properties of nanoscale dielectrics from first principles computations properties of nanoscale...

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



Objectives & methodologyObjectives & methodology




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


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)



Objectives & methodologyObjectives & methodology




High energy density storage systemsHigh energy density storage systems Molecular compositesMolecular composites Polymer:oxide heterostructurePolymer:oxide heterostructure


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 ?


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

+ +


(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


(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

properties of nanoscale dielectrics from first principles computations properties of nanoscale...

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high dielectric constants

materials example of

oxide dielectric properties

oxide heterostructures

constant capacitance

band gap

local band edges profiles

conduction band offset