How does a diode maintain a constant voltage?

A fundamental property of all types of diodes (silicon, germanium, Schottky, LEDs, Zener ...) is to maintain a relatively constant voltage when the current through them varies. How do they do that?

This question can be answered specifically by considering the processes in the semiconductor PN junction. Also, it would be interesting to explain this on a conceptual level by revealing the basic idea. This "philosophical" approach has several advantages: first, it does not require in-depth knowledge of semiconductor devices; second, it would be applicable to all 2-terminal devices that have this property. I will do this using the concept of "dynamic resistance".

In the most general sense, a diode behaves like a resistor that interferes with current creating a voltage drop and heat loss. In the initial sloping part of its IV curve, this "resistor" has a relatively constant high resistance. And if it was really a resistor, the curve would continue in the same direction.

However, when the voltage threshold of the respective diode is reached, the curve abruptly changes its slope and becomes almost vertical. The current continues to change but the voltage stops changing. Why? Here is my simple explanation…

When the current I increases, the diode decreases its static resistance R with the same rate of change. So, the voltage drop across the diode V = I.R does not change.

This is a simple arithmetic trick where we change the multipliers in the opposite direction and at the same rate of change; as a result, the product of multiplication does not change.

Thus, by changing its resistance opposite to the current, this "dynamic resistor" maintains a constant voltage. This clever "diode trick" can be illustrated by a graphical representation:

During the last online exercise (25.11.21) on Semiconductor Devices with group 48a, ITI, FCST of Technical University of Sofia, I used the ZOOM pen to draw moving IV curves on the existing picture in Nicole's lab report; see the video record of the ZOOM meeting (in Bulgarian)  and the screenshot below:

To get the attention of my students at this late class, I told them that I could mimic any diode they wanted with just a variable resistor ("potentiometer")... and if I hid in a big box, they would think that there is a diode inside:-)

It would be interesting for me to know your opinion on my explanation.