Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 7
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2.2 Tertiary Compounds and Heterostructures
In addition to the binary Ill-V nitrides, it is possible to grow trinary compounds
such as AIGaN and InGaN. These compounds have the benefit of allowing for the
tuning of the bandgap of the compound by adjusting the ratio of Ga:AI or Ga:ln. The
fractional composition of the tertiary compound is generally written as AlxGa -xN, where
x is the Aluminum (or Indium) fraction of the alloy. The lattice constant of the alloy turns
out to be simply related to the lattice constants of the two binary compounds the
semiconductor is composed of. This relation is known as Vegard's law and it states that
the lattice constant (or any other parameter which can be related in this way) for the
alloy is given by :
aAIGaN = aAIN X + aGaN (1 - X) (2.2.1)
Many other parameters, such as phonon frequencies  and piezoelectric
constants , can be determined for alloys using Vegard's or a Vegard's-like law.
The bandgap, on the other hand, generally is not linear in the In or Al fraction
used. Generally the dependence of the bandgap on the fraction x is given by a
Vegard's-like relation with an additional bowing parameter b :
Eg(AlxGal_xN) = x Eg(AIN) + (1 - x) Eg(GaN) - b x (1 - x) (2.2.2)
The solid and dashed lines in Figure 2.1 represent this relation for the trinary
compounds derived from the binaries they connect, e.g. the line between AIN and GaN
represents the bandgap of AlxGa-_xN.
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Llopis, Antonio. Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures, dissertation, May 2012; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc115113/m1/17/: accessed November 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .