3.1. BASIC CONCEPTS 85
Figure 3.5: Lattice constants and bandgap energies of ternary and quaternary compounds formed
by using nine group III–V semiconductors. Shaded area corresponds to possible InGaAsP and
AlGaAs structures. Horizontal lines passing through InP and GaAs show the lattice-matched
designs. (After Ref. [18];©c1991 Wiley; reprinted with permission.)
depends on the quality of the heterojunction interface between two semiconductors of
different bandgaps. To reduce the formation of lattice defects, the lattice constant of the
two materials should match to better than 0.1%. Nature does not provide semiconduc-
tors whose lattice constants match to such precision. However, they can be fabricated
artificially by forming ternary and quaternary compounds in which a fraction of the
lattice sites in a naturally occurring binary semiconductor (e.g., GaAs) is replaced by
other elements. In the case of GaAs, a ternary compound AlxGa 1 −xAs can be made
by replacing a fractionxof Ga atoms by Al atoms. The resulting semiconductor has
nearly the same lattice constant, but its bandgap increases. The bandgap depends on
the fractionxand can be approximated by a simple linear relation [2]
Eg(x)= 1. 424 + 1. 247 x ( 0 <x< 0. 45 ), (3.1.19)whereEgis expressed in electron-volt (eV) units.
Figure 3.5 shows the interrelationship between the bandgapEgand the lattice con-
stantafor several ternary and quaternary compounds. Solid dots represent the binary
semiconductors, and lines connecting them corresponds to ternary compounds. The
dashed portion of the line indicates that the resulting ternary compound has an indirect
bandgap. The area of a closed polygon corresponds to quaternary compounds. The