Amrit Palaria Amritanshu Palaria Electrical and Computer Engineering Purdue University Advisors:...

Amrit Palaria

Amritanshu PalariaElectrical and Computer Engineering

Purdue University

Advisors: Gerhard Klimeck

Alejandro Strachan

Multi-scale modeling of nano-material and realistic devices

Amrit Palaria 2

Why material modeling?

Introduction

Challenges in continuing Moore’s law: transistors, interconnectsDesired device properties new material new device/ architecture

ITRS 2007

ITRS 2007 - 1D nanostructure extensions to CMOS

Si nanowire array FET(Wang et al., 2006)

Si nanowire inverter(Cui and Leiber, 2000)

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Introduction

Nanowires - New materials! Properties tunable by size.

• Electrical and optical properties-Can be the most confining electrical conductors - squeeze electrons-Can be defect free-Quantum confinement - tunable optical properties

• Mechanical properties-Can exhibit high strengths

• Thermal properties- Can be designed to conduct heat much better or worse than bulk

• Chemical properties- Dominated by large surface-to-volume ratio


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Introduction

Other applications of silicon nanowires:

Chemical sensors (large surface)

Energy conversion devices

•Thermoelectric devices

•Photovoltaic

•Electrochemical storage (lithium battery electrode)

Chen and Carlen, Univ of Twente

Chan et al., 2008

n

p

npPeng et al., 2005

Garnett and Yang, 2008ZT = S2σT/κ


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Introduction


Example of Carbon

Material details drastically affect electrical properties

Semiconducting/ metallic

1D - carbon nanotubes

Insulating (fullerite)

0D - buckminster fullerene

3D - diamond (sp3)

Insulating

Anisotropically conducting

3D - graphite (sp2)(TEAM 0.5, Berkeley Lab)

Superconducting

2D - graphene(picture by Jannik Meyer)

Dimensionality and bonding affect electrical properties

Amrit Palaria

Introduction

Multi-scale modeling

Semi-classical(BTE)

SUB-MICRONMOSFET

Quantum(NEGF)

NANOTUBES

QuantumMechanics (DFT/ GW)

NANOTUBES

Material ScienceElectrical Engineering

Resolution Generality/ transferabilityAt atomistic level the paths converge

Classical

BULK

Moleculardynamics

COLLOIDS

Mesoparticle

GRAINS

Continuum

BULK

Size ofSystem

Resolution

Size ofSystem

Resolution

Amrit Palaria

Introduction

Multi-scale modeling

Size ofSystem Continuum

MesoparticleMoleculardynamics

QuantumMechanics (DFT/ GW)

Classical Semi-classical(BTE)

Quantum(NEGF)

Eg, m*

Size ofSystem

1. Atomic Structure

2. Tight-binding Model

Resolution Resolution

Amrit Palaria

Introduction

Multi-scale modeling - Vision

Channel Molecularstructure

MD/ DFT

ChannelHamiltonian

Tight BindingStatisticalMechanics

Electrostatics

Poisson

Boltzmann/ NEGF<1nm diameter SiNW

strained Si/Ge/Sinanobars

TB for surfaces

Structural Quantum Mechanics

Amrit Palaria

Geometry morphology and properties of 1 nm silicon nanowires

Objective: Investigate stability and properties of ~1nm diameter 1-D silicon nano-structuresMethod: Multi-scale modeling in time - density functional theory, reactive force field molecular dynamicsResults:•2 categories of energetically most stable Si nanowires (NW) of dia ~ 1nm•Stable wires possess non-diamond geometries•Structural symmetry reduction at wire surface enhances stability and introduces bandgap•Pristine and H passivated wires with new bandgaps and unique properties

Impact:•New materials: possible use in thermoelectrics, photovoltaics, sensors, flexible electronics, CMOS scaling

