5: Hall Effect
- Page ID
- 18970
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In this chapter we discuss another type of inductive energy conversion device, the Hall effect device. While these devices may be made from conductors, they are more often made from semiconductors, like silicon, which are easily integrated into microelectronics. The Hall effect was discovered using gold by Edwin Hall in 1879 [57]. The first practical devices were produced in the 1950s and 1960s when uniform semiconductor materials were first manufactured [57].
Hall effect sensors are used to measure some hard to observe quantities. Without external tools, humans cannot detect magnetic field. However, a small, inexpensive Hall effect sensor can act as a magnetometer. Also, the Hall effect can be used to determine if a semiconductor is n-type or p-type. One of the first applications of Hall effect devices was in computer keyboard buttons [57]. Today, Hall effect devices are used to measure the rotation speed of a motor, as flow rate sensors, in multiple types of automotive sensors, and in many other applications.
- 5.1: Physics of the Hall Effect
- This page covers Hall effect devices that convert magnetic energy to electrical energy via the Lorentz force, highlighting their role as sensors, especially in detecting weak electrical signals. It explains how these devices operate using charge carriers in conductors and semiconductors while detailing the parameters like current density and Hall resistance. Additionally, it reviews a specific silicon-based device that calculates a resistance of 0.09 Ohms and a power output of 1.
- 5.2: Magnetohydrodynamics
- This page discusses magnetohydrodynamic devices that convert magnetic energy to electrical energy using conductive liquids or plasmas, highlighting the distinction from the Hall effect in solids. It explains the Lorentz force equation and the state of plasma, which consists of charged particles.
- 5.3: Quantum Hall Effect
- This page covers the discovery of the quantum Hall effect, detailing Klaus von Klitzing's integer quantum Hall effect (1980) and the fractional quantum Hall effect (1998) by Laughlin, Störmer, and Tsui. It explains how these phenomena in two-dimensional electron gases under low temperatures and strong magnetic fields lead to quantized Hall resistance measurements.
- 5.4: Applications of Hall Effect Devices
- This page discusses Hall effect devices, which are small and affordable semiconductor components categorized into analog and digital types. Analog devices measure magnetic fields with temperature calibration, while digital devices combine sensors and circuitry for digital output. Their applications include temperature, pressure, and current measurement, as well as switches and proximity sensing.
- 5.5: Problems
- This page explains the Hall effect and its use in semiconductor devices for measuring magnetic fields. It covers methods to enhance output voltage, calculations for charge carrier concentration and magnetic flux density, and the consistency of Hall resistance expressions. Additionally, it includes exercises that encourage readers to apply theoretical concepts through practical computations, focusing on the interplay between current, magnetic field, and voltage in Hall effect scenarios.
Thumbnail: Hall effect. (Public Domain; Hajder via Wikipedia)