Transcript TalleyHallEffectSS2012 - The University of the South

The Hall Effect in N-Type and P-Type Semiconductors
Trey Talley C’13
Department of Physics and Astronomy
Sewanee: The University of the South, Sewanee, TN
Introduction
The Lorentz Force
Semiconductors
Many important conduction properties of
doped semiconductors can be measured using
the Hall Effect. The Hall Effect can be clearly
observed in n- and p-type semiconductors
when a current is flowing through the
conductor with a magnetic field that is
perpendicular to the direction of the current
flow. The measurement of the Hall coefficient
can be used to calculate the mobility and the
carrier concentration within these semiconductors.
• Conduction is due to a single carrier type
with charge q and mobility μ.
• When a magnetic field B is applied, then
the carriers of charge q experience a Lorentz
force:
Semiconductors are materials with electrical
conductivity. They are the foundation of
modern electronics: they are used in
computers, telephones, radios, solar cells,
LED’s, and diodes. Semiconductors can be
doped with impurities to modify conductivity
for constructing electronic devices.
F  qV  B

What is the Hall Effect?
• If a conducting material that carries a
current down the x-axis is placed in a
perpendicular magnetic field, a potential
difference (Hall Voltage) is produced along
the y-axis.
• The production of this voltage is known as
the Hall effect, first observed by Edwin Hall
in 1879.
• This force deflects the moving charge
carriers in the material, and thus produces the
Hall effect.
• The Lorentz Force can teach us valuable
information about the movement of the
Intrinsic
semiconductors
are
doped
with
charge carriers in materials.
impurity atoms, making them extrinsic
semiconductors. The presence of these
impurities affects the carrier concentration
and the conductivity of the material. When a
semiconductor is doped, it produces either N
or P type semiconductors.
Doping: N-type and P-type
Semiconductors
My Experiment
Figure 4: This is the N-type silicon wafer that is doped
with Phosphorus. The indium connections are at all four
corners.
Measurements
I took four tables of data. The first two tables are
the van der Pauw resistivity data, and the second
two tables are the Hall measurements that were
taken while the wafer was in a magnetic field B of
1500 G. From the data that was taken, I was able to
ultimately calculate the carrier concentration within
the n- and p-type silicon wafers.
Calculations
Current Amps
J  nqv  v 

2
Area
m
Ey
1
Jx Bz
Figure 2: The Lorentz Fore causes the positive charges in this
RH 
RH 
Ey 
semiconductor to move to the far side of the material.
J x Bz
nq
nq
First, I calculated the current density J by dividing
the current by the area. Next, I calculated the electric
dividing volts per meter. After measuring
field
E
by


First, I used a diamond-tipped scriber to cut a
the magnetic field B with a Hall probe, I was able to
5 by 5 cm. wafer from the n-type and the pcalculate the Hall coefficient R. Then I solved the
• We can learn about the charge transport
type silicon. Next, I melted indium on all
last equation for n, the electron density. This is equal
properties of different materials through the
four corners, and scratched off the native
to the concentration of the charge carriers, which I
behavior of the Hall Voltage.
10
3
oxide layer along the silicon-indium
found
to
be
n  3.41 10 cm .
• The concentration (carrier density),
Why Study the Hall Effect?
Figure 1: The Hall Effect in a material.
mobility, and sign of charge carriers can be
determined.
• Most importantly, the conductivity of
different materials can be determined.
My Experiment
interface. Next, I melted 30 gauge wires to
all four corners. The final product for the Ntype sample is shown below.
Acknowledgements
Thanks to Dr. Peterson, Rodger, Jim, and the P C’13.
Team