The problem is the actual silicon bulk to the diode junction having a varying resistance with both temperature and current. This is solved by selecting the current through the diode so the variation in diode drop with current is exactly equal to the change in resistance, so the voltage stays constant over a small range of temperature. Then you can further select the diodes so the change with temperature and current is roughly the same, but this is not as good as simply selecting the best units at an elevated temperature, and driving them with the correct current. Thus the best are heated to a constant temperature, and the slightly worse ones are not heated but are meant to have a preset current that is individual per diode to get the best performance. 5-6 digits or more need a heated reference, under 4 you can get away with a temperature compensated one.
You cannot make a 4 wire connection on the silicon die itself, any attempt will make a new set of resistors. Best is to make the circuit compensate for the variation.