At null temperature (0 Kelvin), is the current going through a diode (PN junction) null?

At null temperature (0 Kelvin), is the current going through a diode (PN junction) is null, for a positive voltage in a direct polarisation, above the built-in voltage of the depleted region ?

If your answer is yes, could you explain why the energetic electrostatic potential coming from the applied voltage could not play the same role as the thermic potential in presence of non null temperature : why can't the electrons move in the junction at null temperature thanks to the applied voltage at null temperature ?

If your answer is not, then how do you explain that in the Shockley current equation $$I=I_{\text{saturation}} \cdot (e^{V / V_T} -1),$$ one has $$I_{\text{saturation}}=0$$ at null temperature.

Thank you for your kind help

• What are the free electron/hole concentrations at T=0? – Jon Custer Apr 30 at 18:43
• @John Custer Tunneling may still be possible. – my2cts Apr 30 at 18:55
• @my2cts - what initial state tunneling to what final state? And, what is the tunneling probability at T=0? – Jon Custer Apr 30 at 20:27