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⎛ ⎞
∝ ⎜ ⎟⎝ ⎠