Hall effect measurement(홀 측정)

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The importance of the Hall effect is underscored by the need to determine accurately carrier density, electrical resistivity, and the mobility of carriers in semiconductors. The Hall effect provides a relatively simple method for doing this. Because of its simplicity, low cost, and fast turnaround time, it is an indispensable characterization technique in the semiconductor industry and in research laboratories.
1. Introduction
2. The Hall Effect and the Lorentz Force
The basic physical principle underlying the Hall effect is the Lorentz force.
⇒ ns = IB/q|VH|
This transverse voltage is the Hall voltage VH and its magnitude is equal to IB/qnd, where I is the current, B is the magnetic field, d is the sample thickness, and q (1.602 x 10-19 C) is the elementary charge. In some cases, it is convenient to use layer or sheet density (ns = nd) instead of bulk density.
⇒ = |VH|/RSIB = 1/(qnSRS)
If the conducting layer thickness d is known, one can determine the bulk resistivity
(r = RSd) and the bulk density (n = nS/d).
I=nqAvd (A=wd, where vd is the drift velocity)
Fm = IB/nA At equilibrium VHq/w = Fe
3. The van der Pauw Technique
In order to determine both the mobility and the sheet density ns, a combination of a resistivity measurement and a Hall measurement is needed. We discuss here the van der Pauw technique which, due to its convenience, is widely used in the semiconductor industry to determine the resistivity of uniform samples.
The contact occurs in the edges on the sample.
The point of contact is small enough to negligible.
The thickness of the sample is uniform.

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