Single-photon counting MKIDs (microwave kinetic inductance detectors) are light detectors that use
the change in the electric properties of a superconductor due to electron excitations to detect individual
photons. Novel MKIDs are limited by an uncertainty in the down-conversion process from a photon to
a number of excited electrons, called the Fano factor. These Fano-limited MKIDs could be improved if
a method is found to lower the Fano factor, further increasing the resolving power of MKIDs, and pos-
sibly other detectors that rely on pair-breaking. In this report, a Monte Carlo simulation is constructed
to simulate a large number of individual photons incident on a superconductor. The data from the sim-
ulation is then used to calculate the Fano factor. Simulations are performed to test the dependence of
the Fano factor on both the choice of superconducting material (Sn, Nb and Al), and the energy of the
photon incident on the superconductor. F = 0.208 ± 0.003 is found independent of material and photon

energy. The dependency of the Fano factor on the phonon spectrum of the superconductor is tested
and the possible implementation of phonon spectrum tuning in order to improve the Fano factor are
discussed. We find that F can be reduced to F = 0.151 ± 0.003 by implementing a phonon band gap

from 0-2∆. The resolving power of an MKID then improves with up to 24%. To realise this band gap,
holes could be introduced in the superconductor, creating a pattern with a period of approximately 80
nm. The smallest feature size in this pattern would be approximately 40 nm, which is achievable with
current technology. It is unlikely that a perfect 0-2∆ band gap can be created and the real improvement
of F by implementation of a phonon band gap would probably be lower than 24%. We conclude that
improvement of the resolving power of an MKID via the Fano factor is possible in theory, but further
research is required to test the viability of such a band gap and calculate the specific shape and size
of these holes.