1. Hall effect measurements in organic
semiconductors
Edward Burt Driscoll
Paralleling the use of Hall effect measurements used in inorganic conductors
and semiconductors, the Hall effect has been used to analyze charge carrier
characteristics in organic semiconductors. We look at how this field has both
improved organic electronics and been improved by techniques specified for
organic materials.
1
The use of the Hall effect to calculate
majority charge carrier type, density, and
mobility is a common occurrence in the field
of semiconductors, organic and inorganic
alike. However, additional problems arise in
the conducting of Hall effect measurements
of organic materials, which, if not accounted
for or fixed, result in skewed results. Single
crystal samples of organic materials have
yielded strong Hall effect results[1]
, yet high
resistivity causes clear results to be rare
when executing the normal measurements.
Attempts have been made to resolve
the behavior of the Hall effect in organic
semiconductors, either by adding additional
mechanisms[2-5]
, or by making corrections
with variable temperature and magnetic field
strength[6]
. On top of this, imperfections in
the material often lead to charge traps,
which disrupt the current density and charge
carrier mobility[7]
, and accelerates
recombination of exciton pairs, leading to
drops in device performance.
Charge trapping occurs on surface
and grain boundaries in materials, and the
accumulation of such charges results in
strong phonon-charge coupling[8]
. This
coupling effect can control interactions when
the concept is applied to thin films, where a
ORGANIC MATERIALS
2
large proportion of charge transfer occurs on
the surface edge[9]
. In π-conjugated
polymers, charge traps caused by crystal
defects create a minor energy landscape
throughout the device, in addition to the
bimodal electronic energy landscape[10]
.
Although many devices use multiple
materials and are designed in a way to
minimize grain boundary discrepancies,
methods to measure the true electronic
properties of organic materials by correcting
the problems associated with charge
trapping have been explored.
Called “trap-healing”, depositing an
inert, non-conjugating polymer on the
surface of the semiconductor under test
increases the surface conductivity and
allows the samples to go through proper Hall
effect measurements[11]
. However, this only
solves the problem of measuring the Hall
mobility of the sample, which does not carry
over when making a device that may contain
a similar amount of charge traps. In organic
photovoltaics especially, these traps lead to
a higher rate of recombination, an aspect of
semiconducting electronics that researchers
try to minimize.
Another measurement technique that
adds a degree to certainty to the Hall effect

2. 3
is the microwave Hall effect. In this
configuration, shown in Figure 1a, the
sample is bombarded with a constant
stream of microwaves, and the rotation of
the polarity of the microwaves can be used
to find the charge carrier mobility[2]
. The
direction the microwave rotates from center
determines the majority charge carrier, while
the angle value is proportional to the square
root of the mobility[4]
.
The microwave frequency used in this
system varies around 30 GHz[2]
or 33 GHz[3]
.
High energies are used to overcome the
noise caused by the geometry of the
bimodal cavity and outside sources. In 1974,
microwave Hall effect measurements were
Figure
1[4]:
Two
setups
of
the
microwave
Hall
effect
measurement.
(a)
A
simple
microwave
Hall
effect
setup
with
microwaves
traveling
in
a
single
direction
parallel
with
the
magnetic
field.
(b)
A
complex
yet
more
efficient
setup
includes
a
bimodal
cavity
containing
the
sample,
with
microwaves
being
coupled
in
the
cavity
to
the
Faraday
rotation,
and
allows
power
to
be
released
from
the
cavity.
a
b
4
taken for biological compounds, such as
DNA and hemoglobin, at 10 GHz[12]
. These
biological samples are not necessarily being
researched for their electrical properties like
organic materials are currently, so extreme
accuracy was not necessary. However, in
the avenue of organic semiconductors,
higher energies with frequencies much
above 30 GHz could greatly improve the
precision of Hall effect measurements[2]
.
The quantum Hall effect is not a
measurement technique like the microwave
Hall effect, but instead a phenomenon that
occurs in some Hall effect measurements.
As displayed in Figure 2, variations in the
magnetic field strength lead to a slight
quantization of conductance (and therefore
resistance). This is an effect commonly
found in inorganic materials at extremely low
temperatures in high magnetic fields, where
particles behave as in a 2-D field with
cyclotron behavior[13-14]
.
This cyclotron behavior causes the
electrons to take on particular quanta of
momentum, and therefore energy, in what
Figure
2[6]:
The
quantization
of
Hall
resistance
with
respect
to
magnetic
field
strength
in
tetracene.
These
distinct
Hall
plateaus
are
reflective
of
energy
levels
in
cyclotrons,
called
Landau
levels[14,15].

