LEDs can be, have been and are used as voltage references. Standard LEDs in various colors are cheap and hence sensible when wanting a low accuracy low voltage reference. Remember that low voltage Zeners have bad knee characteristics and poor tolerances. Zener diodes do make noise when in the breakdown region. In fact, there are noise generators based on this known principle in antique ARRL handbooks. However, is the LED less noisy than the Zener?
Electronic – LEDs vs. Zeners: what is quiet
noisevoltage-referencezener
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Best Answer
(True) Zener diodes are not generally used as noise sources- 'Zeners' for >6V are actually avalanche diodes.
This paper mentions that a 5V Zener has about 15-20dB less noise than a 12V 'Zener'. So, I'll assume that the (dominant in a 12V 'Zener') avalanche noise is not a factor since you are going to use a true Zener diode.
Both an LED and a Zener will have shot noise, which is proportional to the square root of current, so it may well depend on the relative operating currents. There will also be some thermal noise from the resistive component, which would probably favor a Zener over a small LED.
Usually if noise is concern you should follow a relatively low noise source with a conventional low pass filter or something like a capacitance multiplier. That's how reference chips designed for RF circuits achieve uV wideband noise using relatively noisy bandgap references.