Transport in disordered systems

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Transport in disordered systems

• Interchain hopping in polymers
• Carriers are polaronic
• Mobility for transport between chains is small
• Important in PLEDs and PTFTs
• Transport in disordered systems
• In amorphous systems
• In polycrystaline systems which are not grain
  boundary limited
• Important in photoconductors, OLEDs

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Polymer FETs
LED materials
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Polymer thin-film transistor
Spun polymer film (ordered)
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Polythiophene Ordering
Not good
Good for high mobility

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• Consider the organic crystal lattice
• An electron will see periodic potential as shown
• The Hamiltonian of the system is given as
• H He Hl Hint

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• Interaction of electron and lattice in organic
  crystal
• At a certain instant of time let electron be
  fixed in poisition
• The lattice around it gets distorted due
  interaction
• This creates a potential well around the
  electron
• So if the well is deep then the electron is
  bound
• The setup of electron and the deformed lattice,
  is called polaron.

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Linear dimensions of polaron

• Lp ? a.(4J.M?o2/ A2)
• Small polaron, Lp ?? a
• ? 2J ?? A2/2M?o2
• Large polaron, Lp ?? a
• ? 2J ?? A2/2M?o2

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Holstein equations
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Sirringhaus et al., Science Vol. 280, p 1741
(1998)
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• Bassler disorder model
• Results
• Background

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Assumptions

• The free energy e of each site ( also hold for
  distances between sites)
• e energy measured relative to the center of the
  distribution
• s standard deviation of the distribution
  function
• Energies of adjacent sites are uncorrelated.
• 3. Motion -- no phase memory, each jump is
  unrelated to the previous jump.

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• Monte Carlo ( MC ) simulation
• - an idealized experiment carried out on samples
  of arbitrarily adjustable degree of disorder and
  devoid of any accidental complexity
• - allows to determine which level of
  sophistication is required to reproduce the
  properties of a real world sample and, by
  comparison with theory, to check the validity of
  approximations in analytical treatments that are
  based on the same physical principles.

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Results

• A cubic lattice consisting of 707070 sites
• a 0.6 nm
• Applying periodic B.C.
• ? effective sample size 80008 8
• ? sample length 4.8 µm in the direction of an
  applied electric field

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• The analytical expression for mobility (approx)
• for
• for
• Where, reduced energetic disorder parameter

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Dependence of mobility on temperature
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Field dependence of mobility
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Referrence (Disorder)

• H. Bassler, Phys. Stat. sol. (B) 175, 15(1993)
• Pope Swenberg, Electronic Process in Organic
  Crystals and Polymers
• Borsenberger Weiss, Organic Photoreceptors for
  Xerography

Acknowledgments Shreyas Rajasekhara Wei-Wei
(former students in EE397)