  We derive the photovoltaic conversion efficiency limit for two-terminal
tandem solar cells with a perovskite top cell and silicon bottom cell with an
embedded spectrum splitter. For large-bandgap top-cells a spectrum splitter
strongly enhances the efficiency because of enhanced light absorption and
trapping. A Lambertian spectral splitter shows a significantly improved effect
compared to a planar splitter: we find an ideal efficiency enhancement in the
thermodynamic limit for a 500 nm thick top cell of 6% absolute for bandgaps
above 1.75 eV. Vice versa, the use of a spectral splitter geometry enables the
use of a thinner top cell. Using experimental parameters for perovskite cells
we show that for a top-cell bandgap of 1.77 eV a 2.8% absolute efficiency can
be gained. The calculations in this work show that integration of a spectral
splitter into perovskite/silicon tandem cells with a top bandgap above 1.7 eV
can lead to a large increase in efficiency, even with realistic experimental
losses and non-unity reflection of the spectral splitter.
