Density functional theory calculation of dielectric properties of thin film

1
Properties of nanoscale dielectrics from first
principles computations
Ph. D. Dissertation Proposal
Ning Shi Department of Chemical, Materials
Biomolecular Engineering Institute of Materials
Science, University of Connecticut Major
Advisor Prof. Rampi Ramprasad Associate Advisor
Prof. Pamir S. Alpay Associate Advisor Prof.
Bryan D. Huey
2
Outline

• Motivation
• Modern microelectronics
• High energy density storage systems
• Objectives methodology
• Applications Results
• High-k dielectrics for modern microelectronics
• Position dependent dielectric constant profile in
  heterostructure
• Local band edges profile in heterostructure
• High energy density storage systems
• Molecular composites
• Polymeroxide heterostructures
• Future work

3
Motivation Modern microelectronics High
dielectric constant (High-k) materials

• Moores Law The International Technology
  Roadmap for Semiconductors requires continued
  shrinkage of electronic devices (John Roberson,
  Rep. Prog. Phys. 2006)
• Decrease A for constant capacitance
• Replace SiO2 by other dielectrics (e.g., HfO2, Hf
  silicates, etc.) with larger dielectric constant

(Craig R. Barrett MRS bulletin 2006)

• Bulk high k oxide dielectric properties are
  well determined (Zhao X and Vanderbilt D, Physl
  Rev. B, 2002)

• Dielectric properties of thin film and
  variation at the interface ?

4
Motivation Modern microelectronics Band 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)

Desirable
Undesirable

• Conventional computational approach only
  predict band gap, band offsets
• (V. Fiorentini and G. Gulleril, Physl Rev. B,
  2002 )

The local band edges profiles of the interfaces
at atomic level?
5
Motivation High energy density storage systems
High dielectric constant (High-k) materials
(Q. M. Zhang et al , Nature, 2002)
CuPc polymer composite

• Example of high-k organic composite
• Cu-phthalocyanine polymer composites shows high
  dielectric constants under certain conditions

Pure polymer

• Atomic/molecular origins of high dielectric
  constant?

6
Motivation Energy density storage systemHigh
breakdown strength polymer composites
The incorporation of SiO2 nanoparticles into
polyethylene (PE) increases the breakdown strength

• Example of high E polymer composite
• Improvement of breakdown strength in XLPE with
  SiO2 nanofiller
• The interface between SiO2 and polyethylene plays
  a critical role
• The interface states could act as potential
  electron traps, thereby scavenging hot
  electrons.
• Coupling between hot electrons in polymer and
  phonons in SiO2 can improve breakdown strength

(M. Roy et. al IEEE Trans. on Dielectrics and
Electrical Insulation. 2005)

• Atomic origins of increase of dielectric
  breakdown strength?

7
Objectives

• Development of new first principles computational
  methods
• Position dependent dielectric constant profiles
• Local band edges variation
• Electron-Phonon interaction
• Applications Results
• SiSiO2 and SiHfO2 heterostructures
• CuPc molecular composite and silica nanoparticle
  filled polymer composite

8
Publications

• 1  N. Shi and R. Ramprasad, "The intrinsic
  dielectric properties of phthalocyanine crystals
  An ab initio investigation", Phys. Rev. B, in
  print
• 2   N. Shi , C.G. Tang and R. Ramprasad,
  Electronic properties of Si HfO2 interface, in
  preparation
• 3   N. Shi and R. Ramprasad, "Dielectric
  properties of nanoscale multi-component system A
  first principles computational study", J.
  Computer-Aided Materials Design
• 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", J. Computer-Aided Materials
  Design.
• 5   N. Shi and R. Ramprasad, "Dielectric
  properties of Cu-phthalocyanine systems from
  first principles",
• Appl. Phys. Lett., 89, 102904 (2006).
• 6   N. Shi and R. Ramprasad, "Atomic-scale
  dielectric permittivity profiles in slabs and
  multilayerss",
• Phys. Rev. B., 74, 045318 (2006).
• 7    R. Ramprasad and N. Shi, "Polarizability
  of phthalocyanine based molecular systems A
  first-principles electronic structure study",
  Appl. Phys. Lett., 88, 222903 (2006).
• 8    N. Shi and R. Ramprasad, "Dielectric
  properties of ultrathin SiO2 slabs",
• Appl. Phys. Lett., 87, 262102 (2005).
• 9   R. Ramprasad and N. Shi, "Scalability of
  phononic crystal heterostructures",
• Appl. Phys. Lett., 87, 111101 (2005).
• 10  R. Ramprasad and N. Shi, "Dielectric
  properties of nanoscale HfO2 slabs", Phys. Rev.
  B., 72, 052107 (2005).

