properties of nanoscale dielectrics from first principles computations properties of nanoscale...
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Properties of nanoscale Properties of nanoscale dielectrics from first dielectrics from first
principles computationsprinciples computations
Ning Shi
Department of Chemical, Materials & Biomolecular Engineering
Institute of Materials Science, University of Connecticut
Major Advisor: Prof. Rampi RamprasadAssociate Advisor: Prof. Pamir S. AlpayAssociate Advisor: Prof. Bryan D. Huey
Ph. D. Dissertation Proposal
OutlineOutline Motivation Motivation
Modern microelectronicsModern microelectronics High energy density storage systemsHigh energy density storage systems
Objectives & methodology Objectives & methodology
Applications & ResultsApplications & Results High-k dielectrics for modern microelectronicsHigh-k dielectrics for modern microelectronics
Position dependent dielectric constant profile in Position dependent dielectric constant profile in heterostructureheterostructure
Local band edges profile in heterostructureLocal band edges profile in heterostructure
High energy density storage systemsHigh energy density storage systems Molecular compositesMolecular composites Polymer:oxide heterostructuresPolymer:oxide heterostructures
Future workFuture work
Motivation: Modern microelectronics Motivation: Modern microelectronics High dielectric constant (High-k) materialsHigh dielectric constant (High-k) materials
““Moore’s Law”: The International Technology Roadmap for Semiconductors requires Moore’s Law”: The International Technology Roadmap for Semiconductors requires continued shrinkage of electronic devices continued shrinkage of electronic devices (John Roberson, Rep. Prog. Phys. 2006)(John Roberson, Rep. Prog. Phys. 2006)
Decrease A for constant capacitance Decrease A for constant capacitance
Replace SiOReplace SiO22 by other dielectrics (e.g., HfO by other dielectrics (e.g., HfO22, Hf silicates, etc.) with larger dielectric constant, Hf silicates, etc.) with larger dielectric constant
Dielectric properties of thin film and variation at the interface ?Dielectric properties of thin film and variation at the interface ?
(Craig R. Barrett MRS bulletin 2006)
Bulk high k oxide dielectric properties are well determined Bulk high k oxide dielectric properties are well determined ((Zhao X and Vanderbilt D, Physl Rev. B, 2002)Zhao X and Vanderbilt D, Physl Rev. B, 2002)
Motivation: Modern Motivation: Modern
microelectronics microelectronics Band offsetsBand offsets A good insulating layer: the conduction band offset of the oxide with
respect to silicon has to be greater than 1 eV (John Roberson, Rep. Prog. Phys. 2006)(John Roberson, Rep. Prog. Phys. 2006)
Desirable
The local band edges profiles of the interfaces at atomic
level?
Undesirable
Conventional computational approach only predict band gap, band offsets
(V. Fiorentini and G. Gulleril, Physl Rev. B, 2002 )
Motivation: High energy density storage Motivation: High energy density storage systems systems
High dielectric constant (High-k) materialsHigh dielectric constant (High-k) materials
Example of high-k organic composite:Example of high-k organic composite:
Cu-phthalocyanine: polymer Cu-phthalocyanine: polymer composites shows high dielectric composites shows high dielectric constants under certain conditionsconstants under certain conditions
(Q. M. Zhang et al , Nature, 2002)
Atomic/molecular origins of high dielectric Atomic/molecular origins of high dielectric constant?constant?
Pure polymer
CuPc polymer composite
Motivation: Energy density storage systemMotivation: Energy density storage systemHigh breakdown strength polymer compositesHigh breakdown strength polymer composites
Example of high E polymer composite:Example of high E polymer composite:
Improvement of breakdown strength in XLPE Improvement of breakdown strength in XLPE with SiOwith SiO22 nanofiller nanofiller
The interface between SiOThe interface between SiO22 and polyethylene and polyethylene plays a critical roleplays a critical role
The interface states could act as potential The interface states could act as potential
electron traps, thereby scavenging “hot” electron traps, thereby scavenging “hot” electrons.electrons.
