69
components given as
dAB =
X
CD
Egap
AB + Egap
CD
gap
2 − EABCD
2
(6.2)
In the equation above AB corresponds to the compound for which the distance
measure has to be calculated and the summation index CD corresponds
to other compounds in the set of binary compounds which are combined with
AB to form alloys. Based on the distance measure the compounds with cutoff
distance measures will be clustered together. The clustering of compounds
like ZnO and GaN, CdS and CdSe, ZnTe and CdTe, for which the thermodynamic/
light absorption properties of the solid solutions have already been
explored experimentally complements our study 119, 128, 129. As one would
expect on the chemical grounds, clustering naturally leads to the grouping of
the chalcogenides of the Group 12 elements, chalcogenides of Group 14 elements,
silver halides and the compounds of the trivalent ions with the Group
15 elements. As can be seen from the values close to zero along the block
diagonal in the dendrogram plot that in most of the cases when the mixtures
are formed from compounds in the same group, the resultant bandgaps differ
only by 0.5 eV from the average of the bandgaps. On the other hand, mixing
of the compounds from different groups leads to a significant reduction of
the bandgap with respect to the average of the bandgaps in most of the cases
as shown with the red blocks. The detailed description of the above trend
would require electronic structure analysis of every mixture which is beyond
the scope of the current work.
Figure 6.6(a) and (b) show the bandgap and enthalpy of mixing Hmix of
the mixture as given by equation (6.1). Since, The positive correlation between
the bandgap and the stability 130 renders some of the mixtures metallic due
to the large positive heat of mixing. As one would anticipate that the mixing
of compounds with very different lattice constants will be energetically unfavorable,
the red regions in Figure 6.6(b) manifest the expected trend. For
example, ZnO, GaN, ScN have similar volumes, so their mixture with the tellurides,
selenides or compounds of lead which have much larger volumes result
to significantly positive heat of mixing which in turn leads to zero bandgap
of those mixtures. Thus, exploring mixtures of compounds with similar lattice
constant will have a higher probability of giving compounds with a finite
bandgap.
Combiningly, Figure 6.5 and 6.6 show that the bandgap of most of the
stable mixtures along the block diagonal 1 (bottom left to top right) have
bandgap of 2.5 eV except the block containing the chalcogenides of zinc and