•General method for exploration of new materials

Amrit Palaria, Alejandro Strachan, Gerhard Klimeck

Amrit Palaria 10

Amrit Palaria, Gerhard Klimeck, Alejandro Strachan

Objective: Investigate the electronic bandstructure properties of s-Si/s-Ge/s-Si nanowires with major Ge sectionMethod: •Use realisitc Si-Ge-Si nanowire structures obtained from ReaxFF molecular dynamics•Model the Ge section of the wires using bulk sp3d5s* tight binding parameters modified for strain

Results: •Hole effective mass of wire structured from 2% compressively strained Ge film reduces with decreasing width•General VB shape is dependent on average strain•Non-uniformity of strain plays a role in effective mass and DOS

Impact: •Can provide channel material for faster devices (high gm)

Electronic properties of Si-Ge-Si heterostructures from tight binding

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Amrit Palaria, Gerhard Klimeck, Alejandro Strachan

Objective: Investigate the possibility of simulating surfaces and interfaces with empirical tight bindingMethod: •Investigate sp3d5s* tight binding using bulk with strain parameters for Si slab with (100) surface, modify NEMO-3D for this (in C++)•Use GW results as benchmark •Modify surface atom bulk parameters•Check sensitivity of high symmetry points to bulk parameter modification

Result: •Band-structure of Si(100) surface from TB with modified sigma parameters matches reasonably with GW results

Impact: •Quick and scalable simulation of realistic electronic devices with surfaces or other non-bulk bonds e.g. interfaces

Tight binding parameters for silicon surface

Amrit Palaria

Structures and properties of very small diameter (<1 nm) Si nanowires

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Introduction

Nanowires - New materials! Properties tunable by size.

• Electrical and optical properties-Can be the most confining electrical conductors - squeeze electrons-Can be defect free-Quantum confinement - tunable optical properties

• Mechanical properties-Can exhibit high strengths

• Thermal properties- Can be designed to conduct heat much better or worse than bulk

• Chemical properties- Dominated by large surface-to-volume ratio


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Introduction

Other applications of silicon nanowires:

Chemical sensors (large surface)

Energy conversion devices

•Thermoelectric devices

•Photovoltaic

•Electrochemical storage (lithium battery electrode)

Chen and Carlen, Univ of Twente

Chan et al., 2008

n

p

npPeng et al., 2005

Garnett and Yang, 2008ZT = S2σT/κ


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Introduction

Bandgap increases with decreasing diameter

dia (nm)

Thermoelectric performance can improve with decreasing diameter

Shi et al, 2009

ZT = PT/(κe+κph)

Source: American Society for Testing and Materials (ASTM)

Why worry about such small diameters?

Wire

Liang and Li, 2006

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Silicon nanowires with bulk geometry

Background of small diameter silicon nanowires

Hydrogen passivated surfaceClaim - silicon bulk configuration

•SiNW with dia <2 nm achieved! (Ma et al., Science, 2003)

•Few nm diameter - bulk geometry (Wu et al., Nano Lett., 2005)

~4nm diameterNo surface oxide[110] wire preferred

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Non-bulk geometry wires - role of surfaces

•~1 nm unpassivated wires? (DFT study, Kagimura et al., PRL, 2005)

Background of small diameter silicon nanowires

Simple hexagonal[110]

DFT-GGA<1nm diameter Hexagonal, pentagonal, square cross sectionsMetastableMetallic

•Non CNT structure silicon nanotubes(Bai et al., PNAS 2003)

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Objectives

Introduction

What are the energetically most stable 1-D silicon nanostructures at ~1nm diameter – unpassivated and H-passivated?

What are some electronic properties of these structures?

Can we understand the physics of the surface effect on the stability and properties of these structures?

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Objectives

Introduction


What are some electronic properties of these nanowires?


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Predicting Si nanowire structure

FF-MD

Force-fieldMolecular Dynamics

fs ps nsSimulated Time

ReaxFF-MD (fast and inexpensive)

exploration tool

DFT

Density Functional Theory

SeqQuest/ Abinit (expensive)

Predicting new material

Energy

generalized coordinate

Eb barrier height

refinement tool

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Compression Expansion

Example with compression speed 5A/ns

Using reactive force field MD as exploratory tool


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~1 nm dia silicon nanowiresEnergetically most stable unpassivated wires: tubular

2 categories:Distorted fullerenes (DF)Distorted nanotubes (DNT)

Surface modifies geometry

Very different from diamond bulk or carbon nanotubes!

