  Radioactive noble gas radon ($\mathrm{^{222}Rn}$) is one of the major
background sources below the MeV region in rare event search experiments. To
precisely measure radon concentration in purified gases, a radon detector with
an electrostatic collection method is widely used. In this paper, we discussed
the improvements of a radon detector by installing a new PIN-photodiode
($28\times28$ $\mathrm{mm}$) whose surface area is $2.5$ times larger than that
used previously ($18\times18$ $\mathrm{mm}$). We evaluated the detector's
performance by serially connecting two radon detectors equipped with two types
of PIN-photodiodes. As a result of the calibrations, we found an improvement of
$(3.8\pm2.4)\%$ in the detection efficiencies below $1.0$ $\mathrm{g/m^{3}}$,
while a $10$-$20\%$ improvement occurred above this level. The intrinsic
background of the detector equipped with the large PIN-photodiode was measured
as $0.24^{+0.09}_{-0.05}$ $\mathrm{mBq/m^{3}}$. This background level is
consistent with the radon detector with the small PIN-photodiode, although we
installed the large one. This improvement is useful for applications in radon
emanation measurements from a material, which also emits water from its
surface.
