Carrier Transport in Dirac-band Materials and Their Device Applications

Gaurav Guptagaurav.gupta@nus.edu.sg gauravdce07@gmail.com

PhD DefencePhD Defence

Computational Nanoelectronics and Nanodevices Lab (CNNL)Department of Electrical and Computer Engineering

National University of Singapore 1

29th October, 2015

Motivation

Bi2Se3 3D-TI Properties & Methodology

Carrier Transport Characterizing Resistance Contact Effects

Devices Interconnects Band-Alignment induced Resonance

Outline

2

3

What Device Community is trying to ACHIEVE ?

Present Computing Chips

Robust Transport&

Zero Power (Standby)

Motivation

Future Computing Chips

Large Static and Dynamic Power

Dissipation

4

Why ?

Safely put laptops on lap !!!

No need to repeatedly operate to Replace Implants

Save Lives & Money(Bioelectronics)

Battery Drainage requires operation to replace implant

DataCentre

275 Billion kWh consumed in 2011 by

Data Servers !!!

Save Energy

Motivation

http://www.nanowerk.com/news/id25227_2.jpg 5

How (Our Scope)?Motivation

Dirac-Band Materials

Graphene Heavier Group-IV

2D Group-IV Monolayers Bi2Se3 3D-Topological Insulator

Carrier Transport- Ballistic and Acoustic Phonons

(Chapter 6)Devices - Graphene

electro-optic transistor

(Chapter 3)

Devices - Spin-Separator and

Filter(Chapter 4 and 5)

Carrier Transport- Contact Effects

(Chapter 7)

Carrier Transport- Defects(Chapter 8)

Carrier Transport- Longitudinal & Vertical Transport

(Chapter 9)

Device - Interconnects(Chapter 8)

Devices – Resonance Devices(Chapter 9)

Large Fermi-Velocity Spin-Polarization

2D-TI (QSH Phase)Spins flow on edges

Real Space

Topological Insulator (TI)

6

Ordinary Insulator Topological Insulator

Change in Property (Physical/Electronic)

Trivial Phase

Topological Phase

(non-trivial inverted)

Band-Inversion

Dirac-Bands

A genre of Strong Spin-Orbit Coupling Materials

Motivation

https://www-ssrl.slac.stanford.edu/research/highlights_arc

hive/topological_insulator.htmlhttp://spectrum.ieee.org/image/1876231

3D-TI – Spins flow on Surface

Momentum Space

http://www.nature.com/am/journal/v3/n1/full/am201117a.html

Independent Channels for up and down spin in opposite direction on edges (2D-TI) or surfaces (3D-TI).

Perfect Transport

No Heat Dissipation in the Channel (strictly true only for 2D-TI edge transport)

Electron Transport in Topological Insulators

unless: Spin-Flip Mechanisms (Magnetic Impurities) Break Time-Reversal Symmetry (Magnetic-Field)

Back-scattering Prohibited

7

Excellent Material for Transport and Electronic Devices

Motivation

8

MotivationJ. Burton, Nature Vol. 466 (15 July 2010)

Topological Insulators

9

Objectives of this ResearchMotivation

1. Develop NEGF formalism based Quantum transport Simulator for extensively parallelized computing.

2. Investigate carrier transport through Dirac-Band materials.

3. Apply Dirac-band materials and investigate their feasibility for prospective device schemes.

Motivation

Bi2Se3 3D-TI Properties & Methodology

Carrier Transport Characterizing Resistance Contact Effects

Devices Interconnects Band-Alignment induced Resonance

Outline

10

1. Single Dirac Bands of high Fermi-velocity on each Surface.

Spin Texture (K-Space)

+kx-kx

-ky

+ky(b)

Top Surface

Bottom Surface

Bulk

(a)

Semiconducting

xy

zlayers

[1] Nature Nanotech. vol. 9, no. 3, pp. 218-224, 2014 11

3D-TI Properties & Device

VGS

Source Drain

VDS

xyz

Bi2Se3 TIInsulator

Phenomenological Gate

Bi2Se3 Bulk Bandgap ~ 0.3 eVLargest Bandgap among all proven 3D-TIs Greatest isolation between non-trivial and trivial bands.

