A majority carrier diode (MOS, Schottky) should have no
recovery "porch", just the depletion capacitances to
discharge. A bipolar diode (PN or BJT junction) will in
reality; model quality is always a question and small
signal transistors may simply assume no saturation
and have no proper modeling depending on plans and
laziness.
I would recommend using a series resistor and vpulse,
the forward (V-Vf)/R sets your forward current which
is a primary "knob" on charge stored (QRR). The reverse
time will also be modulated by the impedance and a
stiff voltage source would only be limited by diode
Rs, which might make the timescale unreasonably
short and more to the point, application-unrealistic.