  We study the formation of molecular precursors to dust in the ejecta of
Population III supernovae using a chemical kinetic approach. Our work focuses
on zero-metallicity 20 Msun and 170 Msun progenitors, and we consider
fully-macroscopically mixed and unmixed ejecta. The nucleation stage for small
silica, metal oxides and sulphides, pure metal, and carbon clusters is
described with a new chemical reaction network. We consider the effect of the
pressure dependence of critical nucleation rates, and test the impact of
microscopically-mixed He+ on carbon dust formation. The unmixed ejecta of a 170
Msun progenitor supernova synthesizes ~ 5.6 Msun of small clusters, while its
20 Msun counterpart produces ~ 0.103 Msun. Our results point to smaller amounts
of dust formed in the ejecta of Pop. III supernovae by a factor ~ 5 compared to
values derived by previous studies, and to different dust chemical composition.
Such deviations result from some erroneous assumptions made, the inappropriate
use of classical nucleation theory to model dust formation, and the omission of
the synthethis of molecules in supernova ejecta. Unmixed ejecta of massive Pop.
III supernovae chiefly form silica and/or silicates, and pure silicon grains
whereas their lower mass counterparts form a dust mixture dominated by silica
and/or silicates, pure silicon and iron sulphides. Amorphous carbon can only
condense in ejecta where the carbon-rich zone is deprived of He+. The first
dust enrichment to the primordial gas in the early universe from Pop. III
massive supernova comprises primarily pure silicon, silica and silicates. If
carbon dust is present at redshift z> 6, alternative dust sources must be
considered.
