group the compounds in Figure 6.3 in six different groups based on the geometric
mean of the chemical scale factor 118. The range of geometric mean
of groups is shown in Table 6.1.
The grouping in Figure 6.3 shows an apparent correlation between the
crystal structure and the geometic mean of the chemical scale factor of the
compounds. For very small values of geometric mean (Group 1) the compound
prefers to have the low volume structure i.e. rocksalt or NiAs whereas at larger
values(Group 6) the compound prefer to have more open structure i.e. wurtzite
or zincblende. Few green parts in the Group 1 for compounds like LiF, LiCl
is the artifact of the calculation since these compounds are known to have the
rocksalt structure. On the other hand,the difference in energies of the wurtzite
and rocksalt structure of these compounds as per our calculations is of the
order of 0.05 eV which is small and can be safely ignored. The region of extreme
values of the geometric mean in Figure 6.3 i.e. Group 1 and 6 are the region
of extreme ionicity of the compounds with very small values indicating large
ionicity (more closed structures) whereas very large values showing greater
covalent character (more open structures) 118. On the other hand, the region
of moderate ionicity i.e. Group 2-5 is not dominated by one crystal structure.
Group 2 has large fraction of WZ and NiAs structures, Group 3 ZB structure,
Group 4 RS structure and Group 5 WZ and RS structures.
In Figure 6.4 we show the bandgap of all the compounds. The white regions
in the heatmap show the zero bandgap materials by which we can see that out
of 704 materials in each group very few turn out be semiconducting with the
smallest number of semiconductors in the NiAs structure and the largest number
in the ZB structure. The plot also shows that despite having the similar
heat of formation, the wurtzite and zincblende have quite dissimilar trend in
bandgaps(especially indirect gap) which is a well known phenomenon 126.
Hence, in cases where the WZ and ZB have significantly different bandgaps,
stabilizing the structure with the required bandgap can be achieved efficiently
due to the similar heats of formation.
In addition to modifying the structures to tune the bandgap, bandgap
engineering can also be achieved by making solid solutions of different semiconductors.
The same has been realized in the experiments in recent works
carried out in Domen’s group 119, 3 in which the mixture of GaN and ZnO
has the bandgap of 2.5 eV as opposed to the bandgap of 3.4 eV of the constituent
compounds GaN and ZnO. Thus, these experimental results suggest
that the alloying can be used as a method for the bandgap tailoring. Hence,
guided by the above experiments we also explore the alloys of binary compounds
in the wurtzite structures having the bandgap in the range of 1.0 -
3.5 eV. The stability of the alloy with respect to the constituent compounds