# Two-Dimensional Electron Gas

2DEG

The term two-dimensional electron gas (2DEG) refers to the collection of electrons moving in a two-dimensional plane within a solid material. Electrons can thus move freely in this plane, while they are restricted in the third dimension, either by physical barriers or by a strong magnetic field.

Once such a 2DEG is exposed to a strong perpendicular magnetic field, a quantum Hall effect (QHE) can occur. The magnetic field then splits the energy bands in the material and forces the electrons to discrete quantized energy levels. If the temperature is kept near absolute zero in the process, the electrons fill the lowest energy levels, called "Landau levels." The quantum Hall effect is particularly remarkable because it leads to an extraordinary quantization of electrical resistance.

The quantum Hall effect is often characterized by its filling factors, which are the ratio of the number of electrons per Landau level to the number of magnetic flux quanta in the system. For certain filling factors, the electrical resistances of the 2DEG plateau take only discrete, quantized values, resulting in high precision in the resistance measurement.

In quantum Hall effect sensors, these quantized values of electrical resistance are used to make high-precision measurements of magnetic fields. As the magnetic field changes, the quantized values of resistance also change, resulting in a characteristic pattern of resistance changes. This pattern is measured and analyzed to determine the strength of the magnetic field.

The use of 2DEG and the quantum Hall effect in sensors enables the development of extremely sensitive and accurate magnetic field sensors. These sensors have applications in various fields such as materials characterization, metrology, geophysical exploration, and magnetic resonance imaging (MRI) for medical imaging.