We compare the superconducting phase-diagram under high magnetic fields (up to $H = 45$ T) of Fe$_{1+y}$Se$_{0.4}$Te$_{0.6}$ single crystals originally grown by the Bridgman-Stockbarger (BRST) technique, which were annealed to display narrow superconducting transitions and the optimal transition temperature $T_c gtrsim 14$ K, with the diagram for samples of similar stoichiometry grown by the traveling-solvent floating-zone technique as well as with the phase-diagram reported for crystals grown by a self-flux method. We find that the so-annealed samples tend to display higher ratios $H_{c2}/T_c$, particularly for fields applied along the inter-planar direction, where the upper critical field $H_{c2}(T)$ exhibits a pronounced downward curvature followed by saturation at lower temperatures $T$. This last observation is consistent with previous studies indicating that this system is Pauli limited. An analysis of our $H_{c2}(T)$ data using a multiband theory suggests the emergence of the Farrel-Fulde-Larkin-Ovchnikov state at low temperatures. A detailed structural x-ray analysis, reveals no impurity phases but an appreciable degree of mosaicity in as-grown BRST single-crystals which remains unaffected by the annealing process. Energy-dispersive x-ray analysis showed that the annealed samples have a more homogeneous stoichiometric distribution of both Fe and Se with virtually the same content of interstitial Fe as the non-annealed ones. Thus, we conclude that stoichiometric disorder, in contrast to structural disorder, is detrimental to the superconducting phase diagram of this series under high magnetic fields. Finally, a scaling analysis of the fluctuation conductivity in the superconducting critical regime, suggests that the superconducting fluctuations have a two-dimensional character in this system.
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