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Computational Materials Landscape
Thermodynamics Classical mechanics
kinetic Monte Carlo simulations
Electronic structure methods
Electronic structure simulation based on Density
Functional theory
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Density Functional Theory (DFT)

• Alternative formulation of Quantum Mechanics
• Hohenberg-Kohn-Sham equations for non-interacting
  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
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Density Functional Theory (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

12
Outline

• Motivation
• Modern microelectronics
• High energy density storage systems
• Objectives methodology
• Applications Results
• High-k dielectrics for modern microelectronics
• Position dependent dielectric constant profile in
  heterostructure
• Local band edges profile in heterostructure
• High energy density storage industry
• Molecular composites
• Position dependent permittivity in polymeroxide
  heterostructure
• Local band edges in polymeroxide composites
• Future work

13
Surface/Interface effects in modern
microelectronics

• Bulk high k oxide dielectric properties have been
  well determined (Zhao X and Vanderbilt D, Physl
  Rev. B, 2002)
• Dielectric properties and polarization different
  at surface/interface
• Prior work calculate dipole moment as a function
  of slab thickness
• Dependence of dipole moment versus slab thickness
  provide bulk and surface properties

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Surface/Interface effects in modern
microelectronics
Example a-Quartz SiO2 (0001) thin film

• Dielectric constant obtained from slope
• This work 4.69
• Experiment 4.5
• HfO2 slab shows similar behavior

Slope bulk polarization
None zero y-intercept surface contribution
Dipole moment density as a function of slab
thickness
Shi N. Ramprasad. R. Appl. Phys. Let. 87,
262102 (2005) Ramprasad. R. Shi N. Phys. Rev.
B 72, 052107 (2005)
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Position dependent dielectric permittivity
Density Functional Theory

• Application of finite electric field results in
  charge density displacement
• Position dependent polarization
• Position dependent dielectric permittivity
• Efficient method has been developed to calculate
  position dependent polarization permittivity

N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904
(2006) N. Shi and R. Ramprasad, J.
Computer-Aided Materials Design (2006)
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Position Dependent Dielectric Constant SiSiO2
interface
Si atom
O atom
Si atom
Electric field
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904
(2006) N. Shi and R. Ramprasad, J.
Computer-Aided Materials Design (2006)
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Position Dependent Dielectric Constant SiSiO2
interface
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)
18
Local band edges variation

• Interfacial band edges variation at atomic scale
• Conventional 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) method
  
• Total density of states (DOS) is decomposed in
  terms of its origin from the various atoms of
  the system on a layer-by-layer basis
• Band edges profile at the surface and interface
• Band offsets at interface can be accurately
  determined

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Local band edges of SiHfO2 interface

• Valence band offset
• 3.1 eV
• Expt. 3.0-3.3eV

(M.Oshima et al, Appl. Phys. Lett. 2003)
Band edges variations across the surfaces and
interfaces
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Outline

• Motivation
• Modern microelectronics
• High energy density storage systems
• Objectives methodology
• Applications Results
• High-k dielectrics for modern microelectronics
• Position dependent dielectric constant profile in
  heterostructure
• Local band edges profile in heterostructure
• High energy density storage systems
• Molecular composites
• Polymeroxide heterostructure
• Future work

21
Molecular compositesDielectric Constants of
Cu-Phthalocyanine polymer Composites
Structure of Cu-Phthalocyanine monomer (CuPc)
Dielectric tensor e?CuPc, e?CuPc
Central atom can be metal (Cu, Mg, La, ) or
metal-free (H2)
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Molecular compositesDielectric Constants of
Cu-Phthalocyanine polymer Composites

