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Exppresion for saturation current in GaN based diodes $$J_{s1}=e[\sqrt\frac{D_n}{\tau_n}\frac{n_i^2}{N_D}+\sqrt\frac{D_p}{\tau_p}\frac{n_i^2}{N_A}]$$ For the simplicity, parameters: \$e=10^{-19}, N_D=N_A=10^{16},n_i=10^{-10},D_n=25,D_p=5,\tau_n=\tau_p=10^{-9}\$ at room temperature (T = 300K) i get value ~ \$10^{-50}A/cm^2\$ (too low?), is this the right way to calculate saturation current or am i missing something ?

sorry for my bad english, and thanks in advance

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  • \$\begingroup\$ is e = elementary charge * cross section of device ? \$\endgroup\$
    – johnger
    May 16, 2018 at 19:26
  • \$\begingroup\$ No, e just represents elementary charge, Js = Is (saturation current) * S (cross section), sorry i forgot to mention it in first sentence,... saturation current density \$\endgroup\$
    – Johnny
    May 16, 2018 at 20:07

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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 τp and τn 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.

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).

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