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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