Bi2Se3 3D-TI

2. Spin-Momentum Locking. (Opposite Spin Texture on Opposite Surfaces).3. Spin-Polarized Surface Transport. [1]

2 2x y1 2

2 2x y2 1

p 2 2x y 1 2

2 2x y 2 1

k /m d+k /m ivk -vk 0

d+k /m k /m 0 -ivk +vkH = , (1)

-ivk -vk 0 k /m d+k /m

0 ivk +vk d+k /m k /m

Each layer of Bi2Se3 described in pz orbital basis

v (2.5 eV-Å) is Fermi-velocity, m1 (0.125 eV-1Å-2)and m2 (-0.04 eV-1Å-2) are the orbital masses d (-0.22 eV) is introduced to generate a gaptz (0.35 eV) is hopping b/w adjacent layers tight-binding parameter

z

z

0 0 0 0t 0 0 0T= , (2)0 0 0 00 0 t 0

1 1†1 2 2

†2 3

Η Τ 0

Τ Η Τ

Η= , (3)Τ Η

.

0 .

Fitting parameters extracted from

ab-initio. (Dr. Hsin Lin )

k.p Model in kx-ky space

Tight-Binding Interaction along

z-axis (Nearest Neighbour)

Hamiltonian

12

Bi2Se3 3D-TI

Gupta et al., PRB 89, 245419 (2014)

Se

Bi

Quintuple Layer (QL) (0.943 nm)

Image Courtesy: Huang Wen

L. A. Wray, S. Y. Xu, Y. Q. Xia, D. Hsieh, A. V. Fedorov, Y. S. Hor, R. J. Cava, A. Bansil, H. Lin, and M. Z. Hasan, “A topological insulator surface under strong Coulomb, magnetic and

disorder perturbations,” Nature Physics, vol. 7, no. 1, pp. 32-37, Jan, 2011.

Our Blue Bands superimposed over Experimental DataValidating Model for Slab (1/2)

13

Bi2Se3 3D-TI

Image Courtesy:

Dr. Hsin Lin

Top Surface

Bottom Surface

Layer Number5 10 15 20

|Ψ(z)

|2 D

irac B

and

s

0.6

0.5

0.4

0.3

0.2

0.1

0

(b)

Bottom SurfaceTop Surface

0.2

0.1

0

-0.1

-0.2-0.02 0 0.02

kx ax

En

erg

y (e

V)

(a)

20 QL (ky=0)

Surface Band

ky

ay

kx ax

-0.05 0 0.05

0.04

0

-0.04

(c)

k y a

y

kx ax

-0.05 0 0.05

0.04

0

-0.04

(d)------------- Spin Texture – Conduction Band -------------

Validating Model for Slab (2/2)

14

Bi2Se3 3D-TI

2e fG = dE T(E) (- )

h E(6)

∂∂∫

DOS(E) fn = dE (- )

L E(7)

∂∂∫

Conductance (G)

Linear Free Charge Density (n)

(8)G .L

μ =n e

Mobility (μ)

-1

D0 0 S phGr = (E+iη)I-H -U -Σ -Σ -Σ (1)

Green’s Function (Gr)

†i[DOS(E)] = ([Gr - Gr ]) (5)

2π

Density of States (DOS(E))

†

S DT(E) = Trace(Γ Gr Γ Gr ) (4)Transmission (T(E))

acph[Σ ] = D [Gr] (2)Self-Energy of Phonons

Level Broadening †Γ = i ([Σ - Σ ]) (3)

Modeling Equations (NEGF)

15

Bi2Se3 3D-TI

Good Books for Learning Quantum Transport via NEGF:[1] S. Datta, Quantum Transport: Atom to Transistor, Cambridge Press (2005)[2] S. Datta, Lessons in Nanoelectronics, World Scientific Publishing (2012)

jeff j

1 1(9)

μ μ= ∑

Matthiessen's Rule

1. Ballistic Transport (CPU Cluster) transverse axis in mode space.

2. Acoustic Phonons (CPU Cluster) transverse axis in mode space.

3. Other Defects (GPU Cluster) (Random Distribution – Examined Over Different Concentrations) in Real Space

1. Charge Impurities2. Vacancies3. Edge Roughness

4. Mobility (Phonons) & Mobility (Other Defects Together) Effective Mobility (μeff)

Modeling Scheme

16

Bi2Se3 3D-TI

Tesla C2070 and M2090 in CUDA 5.0 supported by MAGMA 1.3 (Matrix Algebra on GPU and Multicore Architectures) and LAPACK

