That small voltage is possibly an artifact of the simulator.
You are applying DC to the circuit but then simulating in the transient mode when there is no transient source.
What are you trying to determine?
If you want a plot of diode voltage vs. current you can use the .step function to vary a current-source current.
Then using the DC opt point simulation will give you voltage vs. current, as shown below.
I changed the horizontal current axis to exponential (left click on the axis) so the exponential voltage vs. current looks nearly like a straight line.
Look more closely at my simulation.
There is a .step function directive (SPICE Directive under Edit) which steps the current i in the current source ({i}).
And I did a .op simulation, not a transient simulation as I also showed.
Look up the .step function in the Help file if you don't understand.