  Using Scanning tunneling spectroscopy (STS), we report the correlation
between spatial gap inhomogeneity and the zinc (Zn) impurity resonance in
single crystals of
Bi$_{\mathrm{2}}$Sr$_{\mathrm{2}}$Ca(Cu$_{\mathrm{1-}x}$Zn$_{x}$)$_{\mathrm{2}}$O$_{\mathrm{8+}\delta}$
with different carrier (hole) concentrations ($p$) at a fixed Zn concentration
($x$ $\sim$ 0.5 % per Cu atom). In all the samples, the impurity resonance lies
only in the region where the gap value is less than $\sim$ 60 meV. Also the
number of Zn resonance sites drastically decreases with decreasing $p$, in
spite of the fixed $x$. These experimental results lead us to a conclusion that
the Zn impurity resonance does not appear in the large gap region although the
Zn impurity evidently resides in this region.
