Hall Effect: Basics & Research Applications

1. Experiments in M.Sc. Laboratory
(Hall Effect: Basics &
research applications)
By
Dr. C.L. Saini
(clsaini52@gmail.com, clsaini52@uniraj.ac.in)
(Mobile No. : +91-9413119927)
(Assistant Professor)
Solar and H2 storage Laboratory
Department of Physics
University of Rajasthan, Jaipur
JLN Marg Jaipur, Rajasthan – 302004, India
4/8/2020 1UOR Jaipur

2. Hall Effect
In 1879 E. H. Hall observed that when an electrical current (I)
passes through a sample placed in a magnetic field (Bz), a
potential (VH) proportional to the current and to the magnetic
field is developed across the material in a direction
perpendicular to both the current and to the magnetic field.
Hall Effect will be used to study
Some of the physics of charge
transport in metal and
semiconductor samples.
4/8/2020 2UOR Jaipur

3. Standard Hall Effect Experiment
Current from the
applied E-field
Lorentz force from the magnetic field
on a moving electron or hole
e- v
Top view—electrons
drift from back to front
e+ v
E field
e- leaves + & – charge on
the back & front surfaces–
Hall Voltage
The sign is reversed for
holes
4/8/2020 3UOR Jaipur

4. Electrons flowing without a magnetic field
t
d
semiconductor slice
+ _
I I
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5. When the magnetic field is turned on ..
B-field
I qBv
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6. As time goes by...
I
qBv = qE
low
potential
high
potential
qE
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7. Finally...
B-field
I
VH
4/8/2020 7UOR Jaipur

8. • Why is the Hall Effect useful? It can determine the carrier
type (electron vs. hole) & the carrier density (n) for a
semiconductor.
• How? Place the semiconductor into external B field, push
current along one axis, & measure the induced Hall voltage
VH along the perpendicular axis. The following can be
derived:
• Derived from the Lorentz force FE = qE = FB = (qvB).
n = [(IB)/(qwVH)]
Semiconductors: Charge Carrier Density via Hall Effect
Hole Electron
+ charge – charge
BF qv B 
r rr
4/8/2020 8UOR Jaipur

9. 4/8/2020 9UOR Jaipur
Experimental Set-up at Deptt. Of
Physics, UOR Jaipur

10. THE HALL EFFECT: SEMICONDUCTORS
Why use Semiconductors?
 Ideal number of charge carriers
 Charge carriers increase with temperature
What we can learn ?
 Sign of charge carrier
 Charge carrier density
 Charge carrier mobility
 Energy gap
4/8/2020 10UOR Jaipur

11. HALL VOLTAGE

VH 
IB
ned
 RH
IB
d
For simple conductors
Where n = carrier density, d = conductor length
• RH is known as the Hall coefficient
• VH α B  Useful for measuring B-Fields
Gauss-meter Probe uses a
hall sensor
4/8/2020 11UOR Jaipur

12. HALL COEFFICIENT
Semiconductors have two charge carriers
but, for large magnetic fields
Which enables us to determine the carrier density
RH 
ne
2
 ph
2
e(ne
2
 ph
2
)2

RH 
1
(p  n)e
4/8/2020 12UOR Jaipur
Where: n, p represent charge carriers
(e- & h) and corresponding mobility's
are μe and μh

13. 4/8/2020 13UOR Jaipur
Source file: Local Text books which are available in Market

14. The Lorentz Force: Review
F = q[E + (v  B)]
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15. Lorentz Force: Review
The Velocity Filter:
Undeflected trajectories in crossed E & B fields:
Cyclotron motion:
•Orbit radius:
•Orbit frequency:
•Orbit energy:
momentum (p) filter
mass detection
4/8/2020 15UOR Jaipur
B
E
v 
r
mv
qvBmaF rB
2

Bq
p
Bq
mv
r 
m
Bq
f   2
m
RBq
mvK
22
1 222
2


16. Hall resistance-Rxy(ohms)
The classical Hall effect
• Lorentz force likes to deflect jx
• However, E-field is set up which balances Lorentz force
• Balance occurs when Ey = vxBz = Vy/ly
• But jx = nevx (or ix = nevxAx)
Rxy = Vy / ix = RH Bz × (ly /Ax), where RH = 1/ne
Where ly is transverse width of sample and Ax is the transverse cross sectional area
of the sample, i.e. depends on shape of sample
0 2 4 6 8 10
200
0
1200
1000
800
600
400
1400
Slope related to RH
and sample dimensions
Magnetic field (tesla)
Ax
ly
4/8/2020 16UOR Jaipur