Predicting new material0.635

0.637

0.638

0.658

0.673

0.705

0.697

0.708

0.714

(eV/atom)

(eV/atom)

sp2sp3

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~1 nm dia silicon nanotubes

Low symmetryHigh disorder

Predicting new material0.635

0.637

0.638

0.658

0.673

0.705

0.697

0.708

0.714

(eV/atom)

(eV/atom){(E|t),(C10|t/2),D5h}

{(E|t),(C12|t/2),D6h}

{(E|t),D5h}

{(E|t),D6h}

{(E|t),D1h}

{(E|t),(v|t/2)}

{(E|t), C1v}

Amrit Palaria 24

~1 nm dia H passivated silicon nanowires


H

SiSi

HHSiNW

n

nE

EnergyDF1

F1

DNTs and Fs better than or comparable to diamond wires

H : +

Esur:HEsur

Amrit Palaria 25

Objectives

Introduction


2 categories of tubular non diamond-core silicon nanowires:

DFs and DNTs



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Properties of Si nanotubes

Effective masses of ~1 dia silicon nanowires

0 0 0 0 0/ɑF2/ɑF1 /ɑDNT3 /ɑDNT1 /ɑ[110]

F2 F1 DNT3 DNT1110_small

H-passivated

Unpassivated

DF2’ DF1 DNT1DNT3

0 bandgap

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Kohn-Sham bandgaps: the bandgap problem

Same ρ(r)

Non-interacting systemActual interacting system

H[] T[]Vext[]Uee[]

UH []Uxc[]

HKS h2

2m2 vR (r)

vR (r) f [Vext (r

),(r

),Uxc[](r

)]

Kohn-Sham DFT is not designed to determine correct single particle states

Amrit Palaria 28


Kohn-Sham bandgaps: the bandgap problem

DFT not designed to determine correct single particle states.

Yet known to provide:

-almost correct dispersion for filled states in ground state system

-almost correct curvatures of single particle states

-smaller than true bandgapprediction of presence of gap from DFT is correctfor SiNW, the GW bandgap is proportional to K-S bandgap (Zhao et al., 2004)

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(sp3d5s* TB)

Electronic band gaps of bulk like silicon nanowires


For silicon (bulk, surface, bulk-like nanowires):BandgapGW ~ 2*BandgapK-S

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0

0.5

1

1.5

2

2.5

3

3.5

4

0 1avg diameter (nm)

E g

ap (

eV

)

[110] H-pasv hex cs wire GW(Zhao)

[112] H-pasv wire expt Ma

[110] H-pasv wire expt Ma

[110] unpasv hex cs wire DFT-GGA (Akiyama)

unpasv F/DF/DNT structuresDFT-GGA

unpasv Pen and Hexstructures DFT-GGA (Bai)

unpasv SHW structures DFT-GGA

H pasv SiNT DFT-GGA

H pasv rect cs [110] wires

H pasv circ cs [111] wires

DF2''DNT1

F2 F1

DF2''_H

DF1

DF1_H

DNT1_H


Electronic band gaps of ~1 dia silicon nanowires

New bandgaps

Diamond wires (DFT)DFT Visible

(guess)

Amrit Palaria 31


Effective masses of ~1 dia silicon nanowires

0 0 0 0 0/ɑF2/ɑF1 /ɑDNT3 /ɑDNT1 /ɑ[110]

F2 F1 DNT3 DNT1110_small

H-passivated

Unpassivated

DF2’ DF1 DNT1DNT3

Non-diamond wires have high effective masses

Amrit Palaria 32

Investigating mechanical response


Straining F1 using ReaxFF MD at 300K

Sustains 6% strainBulk can sustain only 0.04%

Good strength => Flexible electronics:

118

72

145

Young’s moduli (GPa)

Not too different from bulk(80 GPa for Si bulk)

Amrit Palaria 33

Objectives

Introduction



DFs and DNTs


New bandgaps and effective masses


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What leads to higher gap in lower energy structures?