Coupling between “hot” electrons in polymer Coupling between “hot” electrons in polymer and phonons in SiOand phonons in SiO22 can improve breakdown can improve breakdown strengthstrength
The incorporation of SiOThe incorporation of SiO22 nanoparticles nanoparticles into polyethylene (PE) increases the into polyethylene (PE) increases the breakdown strengthbreakdown strength
Atomic origins of increase of dielectric breakdown Atomic origins of increase of dielectric breakdown strength?strength?
(M. Roy et. al IEEE Trans. on Dielectrics and Electrical Insulation. 2005)
ObjectivesObjectives
Development of new first principles computational methodsDevelopment of new first principles computational methods Position dependent dielectric constant profiles Position dependent dielectric constant profiles Local band edges variation Local band edges variation Electron-Phonon interactionElectron-Phonon interaction
Applications & ResultsApplications & Results Si:SiOSi:SiO22 and Si:HfO and Si:HfO22 heterostructuresheterostructures CuPc molecular composite and silica nanoparticle filled polymer CuPc molecular composite and silica nanoparticle filled polymer
compositecomposite
PublicationsPublications[1] N. Shi and R. Ramprasad, "The intrinsic dielectric properties of phthalocyanine crystals: An ab initio [1] N. Shi and R. Ramprasad, "The intrinsic dielectric properties of phthalocyanine crystals: An ab initio
investigation", investigation", Phys. Rev. B, in printPhys. Rev. B, in print[2] N. Shi , C.G. Tang and R. Ramprasad, “Electronic properties of Si: HfO[2] N. Shi , C.G. Tang and R. Ramprasad, “Electronic properties of Si: HfO22 interface”, in preparation interface”, in preparation[3] N. Shi and R. Ramprasad, "Dielectric properties of nanoscale multi-component system: A first [3] N. Shi and R. Ramprasad, "Dielectric properties of nanoscale multi-component system: A first
principles computational study", principles computational study", J. Computer-Aided Materials DesignJ. Computer-Aided Materials Design[4] M. Yu, G. Fernando, R. Li, F. Papadimitrakopoulos, N. Shi and R. Ramprasad, "Discrete size series [4] M. Yu, G. Fernando, R. Li, F. Papadimitrakopoulos, N. Shi and R. Ramprasad, "Discrete size series
of CdSe quantum dots: A combined computational and experimental investigation", of CdSe quantum dots: A combined computational and experimental investigation", J. Computer-J. Computer-Aided Materials DesignAided Materials Design..
[5] N. Shi and R. Ramprasad, "Dielectric properties of Cu-phthalocyanine systems from first principles",[5] N. Shi and R. Ramprasad, "Dielectric properties of Cu-phthalocyanine systems from first principles", Appl. Phys. Lett., Appl. Phys. Lett., 8989, 102904 (2006). , 102904 (2006). [6] N. Shi and R. Ramprasad, "Atomic-scale dielectric permittivity profiles in slabs and multilayerss",[6] N. Shi and R. Ramprasad, "Atomic-scale dielectric permittivity profiles in slabs and multilayerss", Phys. Rev. B.,Phys. Rev. B., 7474, 045318 (2006). , 045318 (2006). [7] R. Ramprasad and N. Shi, "Polarizability of phthalocyanine based molecular systems: A first-[7] R. Ramprasad and N. Shi, "Polarizability of phthalocyanine based molecular systems: A first-
principles electronic structure study", principles electronic structure study", Appl. Phys. Lett., Appl. Phys. Lett., 8888, 222903 (2006)., 222903 (2006).[8] N. Shi and R. Ramprasad, "Dielectric properties of ultrathin SiO[8] N. Shi and R. Ramprasad, "Dielectric properties of ultrathin SiO22 slabs", slabs", Appl. Phys. Lett., Appl. Phys. Lett., 8787, 262102 (2005)., 262102 (2005). [9] R. Ramprasad and N. Shi, "Scalability of phononic crystal heterostructures", [9] R. Ramprasad and N. Shi, "Scalability of phononic crystal heterostructures", Appl. Phys. Lett., Appl. Phys. Lett., 8787, 111101 (2005). , 111101 (2005). [10] R. Ramprasad and N. Shi, "Dielectric properties of nanoscale HfO[10] R. Ramprasad and N. Shi, "Dielectric properties of nanoscale HfO22 slabs", slabs", Phys. Rev. B., Phys. Rev. B., 7272, 052107 , 052107
(2005).(2005).
