Introduction to Molecular Electronics

Lecture 1

Why Molecular Electronics?• Low-cost devices (OLED, RF-ID,

chemical sensors etc.)• Beyond the Moor’s law: more devices

per unit area and not only• Self-assembly: new old way to

assemble complicated devices• Complex (designer) logical functions• Interacting with living organisms: e.g.

linking biological functions and electronic readout

Conductive organic molecules

“Plastic can indeed, under certain circumstances, be made to behave very like a metal - a discovery for which Alan J. Heeger, Alan G. MacDiarmid and Hideki Shirakawa are to receive the Nobel Prize in Chemistry 2000”.

Particle in a box

• The technique:– Solve Schrodinger equation

between the walls (V=0)– Impose boundary condition at the

walls and find the coefficients

2

2ˆ ˆ

2H E H

m xψ ψ ∂= = −

∂2 2

2(0, ) 0

ikx ikxk k

k

kAe Be Em

L

ψ

ψ

−= + =

=

( ) sin( / ) 1,2,...n x C n x L nψ π= =

Particle in a box: example

• Electronic absorption of b-carotene

22 electrons fill states up to n=11

0.294nm

( )( )2

2 212 11 1

8hE E E n nmL

∆ = − = + −

Energy bands in solids

• Metal – Fermi level lies within a band• Semiconductor (or dielectric) – Fermi level lies in a gap

Metal Semiconductors

p- and n-doped semiconductors

• n-dopedP, As, Sb, Bi

• n-dopedP, As, Sb, Bi

• p-doped(B, Al, Ga, In)

• p-doped(B, Al, Ga, In)

Intermediate case: molecules

Molecular structure

• The Born-Oppenheimer approximation:nuclei can be treated as a stationary

• Valence bond theory:key concepts: spin pairing, sand p bonds, hybridization.

• Bonding-Antibonding orbitals

(1) (2) (2) (1)A B A Bψ = ±

Diatomic molecules

Hybridization

Hydrogen molecule

• Bonding-Antibonding

Bond order – a measure of net bonding in a diatomic molecule:

1 ( *)2

b n n= −

The greater the bond order the shorter the bond and the greater the bond strength

Antibondingunbounds more than bonding bounds!

Diatomic molecules

• s-orbitals are built from atomic s-orbitals and pz-orbitals.

• p-orbitals are built from atomic px and py orbitals

antibonding

bonding

Diatomic molecules

Peierls distortion• 1D delocalized

system is expected to be metallic, however

• Monoatomic metallic chain will undergo a metal-insulator transition at low temperature;

• period doubling leads to opening a gap at p/2

lowering energy

Peierls distortion

• Peierls transition in polyacetylene

Charge-transfer complexes• Charge transfer compounds are formed by two or more types of neutral

molecules one of which acts as a donor and the other is an electron acceptor

D A D A+• −•⎡ ⎤ ⎡ ⎤+ ⎯⎯→⎣ ⎦ ⎣ ⎦

Mixed stacks: not highly conductive

Segregated stacks: strong p-overlap results in delocalizing and high conductivity

Charge-transfer complexes• Example: pyrene (10-12 S·m-1)

and iodine (10-7 S·m-1) form a high conductivity complex with 1 S·m-1.

• Example: TTF (tetrathiafulvalene) and TCNQ (tetracyanoquinodimethane)

• 1:1 mixture shows conductivity of about 5·102 S·m-1 and metallic behaviour below 54K.

Doping of organic semiconductors

• As in inorganic semiconductors, impurities can be added to either transfer an electron to LUMO (p*) or remove electron from HOMO (p).

[ ] ( ) ( )[ ] ( )

2 332

y

n y n

y

n n

nyCH I CH I

CH nyNa CH Na

+ −

− +

⎡ ⎤+ ⎯⎯→⎢ ⎥⎣ ⎦

⎡ ⎤+ ⎯⎯→⎣ ⎦

• Large doping concentration is required 1-50%• Counter ions are fixed while charge on the polymer

backbone is mobile

Quantum Mechanical Tunneling

• the wave nature of electrons allows penetration into a forbidden region of the barrier

• at low voltages (V<<barrier height):

exp( )A Bdσ = −

• at higher voltages the barrier tilt should be taken into account:

202 exp( )sinh

sin( ) 2CkT CVI I BV

CkTππ

⎡ ⎤ ⎛ ⎞= − ⎜ ⎟⎢ ⎥ ⎝ ⎠⎣ ⎦

Variable range hopping

• for disordered materials the charge transfer goes by a process similar to diffusion as the mean free path is of the order of interatomic distance

1/ 40

0 exp TT

σ σ⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

• Mott equation 1/3 for 2D and ½ for 1D1/3 for 2D and ½ for 1D

Charge-space separation

2

mVJ dd

⎛ ⎞⎜ ⎟⎝ ⎠

∼

Shottky and Poole-Frenkel effects• At high applied electric fields (>107 V/m)

0.5

exp EJkTβ⎛ ⎞

∝ ⎜ ⎟⎝ ⎠