The Hall Effects
Richard Beck
141A 2013
Hall Effect
• Discovery
• The physics behind it
• Applications
• Personal experiments
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Discovery
• Observed in 1879
• Edwin Herbert Hall
Via Wikimedia Commons (public
domain)
• Discovered 18 years before the electron
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Principles
• Mobile charges pressed to one side from
Lorentz force, immobile charges unaltered
• Creates internal electric potential, known as
Hall voltage.
• For simple metals, is V =
Richard Beck - Physics 141A, 2013
Note: t
refers to the
thickness of
the metal
along the
direction of
the B-field
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A Visual Representation
From Non-Destructive Testing (NDT) Resource Center
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Hall Coefficient
• Magnitude parameter:
• In metals:
• In semiconductors:
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Triumphs
• Classical Picture: only electrons moving in
same average direction in both hole (p-type)
and electron (n-type) conductivity
• Opposite sign indicates that electrons in
valence bands move in opposite direction
than previously thought
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Applications
• Measurement can tell about charge carrier
mobility, concentration
• Conversely, knowing the above allows for
sensitive measurement of an external B-field
• Resistant to outside contaminants unlike
optical, electromechanical testing
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Hall Probes
Via LessEMF.com
Via the NDT Resource Center
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Rotation Sensing
• Hall Effect sensors capable of switching very
fast, does not distort like capacitative or
inductive sensors
• Contactless sensing
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In Cars
• Used expansively in rotating systems
• Anti-lock brakes, motor feedback, ignition
Via Power Systems Design, Ltd.
Via Draper, 2005
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In Space
• Hall Effect thruster
• Trap electrons in a magnetic field, electrons
ionize propellant, creates thrust
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New Discoveries
• QuantumHall Effect
• Spin Hall Effect
• Anomalous Hall Effect
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Quantum Hall Effect
• Quantization of normal Hall Effect
• Seen at low temperature, high magnetic field
• Very precise, magnitude determined by
Landau levels and electron interaction
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Spin Hall Effect
• Separation of electron spins in currentcarrying object, no magnetic field needed
• Predicted in 1971, observed in 2004 via
emission of circularly polarized light
• Universal, present in metals and
semiconductors at high and low temperature
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Anamolous Hall Effect
• Ferromagnetic materials have internal
magnetic field
Via Toyosaki et al.
2004
• Much larger than normal Hall Effect, but not
well understood ; Possible Berry-phase effect
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Personal Experiments
• Aluminum-doped Germanium 1 sq cm chip
• Van Der Pauw configuration
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Hall Coefficients
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Extrapolated Carrier Mobility
Clear temperature dependence! Has to do with electron energy
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Summary
• Physics of the Hall Effect
• Popular Applications
• Future Potential
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References
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•
•
•
•
•
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Kittel, Charles, Introduction to Solid State Physics, John Wiley & Sons, Inc.. 2005
Kasap, Safa. Hall Effect in Semiconductors, University of Saskatchewan, 2001
Non Destructive Testing Resource Center, http://www.ndted.org/EducationResources/CommunityCollege/MagParticle/Physics/Measuring.ht
m , 2004
Power Systems Design, http://www.powersystemsdesign.com/hall-effect-sensorsdeliver-higher-efficiency-in-brushless-dc-motors?a=1&c=1399#, 2004
Ando, Tsuneya; Matsumoto, Yukio; Uemura, Yasutada (1975). Theory of Hall Effect
in a Two-Dimensional Electron System. J. Phys. Soc. Jpn. 39 (2): 279–288.
Spin effect M.I. Dyakonov (2007). Magnetoresistance due to edge spin
accumulation. Phys. Rev. Lett. 99 (12): 126601
N. A. Sinitsyn (2008). Semiclassical Theories of the Anomalous Hall Effect. Journal
of Physics: Condensed Matter 20 (2): 023201.
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