Limit Efficiency of a Silicon Betavoltaic Battery with Tritium Source

An idealized design of a silicon betavoltaic battery with a tritium source is considered, in which a thin layer of tritiated silicon is sandwiched between two intrinsic silicon slabs of equal width, and the excess charge carriers are collected by thin interdigitated n⁺ and p⁺ electrodes. The opposite sides of the device are covered with a reflecting coating to trap the photons produced in radiative recombination events. Due to photon recycling, radiative recombination is almost ineffective, so the Auger mechanism dominates. An analytical expression for the current-voltage curve is obtained, from which the main characteristics of the cell, namely, the open-circuit voltage, the fill factor, and the betaconversion efficiency, are found. The analytical results are shown to agree with the numerical ones with better than 0.1% accuracy. The optimal half-thickness of this device is found to be around 1.5 μm. The maximal efficiency increases logarithmically with the surface activity of the beta-source and has the representative value of 12.07% at 0.1 mCi/cm² and 14.13% at 10 mCi/cm².