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Organic Electronics Stephen R. Forrest Establishing Common Language Crystal Structure and Binding Chapter 1.4, 2.1-2.4 Week 1-2

Establishing Common Language Crystal Structure and Binding

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Page 1: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Establishing Common LanguageCrystal Structure and Binding

Chapter 1.4, 2.1-2.4

Week 1-2

Page 2: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Objectives: Structure of Organic Solids

• Introduce basic terminology of organic materials• Discuss relationship of crystal structure to properties• Introduce the basic terminology and concepts

of crystals and crystal lattices- Fill in the gaps

• Discuss crystal binding- Physical properties and constants

• Learn about organic lattices and their equilibrium structures- Energy minimization

• Growth and epitaxy

Page 3: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

First: Establishing a vocabulary

(Without a common language, there can be no common understanding)

• Illustration of molecular structure• Basic molecular units and structures• Standard terminologies

3

Page 4: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Benzene, phenyl, aryl

• Benzene: C6H6

• Phenyl: the phenyl group or phenyl ring is a cyclic group of atoms with the formula C6H5. Phenyl groups are closely related to benzene.

• Aryl: A functional group of the form C6H5 attached to a molecule

4

Page 5: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

• Alkanes are the simplest organic molecules, consisting of only carbon and hydrogen and with only single bonds between carbon atoms. Alkanes are the basis for naming the majority of organic compounds (their nomenclature). Alkanes have the general formula CnH2n+2.

• Polyacenes: The acenes or polyacenes are a class of organic compounds, and polycyclic aromatic hydrocarbons made up of linearly fused benzene rings.

5

Page 6: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

• Aromaticity: materials consisting of closed carbon rings where the C bonds are in resonance.

- Double-single bond structure of the molecule allows the bond arrangement to alternate between C atom pairs in the ring.

- To be aromatic the molecule must be planar and have an ODD number of π electron pairs. (see anaromatic)

• Polycyclic Aromatic Hydrocarbon (PAH): organic compounds containing only carbon and hydrogen—that are composed of multiple aromatic rings (organic rings in which the electrons are delocalized)

• Radical: A charged molecule that is either anionic or cationic. A cation is a positively charged molecule, and an anion is negatively charged. An excess electron is typically denoted by a solid dot.

Pentacene anion

Aromatics and Radicals

6

Page 7: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

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�¨Ü ����a����a�Ü ¯~S¯Ü �¨�Ü ¯À�Ü �sÜ ¯~lÜ SÈl¨Ü �T�Ü [ Ü S¦lÜ S¯Ü ¦�{~®Ü S�{�l¨Ü ¯�Ü

lSa~Ü�¯~l¦�Ü Yµ¯Ü ¯~lÜ ¯~�¦jÜSÈ�¨Ü �~¤ �¨Ü S¯Ü S�Ü S�{�lÜ�¯~l¦Ü¯~S�Ü SÜ ¦�{~¯Ü

S�{�lÜ ¯�Ü ¯~lÜ �¯~l¦Ü ¯À��Ü 8�Ü ¯~lÜ Sµ¯~�¦�¨Ü lÈ l¦��l�¯¨Ü ¯~�a��l¨¨Ü �sÜ SÜ

a¦Ì¨¯S�Ü �¨Ü �lS¨µ¦ljÜ ��Ü ¯~lÜ j�¦la¯���Ü  l¦ l�j�aµ�S¦Ü ¯�Ü ¯~lÜT[Ü  �S�l�Ü

JP¤

π-system

Electron density

Anthracene: A classic aromatic molecule

• C14H10• It is a PAH with form C4n+2H2n+4• n=number of rings

7

Page 8: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Conjugation

• a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule

• Conjugation lowers the overall energy of the molecule and increases stability.

• Conjugation is conventionally represented as having alternating single and multiple bonds.

8

Page 9: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

A Few Polyacenes

9

Benzene

Naphthalene

Anthracene

Tetracene

Pentacene

Hexacene

Pyrene

OvaleneAnthanthrene

BenzoperylenePerylene

Coronene

Page 10: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Monomer, Oligomer• Monomer: a molecular complex with a well-defined molecular weight that

consists of a single irreducible unit

• Oligomer: a molecular complex that consists of a few monomer units, where the number of monomers is, in principle, not limited but is always well defined. (e.g. dimer, trimer, tetramer, etc.)

