Tentamen i TNE078 Laddningstransport i organiska och
oorganiska material (5p)
Onsdag den 16 Mars 2005 kl 14.00 - 18.00
Hjälpmedel: engelsk ordbok
Examinator: Xavier Crispin
Preliminära betygsgränser:
tentamen omfattar totalt 38p. För betyg 3 krävs 16p, för betyg 4, 23p, och för betyg 5, 30p.
Språk: The English language is recommended. However, if you have any problems write in
Swedish.
Reminder: Read carefully the questions in order to answer properly and completely!
Lycka till, Good luck!
Part 1, transport in inorganic materials (20p)
1.1. A simple model of energy bands in semiconductors is the spherical parabolic band
model. Give a brief description of it. In the case of silicon, a modification of the model is
often made because of the anisotropic effective mass. Describe the modification.
(2 p)
1.2. What particles are involved in ionized impurity scattering? When can this scattering
mechanism be expected to be important compared to other scattering mechanisms like phonon
scattering? How does the scattering rate for ionized impurity scattering depend (qualitatively)
on the scattering angle, i e the angle between the momenta of scattered and incident particle?
(3 p)
1.3. Consider the Boltzmann transport equation (BTE) in one spatial dimension:
f
f
f f
v F

t
r
p t
 s ( r , p, t )
coll
Explain the physical meaning of the function f and make an interpretation of the different
terms in the BTE. Would you characterize the equation as classical, quantum mechanical or a
mixture? What information is possible to obtain if we have solved the equation and the
function f is known?
(4 p)
1.4. Describe the relaxation time approximation. Which term in the BTE is approximated and
how?
(2 p)
1.5. What is a “wide band gap semiconductor”? Give at least two examples of such materials
and give some advantages (compared to silicon) and possible applications.
(2 p)
1.6. What is the free flight time in a Monte Carlo simulation? Describe at least two different
methods of determining the free flight time.
(3 p)
1.7. The upper figure shows the hole current as a function of time from a Monte-Carlo
simulation of carrier motion in amorphous silicon. The applied voltage was 2 V and the length
of the sample 210-4 cm. The temperature was 245 K. Calculate the drift mobility of the holes
from the MC data, and compare the value with the experimental value obtained from the
lower figure.
(4 p)
2
3
Part 2, transport in organic materials (18p)
2.1. Electron transfer reaction: H2 + H*2+  H2+ + H*2 (2p)
2.1.a) Two molecules, H2 and H*2+, are separated by a fixed distance. They undergo an
electron transfer reaction. Draw the potential energy curve of the reactants and products
versus the reaction coordinate (difference in interatomic distance).
2.1.b) Draw both molecules (bond length) as reactants and products and at the transition state.
2.1.c) From the potential energy curve of one neutral H2 molecule and a positively charged
H2+ molecule, define the internal reorganization energy for the electron transfer reaction.
2.2. Electron transfer and charge transport (3p)
In an un-doped organic crystal at room temperature, the charge transport usually occurs in a
hopping regime between adjacent molecules. In other words, the fundamental event of charge
hopping is a self-exchange electron transfer reaction. In the semi-classical model, the rate of
this reaction is given by the formula:
2.2.a) What are T, t and λ? Explain their physical meaning.
2.2.b) How does “t” depend on the intermolecular distance?
2.2.c) What type of morphology and crystal structure would give rise to the largest charge
carrier mobility?
2.3. Charge transport in neutral conjugated materials (3p)
2.3.a) What is the order of magnitude of the electrical conductivity in un-doped conjugated
polymers?
2.3.b) Does the temperature affect the charge carrier density in un-doped conjugated
polymers? Why?
2.3.c) Give and explain one criterion to estimate if charge carriers travel in a hopping regime
or a band motion regime?
2.3.d) In the band motion and hopping regimes, the charge carrier mobility has different
temperature dependence. What are they?
2.3.e) What is a polaron in a conjugated polymer? Sketch the structure of a polaron for a
conjugated polymer of your choice.
4
2.4. Doped conjugated polymers (3p)
2.4.a) What is ”variable range hopping-VRH” theory?
2.4.b) For what kind of materials is the VRH theory used?
2.4.c) What is Mott’s law? Give it
2.4.d) How can one increase the electrical conductivity of polyaniline in its emeraldine base
form?
2.4.e) How is the conductivity vs. temperature dependence affected by increasing the disorder
in a polyaniline layer?
2.5. Ionic transport (3p)
The 85th edition of the CRC Handbook of Chemistry and Physics gives values of the diffusion
coefficient D in water for Cl- and Na+ of 2.03210-5 cm2/sec and 1.33410-5 cm2/sec,
respectively.
2.5.a) What is the mobility µ of Na+ in water at room temperature (293K)? Of Cl-? What is
the ionic conductivity  of a 0.01M aqueous solution of NaCl?
(1M = 1 mol/liter)
2.5.b) At equilibrium with no applied field, the concentrations will be uniform and equal
everywhere in the above electrolyte. What happens near a metal electrode with an applied
potential of -1V? Assume that the potential in the electrolyte far away from the electrode is
0V and the concentrations are both 0.01M. Sketch the concentration profiles of each of the
above species and the potential within the electrolyte versus the distance from the electrode.
It is OK to approximate the ions as point charges with no volume.
2.5.c) About how close to the electrode must you look to observe concentrations and/or
potential that is different from that observed in the bulk? An order of magnitude is OK, but
state where the estimate comes from.
2.6. Doping and electrochemistry (2p)
Chemists and physicists often use different language to describe the same thing. For example,
chemists talk about oxidation and reduction, while physicists talk about doping and dedoping.
2.6.a) Write a chemical half-reaction for a conjugated polymer (generically or for a specific
material) and indicate whether the half-reaction you wrote is a reduction or an oxidation.
2.6.b) Is the reaction you wrote above a doping or a dedoping process? Which is the more
electronically conductive species? Which is the doped species? Which is the neutral species?
5
2.7. Electrochemical device structure and behavior (2p)
2.7.a) Sketch a lateral (both anode and cathode in the same plane with electrolyte on top)
structure 2 device and indicate how to apply an electric potential. Clearly indicate where the
conducting polymer and the electrolyte are, and which electrode will be the anode and which
will be the cathode when a potential is applied in the direction you indicate.
2.7.b) When a potential is applied to such a device made out a conjugated polymer (like
PEDOT:PSS), a color change is observable. This is called electrochromism. What color does
each side become in a PEDOT:PSS device? If the electrolyte is a poor conductor (few ions,
low mobility), which part of each electrode will switch first? A sketch may be appropriate.
6