Transcript Density functional theory calculation of dielectric

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

Motivation


Outline
Modern microelectronics
High energy density storage systems

Objectives & methodology

Applications & Results

High-k dielectrics for modern microelectronics
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

High energy density storage systems



Position dependent dielectric constant profile in heterostructure
Local band edges profile in heterostructure
Molecular composites
Polymer:oxide heterostructures
Future work
Motivation: Modern microelectronics
High dielectric constant (High-k) materials

“Moore’s 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 ?
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?
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?
Motivation: Energy density storage system
High 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?
Objectives
Development of new first principles computational methods
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
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Position dependent dielectric constant profiles
Local band edges variation
Electron-Phonon interaction
Applications & Results
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Si:SiO2 and Si:HfO2 heterostructures
CuPc molecular composite and silica nanoparticle filled polymer
composite
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. ComputerAided 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 firstprinciples 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).
Computational Materials “Landscape”
L[m]
Thermodynamics
1
macroscopic
regime
10-3
10-6
mesoscopic
regime
kinetic Monte Carlo
simulations
10-9 electronic
structure
10-12 10-9 10-6 10-3
Classical mechanics
Electronic structure methods
1
t[s]
Electronic structure simulation based on Density Functional theory
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
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

Motivation


Outline
Modern microelectronics
High energy density storage systems

Objectives & methodology

Applications & Results

High-k dielectrics for modern microelectronics



High energy density storage industry




Position dependent dielectric constant profile in heterostructure
Local band edges profile in heterostructure
Molecular composites
Position dependent permittivity in polymer:oxide heterostructure
Local band edges in polymer:oxide composites
Future work
Surface/Interface effects in modern microelectronics

z
Bulk high k oxide dielectric
properties have been well
determined (Zhao X and Vanderbilt D,
Physl Rev. B, 2002)
y
Surface
polarization
Bulk
polarization
Electric field
x

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
Surface/Interface effects in modern microelectronics
Dipole moment density (10-12 C/m)
Example: α-Quartz SiO2 (0001) thin film
18
16
Dielectric constant obtained from
slope
This work: 4.69
Experiment: 4.5
14
12
10
8
Slope: bulk polarization
6
HfO2 slab shows similar behavior
4
2
None zero y-intercept: surface contribution
0
0
5
10
15
20
25
slab thickness (Å)
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)
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)
Position Dependent Dielectric Constant
Si:SiO2 interface
x
y
Si atom
O atom
z
Si atom
Si
SiO2
Electric field
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: Si:SiO2 interface
x
y
z
Si
Polarization as a function of z
SiO2
Dielectric constant as a function of z
16
1.6
14
1.4
Dielectric constant
-3
Polarization(×10 C/m2)
1.8
1.2
1.0
0.8
0.6
0.4
0.2
Expt: Si
12
10
8
6
Expt: SiO2
4
2
0.0
-0.2
0
10
20
30
40
0
0
z (Å)
10
20
30
40
z (Å)
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)
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 it’s origin from the
various atoms of the system on a layer-by-layer basis

Band edges profile at the surface and interface
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Band offsets at interface can be accurately determined
Local band edges of Si:HfO2 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
Outline

Motivation


Modern microelectronics
High energy density storage systems

Objectives & methodology

Applications & Results

High-k dielectrics for modern microelectronics



High energy density storage systems



Position dependent dielectric constant profile in heterostructure
Local band edges profile in heterostructure
Molecular composites
Polymer:oxide heterostructure
Future work
Molecular composites:
Dielectric Constants of Cu-Phthalocyanine polymer Composites
Structure of Cu-Phthalocyanine monomer (CuPc)
y
z
x
Dielectric tensor:
εCuPc, εCuPc
Cu
atom
H atom
N atom
C atom
Central atom can be metal (Cu, Mg, La, …) or metal-free (H2)
Molecular composites:
Dielectric 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)

εCuPc~( 20-10 ); ε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
Isolated CuPc Monomer : The Local Permittivity
z
||
 comp
x
Electric field

 comp
Electric field
||
 CuPc

 CuPc

  CuPc
2
||
  CuPc
 15
Dielectric tensor of isolated CuPc molecule: εCuPc~15, εCuPc~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 polymer:oxide composites
Polymer chain:SiO2 interface
x
y
z
C atom
H atom
O atom
Si atom
Polymer
Electric field
SiO2
Si atom
Position dependent dielectric constant in polymer:oxide composites
Polymer chain:SiO2 interface
x
y
z
Polymer
SiO2
Dielectric constant as a function of z
7
Dielectric constant
6
= 0Eapplied/(0Eapplied – P)
5
Expt: SiO2
4
Interior region: dielectric properties
close to single component bulk value
3
Expt: Polymer
2
1
0
20
30
40
50
60
70
Surface/Interface region: dielectric
constant enhancement is consistent
with expt. (P.Murugarai et al., J. Appl. Phys.
2005)
z (Å)
N. Shi and R. Ramprasad, Phys. Rev. B. 89, 102904 (2006)
Local band edges in polymer: oxide composites
SiO2 : vinylsilanediol : polymer
SiO2:vinylsilanediol:C6H14
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?
Future work
Dielectric properties of Si:HfO2 heterojunciton

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 ?
Future work:
The Origin of High Permittivity of CuPc ?


Dielectric tensor of isolated CuPc molecule

Low dielectric constant obtained: εCuPc~15, εCuPc~2

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)
Future Work:
Dielectric breakdown in PE (PVDF) with SiO2 nanofiller
SiO2:vinylsilanediol:C6H14
 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
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.
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)2CH=CH2)
A polyethylene chain is modeled
using C6H14, pvdf chain is
modeled using C6H7F7
SiH4
(Silane)
H
HSi(OH)2CH=CH2
(Vinylsilanediol)
C
Si
O
C6H14
C6H7F7
Attachment of silanes to SiO2 nanoparticle &
incorporation of SiO2 into PE
+
+
Position Dependent Dielectric Constant
(Covalent Single-component Systems)
“Supercell”
x
y
z
System
Electric field
Silicon slab
Polymer (C12H26) slab
Si
In covalent systems, ionic contribution to dielectric constant is negligible
Surface unsaturations result in higher polarizability
Position Dependent Dielectric Constant
(Ionic Single-component Systems)
SiO2 slab (b-cristobalite)
SiO2 slab (a-quartz)
Bulk properties recovered in the slab interior
In ionic systems, ionic contribution to dielectric constant is significant
Surface unsaturations result in higher polarizability
Density of states for SiO2 bulk
Eg(bulksio2)=6.06 eV compare with other DFT-LDA=5.48 eV;
Giant Dielectric Constants in CuPhthalocyanine (CuPc) Composites

Zhang et al

Atomic/molecular origins of high dielectric constant?
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
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
Newton’s second law:
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!