Space charge width in a pn junction
Think: what does it mean for a simplistic diode model, when we apply a voltage which is exactly equal to the built-in junction potential?  The net barrier potential would go to zero.  In that case the diode would become an ideal short-circuit, and even for infinitesimally higher voltage, the current would go to infinity.

So what really happens with large values of Veb is that we must stop using the oversimplified equation, and instead switch to a more-complicated diode model, one which incorporates current-density, the bulk resistivity of n- and p- regions, and perhaps junction-heating effects.

Similar question: what happens when we connect a wire across a power supply, and then reduce the resistivity of the wire to less than zero?  (Obviously we've achieved even more dividee by zeroee than even conventional dividing by zero can produce!)   Or better yet: if we apply a large voltage to an ideal LED, what kind of light would come out? Whew, too complex for me to even imagine.