# Hall Effect Analysis

###### HCS-Hall Effect Measurement System & TFA Thin Film Analyzer

If a **current is applied to a semiconducting device** which is **set into a magnetic field, the so called Hall Effect** can be observed. It is caused by the Lorentz Force, which is affecting the charge carriers to move perpendicular to the magnetic field lines in circular paths.

As a result, there will appear an increase in charge carriers at one side, which will result in an electric field inside the device, perpendicular to the magnet field and current direction, as. The voltage of this field can be measured and is considered as Hall Voltage V_{Hall}.

A steady state will be reached when the force of Hall voltage and the Lorentz force compensate each other, so there is a **proportional relation between Hall Voltage (V _{H}), magnetic field (H), current (I), the so called Hall coefficient (R_{H})**. The Hall coefficient also depends on the thickness of the device (d).

From this relationship, the **Hall Coefficient can be determined** by measuring the Hall Voltage under a given field and current with a known device thickness, following the formula:

\(V_{H} = \frac{R_{H} ⋅ I ⋅ H}{d}\) or \(R_{H} = \frac{V_{H} ⋅ d}{I ⋅ H}\)

Depending on the type of sample (p-type, n-type), the Hall Voltage will be positive or negative and in case of only one charge carrier (electrons or holes) determines the transport, the Charge carrier density n and mobility m can be calculated using the formulas:

\(n = \frac{1 }{R_{H} ⋅ e}\) and \(μ = \frac{R_{H}}{ρ}\)

With e = charge of the carrier and ρ = resistivity of the material.

You can choose between a permanent magnet, which can measure the Hall Voltage at three different Field points (+ field, 0 field and – field) and an electric magnet that can continuously measure during increasing the magnetic field strength, resulting in a more accurate measurement.

## Linseis Products For Hall Effect Analysis

### HCS 1 / 10/ 100

The HCS System (three magnet options) permits the characterization of semiconductor devices, it measures: **mobility, resistivity, charge carrier concentration and Hall constant**

### TFA

Measurement technology for sample **characterization of thin films (TFA)** from 80 nanometers (nm) to 20 micrometers (µm). Integrated **Hall constant** (**charge carrier concentration**, **hall mobility**) and resistivity measurements.

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