## Hall effect analysis

HCS Hall effect measurement system & TFA thin film analysis

When a semiconductor, coursing with an electric current, finds itself nestled in the embrace of a magnetic field, a curious phenomenon unveils itself, known as the Hall effect. This intriguing effect, orchestrated by the graceful hand of the Lorentz force, exerts its influence on the fleet-footed charge carriers journeying through the magnetic realm.

Picture this: the Lorentz force, like a silent conductor, guides the charge carriers along an arc that stands perpendicular to the magnetic field lines. As this orchestra of charge carriers sways in unison, a congregation of them gathers on one side of the semiconductor. This congregation gives birth to an electric field, one that stands defiantly perpendicular to both the magnetic field and the current’s course.

The voltage generated by this field becomes known as the Hall voltage, affectionately referred to as ‘V Hall.’

Now, should a harmonious equilibrium bloom between the electric field of the Hall voltage and the Lorentz force, a proportional trinity is formed, uniting the Hall voltage (V H), magnetic field (B), and current (I). This holy matrimony of variables is known as the Hall coefficient (R H), a parameter that also bears allegiance to the thickness of the semiconductor (d).

Measuring the Hall coefficient necessitates a deft calculation. One must gauge the Hall voltage for a given magnetic field, coupled with the strength of the electric current, and the thickness of the semiconductor. The formula dances as follows:

**\[V_{H} = \frac{R_{H} ⋅ I ⋅ B}{d}\]**

Or, should you desire the Hall coefficient directly:

**\[R_{H} = \frac{V_{H} ⋅ d}{I ⋅ B}\]**

The story, however, unfolds with an added layer of intrigue. Depending on the type of semiconductor (p-type or n-type), a Hall voltage of either positive or negative temperament is bestowed upon us. And if one charge carrier type reigns supreme in the transportation process, one can delve even deeper. By employing an elegant formula, the charge carrier density ‘n’ and mobility ‘m’ of the sample can be unraveled:

**\[n = \frac{1 }{R_{H} ⋅ e}\]**

**\[μ = \frac{R_{H}}{ρ}\]**

Where ‘e’ stands as the charge of the charge carrier, and ‘ρ’ represents the specific resistance of the material.

Introducing the Linseis Hall measuring device, a guardian of knowledge in a vast temperature spectrum, offering a choice between two magnet types. Opt for the steadfast permanence of a magnet that bestows three fixed magnetic field strengths (+ field, 0 field, and – field) or the versatile electromagnet, which whispers the secrets of continuous magnetic field strengths.

Our instruments strictly adhere to both national and international standards, including ASTM F76 – 08 (Standard Test Methods for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors). They are proficient in delivering precise measurements of the Hall coefficient, catering to various elements as per your business requirements. These Hall measurement instruments are versatile and excel in diverse applications, including operating in vacuum conditions when necessary. Data collection is streamlined and easily monitored through the user-friendly Windows operating system.

## 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.

**Do you require a personalized consultation for a specific device?**

**Interested in conducting a test measurement?**

**Don’t hesitate to get in touch with our team of application experts!**