17. Dimension of LHS is resistance but it
is not a resistant conventionally,
Hall resistance (RH)
Hall resistance is expected to increase linearly (straight line) with the magnetic field
for a particular sample.
1980, K.V. Klitzing (1985 Noble prize)
measured that
 The Hall resistance
increase as per plot
shown (stair steps) at high magnetic field
at low temperature (1 K),
this effect is known as
quantum hall effect.
The dashed line show –classical and,
the steps show quantum result
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RH B

18. • Surface current density sx = vxq, where is surface charge density
• Again, RH = 1/e
• However, now: Rxy = Vy / ix = RH Bz
since sx = ix /ly and Ey = Vy /ly
i.e. Rxy does NOT depend on the shape of the sample. This is a v. important aspect of
the QHE
The 2D Hall effect
4/8/2020 18UOR Jaipur

19. The integer quantum Hall effect
Hall conductance quantized in units of e2/h, or Hall resistance Rxy = h/ie2,
where i is an integer. The quantity h/e2 is now known as the "Klitzing"
1 Klitzing 25,813 
Has been measured to 1 part in 108
Very important:
For a 2D electron
system only
First observed in 1980 by
Klaus von Klitzing
•Awarded Nobel prize in 1985
4/8/2020 19UOR Jaipur

20. Quantum Hall effect
For a 2D electron system which can be produced in a MOSFET, in the presence of
large magnetic field strength and low temperature, one can observe the
quantum Hall effect, in which the Hall conductance (σ) undergoes quantum Hall
transitions to take on the quantized values.
Spin Hall effect
The spin Hall effect consists in the spin accumulation on the lateral boundaries
of a current-carrying sample. No magnetic field is needed. It was predicted by
M. I. Dyakonov and V. I. Perel in 1971 and observed experimentally more than 30
years later, both in semiconductors and in metals, at cryogenic as well as at
room temperatures (RT).
Quantum spin Hall effect
2D quantum wells in mercury telluride with strong spin-orbit coupling, in zero
magnetic field, at low temperature, the quantum spin Hall effect has been
recently observed.
4/8/2020 20UOR Jaipur

21. Anomalous Hall effect
In ferromagnetic materials (and paramagnetic materials in a magnetic field), the
Hall resistivity includes an additional contribution, known as the anomalous Hall
effect (or the extraordinary Hall effect), which depends directly on the
magnetization of the material, and is often much larger than the ordinary Hall
effect.
(Note that this effect is not due to the contribution of the magnetization to the
total magnetic field.)
e.g. in nickel, the anomalous Hall coefficient is about 100 times larger than the
ordinary Hall coefficient near the Curie temperature, but the two are similar at
very low temperatures.
There is still debate about its origins in the various materials. The anomalous
Hall effect can be either an extrinsic (disorder-related) effect due to spin-
dependent scattering of the charge carriers, or an intrinsic effect which can be
described in terms of the Berry phase effect in the crystal momentum space (k-
space).
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22. Why use Hall effect?
 Reason for using a particular technology or sensor
vary according to the application.
 Cost, performance and availability are always
considerations.
Hall effect sensor are magnetic field sensor.
Used as current, temperature, pressure,
piston etc.
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Algorithm to use Hall sensor

23. Hall effect sensors can be applied as
 monitoring (flow meters, current sensors),
 positioning (positions sensor, seat belt) or
 safety feedback (interlocks, pressure sensor, RPM sensors) devices for the
automotive market.
4/8/2020 23UOR Jaipur
Practical use of Hall sensors in today life

24. The magnetic piston (1) in this pneumatic cylinder will cause the Hall effect
sensors (2 and 3) mounted on its outer wall to activate when it is fully
retracted or extended.
4/8/2020 24UOR Jaipur

25. Applications in Portable Electronics
In consumer electronics, product acceptance is increasingly determined by:
 the user interface, where sensors provide awareness
 the overall user experience, where a subtle feature can become a wow factor.
The use of Hall effect IC switches are contributing to product acceptance in several
of these applications.
4/8/2020 25UOR Jaipur

26. Polarity-discriminating
omipolar hall effect IC
switches can be used to
control the operation of
multiple displays
Lower cost MP3 players use
jog wheel that moves
clockwise or counterclockwise
to select MP3 songs or scroll
through a list of menu items.
4/8/2020 26UOR Jaipur

27. 4/8/2020 27UOR Jaipur
Thank you
very much
Suggestions are invited for improvement in the ppt file.
Send your feedbacks at Email: clsaini52@gmail.com