electronicstructure
mesoscopicregime
macroscopicregime
1
10-3
10-6
10-9
10-12 10-9 10-6 10-3 1 t[s]
L[m]Thermodynamics
Classical mechanics
Electronic structure methods
kinetic Monte Carlo simulations
Electronic structure simulation based on Density Functional theory
Computational Materials Computational Materials “Landscape”“Landscape”
Density Functional Theory (DFT)Density Functional Theory (DFT) Alternative formulation of Quantum MechanicsAlternative formulation of Quantum Mechanics Hohenberg-Kohn-Sham equations for non-interacting Hohenberg-Kohn-Sham equations for non-interacting
electrons in an effective potential:electrons in an effective potential:
The effective potential contains three contributions:
Self-consistent solution of Kohn-Sham equations resolution results in i, i, total energy
Walter Kohn received the Nobel prize in 1998 for the development of DFT
Density Functional Theory Density Functional Theory (DFT)(DFT)
DFT-Properties:• Total energy
• Forces
• Structure determination
• Charge density, dipole moments
Extensions and enhancements: Local polarization profile Band edge variations, band offsets Electronic structure, defect state energies Electron-Phonons coupling
OutlineOutline Motivation Motivation
Modern microelectronicsModern microelectronics High energy density storage systemsHigh energy density storage systems
Objectives & methodologyObjectives & methodology
Applications & ResultsApplications & Results High-k dielectrics for modern microelectronicsHigh-k dielectrics for modern microelectronics
Position dependent dielectric constant profile in Position dependent dielectric constant profile in heterostructureheterostructure
Local band edges profile in heterostructureLocal band edges profile in heterostructure
High energy density storage industryHigh energy density storage industry Molecular compositesMolecular composites Position dependent permittivity in polymer:oxide Position dependent permittivity in polymer:oxide
heterostructureheterostructure Local band edges in polymer:oxide compositesLocal band edges in polymer:oxide composites
Future workFuture work
Surface/Interface effects in modern Surface/Interface effects in modern microelectronicsmicroelectronics
Bulk high k oxide Bulk high k oxide dielectric properties have dielectric properties have been well determined been well determined ((Zhao X and Vanderbilt D, Physl Rev. B, 2002)
Dielectric properties and Dielectric properties and polarization different at polarization different at surface/interfacesurface/interface
Prior work: Prior work: calculate calculate dipole moment as a dipole moment as a function of slab thicknessfunction of slab thickness
Dependence of dipole Dependence of dipole moment versus slab moment versus slab thickness provide bulk thickness provide bulk and surface propertiesand surface properties
Ele
ctric
fie
ld
Bulkpolarization
Surface polarization
x
z
y
Dipole moment density as a function of slab thickness
Example: α-Quartz SiO2 (0001) thin film
Dielectric constant obtained from slopeThis work: 4.69Experiment: 4.5
HfO2 slab shows similar behavior
Shi N. & Ramprasad. R. Appl. Phys. Let. 87, 262102 (2005)Ramprasad. R. & Shi N. Phys. Rev. B 72, 052107 (2005)
slab thickness (Å)
0 5 10 15 20 25
Dip
ole
mo
men
t d
en
sit
y (1
0-12 C
/m)
0
2
4
6
8
10
12
14
16
18
None zero y-intercept: surface contribution
Slope: bulk polarization
Surface/Interface effects in modern Surface/Interface effects in modern microelectronicsmicroelectronics
Position dependent dielectric Position dependent dielectric permittivity: Density Functional permittivity: Density Functional
TheoryTheory Application of finite electric field results in Application of finite electric field results in
charge density displacementcharge density displacement Position dependent polarization:Position dependent polarization:
