Suppose you've got two 5V1 zeners in parallel. Due to slight differences between the two parts (tolerance on zener voltage), one of them will conduct more current.
simulate this circuit – Schematic created using CircuitLab
The one consuming most current will heat up more. This will probably affect its properties. What kind of equilibrium will be reached? Will the current distribute evenly between them?
I couldn't estimate myself what equilibrium would be reached because...
I got confused by the temperature coefficients. Some zeners tend towards negative, other towards positive temperature coefficients.
Negative temperature coefficients would be the worst-case scenario: the zener voltage would drop when the part heats up, drawing even more current. Nevertheless, while drawing more current the voltage over the diode will increase a little because the zener I-V-Curve is not ideal. This would push some current to the other zener(s) mounted in parallel. But would that be enough to overcome the detrimental effects of a negative temperature coefficient?