  As an appealing concept for developing next-generation solar cells,
intermediate-band solar cells (IBSCs) promise to drastically increase the
quantum efficiency of photovoltaic conversion. Yet to date, a standing
challenge lies in the lack of materials suitable for developing IBSCs.
Recently, a new doping approach, termed non-compensated n-p codoping, has been
proposed to construct intermediate bands (IBs) in the intrinsic energy band
gaps of oxide semiconductors such as TiO$_2$. We explore theoretically the
optimal quantum efficiency of IBSCs based on non-compensated n-p codoped
TiO$_2$ under two different design schemes. The first preserves the ideal
condition that no electrical current be extracted from the IB. The
corresponding maximum quantum efficiency for the codoped TiO$_2$ can reach
52.7%. In the second scheme, current is also extracted from the IB, resulting
in a further enhancement in the maximum efficiency to 56.7%. Our findings also
relax the stringent requirement that the IB location be close to the optimum
value, making it more feasible to realize IBSCs with high quantum efficiencies.
