Odd results from mesh current analysis in a circuit with a diode

Question

I have this circuit:

^{simulate this circuit – Schematic created using CircuitLab}

The reverse saturation current of the diode is 10^-6 A.

I use mesh current analysis to find the current inside the diode:

And putting this into WolphramAlpha gives I2 = 0.99...A so the current inside the diode is 0.

But I dont get it why this is happening.

Also if R1 becomes 100Ω there isnt a real solution to the system of the equation from mesh current analysis.Where am I wrong?

Answer 1

You have the wrong sign for the voltage across the diode. You should be adding instead of subracting here:

(Also I'm not sure where the "+1" term comes from...If it's from inverting the Shockley diode equation, then you have it in the wrong place and forgot to multiply it by \$I_s\$, but you can probably ignore it and get an answer that's close enough to correct)