2.10. TAILORING ELECTRONIC PROPERTIES 73
2.10 TAILORING ELECTRONIC PROPERTIES....................
In many applications we need bandgaps or carrier properties that are not available in naturally
occurring materials. It is possible to tailor electronic properties by using alloys and quantum
wells.
2.10.1 Electronic properties of alloys
Alloys are made from combinations of two or more materials and can be exploited to create
new bandgaps or lattice constants. In Chapter 1 we have discussed how the lattice constant of
alloys changes with composition. To the first order the electronic properties are also given by a
similar relation. Consider an alloyAxB 1 −xmade from materialsAwith bandstructure given by
EA(k)andBwith bandstructure given byEB(k). The bandstructure of the alloy is then given
by
Eall(k)=xEA(k)+(1−x)EB(k) (2.10.1)
Note that the energy averaging is done at the samekvalue. If we make an alloy from a direct
and an indirect material, one does not simply average the bandgaps to get the alloy bandgap.
Instead the bandgaps at the samekvalues are averaged and the bandgap is then given by the
lowest energy difference between the conduction and valence energies.
Basedontheequationabovetheeffectivemassofthealloyistobeaveragedas
1
m∗all=
x
m∗A+
(1−x)
m∗B(2.10.2)
It is important to note that alloys have inherent disorder since they have random arrangements
of atoms. This leads to disorder related scattering discussed in the next chapter.
2.10.2 Electronic properties of quantum wells
Quantum wells offer a very useful approach to bandstructure tailoring. In Section 2.2 we have
discussed electronic properties in quantum wells. In quantum wells electrons behave as if they
are in a 2-dimensional space and acquire properties that are especially useful for many electronic
and optoelectronic applications.
When two semiconductors with different bandgaps (and chemical compositions) form an in-
terface, We need to know how does the conduction band (valence band) on one material line
up with the other materials bands? This information is usually obtained through experiments.
There are three possible scenarios as shown in figure 2.30. In type I structures the layer bandgap
material “surrounds” the bandgap of the small gap material. In quantum wells made from such
materials, both electrons and holes are confined in the same physical quantum well. Most elec-
tronic and optoelectronic devices are based on type I lineup. In type II lineup the conduction
band of material A is below that of the material B, but the valence band of A is above that
of B as shown. In quantum wells made from such materials the electrons and holes are con-
fined in spatially different quantum wells. These structures are useful for applications in the
long wavelength regime, since their “effective” bandgap can be very small. Finally, in type III