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Drexel University
ECE-E302, Electronic Devices
Lab I: Hall Measurement
Hall Measurement
Objective
The objective of this experiment is to study the Hall effect in semiconductors. To do this
we will measure the Hall voltage of an Indium Arsenide sample under different conditions, and
examine a typical application of a Hall device.
Theory
The Hall effect can be achieved by inducing a magnetic field perpendicular to the current
flow direction in a semiconductor. Under such conditions, a voltage is developed perpendicular
to both the current and magnetic field. This voltage is known as the Hall voltage. The origin of
the Hall voltage can be seen by considering the forces on a charged carrier in the presence of a
magnetic field (see figure 1):
F  qE  qv  B
(1)
The first term is due to the total electric field driving the current through the sample. The
second term is due to the Lorentz force on the charged carriers, and tends to deflect the carrier
toward the side of the sample. The direction of the deflection depends on the sign of the carrier’s
charge.
Ix
Bz
z
y
x
Ey
+
–
L
T
W
Ex
Ix
Figure 1. The Hall effect device. Current flows in the positive x-direction. The applied magnetic
field is in the positive z-direction. For a p-type sample an internal electric field develops in the
positive y-direction.
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Drexel University
ECE-E302, Electronic Devices
Lab I: Hall Measurement
Consider the example illustrated in Figure 1. Let’s assume that we have a p-type
semiconductor bar. The applied electric field and the current are in the positive x-direction, the
applied magnetic field is in the positive z-direction. The y-component of the force is:
Fy  qE y  qv xB z
(2)
This equation implies that unless something happens, all carriers moving in the sample will
experience a force that will drive them toward one side of the sample. In this case, the holes
would move in the negative y-direction.
If a number of holes were to collect at the right side of the sample, that side would take
on a positive charge relative to the left side. This sets up an internal electric field in the +ydirection. Note that the only applied electric field is in the +x-direction. The force due to the
internal electric field opposes the Lorentz force. To maintain a steady flow of current through the
sample, we must have a balance of forces:
E y  v x Bz
(3)
resulting in no net force on the carriers in the y-direction. The internal field can be set up by
moving the holes only slightly to the right.
The presence of the internal field can be detected by measuring the voltage developed
across the sample:
Ey 
Vy
w
(4)
where w is the width of the sample. This is known as the Hall voltage.
Carriers subject to an electric field move with a velocity called the drift velocity. The hole
current in our sample can be written as
Ip  qpv d A
(5)
where +q is the hole charge, p is the hole density in #/cm3, vd is the drift velocity, and A is the
cross sectional area of the sample. If we convert this to an equation for the current density vector,
where the magnitude J = I/A and the direction is parallel to the drift velocity, we have
J p  qpv d
(6)
The drift velocity is related to the electric field driving it through a proportionality
constant known as the mobility:
v d   pE for holes, v d   nE for electrons
(7)
Substituting this into the current density equation, we get
J p  qp pE for holes, J n  qn nE for electrons
Using this relationship in our equation for the field Ey, we get:
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(8)
Drexel University
ECE-E302, Electronic Devices
Lab I: Hall Measurement
E y  v x Bz 
Jx
B  R H J xB z
qp z
(9)
where RH =1/qp is called the Hall coefficient. You can also show that RH = –1/qn for n-doped
samples.
We can also extend this model to consider the Hall effect when both electrons and holes
are present, resulting in the following equation (for small fields):
RH 
1
q
p
p
2
p
p


 n 2
n
 n n
2
(10)
Applications
1) Doping concentration
Equation (9) can be rearranged as
RH 
Ey
JxB

V y
W

IB WT
TV y
IB
(11)
We see that we can use measurements of the Hall voltage, magnetic field, current, and
sample thickness to determine the Hall coefficient for any sample. From the Hall coefficient we
can derive the doping density, p or n. This measurement is a diagnostic tool for determining the
doping level in the sample.
2) Mobility
If a measurement of sample resistance R is made, you can calculate the resistivity
R 
Vx I x
L
RWT
, so  