Unpassivated wires

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What leads to gap in lower energy structures?

Symmetry of structure same symmetry of HOMO and LUMO

bohr-3/2

bohr-3/2

bohr-3/2

bohr-3/2

Loss of structure symmetry loss of similarity in symmetries of HOMO and LUMO

y

x

z


Amrit Palaria 36

Comparison with Si (100) surface

Symmetry breaking of structure redistributes HOMO e- among atoms


Perfect fullerene

Similar to Si(100) symmetric to asymmetric reconstruction

Distorted fullerene

A’A

DF1F1

A A’

Si (100) p(2X1) surface reconstruction

Asymmetric

Symmetric

F1 and DF1

AA’DF1

F1

-+

Amrit Palaria 37

Objectives

Introduction



DFs and DNTs


New bandgaps and effective masses

Can we understand the physics of surface effect on the stability and properties of these structures?

Loss of structural symmetry leads to enhanced stability and redistribution of HOMO electrons among atoms leading to a bandgap

Amrit Palaria

Investigating realistically strained Si/Ge/Si nanobars

Amrit Palaria 39

Strained Si/Ge/Si hetero nanobars

Periodic

The structure

Amrit Palaria 40

Objectives

What are the confinement effects on electronic bandstructure?

What are the strain effects? How does MD relaxed differ from homogeneous uniaxially or biaxially strained wire? Are the properties of MD relaxed wires good or bad for devices?

Does non-uniformity of strain play any role?


Amrit Palaria 41

H = 6.39 nm, W = 20.09 nm

Transverse strain vs W and H

W

Square Ge sections - almost uniaxial strain

Park et al., JAP, 2009

ReaxFF MD

Virtual SiGeSiGeSi

SiO2

SiO2

SiGeSi

Virtual SiGe

-2%-2%

2%2%

2%2% -2%

-2%2%2%

2%-2%

LongitudinalTransverse

LongitudinalTransverse

Strain relaxes

HW

Hashemi et al., 2007

W: 30-300nm

Hashemi et al., 2007

Introduction


Amrit Palaria42

Structures and Method


Periodic

EV > 0.4eVp-type device

H ~ 7 nmH ~ 10 nm

W: 8-41 nm

sp3d5s* tight binding with strain corrections (Boykin et al., 2002) and surface passivation (Lee et al., 2004)

Amrit Palaria 43

Strains


Longitu

dinal

(perio

dic)

H

WH~7nm

W~8nm

W~12nm

W~30nm

Amrit Palaria 44

Strains


Variation of bond strains in MD relaxed wires

Compared with uniformly uniaxial and uniformly biaxial wires with 2% compression in longitudinal direction

Asterisks: peaks of distributionGreen dotted line: average transverse strain

Amrit Palaria 45

Confinement effect


Bulk: (0, 0, 0) to (0, 0, /ɑ)Slab:(0, 0, 0) to (0, 0, /ɑ)Wire:(0, 0, 0) to (0, 0, /ɑ)

Bulk: (/ɑ, /ɑ, 0) to (/ɑ, /ɑ, /ɑ)Slab:(/ɑ, /ɑ, 0) to (/ɑ, /ɑ, /ɑ)Wire:(0, 0, 0) to (0, 0, /ɑ)

bulkslabwire: •Bandgaps increase•Effective masses degrade

CB edge VB edgeBand edgesEffective masses

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Ge wires


CB VB

• Shifts in band edges• Changes in band curvatures

Amrit Palaria 47

Band edges in Ge wires


Filled symbols: H~7nmOpen symbols: H~10nm

• Bandgaps increase with decreasing widths

• MD relaxed has smallest bandgap (smaller by about 0.1eV than uniaxial wire)

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Electron effective masses in Ge wires



• Branches switch at band edge, causing the effective masses to oscillate with changing widths.