3.2.1 (Linear Algebra Package) librariesMax. Size Unit-Cell : 244 MB ;

Device Hamiltonian for RGF : 14 GB ; Data Section : 45 GB

Motivation

Bi2Se3 3D-TI Properties & Methodology

Carrier Transport Characterizing Resistance Contact Effects

Devices Interconnects Band-Alignment induced Resonance

Outline

17

Nano Lett. 10 (1), 2010

Many Experimentalists have observed

Metallic Trend

Insulating Trend

Few Experiments have shown

Nature Communications 3 (757), 2012

Yet, Everybody Claims to be

capturing Transport through Topological

Surface band !!!

At least Four Groups have observed

maxima

Reason never been discussed

PRL 106 (196801), 2011

Two Disputes: a) Resistance vs Temperature

18

Carrier Transport

Magnitude of dimensionless electron-phonon coupling constant λ :

Range 0.08 to 0.43

Weak Strong

Theory Thalmeier, PRB 83, 125314 (2011)

Giraud et al. PRB: 83, 245322 (2011) & 85, 035441 (2012)

ARPESPark et al., New Jour Phys 13, 013008 (2011); Pan et al. PRL 108,187001 (2012)

Hatch et al., PRB (R) 83, 241303 (2011)

Helium Scattering

Zhu et al., PRL 108,185501 (2012)

electron trajectory

spin

Two Disputes: b) Strength & Role of Acoustic Phonon

19

Carrier Transport

Temperature (K)50 150 250

Resi

sta

nce

(Ω

)

1600

1200

800

400

0

TI DS

VDS

0.01 eV

0.05 eV

Ef = 0.05 eV

μS μD

0.16 eV

Ef = 0.2 eV0.2 eVμS μD Temperature (K)

Resi

sta

nce

(x

Wid

th)

(ohm

s-μm

)

0.05 eV0.06 eV

0.1 eV0.2 eV

100 200

2000

1500

1000

500

50 150 250

0.025 eV0.050.06

0.10.2

Experiment* Our Simulation

*S.S. Hong, J.J. Cha, D.S.Kong, Y. Cui, Nat Commun, 3 (2012) 757

Explained all controversial Experimental Data (> 50 K) published on Resistance Measurements on 3D-TI [1]

[1] Gupta et al., PRB 89, 245419 (2014)

Provided microscopic picture of transport mechanism in 3D-TI accounting for number of physical and electronic parameters

Role of Acoustic Phonons in 3D-TI

20

xy

z

Carrier Transport

21

Thickness-dependent [1] & Thickness-independent [2]

Transport

[1] Kim et al., PRB 84 (073109), 2011 [2] Bansal et al., PRL, 109 (116804), 2012

15 20 25 30 35 40 Slab Thickness (QL)

103

102

Res

ista

nce

(oh

ms-

μm

)

0.0 eV

0.15 eV

0.075 eV

0.2 eV

(a)

Current Density (μA/μm)

Dra

in C

urr

ent

(μA

/μm

)50 150 250

40

30

20

10

(e)

Temperature (K)

En

ergy

(eV

)

2 4 6 8 10 12

0.1

0

-0.1

T = 300 K 0.5

0.3

0.1

(f)

En

ergy

(eV

)

(d)

2 4 6 8 10 12

0

-0.1

-0.2

VDS = 0.16 V 2

1

0-0.1 0 0.1

100

50

0

-50

-100

(b)

Dra

in C

urr

ent

(μA

/μm

)

VDS (Volts)

Dra

in C

urr

ent

(μA

/μm

)

(c)

2 4 6 8 10 12

10

6

2

0.040.06 0.080.02

Layer Number

Ballistic Transport: QL, VDS, TCarrier Transport

Gupta et al., Physica E, 74, 10-19 (2015)

Layer Number

Layer Number

VDS

1 10 100 1000

251 316 398 501

0.12

0.10

0.08

0.06

0.04

T = 50 K

30 100 900

0.1 1 10 1000.2

0.1

0

T = 250 K

Δ f

SD x

100

0

(a) (b)