Pt N N

N N

n

b.#a.# c.#

Pt N N

N N

n

b.#a.# c.#

mer (Greek: meros)-part

10

Page 11: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

thiophene

dibenzofuranindolizine

oxazole thiazole

imidazole isoindole

Heterocycles

Metalorganics

Ir(ppy)3 Ir(ppy)2acac

Ligand

PtOEP CuPc

Porphyrins Phthalocyanines

ligand: Latin: can be tied

Page 12: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Dendrimer, Polymer

(b)$(a)$

Pt N N

N N

n

b.#a.# c.#

• Dendrimer: An oligomer that is built with repeat units radiating (like dendrites) from a central core. Each concentric repeat unit is a generation. (a) 54 ferrocene (so named due to the 54 ferrocene groups on its periphery), and (b) a 4th generation dendrimer.

• Polymer: a molecular complex consisting of an undefined number of monomeric repeat units and hence undefined molecular weight.

12

Page 13: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

At what point does the molecular picture give way to the solid?

Eg#

BW# Conduc,on##Band#

Valence#Band#

DOS#

Energy#

(a)#

Eg#HOMO#

Energy#

HOMO:1#HOMO:2#

•  ##•  ##•  ##•  ##

•  ##•  ##•  ##•  ##

•  ##•  ##•  ##•  ##

LUMO+2#LUMO+1#LUMO#

•  ##•  ##•  ##•  ##

(b)#

DOS#Eg#

BW# Conduc,on##Band#

Valence#Band#

DOS#

Energy#

(a)#

Eg#HOMO#

Energy#

HOMO:1#HOMO:2#

•  ##•  ##•  ##•  ##

•  ##•  ##•  ##•  ##

•  ##•  ##•  ##•  ##

LUMO+2#LUMO+1#LUMO#

•  ##•  ##•  ##•  ##

(b)#

DOS#Eg#

BW# Conduc,on##Band#

Valence#Band#

DOS#

Energy#

(a)#

Eg#HOMO#

Energy#

HOMO:1#HOMO:2#

•  ##•  ##•  ##•  ##

•  ##•  ##•  ##•  ##

•  ##•  ##•  ##•  ##

LUMO+2#LUMO+1#LUMO#

•  ##•  ##•  ##•  ##

(b)#

DOS# ? ?

Page 14: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Crystal Morphologies

14

• Electrical conduction– Range from conducting to insulating

• Solid state: not liquids or gases• Organics found and exploited in all morphological types

Structure determines electronic properties

Types of solids

CrystallineAmorphous Polycrystalline

Page 15: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Crystal Structure

15

Lattice

Unit cell

Periodic arrangement of atoms in a crystal

Small volume of crystal that may be used to reproduce the entire crystal—space filling

Primitive unit cell

Smallest unit cell that describes the crystal Body centered

cubic (BCC)

Simple cubic

lattice constant

a

Lattice constant is a material parameter

Page 16: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Lattices

a"b" R=la+mb$

Translation vector: R=la+mb+nc

A translation vector moves a R point to an equivalent point in the lattice

Volume: VCell = a • (b× c)

Page 17: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Common Semiconductor Crystal Structures

17

Diamond Zinc Blende

÷øö

çèæ 0,

2,2aa

÷øö

çèæ

4,4,4

aaa

(Si, Ge) (GaAs, InP, AlSb, …)

Ga

As

Page 18: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Bravais Lattices• These lattices define the crystal structure

!

Lattice System Bravais Lattice

Triclinic

Monoclinic

Orthorhombic

Tetragonal

Rhombohedral

Hexagonal

(pcc) (bcc) (fcc)

Cubic

!

Almost all organics fallInto these lattice types

Can you think of a moleculeThat fits this structure?

coordination #=12 (fcc)

Page 19: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Reciprocal Lattice

• Condition of self transformation: ψ(r)=ψ(r+R) ~

• Then G is the reciprocal lattice vector:

• The reciprocal lattice defined by G, has an identical symmetry to the physical lattice defined by R.

