Paralleling IGBT modules

I'm not sure why the IGBTs would share the current since they're paralleled, unless external circuitry (series inductance, resistance, gate resistors) forces them to do so?

I would be pretty leery of paralleling these modules. As far as the PN diodes go, reverse recovery currents in PN diodes (especially if they are hard switched to a reverse voltage) are usually not limited by their internal semiconductor operation until they reach "soft recovery" (the point where the reverse current decays). They are usually limited by external circuitry (resistance, inductance, IGBT gate resistance). A perfect example: the traditional diode reverse recovery measurement test externally limits the reversing current to a linear falling ramp by using a series inductance. If you could reverse the voltage across the diode in a nanosecond, you would see an enormous reverse current spike.

Even though diode dopings are pretty well controlled these days, carrier lifetimes are not necessarily. Since one diode might "turn off" (go into a soft reverse current decreasing ramp, where the diode actually DOES limit its own current) before the other, you may end up with all the current going through one diode for a least a little while (the motor will look like an inductor, for all intents and purposes, during the diode turn-off). Probably better to control the max diode current externally for each driver.

Paralleling IGBT modules where the IGBT but not the diode has a PTC is commonly done at higher powers. I personally have never done more than 3 x 600A modules in parallel but if you look at things like high power wind then things get very "interesting". It is all a matter of analysis, good thermal coupling, symmetrical layout and current de-rating. Once you get too many modules in parallel then the de-rating gets out of hand without some kind of passive or active element to ensure current sharing. Then you know it is time to switch to a higher current module or a higher voltage lower current for the same power. The relative proportion of switching losses vs conduction losses also has a big part to play.