I have a pile of bluish white LEDs salvaged from Christmas lights. They look like ordinary LEDs, with one electrode having a little cup with the light emitter, and the other with a tiny wire going to the top of the emitter. When I apply a milliamp or so from a 9v supply, they light up just fine. If I apply 10 microamps or so, they barely light when power is applied, then get brighter over the next few seconds. It is clearly visible to the eye, and makes them useless for making optisolators with. Obviously the LEDs used in commercial optoisolators don't have this problem. Why do these LEDs do this, and what kinds of LEDs do it?
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Bare LEDs are generally quite fast. The ones with phosphor to re-emit a different color are slower. How much slower depends on the phosphor. White LEDs, for example, have phosphors. Those would be silly in a opto-isolator.
Commercial opto-isolators use infrared LEDs, usually in the 9xx nm wavelength.
Look at the current spec for commercial opto-isolators. Note that they require significantly more than 10 µA of input current to work. What a LED does with only 10 µA is irrelevant to opto-coupler use since they aren't being run at such low currents. Usually a few mA is expected.