• High dielectric constant has observed in CuPc
  composite
• ( Hari Singh Nalwa, handbook of
  low and high dielectric constant materials and
  their applications)
• Prior semi-classical simulation indicates
• (R. Ramprasad and N. Shi, Appl.
  Phys. Lett. 89, 102904 2006)
• e?CuPc( 20-10 ) e?CuPc( Infinity-3 ) from
  classical ellipsoid model for isolated CuPc
  molecule
• Full ab initio method was applied to
  accurately determine the dielectric properties of
  isolated molecule
• Position dependent permittivity for CuPc

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Isolated CuPc Monomer The Local Permittivity
Dielectric tensor of isolated CuPc molecule
e?CuPc15, e?CuPc2
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904
(2006) R. Ramprasad and N. Shi, Appl. Phys.
Lett. 89, 102904 (2006)
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Position dependent dielectric constant in
polymeroxide composites Polymer chainSiO2
interface
O atom
H atom
C atom
Si atom
Si atom
Electric field
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Position dependent dielectric constant in
polymeroxide composites Polymer chainSiO2
interface
Polymer
SiO2

• e0Eapplied/(e0Eapplied P)

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)
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Local band edges in polymer oxide composites
SiO2 vinylsilanediol polymer
Band gap of polyethylene
Valence band offset
Defect state at interface Electron trap
Band gap variation across interface
Interaction of the phonons in SiO2 with the
interface states?
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Dielectric properties of SiHfO2 heterojunciton
Future work

• Position dependent dielectric constant profile
• 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 ?
28
Future workThe Origin of High Permittivity of
CuPc ?

• Dielectric tensor of isolated CuPc molecule
• Low dielectric constant obtained e?CuPc15,
  e?CuPc2
• BUT it is the dielectric constant for monomer
  only!
• Pc monomer can oligomerize stack
• ( Hari Singh Nalwa, handbook of low and
  high dielectric constant materials and their
  applications)
• Different arrangement of the Pc monomers
• Stacking may result in increased dielectric
  constant, but also increased losses
• Stacked CuPc H2Pc sheets

(Q. M. Zhang et al , Nature, 2002)
(M. guo et al , Jacs, 2006)
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Future Work Dielectric breakdown in PE (PVDF)
with SiO2 nanofiller
SiO2vinylsilanediolC6H14

• 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

• Electron-Phonon coupling
• Phonon frequency and eigenmodes will be
  determined
• Atoms will be displaced according to the phonon
  eigenmodes
• Electronic level shifts provide the degree of
  coupling

Systematic investigation of breakdown increase
mechanism to aid the design of future dielectric
materials
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Acknowledgements
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.
Thank you
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Atomic-level Models Silane Polymer

• Silane-based precursors are used to create sites
  for the subsequent binding of polymers such as
  polyethylene
• Here, we have studied Silane (SiH4) and
  Vinylsilanediol (HSi(OH)2CHCH2)
• A polyethylene chain is modeled using C6H14, pvdf
  chain is modeled using C6H7F7

HSi(OH)2CHCH2 (Vinylsilanediol)
SiH4 (Silane)
H
C
Si
O
C6H7F7
C6H14
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Attachment of silanes to SiO2 nanoparticle
incorporation of SiO2 into PE


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Position Dependent Dielectric Constant(Covalent
Single-component Systems)
In covalent systems, ionic contribution to
dielectric constant is negligible Surface
unsaturations result in higher polarizability
34
Position Dependent Dielectric Constant(Ionic
Single-component Systems)
Bulk properties recovered in the slab interior In
ionic systems, ionic contribution to dielectric
constant is significant Surface unsaturations
result in higher polarizability
35
Density of states for SiO2 bulk
Eg(bulksio2)6.06 eV compare with other
DFT-LDA5.48 eV
36
Giant Dielectric Constants in Cu-Phthalocyanine
(CuPc) Composites

• Zhang et al

• Atomic/molecular origins of high dielectric
  constant?

37
Layer-decomposed Density of States (LaDOS) SiO2
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
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Atomic Relaxation
It 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 Newtons second law
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Atomic Relaxation
To get a rapid convergence it is necessary to
have a good choice of the step length.
Local minima
Global minima
However, the system might get trapped in a local
minima, so it is sometimes necessary check
different reconstructions and compare the surface
energies!