Download Fullerene C60 Single bond 1.46A Double bond 1.40 A Truncated

Fullerene C60
Valence electrons
Single bond 1.46A
Double bond 1.40 A
Truncated icosahedron 20 hexagons
(120 sigma states)
12 pentagons (60 double bonds)
Because of van der Waals forces C60
can form a solid with lattice constant
of 1.42 nm and first neighbor distance
10.0 A with large cohesive
energy 1.6 eV /molecule
Euler Theorem states that a
closed surface can be formed by
12 pentagons and arbitrary hexagons
Ane single bonds
Ene double bonds
Yne triple bonds
CH4
C2H4
Conjugation is alternation of single and double bonds and is a key in the conduction in
polymers.
Unfortunately many polymers are fully saturated like polyethylene ( should be poly-ane)
Same conductivity of
intrinsic silicon
unsaturated
Trans = out
(10-5 /Ohm.cm)
Conjugated polymer
Cis= in
(10-9 /Ohm.cm)
Trans and cis isomers in the case of double bonds because they cannot rotate
Instability in linear metal brings to gap opening
Actually the polyacetylene become semiconducting ( with conducibility of the order of the
intrinsic silicon in the case of the trans and gap of 1.9 eV)
A synthetic metal becomes semiconducting by the opening of a gap and distortion of the
polymer. Conjugated system with alternation of single and double
bonds. The double bond is stronger and shorter.
Degeneration is lost!
Distortion occurs through the existence (T>0K)of a vibronic coupling between
electrons and vibrational modes. In polyacetylene C-C antisymmetric stretching
( opposite directions)
Polyacetylene: The extended π-bonds are partially delocalized in space along the length
of the molecule and are thus similar to the extended energy bands that are formed when
atoms are combined to form a crystal. This is the reason for the little conductivity
By slightly perturbing this system a
Delocalized system is obtained
Attention Breaking of one chain has catastrophic consequence, so
with breaking or cleaving we intend transformation from a double to
a single bond and it is equivalent to the excitation of two electrons
in the conduction band.
Doping
MacDiarmid, Heeger in the 1977 found that conducibility of
polymers can be increased from 10-5 Ω−1cm-1 to 103 Ω−1cm-1
The mechanism is based on redox
transfer process and conjugated system
with π system with low energy is perfect
to transfer electron from double to
single bonds
Polypyrroles and polythiophenes are
obtained from monomers after oxidation
and polymerization and are among the
preferred candidates
Chemical doping can be obtained by electron acceptors ( Br2, SbF5,
WF6 e H2SO4) or electron donors ( alkali metals) after 1%mol.
People considered that
conductivity was depending
on the formation of partially
empty electronic band, but
the experiments showed that
it was the transport of
charged carrier without spin.
This can be explaind by the
Bipolaron
Why the polaron?
To make stable a ionized
state is sufficient that the cost
of the distortion (Edis) is
compensated by the much
less ionization energy.
Oxidation ends with a charge in a level inside the gap and a distorted crystal that we call
polaron, is the responsible of the change from a single to double bond and of the color of
the material
Polaron obtained by an acceptor impurities ( Br or I ) atoms which attracts an efrom the π-state leaving a mobile hole ( spin-less).
Such a polaron is characterized by a low effective mass.
Polaron is the coupling radical-cation has a large radius and is typical
of long molecules.
Poly-p-phenylene (PPP)
If we promote another electron in the neutral chain we form a second polaron
If we remove the radical we have a bipolaron
This second effect is particularly preferred because of the strong reduction of ionization energy
In spite of the repulsion between the two cations
Of course by doping with an electron donor we have negative polarons
According to the symmetries we have also excitons ( with visible luminescence)
The polarons (p) have always unpaired electrons
The bipolaron (bp) is always fully empty or occupied so it has no spin as observed!
P+
Positive (acceptors)
P-
Negative (donors)
Polyacetylene is degenerate and follows another way ( creation of solitons)
b) and c) have same
distortion energy but
only less repulsion
The consequence is that
two solitons depart
away one from the other
