The high electron-mobility transistor (HEMT) is a complicated heterostructure device used only when extremely-high performance is necessary. The HEMT uses a concept called modulation doping, and is sometimes called a modulation-doped field-efect transistor (MODFET). While in the early 1990s many believed that new materials (e.g. gallium arsenide) and new device structures (e.g. the HEMT) would compete with silicon CMOS, it appears that with shrinking lithographic dimensions the dominance of silicon CMOS is increasing. Still, the HEMT is a fairly interesting device that has been used commercially in high-frequency circuits.
The HEMT uses a heterojunction between two similar materials. Some junctions described in the literature are GaAs/AlGaAs, GaN/AlGaN, and InAs/AlSb. Below is a diagram of a HEMT assuming a GaAs/AlGaAs heterojunction.
n+ GaAs \ _______ /n+ GaAs
_________\ | Gate | /____________
\__|_______|__/ n+ AlGaAs
--------------------------------------2d electron gas
The HEMT is obviously a very complex device both to analyze and fabricate. The heterojunctions are made by epitaxial growth techniques (typically MBE). The top n+ GaAs layers are created to make ohmic contacts to the source and drain. The AlGaAs/GaAs heterojunction creates a quantum well of low electron energies at the interface. Electrons from the heavily doped AlGaAs are attracted by these low energy states and form a two-dimensional electron gas at the interface.
So what's the purpose for this complicated structure? Conductivity is greatly reduced by the presence of dopant ions, since these act as impurities that scatter carriers. In the HEMT structure, the electrons from the n+ AlGaAs are moved into the quantum well under the undoped AlGaAs "buffer layer." Since this area is undoped, the electrons in the 2-d electron gas have very high conductivity. The gate controls the conductivity of the 2-d channel in a similar way to the gate of a MESFET.
My personal opinion: The HEMT is not a serious competitor with the silicon MOSFET. It is far too expensive and difficult to fabricate. Like the MESFET, it would require new, deleterious circuit techniques. Furthermore, there is strong reason to believe that silicon CMOS will continue to shrink to ~50nm dimensions with the incorporation of silicon on insulator technology. Because of short-channel effects, it seems impossible to me that the HEMT and MESFET could be nearly as small.
Reference: Semiconductor Devices by Jasprit Singh