the hall effects
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The Hall Effects
Richard Beck141A 2013
Hall Effect
• Discovery
• The physics behind it
• Applications
• Personal experiments
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Discovery
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Via Wikimedia Commons (public domain)
Richard Beck - Physics 141A, 2013
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 =
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Note: t refers to the thickness of the metal along the direction of the B-field
A Visual Representation
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From Non-Destructive Testing (NDT) Resource Center
Richard Beck - Physics 141A, 2013
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
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Via LessEMF.comVia the NDT Resource Center
Richard Beck - Physics 141A, 2013
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
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• Used expansively in rotating systems
• Anti-lock brakes, motor feedback, ignition
Via Power Systems Design, Ltd. Via Draper, 2005
Richard Beck - Physics 141A, 2013
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 current-carrying 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
• Much larger than normal Hall Effect, but not well understood ; Possible Berry-phase effect
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Via Toyosaki et al. 2004
Richard Beck - Physics 141A, 2013
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
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Clear temperature dependence! Has to do with electron energy
Richard Beck - Physics 141A, 2013
Summary
• Physics of the Hall Effect
• Popular Applications
• Future Potential
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References• 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.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Measuring.htm , 2004
• Power Systems Design, http://www.powersystemsdesign.com/hall-effect-sensors-deliver-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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