Position dependent dielectric permittivity:Position dependent dielectric permittivity:
Efficient method has been developed to Efficient method has been developed to calculate calculate position dependentposition dependent polarization & polarization & permittivitypermittivity
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904 (2006) N. Shi and R. Ramprasad, J. Computer-Aided Materials Design (2006)
Position Dependent Dielectric Position Dependent Dielectric ConstantConstant
Si:SiO2 interface y
x
z
Si atom
Si atom O atom
Electric field
Si SiO2
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904 (2006) N. Shi and R. Ramprasad, J. Computer-Aided Materials Design (2006)
Position Dependent Dielectric Constant:Position Dependent Dielectric Constant: Si:SiO2 interface
Si SiO2
yx
z
Polarization as a function of z
z (Å)
0 10 20 30 40
Po
lari
zati
on
(×10
-3C
/m2 )
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Dielectric enhancements at the surface/interface are consistent with expt.(Perkins C. M. et al Appl. Phys. Lett. 2001)
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904 (2006)
Dielectric constant as a function of z
z (Å)
0 10 20 30 40
Die
lectr
ic c
on
sta
nt
0
2
4
6
8
10
12
14
16
Expt: SiO2
Expt: Si
Local band edges variationLocal band edges variation
Interfacial band edges variation at atomic scaleInterfacial band edges variation at atomic scale Conventional band line-up method only predicts band offsetsConventional band line-up method only predicts band offsets ((P.Peacock, K. Xiong, K. Tse and J. Robertson, Phys. Rev. B 2006)
Layer-decomposed Density of States (LaDOS) methodLayer-decomposed Density of States (LaDOS) method Total density of states (DOS) is decomposed in terms of it’s Total density of states (DOS) is decomposed in terms of it’s
origin from the various atoms of the system on a layer-by-origin from the various atoms of the system on a layer-by-layer basislayer basis
Band edges profile at the surface and interfaceBand edges profile at the surface and interface
Band offsets at interface can be accurately determinedBand offsets at interface can be accurately determined
Valence band offset: 3.1 eV Expt.: 3.0-3.3eV
Local band edges of Si:HfOLocal band edges of Si:HfO22 interfaceinterface
Band edges variations across the surfaces and interfaces
(M.Oshima et al, Appl. Phys. Lett. 2003)
OutlineOutline Motivation Motivation
Modern microelectronicsModern microelectronics High energy density storage systemsHigh energy density storage systems
Objectives & methodologyObjectives & methodology
Applications & ResultsApplications & Results High-k dielectrics for modern microelectronicsHigh-k dielectrics for modern microelectronics
Position dependent dielectric constant profile in Position dependent dielectric constant profile in heterostructureheterostructure
Local band edges profile in heterostructureLocal band edges profile in heterostructure
High energy density storage systemsHigh energy density storage systems Molecular compositesMolecular composites Polymer:oxide heterostructurePolymer:oxide heterostructure
Future workFuture work
Structure of Cu-PhthalocyanineCu-Phthalocyanine monomer (CuPc)z
x
y
C atom
H atom
N atom
Cu atomDielectric
tensor: εCuPc,
εCuPc
Central atom can be metal (Cu, Mg, La, …) or metal-free (H2)
Molecular composites:Molecular composites:Dielectric Constants of Cu-Phthalocyanine polymer Dielectric Constants of Cu-Phthalocyanine polymer
CompositesComposites
Molecular composites:Molecular composites:Dielectric Constants of Cu-Phthalocyanine polymer Dielectric Constants of Cu-Phthalocyanine polymer
CompositesComposites High dielectric constant has observed in CuPc High dielectric constant has observed in CuPc
compositecomposite ( Hari Singh Nalwa, handbook of low and high dielectric constant materials and their applications)
