Résumé
We study the formation of molecular precursors to dust in the ejecta of Population III supernovae (Pop. III SNe) using a chemical kinetic approach to follow the evolution of small dust cluster abundances from day 100 to day 1000 after explosion. Our work focuses on zero-metallicity 20 M-circle dot and 170 M-circle dot progenitors, and we consider fully macroscopically mixed and unmixed ejecta. The dust precursors comprise molecular chains, rings, and small clusters of chemical composition relevant to the initial elemental composition of the ejecta under study. The nucleation stage for small silica, metal oxides and sulfides, pure metal, and carbon clusters is described with a new chemical reaction network highly relevant to the kinetic description of dust formation in hot circumstellar environments. We consider the effect of the pressure dependence of critical nucleation rates and test the impact of microscopically mixed He+ on carbon dust formation. Two cases of metal depletion on silica clusters (full and no depletion) are considered to derive upper limits to the amounts of dust produced in SN ejecta at 1000 days, while the chemical composition of clusters gives a prescription for the type of dust formed in Pop. III SNe. We show that the cluster mass produced in the fully mixed ejecta of a 170 M-circle dot progenitor is similar to 25 M-circle dot whereas its 20 M-circle dot counterpart forms similar to 0.16 M-circle dot of clusters. The unmixed ejecta of a 170 M-circle dot progenitor SN synthesize similar to 5.6 M-circle dot of small clusters, while its 20 M-circle dot counterpart produces similar to 0.103 M-circle dot. Our results point to smaller amounts of dust formed in the ejecta of Pop. III SNe by a factor of similar to 5 compared to values derived by previous studies, and to different dust chemical compositions. Such deviations result from some erroneous assumptions made, the inappropriate use of classical nucleation theory to model dust formation, and the omission of the synthesis of molecules in SN ejecta. We also find that the unmixed ejecta of massive Pop. III SNe 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 sulfides. Amorphous carbon can only condense via the nucleation of carbon chains and rings characteristic of the synthesis of fullerenes when the ejecta carbon-rich zone is deprived of He+. The first dust enrichment to the primordial gas in the early universe from Pop. III massive SN comprises primarily pure silicon, silica, and silicates. If carbon dust is present at redshift z > 6, alternative dust sources must be considered.