Bottom Surface DOS (/eV/μm)22

Phonon Scattering Δ fSD (Top Horizontal scale in Magenta)

Solid Color Lines: Surface DOS) (Bottom horizontal scale in Black)

Dashed Color Lines: Transmission(Top horizontal scale in Magenta)

Ballistic Weak Acoustic (λ = 0.08)

Strong Acoustic (λ = 0.25)

DOS Spread α Strength of Phonon Scattering

En

ergy

(eV

)

DOS for Bulk Band

Band-Edge

Density of States : DOS

ε

En

ergy

(eV

)Transmission and ΔfSD

Ef = 0.1 eV Lx = 30 nm55

50

45

40

Res

ista

nce

(Ω

-μm

)

Temperature (K)50 100 150 200 250

Carrier Transport

23

FM/NM Contacts (1/2)

0 40 80 120 160 Temperature (K)

|V(M

)-V

(-M

)| (μ

V) 5

3

1

(c)Experiment [1]

0 50 100 150

0.3

0.2

0.1

Temperature (K)

SP

Dra

in E

nd

(d)Simulation [2]

2.5

1.5

0.5

2 4 6 8 10Layer Number

2 4 6 8 10Layer Number

0 K 300 K 300 K (Phonon)

(a) (b)

+y SM-y SM

Cu

rren

t (μ

A/μ

m) 2.5

1.5

0.5

[1] Nature Nanotech. vol. 9, no. 3, pp. 218-224, 2014[2] Gupta et al., Scientific Rep. 5 (9479), 2015

FM Source – Bi2Se3 Drain

Current on surface layers

As per spin-texture

Gate

Source DrainBi2Se3 TI

x

yz

θϕ

M TS-CB

BS-CB

Carrier Transport

“Contact” Magnetization Vector

SM DM

24

Gate

Source DrainBi2Se3 TI

x

yz

θϕ

M

Carrier Transport

Current on surface layers As per spin-texture ???

FM/NM Contacts (2/2)

5

0

0.5

0

Cu

rren

t (μ

A/μ

m)

(+y)FM-TI-NM

NM-TI-NM

2 4 6 8 10Layer Number

NM-TI-(+y)FM

SM

DM

S D

+y

TS-CB

BS-CB

S D-y

Cu

rre

nt

(nA

/μm

)

exTI Source

Transport Direction (nm)

0

-0.4

-0.8

20 40 60 80

(a)

25

(−y) 100 % DM FM Drain @ ky = 0

Contact Effects - Theory

1

0.6

0.2

(b)

20 40 60 80

f S =

1, f

D =

0f S

= 0

, fD =

1

Carrier Transport

TS-CB BS-CBLayer 10 Layer 1

S D-y

+=

Layer 10 Layer 9 Layer 8 Layer 7 Layer 6Layer 5 Layer 4 Layer 3 Layer 2 Layer 1

Current on surface layers is as per spin-texture, but so do contact dependent transmission and reflection

26

Transport Key-Points1. 3D-TI exhibits complex transport behaviour, where resistance

is a function of at least:(a) Fermi-level (b) Temperature (c) slab thickness (d) channel length (e) channel bias (f) electron-phonon (e-ph) coupling.

2. Observing insulating trend DOES NOT necessarily imply operation in the surface bands for a given 3D-TI. Just e-ph coupling may be weak.

3. FM source contacts may reduce bulk transport (effective contribution) by forcing current through the surface.

4. FM contacts may be used for generating negative surface current as a signature of 3D-TI.

5. FM contacts may result in seemingly contrasting observations w.r.t. expectations from surface spin-texture.

Carrier Transport

Motivation

Bi2Se3 3D-TI Properties & Methodology

Carrier Transport Characterizing Resistance Contact Effects

Devices Interconnects Band-Alignment induced Resonance

Outline

27

Figure from ITRS 2005 Interconnect Chapter

Present Status Cu Interconnects

1997: IBM announced transition to Cu interconnects from Al.

Less Resistive Speed ↑ More Durable and Scalable than Al

Present Challenges with Cu: High Resistivity Electro-migration Grain Boundary Issues Side Wall scatterings

Alternate Material ???