Soliton has a specific energy diagram and no spin
Other possibilities also exist!
In general benzenoid configuration is obtained ( aromatic )
And the soliton is not stable.
Organic LED
If the interaction between electrodes and polymer is weak the following energy schemes is
obtained starting from isolated materials electronic energies.
3.0 eV
2.9 eV
5.2 eV
5.0 eV
Recently, a record
efficiency of 110 lumen/W was reported for doped small molecules LEDs, which is over
50% higher than for inorganic LEDs
Organic FET: unintentionally doped p-type MISFET
At V=Vflat band fermi levels are equilibrated
Polymeric solar cells
By means of polarons
In the polymeric solar cell a big
issue is the interplay between
polaron localization and lifetime.
To improve efficiency both must be
increased.
Typically to improve the lifetime of
the exciton/polaron a blend of
PCBM is used. Lifetime increased
allows to the exciton ( induced by
the photon) to reach the boundary
of P3HT/PCBM where it splits.
Unfortunately the charge transport
occurs by the polaron and the
increase of localization leads to a
decrease of the photovoltaic
performance.
Conductivity in organic materials
Energy diagram
organic crystals ( anthacene,
pentacene.... ) compared to
inorganic (10−1 m2/ Vs) :
μ≈T −n
small width of electronic
bands due to to weakness of
bond ( van der waals, London
forces) and prevalence of
localized process
µ ∼ 10−3 m2/ Vs
Conjugated polymers
poor crystal order because
of defects like kinks or chain
twist ( power law is not valid)
µ ∼ 10−10 10−5 m2/ Vs
Organic crystals and polymers have two main differences with other
Solids
~0.5 eV
Existence of singlet and triplet states like in gas
Poses limit in OLED efficiency
Localized excitons
Poses limit in solar cells devices
Organic devices
Optical properties are related to molecular energy levels and structure
Conduction models using hopping ( activation energy + dependence on the field)
1) phonon assisted hopping between localized states
Phonon energy density
γ
localization
These models needs several
adjustements in terms of many
body energies, trapping states. In
general disorder is introducing a
broad range of electron energies.
Rij
C
C
C
C
Problem: polaronic model gives activation energy too low (1~10mV)
2) disordered induced gaussian density of states ( both energy and position)
Explain the high voltage behavior
Based on
1) optical absorption tails of gaussian shape
2) interaction of carriers with random dipoles has gaussian DOS
transport level
Equilibrium level
Mobility is field dependent
and the the result is not
Arrhenius like
Mobility dependence from T and F( electric field)
μ (T )=μ 0 exp[−(2 σ DOS /3k B T )2 ]∗ f ( F )
It is not Arrhenius like ( ~ exp-(A/kT)
Where A (~100 mV) is the activation energy of the mobility)
At low voltages Arrhenius like equation is
Predicted but a space charge limited model must be used with current increasing less with
Voltage: this is due to correlation of charge during injection
Arrhenius ?
9ϵμ V
J 0=
3
8 Lx
2
As a function of film
thickness and zero
field mobiliy and
Arrhenius type
equation
Hole diode :space charge limited current one type carrier
High doping (cathode)
insulating
High doping (anode)
Shift of the V max
The electric field F=Φ0/Lx (Φ0 is the
applied voltage ) is not uniform
because of the presence of injection
of charge across the sample. The
voltage depends nonlinearly on the
current, ( Ohm law no more valid).
The transport is called
SPACE CHARGE LIMITED
TRANSPORT
In the present case application of an
electric field to the n+-i-n+ makes
some electron to overcome the
barrier by decreasing the potential
barrier by V(x)=-eΦ(x)
mobility=dissipation
n x=−J 0 /e  F  x
LARGE BIAS TO NEGLECT
DIFFUSION TERM
 = F

In fact 
J =−e v n=e  n F
 F  x≫ D dn  x/ dx
By the Poisson equation d2Φ/dx2=-dF/dx= -ρ(x)/ε= en(x)/ε
dF J 0
F
=
dx e 
−d 
=F=0
dx
Boundary conditions consider the virtual
cathode approximation with the potential
Maximum at x =0.
The approximation is valid at large electric field
almost common in short structures.
1/2
2J
F x=− 0 
e
We chose the negative sign of the electric field
Because of the conventional electron motion
x 1/2
The current voltage characteristic can be obtained by the total voltage drop Φ0
8J 0
  x=−∫0 dx F  x=

9
x
2
1 /2
x3 / 2
J 0=
9   0
8 L3x
Mott-Gurney law