A
L
L WT
(12)
Since the conductivity σ = 1/ρ is equal to qµpp, the mobility µp is just the ratio of the
Hall coefficient and the resistivity. Measurements of the Hall coefficient and the resistivity over a
range of temperatures yield plots of majority carrier concentration and mobility vs. temperature,
very useful data to have for semiconductors.
3) Current measurement
Another real-world application of Hall effect devices is as a sensor for current
measurement. A current (dc or ac) passing through a wire (figure 2) generates a magnetic field:
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Drexel University
ECE-E302, Electronic Devices
Lab I: Hall Measurement
B 
 oI w
2 r
(13)
where Iw is the current flowing in the wire, and r is the radial distance from the wire. If a Hall
device is placed near the wire and a constant current Is is passed through it, the magnetic field
generated by the wire will induce a Hall voltage Vy in the device.
Hall sensor
Wire
B-field
Figure 2. End view of a current carrying wire. Current is flowing into the page, so using the righthand-rule, the magnitic field flux circles the wire in a clockwise sense.
Solving equation 11 for B, we see
B 
TVy
IsRH
(14)
Setting equations 13 and 14 equal and solving for Iw,
Iw 
2rV y T
 oIsRH
(15)
Thus, if we know the details of the sensor and the distance of the sensor from the wire, and
measure the Hall voltage we can make a “non invasive” determination of the current flowing in
the wire.
Experiments
A commercial Hall device will be used in this lab. This removes the need to solder two or
three contacts to a semiconductor bar. The Hall device has four leads as shown in figure 3, and is
constructed of Indium Arsenide. The Hall device used in this experiment has an impedance of
around 50 Ω across the Ic contacts, and the maximum Ic is 25 mA.
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Drexel University
ECE-E302, Electronic Devices
Lab I: Hall Measurement
(W)
+
Ic
V
(G)
V
(G)
–
(W)
A
Figure 3. Measurement of Hall voltage
Notice: The outside two leads of the Hall device (G in the above figure) are used to apply control
current Ic. The inner two leads (W in the above figure) are used to measure Hall voltage.
Procedure
1. Hall Offset Voltage (without magnetic field)
Setup the circuit as in Fig 3. Place a 500 Ω resistor in series with the DC power supply to
limit the control current Ic. With no magnetic field present, measure Hall Offset voltage VH-off
on the DVM as you vary the control current Ic from zero to 25 mA (DC) in 5 mA steps by
changing DC supply voltage.
2. Hall Voltage under DC magnetic field
a) Place the Hall generator in between the pole and the keeper of the small horseshoe magnet.
Adjust the screw so the keeper almost touches the Hall device. Vary the control current Ic
from zero to 25 mA in 5 mA steps and measure the corresponding Hall voltage VH-mag.
b) Without changing the screw adjustment, measure the magnet's strength B on the Gauss meter
(1 K Gauss = 0.1 Tesla).
c) Determine the Hall Coefficient RH = VH*T/ (B * Ic), where VH = VH-mag – VH-off , T is
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Drexel University
ECE-E302, Electronic Devices
Lab I: Hall Measurement
the thickness of the Hall device and T = 0.1 mm = 10-4 m .
d) Determine your Hall generator's "product sensitivity" Kp = VH / (B * Ic).
e) Find the doping concentration of the device p = 1 / (q * RH ), where q=1.6E-19 Coulomb.
Be careful with units: VH (volt), Ic (Amp), B (Tesla), T (meter), Kp (volt/Tesla.Amp), p (m-3)
3. Application of Hall device as a Gauss meter
Now that you know the sensitivity of your Hall device, you can use it as a sensor –– you
can measure unknown magnetic fields.
An electromagnet can be used to produce a voltage controlled magnetic field. Use your
Hall device to measure the magnetic field produced by the electromagnet. The electromagnet
used in this lab consists of hundreds of turns of magnet wire wound on a one-inch torroid. The
coil has a resistance less than 50 Ω and its MAXIMUM CURRENT is 150 mA.
Set the control current Ic to 15 mA. Vary the magnet current Im from 150 mA down to 0
in at least seven steps, including at least one value of Im less than 10 mA. For each Im, measure
the Hall voltage VH. Use the value of Kp found in Part 2 (Kp at Ic = 15 mA) to calculate the field
strength B = VH / (Ic * Kp) at various magnet currents Im used.
Report
1. Introduction: Objective and Theory
2. Data sheet and calculations:
1) Plot of Hall voltage VH ( = VH-mag – VH-off ) vs. control current Ic
2) Determination of Hall coefficient RH, Hall device sensitivity Kp and doping density p
3) Plot of (calculated) coil magnetic field B vs. coil current Im
3. Discussion of the results
4. Questions
1) Can the Hall effect be observed in a metal?
2) Can the Hall effect be used to determine experimentally what type of doping (n- or ptype) of a sample?
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