Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$ (0$leq x leq$1.00) single crystals with high-quality have been grown successfully using the travelling-solvent floating-zone technique. The patterns of X-ray diffraction suggest high crystalline quality of the samples. After post-annealing in flowing oxygen at 600 $^o$C, the crystals show sharp superconducting transitions revealed by AC susceptibility. The hole concentration $p$ is deduced from superconducting transition temperature ($T_c$), which exhibits a linear relation with La doping level $x$. It ranges from the heavily overdoped regime ($p approx$ 0.2) to the extremely underdoped side ($p approx$ 0.08) where the superconductivity is absent. Comparing with the superconducting dome in Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+delta}$ system, the effects from out-of-plane disorders show up in our samples. Besides the La doping level $x$, the superconductivity is also sensitive to the content of oxygen which could be tuned by post-annealing method over the whole doping range. The post-annealing effects on $T_c$ and $p$ for each La doping level are studied, which give some insights on the different nature between overdoped and underdoped regime.
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