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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)
Amrit Palaria 3
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
Why material modeling?
Amrit Palaria 4
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
Why material modeling?
Amrit Palaria 5
Introduction
Why material modeling?
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
Amrit Palaria 11
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
Amrit Palaria 13
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
Why material modeling?
Amrit Palaria 14
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
Why material modeling?
Amrit Palaria 15
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
Amrit Palaria 16
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
Amrit Palaria17
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)
Amrit Palaria 18
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?
Amrit Palaria 19
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 nanowires?
Can we understand the physics of the surface effect on the stability and properties of these structures?
Amrit Palaria 20
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
Amrit Palaria 21
Compression Expansion
Example with compression speed 5A/ns
Using reactive force field MD as exploratory tool
Predicting new material
Amrit Palaria 22
~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
Amrit Palaria 23
~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
Predicting new material
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
What are the energetically most stable 1-D silicon nanostructures at ~1nm diameter – unpassivated and H-passivated?
2 categories of tubular non diamond-core silicon nanowires:
DFs and DNTs
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?
Amrit Palaria 26
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
Amrit Palaria 27
Properties of Si nanotubes
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
Properties of Si nanotubes
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)
Amrit Palaria 29
(sp3d5s* TB)
Electronic band gaps of bulk like silicon nanowires
Properties of Si nanotubes
For silicon (bulk, surface, bulk-like nanowires):BandgapGW ~ 2*BandgapK-S
Amrit Palaria 30
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
Properties of Si nanotubes
Electronic band gaps of ~1 dia silicon nanowires
New bandgaps
Diamond wires (DFT)DFT Visible
(guess)
Amrit Palaria 31
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
Non-diamond wires have high effective masses
Amrit Palaria 32
Investigating mechanical response
Properties of Si nanotubes
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
What are the energetically most stable 1-D silicon nanostructures at ~1nm diameter – unpassivated and H-passivated?
2 categories of tubular non diamond-core silicon nanowires:
DFs and DNTs
What are some electronic properties of these structures?
New bandgaps and effective masses
Can we understand the physics of the surface effect on the stability and properties of these structures?
Amrit Palaria 34
What leads to higher gap in lower energy structures?
Properties of Si nanotubes
Unpassivated wires
Amrit Palaria 35
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
Properties of Si nanotubes
Amrit Palaria 36
Comparison with Si (100) surface
Symmetry breaking of structure redistributes HOMO e- among atoms
Properties of Si nanotubes
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
What are the energetically most stable 1-D silicon nanostructures at ~1nm diameter – unpassivated and H-passivated?
2 categories of tubular non diamond-core silicon nanowires:
DFs and DNTs
What are some electronic properties of these structures?
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?
Strained Si/Ge/Si hetero nanobars
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
Strained Si/Ge/Si hetero nanobars
Amrit Palaria42
Structures and Method
Strained Si/Ge/Si hetero nanobars
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
Strained Si/Ge/Si hetero nanobars
Longitu
dinal
(perio
dic)
H
WH~7nm
W~8nm
W~12nm
W~30nm
Amrit Palaria 44
Strains
Strained Si/Ge/Si hetero nanobars
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
Strained Si/Ge/Si hetero nanobars
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
Amrit Palaria 46
Ge wires
Strained Si/Ge/Si hetero nanobars
CB VB
• Shifts in band edges• Changes in band curvatures
Amrit Palaria 47
Band edges in Ge wires
Strained Si/Ge/Si hetero nanobars
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)
Amrit Palaria 48
Electron effective masses in Ge wires
Strained Si/Ge/Si hetero nanobars
Filled symbols: H~7nmOpen symbols: H~10nm
• 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.
Amrit Palaria 49
Hole effective masses in Ge wires
Strained Si/Ge/Si hetero nanobars
Filled symbols: H~7nmOpen symbols: H~10nm
• 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!
Amrit Palaria 50
Valence bands of MD relaxed wires
Strained Si/Ge/Si hetero nanobars
Degradation in effective mass appears to come from faster curving of valence bands to become concave up
Amrit Palaria 51
Comparison of Valence bands
Strained Si/Ge/Si hetero nanobars
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?
Strained Si/Ge/Si hetero nanobars
• 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?
Strained Si/Ge/Si hetero nanobars
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
Strained Si/Ge/Si hetero nanobars
Amrit Palaria 55
Why MD relaxed is different?
Strained Si/Ge/Si hetero nanobars
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?
Strained Si/Ge/Si hetero nanobars
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
Using reactive force field MD as exploratory tool
Predicting new material
Anneal
Regular trial structure
Fully relaxed structure
PESE
Variable representing degree of freedom
Amrit Palaria 59
Predicting new material
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
Using reactive force field MD as exploratory tool
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
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