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# Hall Effect Measurements are Essential for Characterizing High Carrier Mobility in Materials

- Monday, 01 August 2011

The Hall effect can be observed when the combination of a magnetic field through a sample and a current along the length of the sample create an electrical current perpendicular to both the magnetic field and the current, which in turn creates a transverse voltage perpendicular to both the field and the current. The underlying principle is the Lorentz force: the force on a point charge due to electromagnetic fields.

Hall effect measurements are invaluable for characterizing semiconductor materials, whether they are silicon-based, compound semiconductors, thin-film materials for solar cells, or nanoscale materials like graphene. The measurements span low-resistance (highly doped semiconductor materials, high-temperature superconductors, dilute magnetic semiconductors, and GMR/ TMR materials) and high-resistance semiconductor materials, including semi-insulating GaAs, gallium nitride, and cadmium telluride.

A Hall effect measurement system is useful for determining various material parameters, but the primary one is the Hall voltage (V_{H}). Carrier mobility, carrier concentration (n), Hall coefficient (R_{H}), resistivity, magnetoresistance (R_{B}), and the carrier conductivity type (N or P) are all derived from Hall voltage.

As researchers develop next-generation ICs and more efficient semiconductor materials, they’re particularly interested in materials with high carrier mobility, which is what’s sparked much of the interest in graphene. This oneatom-thick form of carbon exhibits the quantum Hall effect and, as a result, relativistic electron current flow. Researchers consider Hall effect measurements crucial to the future of the electronics industry.

Materials with high carrier mobility allow creating devices that obtain maximized current flow at lower power levels, with faster switching times and higher bandwidth. A manipulation of Ohm’s Law (Figure 1) shows the importance of carrier mobility in maximizing current. The current is directly proportional to carrier mobility.

The options for maximizing current flow through a device include increasing voltage, charge carrier concentration, the cross-sectional area of the sample, or the mobility of the charge carriers. All but the last of these have serious disadvantages.

### Measuring Mobility

The first step in determining carrier mobility is to measure the Hall voltage (V_{H}) by forcing both a magnetic field perpendicular to the sample (*B*) and a current through the sample (*I*). This combination creates a transverse current. The resulting potential (V_{H}) is measured across the device. Accurate measurements of both the sample thickness (*t*) and its resistivity (*ρ*) are also required. The resistivity can be determined using either a four-point probe or the van der Pauw measurement technique. With just these five parameters (*B*, *I*, *V _{H}*,

*t*, and resistivity), the Hall mobility can be calculated:

Both Hall voltages and the measured van der Pauw resistivity are typically quite small, so the right measurement and averaging techniques are critical for accurate mobility results.

Figure 2 illustrates the measurement configurations for both the Hall voltage and the van der Pauw resistivity measurement. The two measurement configurations both use four contacts and involve forcing a current and measuring a voltage. However, in addition to different connection schemes, the Hall voltage measurements require a magnetic field.

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