We construct a semi-analytical model which includes a novel implementation of dust size evolution and the resulting H2 formation on dust grains in the early universe. We investigate the cosmic star formation rate and the reionization history, taking into acount the initial mass function transition from Pop III to Pop II stars due to dust cooling. We derive the star formation efficiencies for various host dark matter halo masses and discuss effects of the value of critical dust-to-gas mass ratio, 𝒟cr, on the reionization history. We conclude that the reionization completes before z = 6 in the case of the fiducail value Dcr = 7.4×10−8.

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