Mapping the Photon Detection Efficiency of VUV Sensitive SiPMs from the Ultra-Violet to the Near Infra-Red

We present a flexible analytic model describing the Photo-Detection Efficiency (PDE) for P-on-N silicon photomultipliers. This model can be used for device characterization, PDE extrapolation from limited data or design optimization. The model uses six device specific parameters to describe PDE for a large range of wavelengths, angles of incidence, voltages and temperatures. Refractive index data taken from literature are inputs to the model, which also allows the prediction of PDE for devices operated in dense media. We present the measurement of the absolute PDE from 350-830~nm at 163~K for two UV sensitive devices: Hamamatsu VUV4 and the Fondazione Bruno Kessler VUV-HD3. Additional measurements of relative PDE versus angle are performed. We successfully fit the model to the data and show its predictive power, extrapolating the PDE to new wavelengths and to operation in liquid argon and xenon. Lastly we investigate optimizing efficiency for specific applications in astroparticle physics and quantum computing.