Prior semi-classical simulation indicatesPrior semi-classical simulation indicates:: (R. Ramprasad and N. Shi, Appl. Phys. Lett. 89, 102904 2006)
εεCuPcCuPc~( 20-10 ); ~( 20-10 ); εε
CuPcCuPc~( Infinity-3 ) from classical ~( Infinity-3 ) from classical ellipsoid model for isolated CuPc moleculeellipsoid model for isolated CuPc molecule
Full “Full “ab initioab initio” method” method was applied to was applied to accurately determine the dielectric properties of accurately determine the dielectric properties of isolated molecule isolated molecule
Position dependentPosition dependent permittivity for CuPc permittivity for CuPc
Isolated CuPc Monomer : The Local Isolated CuPc Monomer : The Local PermittivityPermittivity
CuPc
||CuPc
15|| CuPc
Electric field
x
z
Ele
ctri
c fi
eld
2 CuPc
comp
||comp
Dielectric tensor of isolated CuPc moleculeDielectric tensor of isolated CuPc molecule: : εεCuPcCuPc~15, ~15,
εεCuPcCuPc~2~2
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904 (2006) R. Ramprasad and N. Shi, Appl. Phys. Lett. 89, 102904 (2006)
Position dependent dielectric constant in Position dependent dielectric constant in polymer:oxide compositespolymer:oxide composites
Polymer chain:SiO2 interface
y
x
z
Si atom
O atomH atomC atom
Electric field
Si atom
Polymer SiO2
= 0Eapplied/(0Eapplied – P)
yx
z
Interior region: dielectric properties close to single component bulk value
Surface/Interface region: dielectric constant enhancement is consistent with expt. (P.Murugarai et al., J. Appl. Phys. 2005)
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904 (2006)
Polymer SiO2
Dielectric constant as a function of z
z (Å)
20 30 40 50 60 70
Die
lectr
ic c
on
sta
nt
0
1
2
3
4
5
6
7
Expt: SiO2
Expt: Polymer
Position dependent dielectric constant in Position dependent dielectric constant in polymer:oxide compositespolymer:oxide composites
Polymer chain:SiO2 interface
Local band edges in polymer: oxide Local band edges in polymer: oxide composites SiOcomposites SiO2 2 : vinylsilanediol : : vinylsilanediol :
polymerpolymer
Interaction of the phonons in SiO2 with the interface states?
Band gap of polyethylene
Valence band offset
Defect state at interface: Electron trap Band gap variation across interface
SiOSiO22:vinylsilanediol:C:vinylsilanediol:C66HH11
44
Dielectric properties of Si:HfODielectric properties of Si:HfO22 heterojuncitonheterojunciton
Position dependent dielectric constant Position dependent dielectric constant profileprofile Complex interface between Si and HfO2
New phases and defects form at the interface
Effects of defects and interfacial layer on dielectric properties and local band edge
positions ?
Future workFuture work
Dielectric tensor of isolated CuPc moleculeDielectric tensor of isolated CuPc molecule Low dielectric constant obtained: Low dielectric constant obtained: εε
CuPcCuPc~15, ~15, εεCuPcCuPc~2 ~2
BUT it is the dielectric constant for monomer only!BUT it is the dielectric constant for monomer only! Pc monomer Pc monomer can oligomerize & stack ( Hari Singh Nalwa, handbook of low and high dielectric constant materials and their applications)
Different arrangement of the Pc monomersDifferent arrangement of the Pc monomers Stacking may result in increased dielectric constant, but Stacking may result in increased dielectric constant, but
also increased losses: also increased losses: Stacked CuPc & HStacked CuPc & H22Pc sheetsPc sheets
Future work:Future work:The Origin of High Permittivity of CuPc ?The Origin of High Permittivity of CuPc ?
N
NN
N
N
NN N
N
NN
N
N
NN N
N
NN
N
N
NN N
N
NN
N
N
NN N
HOOC COOH HOOC COOH
COOH
COOH
COOH
COOH
COOHHOOCCOOHHOOC
HOOC
HOOC
HOOC
HOOC
M
M
M
M
M = Co2+, Cu2+, Ni2+
C
O
OO N
styrene or isoprene
TMPc TMPcNMRP, 110 °CC
O
OO N
PS or PI
A
B
0 5 10 15 20 25
50
100
150
200
250
RI (
a.u.