28

Devices

Effect of Defects on Mobility

1. Robustness to edge roughness.

2. Unlike De-facto samples [1], defect compensated samples [2] have roughly ballistic mobility.

[1] F. X. Xiu et al., Scientific Reports 2, Article number: 669 (2012) [2] S. S. Hong et al., Nature Communications 3, Article number: 757 (2012) 29

Devices

Ef = 0.100 eVEf = 0.175 eV Ef = 0.125 eVEf = 0.150 eV

Edge Roughness

2% Defects

10% Defects

250200150

250200150

100 200 300

Charge Impurities5 x 1018cm-3

2 x 1019cm-3

6 x 1019cm-3

200

130

80

120

70

5020 100 200 300

Vacancies250

150

200

100

100 30 100 200 300

5 x 1018cm-3

2 x 1019cm-3

6 x 1019cm-3

Mo

bili

ty (

cm

2 /V

/se

c)

Temperature (K)

10QL - 80 nm long - 60 nm wide

Effect of Phonons on Mobility

1. Phonons significantly degrade mobility with temperature.2. Ballistic Mobility increases with wire length.3. Defects (low conc.) hardly affect ballisticity of TI.4. Phonon scattering scales with wire length.

30

Devices

Wire Length (nm)50 100 150

Defects

Acoustic Phonons

300 K180

140

100

60

20

Mo

bili

ty (

cm

2 /V

/se

c)

Ef = 0.100 eVEf = 0.175 eV Ef = 0.125 eVEf = 0.150 eV

Temperature (K)0 100 200 300

200

150

100

50

AcousticPhonons

80 nm long

Net Mobility and Comparison1. 300K Bulk Cu Mobility ~ 30 cm2/V/s Comparable to Bi2Se3 TINano Letters 11 1925-7 (2011) observed 10 cm2V−1sec−1

at 245 K for 3.5 nm thick sample in which inter-surface scattering would be much stronger than 10-13 QL samples, while Thin Solid Films 534 659-65 (2013) observed 23 cm2V−1sec−1 at room temperature for 30 nm thick sample.

2. 300K Cu σ ~ 2.5-3.3 x 107 (Ω-m)-1

2K Bi2Se3 σ ~ 8.9-34.5 x 103 (Ω-m)-1

High electron density in CopperLow Density of States near Dirac-Point :3D-TI

Cu vs Bi2Se3 3D-TI

GNR vs SWCNT vs Bi2Se3 3D-TI1. GNR and SWCNT : small electron-phonon coupling BUT Low DOS

issue near Dirac-Point.2. GNR can be stacked (MLGNR-AsF5 doped) / SWCNT Bundled.3. 3D-TI not scalable like GNR or SWCNT+ phonon effect.

31

Devices

Gupta et al., Scientific Rep. 4, 6838 (2014)

Temperature (K)

140

100

60

2050 100 200 300

Mo

bili

ty (

cm

2 /V

/se

c)

0.100 eV

0.175 eV

Ef 0.075 eV

0.125 eV

0.150 eV

IEDM 2008 & 2010 (UCSB)

Inference for Interconnects1. ITRS 2011 probably assumed only surface transport and

overlooks “scattering” from defects and especially phonons.

2. Pros:1. High Mobility at low temperature.2. ‘Some’ immunity to impurities and edge roughness.

3. Cons:1. Room-Temperature Operation is an issue (phonon)2. Low Density of States near Dirac-point.

4. At least need: 3D-TI with much larger bulk-band gap and very weak e--ph coupling

5. Thin Bi2Se3 3D-TI may not be right material for this application.

32

Devices

IEDM 2013We successfully convinced Device Community to remove 3D-TI from interconnects chapter at least for now No Longer in ITRS 2013

33

Channel (Ch) Material : Graphene

Dielectric

Insulator (Tunnel)

Ch 2

Ch 1

VBG

xy

z

e- flow

VTG

symFET

[1, 2]

μn

μp

[1] Pei Zhao et al. IEEE Trans. in Elec. Devices, 60, 951-957 (2013)[2] R. M. Feenstra et al. J. Appl. Phys. 111, 043711 (2012)

qVDS = 2ΔE

ΔEqVDS

qVDS < 2ΔE

ΔE

Ch 2

Ch 1z

qVDS > 2ΔE

qVDS

μp

μn

2ΔE/q

VDS

orVTG

ID

Resonant State: High Transmission Very High Selectivity (Ratio) Independent of Temperature

