The fit above consisted of two fits, the first for current of the lower part of the curve and a second fit to determing the diode current as a function of the first current. Both curves are easy to fit. The rms residual is still large compared to the precision of the measurements which was 0.01 mA for the current and the 0.01 volts for the voltage. In the plot of the residuals below one sees large deviations at the higher currents. The relative deviations (residual/current) are of the same magnitude for all currents
The current being a function of a current is consistent with a controlled breakdown. There is also a certain amount of noise present and the current fluctuates some due to a statistical component. The largest contribution to the rms deviation is from the upper portion of the curve.
Supplemental: The correlation among neighbouring residuals near I = 0 mA indicates that the fitted functions are not quite right but this error is small compared to larger residuals which may have contributed to errors in the values of u and v.