• It is then straightforward to show that the primitive reciprocal lattice vectors are defined by the following relationships:

• What is the relationship between the unit cell volume in reciprocal to real space?

eiGir = eiGi(R+r )

G iR = 2π

a = 2π b× c

VCell b = 2π c × a

VCell c = 2π a × b

VCell

Page 20: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Miller Indices

20

Need a method to describe crystalline direction/planes

plane ( h k l )

direction [ h k l ]

h k l are Miller indices defining the plane or direction

Page 21: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Defining Crystal Directions and Planes

• Miller indicies

• Miller indices: h, k, l, are the lowest integers that are the inverse of the intercepts between the plane and the axes

• (a,b,c) define plane• {a,b,c} define set of equivalent planes (e.g. (100), (010), (001), etc. for cubic lattice)• [a,b,c] for lattice direction• <a,b,c> for set of equivalent lattice directions

(100)% (101)% (212)%

Page 22: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Determining Miller Indices

22

1. Find intercepts (as multiple of a lattice constant)

2. Take reciprocal

3. Multiply by lowest common denominator

x

z

y

intercepts at (1, 2, ∞)

reciprocal (1, 1/2, 0)

LCM (2, 1, 0)

(210) plane

Vector perpendicular to plane is [210] direction

Page 23: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Example: Miller Index

23

Determine the representation of the plane below

a

a

a2/3 a

x

y

z

Page 24: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Ionic Bonds

For a solid, pairwise ionic interactions must be summed over all N ions, which leads to a net attractive energy of:

Uij (r) = ± q2

4πε0 ri − rj

Uattract (r) =q2

4πε01Rij

− 1Rij − a

⎝⎜

⎠⎟

i, j

N

Similar atoms

Oppositely charged atoms

δ- δ+

NaCl (fcc)TTF-TCNQ: charge transfer complex

α fcc = 6 − 122+ 8

3− 62+ ...⎛

⎝⎜⎞⎠⎟= 1.7476

Utot (r) =σrm

− αq2

4πε01r

Uattract

Madelung Constant ⇒

Page 25: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Equilibrium Crystal Structure

∂Utot

∂r r=r0

= 0

!1#

!0.5#

0#

0.5#

1#

0# 1# 2# 3# 4# 5# 6# 7#

Poten&al)of)an)Ionic)Solid)

r/r0$Utot(r)/Utot(r

0)$

Repulsion##A6rac:on#

Utot (r0 ) = − 1σ

αq2

4πε0m⎛⎝⎜

⎞⎠⎟

m⎡

⎣⎢⎢

⎦⎥⎥

1m−1

(1−m) = αq2

4πε0m⎛⎝⎜

⎞⎠⎟1r0(1−m)

k = ∂2U(r)∂r2 r=r0

= αq2

2πε0m⎛⎝⎜

⎞⎠⎟1r03 (1−m)

Force constant

r0 =mσαq2

4πε0⎡⎣⎢

⎤⎦⎥

1/(m−1)

≈ mσαq2

4πε0⎡⎣⎢

⎤⎦⎥

1/m

Utot (r) =σrm

− αq2

4πε01r

Equilibrium condition

Page 26: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Covalent BondingShared electron systems between ionic cores

H2, Si, Ge, C….

Organic Molecules with C-C bondse.g. Anthracene

H = −

2

2m∇r2 − 2

2Mi

∇Ri

2 +V (r,Ri )i∑

HΨ(r,R) = ΕΨ(r,R)

V (r,R1,R2 ) = − q2

4πε01

r −R1

+ 1r −R2

− 1R1 −R2

⎝⎜⎞

⎠⎟

It’s complicated as N increases!

H2+

Page 27: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Solutions to the H2+ Molecule

anti-bonding orbital

bonding orbital

- Two solutions exist

electron density concentrated between ionic cores

electron density concentrated repelled

Page 28: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

van der Waals bonding• Purely electrostatic instantaneous induced dipole-induced dipole interaction

between π-systems of nearby molecules.

