Two Dimensional Electron Systems
At present, there are mainly three types of 2-D electron systems acheived in experiment
- MOSFET-Metal Oxide Semiconductor Field Effect Transistor
- Superlattice
- Liquid Helium Surface
In MOSFET, inversion layers are formed at the interface between a semiconductor and an insulator or between two semiconductors, with one of them acting as an insulator. The system in which the Quantum Hall Effect(QHE) was discovered has Si for the semiconductor, SiO
for the insulator. Figure 2 is a schematic side view of a silicon MOSFET showing the aluminum gate, the SiO insulator and the p-type Si crystal substrate. The principle of the inversion layer is quite simple. It is arranged that an electric field perpendicular to the interface attracts electrons from the semiconductor to it. These electrons sit in a quantum well created by this field and the interface. The motion perpendicular to the interface is quantized and thus has a fundamental rigidity which freezes out motional degrees of freedom in this direction. The result is a two-dimensional system of electrons. Further, the wavelengths of these electrons are long so that an effective mass approxiamtion with parabolic bands is quite good. The total self-consistent potential seen by the electrons is conveniently described by the picture of "band bending". That is to say, the periodic lattice potential gives rise to energy bands, and the slowly varying electric potential then is regarded as bending these bands. Figure 3 gives the schematic diagram for this process.(Charge density
)
for the insulator. Figure 2 is a schematic side view of a silicon MOSFET showing the aluminum gate, the SiO insulator and the p-type Si crystal substrate. The principle of the inversion layer is quite simple. It is arranged that an electric field perpendicular to the interface attracts electrons from the semiconductor to it. These electrons sit in a quantum well created by this field and the interface. The motion perpendicular to the interface is quantized and thus has a fundamental rigidity which freezes out motional degrees of freedom in this direction. The result is a two-dimensional system of electrons. Further, the wavelengths of these electrons are long so that an effective mass approxiamtion with parabolic bands is quite good. The total self-consistent potential seen by the electrons is conveniently described by the picture of "band bending". That is to say, the periodic lattice potential gives rise to energy bands, and the slowly varying electric potential then is regarded as bending these bands. Figure 3 gives the schematic diagram for this process.(Charge density)
Another type of two-dimensional electron system is formed in the heterostructures of two semiconductors. Using molecular beam epitaxy(MBE) technique, people can grow two semiconductors alternately to form a one dimensional sandwich like structure. Each layer has a width of about several nanometers. They are called superlattice. They can also be grown by metal-organic chemical vapor deposition(MOCVD). For example, in GaAs-Ga
superlattice, a certain controlled number of layers of GaAs is followed by an almost perfectly matched sequence of layers of GaAlAs. The GaAlAs is deliberately doped n-type, which puts mobile electrons into its conduction band. These electrons will migrate to fill the few holes on the top of the GaAs valence band but most of them will end up in states near the bottom of the GaAs conduction band. However, there is a positive charge left on the donor impurities which attracts these electrons to the interface and bends the bands in the process. This is the source of the electric field in this system. The transfer of electrons from GaAlAs to GaAs will continue until the dipole layer formed from the positive donors and the negative inversion layer is sufficiently strong. This dipole layer gives rise to a potential discontinuity which finally makes the Fermi level of the GaAs equal to that of the GaAlAs. Figure 4 shows the band structure. (Charge density
)
superlattice, a certain controlled number of layers of GaAs is followed by an almost perfectly matched sequence of layers of GaAlAs. The GaAlAs is deliberately doped n-type, which puts mobile electrons into its conduction band. These electrons will migrate to fill the few holes on the top of the GaAs valence band but most of them will end up in states near the bottom of the GaAs conduction band. However, there is a positive charge left on the donor impurities which attracts these electrons to the interface and bends the bands in the process. This is the source of the electric field in this system. The transfer of electrons from GaAlAs to GaAs will continue until the dipole layer formed from the positive donors and the negative inversion layer is sufficiently strong. This dipole layer gives rise to a potential discontinuity which finally makes the Fermi level of the GaAs equal to that of the GaAlAs. Figure 4 shows the band structure. (Charge density)
Two-dimensional electron system can also be formed in the surface of liquid Helium. There exists a potential barrier of about 1eV in the surface of liquid Helium which prevents electrons from transmitting into the liquid. On the other hand, the mirror potential attracts the electrons in the surface, resulting a 2D electron system.(Charge density
)
)Quantum Hall effect has been observed in the first two types.
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