Dust grains play a crucial role in the formation and evolution history of stars and galaxies in the early universe. We investigate the formation of dust grains in the ejecta of Population Ⅲ supernovae, including pair-instability supernovae, which are expected to occur in the early universe, applying a theory of non-steady state nucleation and grain growth. Dust formation calculations are performed for core-collapse supernovae with progenitor mass M_(pr) ranging from 13 to 30 solar mass and for pair-instability supernovae with M_(pr) = 170 and 200 solar mass. In the calculations, the time evolution of gas temperature in the ejecta, which strongly affects the number density and size of newly formed grains, is calculated by solving the radiative transfer equation, taking account of the energy deposition of radioactive elements. Two extreme cases are considered for the elemental composition in the ejecta, unmixed and uniformly mixed cases within the He core, and formation of CO and SiO molecules is assumed to be complete. The results of calculations for core-collapse supernovae and pair-instability supernovae are summarized as follows: in the unmixed ejecta, a variety of grain species condense, reflecting the difference of the elemental composition at the formation site in the ejecta; otherwise only oxide grains condense in the uniformly mixed ejecta. The average size of newly formed grains spans a range of 3 orders of magnitude, depending on the grain species and the formation condition, and the maximum radius is limited to less than 1 μm, which does not depend on the progenitor mass. The size distribution function of each grain species is approximately lognormal, except for Mg silicates, MgO, Si, and FeS in the unmixed case and Al_2O_3 in both cases. The size distribution function summed up over all grain species is approximated by a power-law formula whose index is -3.5 for the larger radius and -2.5 for the smaller one; the radius at the crossover point ranges from 0.004 to 0.1 μm, depending on the model of supernovae. The fraction of mass locked into dust grains increases with increasing the progenitor mass: 2%-5% of the progenitor mass for core-collapse supernovae and 15%-30% for pair-instability super-novae whose progenitor mass ranges from 140 to 260 solar mass. Thus, if very massive stars populated the first generation of stars (Population Ⅲ stars), a large amount of dust grains would be produced in the early universe. We also discuss the dependence of the explosion energy and the amount of ~(56)Ni in the ejecta, as well as the efficiency of formation of CO and SiO molecules, on the formation of dust grains in the ejecta of supernovae.
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