Band-Alignment induced ResonanceDevices

Application

Analog Frequency Doubler

Resonant Devices can also be used for Analog

(a) Multipliers (b) Oscillators

[1] Pei Zhao et al. IEEE Trans. in Elec. Devices, 60, 951-957 (2013)

Freq. (id) = 2 x Freq. (vds or vgs)

Can 3D-TI provide Spin + Resonance Functionality for non-

volatile electronics ?(both need surface-bands)

ID

VDS or VGSInput:vds or vgs

Output: id

[1]

Bias-Point

34

Devices

Device Principlex

yz

μS

μD = μS – VDS

VGS < 0

VGS > 0Δ

VDS = 2 Δ

Top Gate

SourceDrain

Bi2Se3 TI

Bottom Gate

Dielectric

VDS

VTG

VBG = VTG= VGS

35

Devices

Potential Gradient

B

C

Design-A

Design-B & C

Source

Drain

Bottom Gate

VDS

VTG= VGS

VBG = 0

VGS = -Δ

VGS = -2 Δ

μS

μD = μS – VDS

VGS < -2Δ

Δ

Δ

VGS > -2Δ VDS = 2 Δ

Gupta et al., Scientific Rep. 4, 6220 (2014)

0.04

0.02

0

-0.02

-0.04-0.2 0 0.2

kya

−0 Δ

kya

−2 Δ

-0.2 0 0.2kya

−1 Δ

-0.2 0 0.2

Resonant Condition (0 K) – Design AEn

erg

y (e

V) 1.5

1

0.5

0

Δ = 0.04 eV

μS

μD

-Δ

Mode MismatchVGS = -0Δ

Δ μS

μD

Δ

-Δ

Mode MatchVGS = -1Δ

μS

μD

Δ

-Δ

Mode MismatchVGS = -2Δ

ModeFiltering Fermi-Velocity VB < CB

36

Devices

Transmission @

Results: Design-A

Resonance at :VGS = -Δ

Δ = 0.04 eV300K200K100K0KT :Δ : 0.04 eV0.06 eV0.025 eV

250

150

50

Gate Voltage (VGS / Δ)-2 -1.5 -1 -0.5 0

1.188

1.257

1.295

Cur

rent

(μA

/μm

)

IRI0

Ratio: IR

I0

Ratio is quite small Current at VGS = 0 is slightly more than at – 2Δ Local minima on either sides of resonance peak.

37

Devices

Gupta et al., Scientific Rep. 4, 6220 (2014)

Results show collective effect of: Band-Alignment induced Resonance. Mode-mismatch at Contacts Effect of gate potential on channel DOS.

Δ

200

160

120

-2 -1.5 -1 -0.5 0

Cur

rent

(μA

/μm

)

1.257

1.230

1.176

1.120

Gate Voltage (VGS / Δ)

T

T = 0 K

VGS

-0Δ -1Δ -2Δ

Ratio and asymmetry worsen with increase in temperature

Vertical Transport: Design B35

25

15

5

30

20

10

1

Sla

b L

aye

r

5 10 15 20 25 30 35

Current Density(μA/μm)

Transport Direction (nm)

38

Devices

Source

Drain

Bottom Gate

VDS

VTG= VGS

VBG = 0

Current flows both along longitudinal (x-axis) and vertical (z-axis) direction

Transport in Design-B (0K)En

erg

y (e

V)

kya

0.04

0.02

0

-0.02

-0.04

(b) (c)

−1 Δ −0 Δ

(d) (e) (f)

−2 Δ−4 Δ −3 Δ

0 0.5 1 1.5

-0.1 0.1kya kya kya kya

Resonance is visible, But: Ratio < 1

Loss in Device Gain

Large Asymmetry Signal Distortion

40

30

20

(Fo

r Δ =

0.0

2 e

V)

100

50

(Fo

r Δ =

0.0

4 e

V)

-4 -3 -2 -1 0 Gate Voltage (VGS / Δ)

(a) Current (μA/μm)

0.981

0.948

39

Devices

-0.1 0.1 -0.1 0.1 -0.1 0.1 -0.1 0.1

No mode mismatch b/w channel and contactsVDS = 2 Δ

Transport in Design-CEn

erg

y (e

V)

