Hall Effect and Conductivity Measurements in Semiconductor Crystals and Thin Films

Abstract

The principle of the Hall effect and its application to the characterization of semiconductors are described. The physical origin of the Hall effect, discovered by Edwin H. Hall in 1879, is the Lorentz force acting on the charge carriers in a solid. The Hall voltage, which is generated perpendicular to the current flow in the sample, is proportional to the carrier mobility in the sample. Its sign depends on the type of the (majority) charge carrier (electrons or holes) and can be used to determine if a semiconductor is n‐ or p‐type. From the measured Hall voltage, the carrier concentration n of the Hall sample can be determined. In combination with a conductivity (σ) measurement, the Hall mobility μ H of the sample can be calculated according to μ = σ/( qn ). Though in principle simple, the preparation of the Hall measurement samples and the interpretation of the measurements needs some care and the appropriate theory for the charge carrier transport in semiconductors. The normal Hall effect can be explained by a semiclassical theory, while the quantum Hall effect, discovered by von Klitzing in 1980, is a true quantum effect, which occurs only at very high fields at low temperatures in two‐dimensional electron gases. The so‐called von Klitzing constant R K = h / e 2 = 25812.807557(18) Ω, which is extracted from a quantum Hall measurement, can be used for the definition of the international standard for resistance. Today, the (normal) Hall effect finds applications for the characterization of semiconductors and mainly for Hall sensors (produced in numbers of billions/year) for the measurement of magnetic fields, for noncontact (proximity) switches, speed detectors, position, and current sensors.

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