  It is well established that the hole density in the prototypical
superconductor La$_{2-x}$Sr$_x$CuO$_4$ is very inhomogeneous due to Sr-dopant
induced disorder. On the other hand, until recently it is widely believed that
the hole distribution in HgBa$_2$CuO$_{4+\delta}$ and
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ doped by interstitial oxygen is much more
uniform. Recent nuclear magnetic resonance measurements indicate, however, that
the charge inhomogeneity in HgBa$_2$CuO$_{4+\delta}$ is close to that in
La$_{2-x}$Sr$_x$CuO$_4$. Calculations performed in the present paper confirm
this observation. We also show that the charge inhomogeneity is most pronounced
at the surface layer that can be probed by scanning tunneling microscope. Our
simulations demonstrate that, despite having similar amplitudes of charge
inhomogeneity, the hole mean free path in HgBa$_2$CuO$_{4+\delta}$ is
substantially longer than that in La$_{2-x}$Sr$_x$CuO$_4$. The screening of
Coulomb repulsion in HgBa$_2$CuO$_{4+\delta}$ is also stronger. These two
reasons might explain the difference in superconducting critical temperatures
between these two compounds.
