A Zener diode is made to be robust enough to handle a large flow of breakdown current at high reverse-bias voltage (instead of blowing up or otherwise damaging the diode, it conducts). How are Zeners engineered? I don't know many of the details, but I think it has to do with having a large amount of doping and a small depletion region, so that you get a very high electric field and high tunneling probability for electrons to jump the gap between materials. Presumably other physical characteristics matter for allowing the diode to handle current.