• MD relaxed has close to or higher effective mass than uniaxial.

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Hole effective masses in Ge wires



• MD relaxed band edge effective mass remains close to uniaxial.

• Average effective mass is smaller than even uniaxial for smalle widths and increases with increasing width!

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Valence bands of MD relaxed wires


Degradation in effective mass appears to come from faster curving of valence bands to become concave up

Amrit Palaria 51

Comparison of Valence bands


Valence bands have shape like uniaxial for W 12.7 nm and like biaxial for W 31.3nm

Valence bands have shape like uniaxial for W 12.7 nm and like biaxial for W 31.3nm

Amrit Palaria 52

Is it only about average transverse strains?Is non-homogenity of MD relaxed wire important?


• Homogeneous wires with strain like MD relaxed (strain in between uniaxial and biaxial) exhibit behavior in between uniaxial and biaxial wires

• Non-homogenity in the MD relaxed wire clearly plays a role

Simulate homogeneous wires with average in all directions like MD relaxed wires

Amrit Palaria 53

Is it only about average transverse strains?Is non-homogenity of MD relaxed wire important?


Strain non-uniformity in MD relaxed wires with 2% compression along longitudinal direction causes :

•Bandgap to be lower (and VB edges shifted further up) than uniform strain cases

•Hole effective mass to be lower than uniform uniaxial case for small width wires and higher than biaxial case for large width wires

•Hole effective mass to decrease monotonically with decreasing width (cross-section) for a given height of wire

Amrit Palaria 54

What does this imply?

GS

DSm V

Ig

gm WCgvT for ballistic gm W(m*)-0.5

For given length: gm WCgeff for scattered gm

W(m*)-1

The closer we can pack the wires, the better.

155.11

2 m

m

g

g

=2 for scattered

for ballistic

1

2

1

2

1

2

1

2

*

*

m

m

W

W

n

n

g

g

m

m

=0.5 for ballistic=1 for scattered

For same area:

<1

2S

36 nm

6 nm

S D

36 nm

1 m*1=0.33

D

8 nmm*2=0.11


Amrit Palaria 55

Why MD relaxed is different?


0 to -0.01 eV of valence bands at the VB edge in the (7,13) MD relaxed wire

Characterisitcs of electronic state distribution in VB of (7,13) MD relaxed wire

Per bond

States/bond are high even for strains removed from average

Total

Amrit Palaria 56

Why MD relaxed is different?


Hole effective mass contribution in the MD relaxed wires

Characterisitcs of effective mass contribution in VB of MD relaxed wires

Per bond

Effective mass contribution/bond is high even for strains removed from average

Total

Amrit Palaria 57

Conclusion

Used different methods at different scales to:

• Predict stable structures of small diameter (~1nm) Si nanowires and understand their properties and effects of surface

• Show that strain engineering combined with nano-sizing (nano-structuring) can provide useful new material structures for electronics

Amrit Palaria 58



Anneal

Regular trial structure

Fully relaxed structure

PESE

Variable representing degree of freedom

Amrit Palaria 59


Starting unit cell geometri

es

Unit cells per

simulation cell

Strain ranges

Strain rates

Temperatures

PentagonHexagon

56101112

-37.50 to -12.50 %

-25.00 to -8.30 %

-20.87 to -4.17%

0.04167 % / ps

0.41667 % / ps

0.83333 % / ps

300K600K


Amrit Palaria 60

Contrasting computational and experimental procedure

Outlook

CVD

Au seeding in supercritical fluid

Abrasive mould methodPreserve crystallinity

Amrit Palaria 61

Future directions

Outlook

How to fabricate?

Electrical conductivity: DOS, scattering, electrostatic effects

Thermal conductivity: phonon, electron

Doping effects?

Simulation of devices

Other possibilities, e.g. intercalation

Date post:	25-Dec-2015
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Amrit Palaria Amritanshu Palaria Electrical and Computer Engineering Purdue University Advisors:...

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