3. 5
are referred to as Landau levels[14]
. This
cyclotron behavior, when restricted to a
specific area like the device under test,
results in localized cyclotron states in the
interior of the sample, and edge states on
the sides, due to the incapability of the
electrons to escape the material. This
creates a Hall current on the edges of the
material, and is therefore referred to as
creating a topological insulator[15]
. Although
particularly associated with inorganic
semiconductors, the quantum Hall effect has
been measured in organics[6]
, and
particularly in graphene[16]
. In graphene, the
ground state at low temperatures shows a
quantum Hall effect due to its spin-orbit
coupling when placed in a magnetic field.
The identification of the momentum levels
with electron spin has led this effect to be
dubbed the quantum spin Hall effect, as
other quantum effects can be noted[17]
.
The quantum Hall effect has also
been noted in tetracene and pentacene, two
basic benzene-based organic compounds.
At 1.7 K, both materials, in crystalline form,
displayed a quantized magnetoresistance
and Hall resistance with varied magnetic
field strength and charge carrier
concentration[6]
. With its appearance in
these organic materials, there is a very good
chance that the quantum Hall effect can be
observed in further, more complex, organic
materials, albeit possibly with much more
disorder.
Another form of the Hall effect, which
is apparent in ferromagnets and
paramagnets, is the anomalous Hall effect.
Much like the quantum Hall effect, it arises
from spin-orbit coupling in ferromagnets
apart from a magnetic field, or in
paramagnets in a magnetic field[13]
. Due to
the similarity in the anomalous Hall effect to
the quantum spin Hall effect, it is referred to
also as the quantum, or quantized,
anomalous Hall effect[17]
.
This effect has not been found in
organic materials, as ferromagnetism and
paramagnetism are not common
occurrences in anything aside from metals
6
and semi-metals. This is most likely not a
useful effect in the study of organic
semiconductors and other organic electronic
devices.
The full limit of Hall effect
measurements in organic materials has not
been met, as variation of the measurement
technique can lead to better and more
versatile measurements. Also, since the
conduction mechanisms of organic
semiconductors have not been fully
understood, phenomena in the Hall effect
measurements of Hall voltages and Hall
resistances, along with the carrier mobility of
the substance, with respect to temperature,
magnetic field strength, and carrier
concentration have not been fully explained.
Material deficiencies that occur all too
often in organic materials, even in pure
crystals, create problems in both device
measurement and performance. Charge
traps caused by surface and grain
discrepancies have not been fully solved,
although the former has been helped with
trap-healing techniques[11]
. On top of these
material issues, problems that arrive from
traditional Hall effect measurement
techniques exacerbate the problems, among
those electrode connections. However,
using microwaves to measure the Hall effect
gives promising results in more accurate
measurements and usefulness a wider array
of materials. The microwave Hall effect, with
microwave frequencies on the order of 10-
33 GHz, has provided accurate
measurements in biological materials[12]
,
along with organic materials[2-3]
.
Investigating the measurements
compiled in Hall effect measurements,
patterns in inorganic semiconductors have
become visible in some organic materials.
The quantum spin Hall effect, found in
inorganics[14-116]
, has also been found when
the same analysis is applied to low-
temperature graphene[16]
, tetracene, and
pentacene[6]
. More phenomena found in Hall
effect measurements of inorganic materials
could be applied to organic materials in
further research. Though some, like the

4.
7
anomalous Hall effect, are not visible in
organic compounds, further testing could
yield viable data to figure out charge
movement mechanisms in organic
semiconductors beyond the buzzword
“hopping”.
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