Carbon and Hybridization

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Organic Semiconductor EE 4541.617A 2009. 1^stSemester

2009 3 10

Changhee Lee, SNU, Korea 1/22

Changhee Lee

School of Electrical Engineering and Computer Science Seoul National Univ.

[email protected] 2009. 3. 10.

Carbon and Hybridization

Electronic Configuration of carbon: C=1s

²

2s

²

2p

²

2s 2p

hybridization: sp, sp

²

, sp

³

~4 eV

Covalent bonding energy for the s orbital:

3~4 eV per bond

2s y p, p , p

“In carbon, three possible hybridizations occur: sp, sp

²

, and sp

³

; other group IV elements such as Si, Ge exhibit primarily sp

³

hybridization. Carbon differs from Si and Ge insofar as carbon does not have inner atomic orbitals except for the spherical 1s orbitals, and the absence of nearby inner orbitals facilitates hybridizations involving only valence s and p orbitals for carbon.”

Ref. R. Saito et al.“Physical Properties of Carbon Nanotubes” (Imperial College Press, 1998, Singapore) p.5.

+ = 2 ( )

1

s

1

φ φ

p_x

ϕ = +

+ =

0

, 0 ,

1

, 1

: lity

Orthonorma ϕ

₁

ϕ

₁

= ϕ

₂

ϕ

₂

= ϕ

₁

ϕ

₂

= ϕ

₂

ϕ

₁

= sp hybridization

) 2 (

1 2

s

2

φ φ

p_x

ϕ = −

(2)

Ethylene (C

₂

H

₄

)

1 Molecules: Chemical Bonds

π∗ (antibonding orbital) C C

p

_z

2 β p

_z

Energy

β α −

−

= E

β

) 2 (

1

2 1

*

φ φ

ψ

_π

= −

Changhee Lee, SNU, Korea 3/22

) 2 (

1

2

1

φ

φ ψ

_π

= +

π (bonding orbital) C C

β α +

+

= E

Benzene Molecule

Number of π-electrons: N=6 ), (n 0 , 1, 2, 3)

6 cos( 2

2 = ± ±

+

= n

E α β π

β

α − 2 E

β α +

β α −

β α +

β α −

+1 - 1

+2 - 2

3

6 2π

β β α −

β α − 2

HOMO LUMO

Changhee Lee, SNU, Korea

Molecular orbitals

4/22

β α + 2 β

α +

Energy states β

α +

0 6

β α + 2

β

α + HOMO

R. M. Nix, An Introduction to Molecular Orbital Theory, (http://www.chem.qmul.ac.uk/software/download/mo/)

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π^∗band

E

_g

∝ 1/Ν

_π

Polyacenes and para-phenyls

Anthracene

Naphthalene Tetracene Pentacene

Biphenyl P-Terphenyl

πband

π^∗band

LUMO

Changhee Lee, SNU, Korea 5/22

Energy Band Structure

Poly(p-phenylene) PPP

p y

P-Quaterphenyl

HOMO E

_g

πband

0

2

(eV)

HOMO-LUMO gaps of polyacenes

HOMO-LUMO gap decreases with increasing π-conjugation.

4

6

8

lectron binding energy (

Gas Solid

Eg~5 3.9 3.1 2.2

Anthracene

Naphthalene Tetracene Pentacene

Benzene 10

E ^Gas

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Widths of HOMO and LUMO Bands

LUMO

HOMO

naphthalene anthracene tetracene pentacene

Y. C. Cheng, et al., J. Chem. Phys. 118,3764 (2003)

Molecules Æ Macromolecules: HOMO, LUMO and Bands

Keep adding molecules

erg y π∗ band

E

LUMO

En e

π band

E

_g

HOMO

• The average energy separation between MOs decrease as n increases ÆFormation of bands.

• The HOMO-LUMO separation, ∆E = EHOMO – ELUMO, decreases as n increases.

• Energetically favored electron excitation is from the HOMO to the LUMO

• The interchain transfer integral (t) expresses the ease of charge transfer between two interacting chains: The larger the band- width (the magnitude of transfer integral), the higher the mobility.

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π-conjugated Polymers: Energy bandgap

n E K

n

E

_g^opt

( ) =

_g^opt

( ∞ ) −

chain length n Energy gap (HOMO-LUMO) decreases with increasing π-conjugation.

E (k)

a

Equidistant C-C bond

1D metal

1-d system

E

_F

a

− π

a 2

− π 0

a 2

π

a π

Wavevector k

(6)

2a

Bond alternation (dimerization)

semiconductor a

Equidistant C-C bond

1-D metal

E = E

_pz

- β - 2 t cos ka

Peierls instability ÆEnergy Band gap

Sir Rudolf E. Peierls

(CH)

_x

E

_F

E

_g

Peierls Gap

E (k)

1907-1995

0 π/2a

−π/2a

−π/a π/a

Wavevector k

R.E. Peierls Quantum Theory of Solids(Oxford University, London Chap.5(1955).

