
1000
2000
3000
4000
5000
Φ
,
SB
=0.4eV
InGaAs SBFET
Si SBFET
Φ
,
SB
=0.2eV
Maximum G
M
(uS/um)
Body Thickness (nm)
23456
0
1000
2000
3000
4000
5000
Rsd = 200 Ω-um
Rsd = 500 Ω-um
(b) InGaAs MOSFET
(a)
Authorized licensed use limited to: Purdue University. Downloaded on July 17, 2009 at 16:33 from IEEE Xplore. Restrictions apply.
    • "One solution might be the turn from conventional Silicon SB MOSFETs to III-V Schottky barrier (III-V SB) MOSFETs as reported in [7]. III-V MOSFETs with doped S/D suffer from high series resistances which significantly degrade the on-current I on [7], [8], [9]. Investigations recommend this change regarding experimental results with improved slope and I on /I off ratio performance due to III-V material properties as improved masses and higher mobilities [10], [11]. "
    [Show abstract] [Hide abstract] ABSTRACT: In this paper we present a model for III-V Schottky barrier (Double-Gate) MOSFET devices including two dimensional effects on the main current transport mechanisms. A detailed way of the two-dimensional modeling approach with the primary current components is given. A comparison and verification with TCAD FEM simulation data is done with the model current equations.
    Conference Paper · Jun 2016 · Solid-State Electronics
    • "6 shows m 2D as a function of the well thickness. As expected, and consistently with other works [23,24], the in-plane effective mass increases when the well thickness is decreased. The masses extracted from the NP-EMA track the DFT results, since NP-EMA calculations were based exactly on the m 3D and a 3D parameters of the bulk crystal extracted from the DFT results. "
    [Show abstract] [Hide abstract] ABSTRACT: We present and thoroughly compare band-structures computed with density functional theory, tight-binding, k·p and non-parabolic effective mass models. Parameter sets for the non-parabolic Γ, the L and X valleys and intervalley bandgaps are extracted for bulk InAs, GaAs and InGaAs. We then consider quantum-wells with thickness ranging from 3nm to 10nm and the bandgap dependence on film thickness is compared with experiments for In0.53Ga0.47As quantum-wells. The impact of the band-structure on the drain current of nanoscale MOSFETs is simulated with ballistic transport models, the results provide a rigorous assessment of III–V semiconductor band structure calculation methods and calibrated band parameters for device simulations.
    Full-text · Article · Oct 2015
    • "Electron-phonon scattering has been implemented within the NEGF framework in the effective mass based device simulator nanoMOS [15,192021. NanoMOS is deployed for public use at www.nanoHUB.org, "
    [Show abstract] [Hide abstract] ABSTRACT: A formalism for incorporating electron-phonon scattering into the nonequilibrium Green's function (NEGF) framework that is applicable to planar MOSFETs is presented. Restructuring the NEGF equations in terms of approximate summation of transverse momentum modes leads to a rigorous and efficient method of solution. This helps to drastically reduce the computational complexity, allowing treatment of both quantum mechanics and dissipative electron-phonon scattering processes for device sizes from nanometers to microns. The formalism is systematically benchmarked against Monte Carlo solutions of the classical Boltzmann transport for model potential profiles. Results show a remarkably close agreement between the two methods for variety of channel lengths and bias conditions, both for elastic and inelastic scattering processes.
    Full-text · Article · Sep 2012 · Solid-State Electronics
Show more