(b) (c) −1 Δ −0 Δ(d) (e) (f)

−3 Δ−4 Δ −2 Δ

0 0.5 1 1.5

0.04

0.02

0

-0.02

-0.04

40

Mode mismatch b/w channel and contacts

Combines worse of Design-A and B

Devices

No Resonance is observed. Minima not at -2Δ because of still some weak mode-matching for vertical transport.

kya-0.1 0.1

kya kya kya kya-0.1 0.1 -0.1 0.1 -0.1 0.1 -0.1 0.1

36

32

28

120

110

100

-4 -3 -2 -1 0Gate Voltage (VGS / Δ)

(a)

VDS = 2 Δ

(Fo

r Δ =

0.0

2 e

V)

(Fo

r Δ =

0.0

4 e

V)

Current (μA/μm)

Inference for Resonant Device

41

Devices

1. Therefore, the results show collective effect of: Band-Alignment induced Resonance. Mode-(mis)match at Contacts Effect of gate potential on channel DOS.

2. Larger band-gap 3D-TI may improve the ratio by providing larger energy-window for device operation.

3. Assumption of pure vertical transport in literature is inappropriate.

4. Order of performance: Design-A > Design-B > Design-C

5. Design-A performance may be slightly improved by limiting transverse modes [1].

6. In my opinion, none of the three designs is suitable especially for Room-Temperature.

[1] Gupta et al., Nanoscale 4, 6365-6373 (2012)

42

Major Results1. Quantum transport Simulator based on NEGF was developed for 3D-

TI and 2D Group-IV monolayers, that exploits heavy parallelism on GPU and CPU Clusters.

2. By investigating carrier transport through Bi2Se3 3D-TI, we: Provided fundamental insights in device transport and scattering

mechanisms. explained contrasting experimental data on resistance

characterization. explained spin-polarized current experiment via FM contacts and

current distribution across layers. suggested new transport-based methods of validating 3D-TI.

3. By investigating 3D-TI devices via Bi2Se3 as example, we: Appraised number of assumptions in existing TI literature Showed thin Bi2Se3 3D-TI may have limited promise for interconnects Showed although resonance can be obtained by band-alignment

operation, its magnitude needs significant enhancement for real applications.

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Future Works

1. Reason for100o scattering angle threshold

Phys. Rev. Lett. 112, 136802 (2014)

Study evolution of decoherence in 3D-TI . Quantum mechanically simulate the scattering mechanism via Wigner Transport Formalism.

2. AlN substrate effectuating gapless Dirac band in 3QL Bi2Se3

ACS Nano, 2014, 8 (7), pp 6614–6619

Ab-initio simulations for heterostructure Transport properties investigation via NEGF

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Publications (Journals)[1] Gaurav Gupta, Mansoor Bin Abdul Jalil, Bin Yu and Gengchiau Liang, "Performance evaluation of electro-optic effect based graphene transistors", Nanoscale 4, 6365-6373 (2012).

[2] Gaurav Gupta, Hsin Lin, Arun Bansil, Mansoor Bin Abdul Jalil, Cheng-Yi Huang, Wei-Feng Tsai and Gengchiau Liang, “Y-Shape Spin-Separator for two-dimensional Group-IV Nanoribbons”. Applied Physics Letters 104 (3), 032410 (2014).

[3] Gaurav Gupta, Hsin Lin, Arun Bansil, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Role of Acoustic Phonons in Bi2Se3 Topological Insulator Slabs: A Quantum Transport Investigation”. Physical Review B 89, 245419 (2014).

[4] Gaurav Gupta, Mansoor Bin Abdul Jalil, and Gengchiau Liang, “Effect of Band-Alignment Operation on Carrier Transport in Bi2Se3 Topological Insulator”, Scientific Report 4, 6220 (2014).

[5] Gaurav Gupta, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Evaluation of mobility in thin Bi2Se3 Topological Insulator for prospects of Local Electrical Interconnects”. Scientific Reports 4, 6838 (2014).

[6] Mohammad Abdullah Sadi*, Gaurav Gupta* and Gengchiau Liang, “Effect of phase transition on quantum transport in group-IV two-dimensional U-shape device”, Journal of Applied Physics 116, 153708 (2014). (*Authors contribute equally)

[7] Gaurav Gupta, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Contact Effects in thin 3D-Topological Insulators: How does the current flow ?”, Scientific Reports 5, 9479 (2015).