M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 82, 1959

(1999)

Organic Semiconductor EE 4541.617A 2009. 1^stSemester 4.0

3.5

3.0 _R ^S ⁿ ^R ⁿ

PPP 3.0 eV PPV 2.4 eV Poly(3-octylthiophene)

P3OT 2.21 eV

Poly(2,5-pyridinediyl) PPY 3.1 eV MEH-PPV

2.25 eV

PFO 3.01 eV

n n

N N

π- π* Energy Gap of Conjugated Polymers

2.5 2.0 Band Gap (eV) 1.5

n

R ⁿ ⁿ

n OR

RO

S n

trans-Polyacetylene PA 1.5 eV

Polydiacetylene PDA 1.7 eV

Polythiophene PT 2.0 eV Poly(thienylenevinylene)

PTV 1.8 eV

Changhee Lee, SNU, Korea 12/22

1.0 0.5

0.0Ref. N. C. Greenham and R. H. Friend, Solid State Physics 49, 1 (1995) p.13; A. Monkman et al., Phys. Rev. Lett. 86, 1358 (2001)

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Polyacetylene: SSH Hamiltonian

Su-Schrieffer-Heeger Hamiltonian

) )](

( [ ) 2 (

2

, ¹ ¹^, ^, ^, ¹^,

0 2 1 . 2

s n s n s n s n n n s

n n

n n n

electronic elastic

kinetic

c c c c u u t u

K u M u

H H H H

+ + +

+ +

+

− + − +

− +

=

+ +

=

∑

∑ α

2

1 α

²

eV 4 . 1 : (CH)

_x

E

_g

∝

N b E a

c

g

= +

2 . where , 2 )]

1 1 [-(

exp 16 2 : gap Peierls

K πt λ α t λ

Δ

o

+ =

=

) (E E D

t

o

2

N

c

Conjugation length

²^t^o Δo

Δo

− 0 to

−2

π π*

o

E

g

= 2 Δ 2a

π Δ

o

Δ

o

−

t

o

− 2

0 E

^g

= 2 Δ

^o

DOS and Absorption

O

pol [2 metho 5 (2’ eth l he lo ) l 4 phen lene in lene]

Density of States (DOS):

Square-root singularity in 1-d.

T. W. Hagler et al., Phys. Rev. B 51, 14199 (1995)

dE E E

g

E E dN

D = ( ) ∝ 1 − )

(

poly[2-methoxy-5-(2’-ethyl-hexyloxy)-l,4-phenylene vinylene]

MEH-PPV

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PL and Absorption of Conjugated Polymers

poly (9-hexyl-9-(2'-ethyl-hexyl)-fluorene-2,7-diyl) (HEH-PF)

E. K. Miller, G. S. Maskel, C. Y. Yang, A. J. Heeger, Phys. Rev. B 60, 8028 (1999)

//

poly(9,9-dioctylfluorene) PFO

Polarized absorption, PL and EL

C₈H₁₇ C₈H₁₇

⊥

//

K. S. Whitehead, M. Grell, D. D. C. Bradley, M. Jandke and P. Strohriegl, App. Phys. Lett. 76, 2946 (2000).

⊥

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• Strong electron-phonon coupling:

π-electron bond densities directly determine the geometric structure, e.g., butadiene, C

⁴

H

⁶

.

Electron-Phonon coupling

1.33 Å

1.33 Å 1.47 Å

• Vibronic progressions in optical absorption and photoluminescence spectra

• Stokes shift between optical absorption and emssion

* Charge transfer or low energy charge-excitations (via dong or photoexcitation) strongly affects the p-electron bond densities Æ geometric structure.

Stokes shift between optical absorption and emssion.

• Polaron formation

A B

S

⁰

Polyacetylene (CH)

_x

Soliton

S (neutral Soliton)

π∗-band

π∗-band π∗-band

π-band

S

⁺

Charge Q = +1

Spin S = 0 π-band

S

⁰

Charge Q = 0

Spin S = 1/2

S - Charge Q = -1

Spin S = 0

π-band

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π∗-band π∗-band

P−

E

P+

E

+

−−

= _P _P

g E E

E

Polaron

Polaron = charge + lattice distortion

hole polaron (P⁺) electron polaron (P^-)

π-band π-band

π-band π-band π-band

hole polaron (P⁺) π∗-band

electron polaron (P^-) π∗-band E_optical

π∗-band Singlet exciton (P^-···P⁺)

P−

E

P+

E

E_g

Exciton Energies of π -Conjugated Polymers

A. Monkman et al., Phys. Rev. Lett. 86, 1358 (2001)

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Organic Semiconductor EE 4541.617A 2009. 1^stSemester 1.0

0.8 0.6 0.4

orbance (arb. unit)

Alq3

N O

N O N OAl

E_optical~ 2.75 eV

Bandgap, Exciton binding energy

0.2 0.0

Abso

700 600 500 400 300

Wwavelength (nm)

optical

S. F. Alvarado, L. Rossi, P. Muller, P. F. Seidler, W. Riess, IBM J. Res. Dev. 45,89 (2001)

Alq3

From z–V measurements, E_gsp= 2.96 ±0.13 eV.

Threshold for optical absorption: Ea = 2.75 eV, ÆE_b= 220 ±130 meV.

Energy levels of π-conjugated molecule in the gas, crystalline and amorphous state

eff b eff G

S

I P E

I = −

⁺

− (

⁺

) Solid-state ionization potential

•Weak van der Waals interaction between molecules ÆEach molecule keep its molecular levels which are shifted due to the interaction with surrounding molecules in the solid-state.

eff b eff G

S

A P E

A = +

⁻

+ (

⁻

) Solid-state electron affinity

gy level

Gaussian density of localized states FWHM: ~ 200 meV

Ener g

Density of state

transport states trap

states impurity trap

states