Why is the current like this?
The current looks like it does because the diode is non-linear at the low voltage provided by the source. 

It may be helpful to mention here the diode equation for a p-n junction:
$$
I=I_0(e^{V/\eta V_T}-1)
$$
where 
\$V\$ is voltage across the diode, \$I_0\$ is its reverse saturation current, \$V_T = kT/q\$ is the thermal voltage (about 26mV at room temp) and \$\eta\$ is approx 2 for silicon.

See also Shockley_diode_equation for more details.