  Among the Fe-based superconductors, Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ is unique in
that its crystal structure is the simplest and the electron correlation level
is the strongest, and thus it is important to investigate the
doping($x$)-temperature ($T$) phase diagram of this system. However, inevitably
incorporated excess Fe currently prevents the establishment of the true phase
diagram. We overcome the aforementioned significant problem via developing a
new annealing method termed as "Te-annealing" wherein single crystals are
annealed under Te vapor. Specifically, we conducted various magnetotransport
measurements on Te-annealed superconducting Fe$_{1+y}$Te$_{1-x}$Se$_{x}$. We
observed that crossover from the incoherent to the coherent electronic state
and opening of the pseudogap occurs at high temperatures ($\approx$ 150 K for
$x$ = 0.2). This is accompanied by a more substantial pseudogap and the
emergence of a phase with a multi-band nature at lower temperatures (below
$\approx$ 50 K for $x$ = 0.2) before superconductivity sets in. Based on the
results, the third type electronic phase diagram in Fe-based high-$T_c$
superconductors is revealed.