A"

B"

A"

B"

t=t0" t>t0"

Φ(r) = 1

4πε0ε r

qr+ p i r

r3 + 12

Qij

rirj

r5i, j∑ + ⋅⋅⋅

⎣⎢⎢

⎦⎥⎥

Multipole potential is from expansion

Monopole dipole quadropole

Medium around the dipole is polarized

p = rρ(r)d 3r∫ : Dipole moment

E(r) = 3n̂(p i n̂)− p

4πε0ε rr3

: Field from dipole moment

Er =2pcosθ4πε0ε rr

3

Eθ =psinθ4πε0ε rr

3

Eφ = 0

Page 29: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Dipole interactions

U = −p i E(r)r1"

p2" r12n̂12

p1"

r2"

O$

Fixed dipoles

Applying Boltzmann statistics to the energy as a function of angle, it can be shown:

For p1=p2

Keesom interaction:

Important relationships:

U = − 12kx2 (in one dimension for an SHO)

⇒ ′U = F = −kx⇒ ′′U = −k⇒Bulk modulus = B =Vol ′′U( ) = −Vol k( )

= force constant = compressibility of the solid

U(r12 ) = − 2p4

3 4πε0ε r( )kTr6 = − ADD

r6

E(r) = 3n̂(p i n̂)− p

4πε0ε rr3

U r12( ) = p1 i p2 − 3 n̂12 i p1( ) n̂12 i p2( )

4πε0ε rr123 = p2

4πε0ε r

p̂1 i p̂2

r123 −

3 r12 i p̂1( ) r12 i p̂2( )r12

5

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

Page 30: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Van der Waals interaction

Induced dipoles depend on the polarizability (α) of the molecule (which may different from

the medium, εr: pind (r) =αE(r)

θ" n̂12

r12$

U (r12 ) = −

Adisp

r126

: Dispersion interaction

U(r) = 4ε σr

⎛⎝⎜

⎞⎠⎟12

− σr

⎛⎝⎜

⎞⎠⎟6⎡

⎣⎢

⎦⎥ : Lennard-Jones 6-12 potential

For van der Waals, the induced dipoles are parallel (p̂1 = p̂2 )

Then our energy equation reduces to:U == p1p24πε0ε rr12

3 1− 3cosθ{ } ≈ − p1p22πε0ε rr12

3

The field from one dipole at the other: E r( ) = 3n̂ p i n̂( )− p

4πε0ε rr123 ≈ p1

2πε0ε rr123

⇒ p2 =2α p1

4πε0ε rr123

From which we get the “London interaction energy”: UvdW = − α p12

πε0ε r( )r126

Page 31: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

van der Waals Coefficients Between atoms

-1

-0.5

0

0.5

1

0 1 2 3 4 5 6 7

U(r)/U(r0)

r/r0

1/r

1/r6

Atoms i-j r0,ij

Å

ε ij

kcal mol-1 C-C 4.00 0.150 C-N 3.75 0.155 C-O 3.60 0.173 C-S 4.00 0.173 C-H 3.00 0.055 N-C 3.75 0.155 N-N 3.50 0.160 N-O 3.35 0.179 N-S 3.75 0.179 N-H 2.75 0.057 O-C 3.60 0.173 O-N 3.35 0.179 O-O 3.20 0.200 O-S 3.60 0.200 O-H 2.60 0.063 S-C 4.00 0.173 S-N 3.75 0.179 S-O 3.60 0.200 S-S 4.00 0.200 S-H 3.00 0.063 H-C 3.00 0.055 H-N 2.75 0.057 H-O 2.60 0.063 H-S 3.00 0.063 H-H 2.00 0.020

!

Ucrystal =12

U(Rij )i≠ j∑ : Equilibrium crystal structure found by calculating and then minimizing all

atom-atom potentials over N atoms in molecules in solid- Local vs. global minima?- Huge numbers of degrees of freedom (6 per molecule!)- Thermodynamics important (different structures with different kBT)

PkT

= NV

+ B2 T( ) NV

⎛⎝⎜

⎞⎠⎟2

+ B3 T( ) NV

⎛⎝⎜

⎞⎠⎟3

+ .....

Virial coeff’ts from vdWinteractions

• Deviations from ideal gas law

Coulomb=long range

vdW=short range

Page 32: Establishing Common Language Crystal Structure and Binding

Organic ElectronicsStephen R. Forrest

Hydrogen bonds

• Directional• Coulombic

UH (r) = −δ + pcosθr2

O-H bond: 1ÅO…H bond: 1.6 -1.8 Å

O − H ⋅⋅⋅O : Must be linear otherwise O-O repulsion dominates

H⋅⋅⋅O and H⋅⋅⋅N are usually only important

Precise form of potential (Coulombic, exponential) usually not critical