[8] Gaurav Gupta, Hsin Lin, Arun Bansil, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Carrier Transport in Bi2Se3 Topological Insulator Slab”. Physica E: Low-dimensional Systems and

Nanostructures 74, 10-19 (2015).

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Publications (Conferences)[1] Gaurav Gupta, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Comparison of Electro-Optic Effect based Graphene Transistors,” 2012 International Conference on Solid State Devices and Materials (SSDM 2012) September 25-27, 2012, Kyoto International Conference Center, Kyoto, Japan.

[2] Gaurav Gupta, Argo Nurbawono, Minggang Zeng, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Theoretical study on Topological Insulator based Spintronic Tristable Multivibrator,” 2013 International Conference on Solid State Devices and Materials (SSDM 2013) September 24-27, 2013, Hilton Fukuoka Sea Hawk, Fukuoka, Japan.

[3] Gaurav Gupta, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Is Sub-10nm Thick 3D-Topological Insulator Good for the Local Electrical Interconnects?”, IEEE International Electron Devices Meeting (IEDM 2013) December 9-11, 2013, Washington DC, USA. (Travel Grant Award: $860)

[4] Gaurav Gupta, Mansoor Bin Abdul Jalil and Gengchiau Liang, “Band-Alignment Induced Current Modulation in Bi2Se3 Topological Insulator,” 2014 International Conference on Solid State Devices and Materials (SSDM 2014) September 8-11, 2014, Tsukuba International Congress Center, Tsukuba, Ibaraki, Japan. (Travel Grant Award: Yen 70000)

[5] Mohammad Abdullah Sadi*, Gaurav Gupta*, and Gengchiau Liang, “Effect of Phase Inversion on Quantum Transport in Group IV Two-Dimensional U-shape Device,” 2014 International Conference on Solid State Devices and Materials (SSDM 2014) September 8-11, 2014, Tsukuba International Congress Center, Tsukuba, Ibaraki, Japan. (*Authors contribute equally)

[6] Gaurav Gupta and Gengchiau Liang, “Quantum Transport in Two-Dimensional Group-IV monolayers and Topological Insulators”, World Congress of Smart Materials (WCSM 2015), March 23-25, 2015, Busan, Republic of Korea. (Invited Talk)

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Publications (Others)

Book-ChaptersIn-Press

[1] Gaurav Gupta, Minggang Zeng, Argo Nurbawono, Wen Huang, and Gengchiau Liang, “Applications of Graphene Based Materials in Electronic Devices,” Chapter 19, Volume 6 (Applications and Industrialization), Graphene Science Handbook, CRC, in press.

[2] Wen Huang, Argo Nurbawono, Minggang Zeng, Gaurav Gupta, and Gengchiau Liang, “Electronic structure of graphene based materials and their carrier transport properties,” Chapter 26, Volume 2 (Nanostructure and Atomic Arrangement) of Graphene Science Handbook, CRC, in press.

Patents[1] Hsin Lin, Wei-Feng Tsai, Chen-Yi Huang, Horng-Tay Jeng, Tay-Rong Chang, Gaurav Gupta, Gengchiau Liang and Arun Bansil, “Transition Metal Dichalcogenides-Based Spintronic Devices”, US Provisional Application No.: 62/058,437, Priority Date: 1st October 2014.

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Supervisors: Assoc. Prof. Gengchiau Liang Assoc. Prof. Mansoor Bin Abdul Jalil

Collaborators: Dr. Hsin Lin (NUS/Northeastern University) Prof. Arun Bansil (Northeastern University) Prof. Bin Yu (New York University)

Funding Agencies:MOE, ASTAR, NRF, NUS Research & PGF Scholarship

PhD Committee for helping me to improve the Thesis

Mentors, Friends and Colleagues

Mom, Dad and Sister

Acknowledgement

Thank You All for listening

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Gaurav Guptagaurav.gupta@nus.edu.sg gauravdce07@gmail.com

Computational Nanoelectronics and Nanodevices Lab (CNNL)Department of Electrical and Computer Engineering

National University of Singapore