  The superconducting Cu_xBi_2Se_3 is an electron-doped topological insulator
and is a prime candidate of the topological superconductor which still awaits
discovery. The electrochemical intercalation technique for synthesizing
Cu_xBi2Se3 offers good control of restricting Cu into the van-der-Waals gap and
yields samples with shielding fractions of up to ~50%. We report essential
details of this synthesis technique and present the established superconducting
phase diagram of T_c vs x, along with a diagram of the shielding fraction vs x.
Intriguingly, those diagrams suggest that there is a tendency to spontaneously
form small islands of optimum superconductor in this material.
