Not sure why picture looks blurry so attached it again:

The reverse current is due to the GMIN conductance (1e-12mho) ngspice inserts to all nodes vs ground to improve convergence. You can lower the GMIN with

.options GMIN=1e-14

GMIN=x resets the value of GMIN, the minimum conductance allowed by the program.
The default value is 1.0e-12.

That said, I don't expect the reverse current of these diodes to be accurate.

Thank you Stefan! Will try it out. And thanks for the heads up with the accuracy issue. I guess I'll put some test structure and measure the reverse biased current in the lab