If you reduce RELTOL and maximum time step, you'll see that clear right up to a nice crisp knee.
Which is not actually physically representative, as breakdown is a noisy process that SPICE transient simulation doesn't know about.
Zener and avalanche breakdown aren't the same thing, and both are relevant to an actually 6.2V device. Higher breakdown voltages are avalanche dominant, and the knee is fairly sharp with a consistent positive tempco. Lower voltages are softer, and the tempco varies (but is generally negative IIRC?). SPICE may not know about this either (the diode BV, IBV parameters are well suited to modeling avalanche breakdown at DC, but not so much zener breakdown or AC noise effects).
I don't remember what noise effects occur in zener breakdown (which is a tunneling phenomenon, so I expect it at least has full shot noise, but beyond that, I don't know). But avalanche is a very noisy phenomenon, because it's the solid state equivalent of a spark discharge. When the electric field across a junction is high, thermally generated electron-hole pairs are accelerated across it. If the field is strong enough that the charge carriers attain enough speed to break more electrons / holes free after a collision, then a runaway process can occur, where one charge carrier bounces off an atom or defect, freeing more charges, and so on, until a huge cone of charge is suddenly zipping across the junction.
Avalanche is a very fast phenomenon, under a nanosecond by the time it reaches the terminals. Avalanche breakdown of certain BJTs (planar epitaxial I think?) can result in peak currents of several amperes, drawn through a nominally ~200mA transistor, turning on in less than a nanosecond (when the transistor normally takes tens of ns to do any sort of switching or amplification). Essentially, the entire volume of the chip turns into a short circuit due to runaway avalanche.
Avalanche diodes are usually constructed in such a way as to minimize this runaway effect, but the random surge effect is present nonetheless. It's particularly easy to see at low currents, where the voltage rises slowly, then jumps down suddenly by a random amount, which reduces the electric field enough to prevent further avalanches, then it starts rising again, and so on.
Tim