  The ubiquity of planets poses an interesting question: when first planets are
formed in galaxies. We investigate this problem by adopting a theoretical model
developed for understanding the statistical properties of exoplanets. Our model
is constructed as the combination of planet traps with the standard core
accretion scenario in which the efficiency of forming planetary cores directly
relates to the dust density in disks or the metallicity ([Fe/H]). We
statistically compute planet formation frequencies (PFFs) as well as the
orbital radius ($<R_{rapid}>$) within which gas accretion becomes efficient
enough to form Jovian planets. The three characteristic exoplanetary
populations are considered: hot Jupiters, exo-Jupiters densely populated around
1 AU, and low-mass planets such as super-Earths. We explore the behavior of the
PFFs as well as $<R_{rapid}>$ for the three different populations as a function
of metallicity ($-2 \leq$[Fe/H]$\leq -0.6$). We show that the total PFFs
increase steadily with metallicity, which is the direct outcome of the core
accretion picture. For the entire range of the metallicity considered here, the
population of the low-mass planets dominates over the Jovian planets. The
Jovian planets contribute to the PFFs above [Fe/H]-1. We find that the hot
Jupiters form at lower metallcities than the exo-Jupiters. This arises from the
radially inward transport of planetary cores by their host traps, which is more
effective for lower metallicity disks due to the slower growth of the cores.
The PFFs for the exo-Jupiters exceed those for the hot Jupiters around
[Fe/H]-0.7. Finally, we show that the critical metallicity for forming Jovian
planets is [Fe/H]-1.2, which is evaluated by comparing the values of
$<R_{rapid}>$ between the hot Jupiters and the low-mass planets. The comparison
intrinsically links to the different gas accretion efficiency between them.