)
Retension time (min)
unfunc.Cu-TPc
Cu-TPc(C18)16C - SEC
(Q. M. Zhang et al , Nature, 2002) (M. guo et al , Jacs, 2006)
Future Work:Future Work: Dielectric breakdown in PE (PVDF) with SiODielectric breakdown in PE (PVDF) with SiO22
nanofillernanofiller
Electron-Phonon coupling Electron-Phonon coupling Phonon frequency and eigenmodes will be determinedPhonon frequency and eigenmodes will be determined Atoms will be displaced according to the phonon eigenmodesAtoms will be displaced according to the phonon eigenmodes Electronic level shifts provide the degree of couplingElectronic level shifts provide the degree of coupling
The defects state can act as the electron traps
The energy of “hot” electrons can be lost by interaction with phonon in SiO2
Other inorganic dielectrics (Al2O3) will be considered to assess the role played by SiO2
Systematic investigation of breakdown increase mechanism to aid the Systematic investigation of breakdown increase mechanism to aid the design of future dielectric materialsdesign of future dielectric materials
SiOSiO22:vinylsilanediol:C:vinylsilanediol:C66HH1144
AcknowledgementsAcknowledgements
I wish to express my sincere gratitude to my advisors, Dr. Rampi Ramprasad, Dr. Pamir S. Alpay, Dr. Bryan D. Huey, Dr. Steve Boggs and Dr. Puxian Gao for all the help and guidance they offered throughout this study.
I would like to thank Dr. Gayanath Fernando, Dr. Lei Zhu, and Dr. Thomas A. P. Seery whose suggestions and guidance was always much appreciated.
I would like to give thanks to my friends and our group members: Haibo Qu, Zhangtang Luo, Shurui Shang, Chunguang Tang, and Thomas Sadowski with their suggestions and discussions.
Partial support of this work by grants from the ACS Petroleum Research Fund and the Office of Naval Research is gratefully acknowledged.
Atomic-level Models – Silane & Atomic-level Models – Silane & PolymerPolymer
Silane-based precursors Silane-based precursors are used to create sites for are used to create sites for the subsequent binding of the subsequent binding of polymers such as polymers such as polyethylenepolyethylene Here, we have studied Here, we have studied
Silane (SiHSilane (SiH44) and ) and Vinylsilanediol Vinylsilanediol (HSi(OH)(HSi(OH)22CH=CHCH=CH22))
A polyethylene chain is A polyethylene chain is modeled using Cmodeled using C66HH14, 14, pvdf pvdf chain is modeled using chain is modeled using CC66HH77FF77
SiH4
(Silane)
HSi(OH)2CH=CH2
(Vinylsilanediol)
C6H7F7
Si
H
C
O
C6H14
Attachment of silanes to SiOAttachment of silanes to SiO22 nanoparticle & incorporation of nanoparticle & incorporation of
SiOSiO22 into PE into PE
+ +
Position Dependent Dielectric Position Dependent Dielectric ConstantConstant
(Covalent Single-component (Covalent Single-component Systems)Systems)
System
“Supercell”
Electric fieldz
x
y
In covalent systems, ionic contribution to dielectric constant is negligibleSurface unsaturations result in higher polarizability
Si
Silicon slab Polymer (C12H26) slab
Position Dependent Dielectric Position Dependent Dielectric ConstantConstant
(Ionic Single-component Systems)(Ionic Single-component Systems)
Bulk properties recovered in the slab interiorIn ionic systems, ionic contribution to dielectric constant is significant
Surface unsaturations result in higher polarizability
SiO2 slab (-quartz)SiO2 slab (-cristobalite)
Density of states for SiODensity of states for SiO22 bulkbulk
Eg(bulksio2)=6.06 eV compare with other DFT-LDA=5.48 eV;
Giant Dielectric Constants in Giant Dielectric Constants in Cu-Phthalocyanine (CuPc) Cu-Phthalocyanine (CuPc)
CompositesComposites Zhang Zhang et alet al
Atomic/molecular origins of high dielectric constant?Atomic/molecular origins of high dielectric constant?
Layer-decomposed Density of States (LaDOS) Layer-decomposed Density of States (LaDOS) – SiO– SiO22 surface surface
Bulk SiO2
band gap
Deviations from bulk band gap can be seen close to surfaces
These manifest as the extra features in the total DOS of previous slides
Atomic RelaxationAtomic RelaxationIt is necessary to relax the forces on the atoms in order to find the lowest energy ground state of the crystal.
Calculate the forces on the atoms:
The ions are so heavy that they can be considered classical
Move the atoms according to the discretized version of Newton’s second law:
Atomic RelaxationAtomic RelaxationTo get a rapid convergence it is necessary to have a good choice of the step length.
However, the system might get trapped in a local minima, so it is sometimes necessary check different reconstructions and compare the surface energies!
Local minimaGlobal minima