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8.5. COMPOUND SEMICONDUCTOR HETEROSTRUCTURES 119<br />

/(0+/-#12<br />

!<br />

,-. *<br />

*&'+<br />

+%+2')!2<br />

3!+%/<br />

!"#$%&'()<br />

inversion layer<br />

conduction band<br />

μ (semiconductor)<br />

E c<br />

-eφ(z)<br />

E v<br />

-eφ(z)<br />

#<br />

"<br />

μ (metal)<br />

eV<br />

valence band<br />

(chemical potentials<br />

do not have to line<br />

up, because insulator<br />

blocks current flow.)<br />

"<br />

Metal<br />

Insulator<br />

p-type semiconductor<br />

Figure 8.19: Band bending induces inversion layer in a MOSFET: applying a positive voltage<br />

to the gate electrode causes an electric field across the insulating oxide layer, which penetrates<br />

some distance into the semiconductor. This causes a varying potential φ(x) close to the surface<br />

<strong>of</strong> the semiconductor. If the resulting band-bending at the semiconductor/oxide interface becomes<br />

larger than the energy gap E g , then the conduction band edge falls below the chemical<br />

potential at the surface, causing an inversion layer to form.<br />

enough that the levels within it are quantised. New and potentially useful effects arise from<br />

the quantisation <strong>of</strong> energy levels in such quantum well structures (see below). Because the<br />

semiconductor in a MOSFET has to be doped in the region were the inversion layer can form,<br />

the electronic mean free path, and thereby the mobility, in the quantum well structure is small,<br />

which restricts its usefulness.<br />

8.5 Compound semiconductor heterostructures<br />

8.5.1 Bandstructure engineering<br />

Another way to make an inversion layer is to change the semiconductor chemistry in a discontinuous<br />

fashion within the same crystal structure. Epitaxial, atomic layer-by-layer growth<br />

allows the chemical composition and doping to be manipulated in fine detail. Such devices<br />

<strong>of</strong> compound semiconductors are used, for example, in semiconductor lasers for optical discs,<br />

in high speed electronics (e.g. cellphones) and high-speed lasers in telecommunications. This<br />

technology has also enabled fundamental science, by preparing very high mobility electron systems<br />

(e.g. for the quantum Hall effects), making “quantum wires” that are so thin as to have<br />

quantised levels, and for studies <strong>of</strong> the neutral electron-hole plasma as a possible superfluid.<br />

Alloys <strong>of</strong> compound semiconductors, e.g. Al 1−x Ga x As, allow one to continuously vary the<br />

optical gap and the position <strong>of</strong> the band edges by varying the composition x. Two different<br />

semiconductors will - when referred to the vacuum potential at infinity - have bands that will

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