# NEGF analysis of InGaAs Schottky barrier double gate MOSFETs

**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

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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

d

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

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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)

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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

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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.

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[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)

- CitationsCitations12
- ReferencesReferences15

- "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.- "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.- "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.

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