So I understand that LED's have a maximum current (like 20mA for instance), but scientifically why is this?
Using the water analogy it seems like a high voltage would be the thing that would mess up something (I like to think of it like a huge amount of "pressure" blowing out a pipe or something). Why would a rate of electron flow damage something?
It's difficult to come up with an analogy because the usual analogies for electrical systems are fluid systems. A great thing about fluid systems is that the working fluid is also good at cooling things, and most people's practical experience with fluid systems involves rates of flow where heating is not very significant.
So let's try a different analogy: a string being pulled through the resistance of your fingers. Your fingers are the LED, and the voltage drop of the LED is analogous to the difference in tension of the string on either side of your fingers. Current is analogous to the rate at which the string is being pulled.
Will your fingers be damaged if the string is pulled too fast? Yes: we call it "rope burn". This will happen even if you adjust the resistance of your fingers to maintain a constant difference in tension on the rope regardless of its speed (analogous to the approximately constant voltage drop of the LED).
The reason is that the rate of work done, and thus, the heat generated, is the product of the force your fingers apply to the rope and the rate at which the rope is moving through your fingers. You can get a rope burn by squeezing too hard, or moving the string too fast.
"Rate of work" or "rate of energy" is called power. One way to define it, for mechanical systems, is the product of force (\$F\$) and velocity (\$v\$):
$$ P = Fv $$
Since power is a rate of energy it should be in units of energy per time. In SI units, thats joules per second, also known as the watt. So, however fast the rope is moving, and however much force your fingers are applying to it, you are doing work at the rate of some number of joules per second. This energy can't vanish: it becomes heat in the rope and your fingers. Once you exceed your body's ability to transfer heat away from your fingertips your skin gets too hot and you are burned.
The analogy for electrical systems is that power is the product of voltage and current:
$$ P = VI $$
\$V\$ is approximately constant for an LED, but if you increase \$I\$ enough, you generate heat faster than it can radiate to the ambient environment. The LED gets too hot and is damaged.
There's a forward voltage drop of a couple volts across the LED. This Voltage drop times the Current is the Power dissipated in the device. It creates light, but also heat. It's the heat that kills the LED.
TL;DR: Flowing current creates heat, and for LEDs, heat kills the part.
Whenever electrons flow through a conductor, Joule heating happens. This is partly because of what heat really is, particles that makes up the object moving around, and having electrons pulled through it guarantees that some electrons will collide into something and have its energy transferred into that particle, heating it up.
When the LED is overloaded the excessive heating will cause the fragile bonding as well as the die itself to change. None of those change is constructive and eventually the heat destroys the part. For LEDs they burn out and maybe blow apart, for some other parts they can burst into flames.
Here's another way of looking at what some others have said:
The conversion of current to light is not 100% efficient, so the remainder of the energy not converted to light is heat.
Each electronic component has something called a "thermal resistance" measured in degrees Kelvin/Watt which says how easily the "waste energy" above gets out of the die to the PCB (typically the cathode for an LED) as heat. This is specified in the datasheet.
In addition, each electronic component has a maximum junction temperature, Tj at which it can operate according to the rest of the specified parameters in the datasheet.
With this information, given a constant thermal resistance, Rth, a fixed maximum power rating LED, Pdiss_max, and a constantly increasing power source driving the LED, what will happen is you will drive the junction temperature above its maximum rating and likely de-solder the wire bonds from inside the chip, rendering it inoperable.
Good question!
There's only a certain amount that that size of material can handle. Take a filament for example. Just the right size to glow but not burn up. It is being overwhelmed with electricity, there's only so much it can handle before it burns out. Same with LEDs. Depends upon the amount and type of material.
All nice answers. I just wanted to add that if there was no non-radiative recombination in the LED's, then there would be much less heat and one could push more current through before it heats up... (Think newer high efficiency LED's)
Actually I found the water analogy pretty effective. A pipe will break apart If a massive quantity of water would transit into it. More specifically, it will melt down as a fluid flowing generates a small quantity of heat like any other material do
:P). \$\endgroup\$