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.
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