We report the structural, magnetic and electronic transport properties of SrFe$_{2-x}$Cu$_x$As$_2$ single crystals grown by self-flux technique. SrCu$_2$As$_2$ and SrFe$_2$As$_2$ both crystallize in ThCr$_2$Si$_2$-type (122-type) structure at room temperature, but exhibit distinct magnetic and electronic transport properties. The x-ray photoelectron spectroscopy(XPS) Cu-2p core line position, resistivity, susceptibility and positive Hall coefficient indicate that SrCu$_2$As$_2$ is an sp-band metal with Cu in the 3d$^{10}$ electronic configuration corresponding to the valence state Cu$^{1+}$. The almost unchanged Cu-2p core line position in SrFe$_{2-x}$Cu$_x$As$_2$ compared with SrCu$_2$As$_2$ indicates that partial Cu substitutions for Fe in SrFe$_2$As$_2$ may result in hole doping rather than the expected electron doping. No superconductivity is induced by Cu substitution on Fe sites, even though the structural/spin density wave(SDW) transition is gradually suppressed with increasing Cu doping.
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