GaN saturation current
Maybe because the "... ideal saturation current is much lower than a practical device’s current at low voltages."


  The matching process of simulation to the experimental device started with the
  dark I-V curve, which is the forward characteristic of the device when the
  device is not stimulated by an external beta source. The dark I-V curve is
  composed of different regions. These regions are controlled by various
  physical parameters within the device. The space charge generation region is
  controlled by the diffusion of charge carriers within the device. This
  current, also called saturation current, can be calculated for an ideal diode
  using Equation 5.
  
  $$I_{s}=qA\left(\sqrt\frac{D_n}{\tau_n}\frac{n_i^2}{N_D}+\sqrt\frac{D_p}{\tau_p}\frac{n_i^2}{N_A}\right)$$
  
  The parameters used in the equation are q for elementary charge; A for the
  cross-sectional area of the device; Dn and Dp for
  the diffusion constants in GaN of electrons and holes, respectively; and
  &tau;p and &tau;n for the lifetime of the electrons
  and holes in GaN, respectively; ni for the intrinsic carrier
  concentration of GaN; ND for the donor doping concentration; and
  NA for the electron doping concentration. Thus, the space charge
  generation current is controlled by these physical parameters of the device.
  The space charge generation current was matched by using the proper dimensions
  and doping concentrations of the real device. However, due to the extremely
  low value of saturation current the intrinsic carrier concentration of GaN,
  the ideal saturation current is much lower than a practical device's current
  at low voltages. This extra current is due to other physical parameters within
  the device, such as trap-assisted tunneling and shunt resistance.
  
  &mdash; Modeling and Simulation of a Gallium Nitride (GaN) Betavoltaic Energy Converter (W.B. Ray II, M. S. Litz, J. A. Russo)


An approach for a more realistic model could be Thermal Study of Gallium Nitride - Metal Contact (S. S. Al-Ameer).