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Suppose you have an LED that emits a spectrum of colours such that the resultant colour emitted is white. Will changing the temperature if the LED itself change the composition of the light's colour spectrum, hence changing its resultant colour?

My immediate answer to this is no but after a bit of research, I came accross this graph:

enter image description here

The website states that:

Figure 9 shows the light output of several LEDs as a function of junction temperature. The temperature dependence is much less for InGaN LEDs (e.g., blue, green, white) than for AlGaInP LEDs (e.g., red and yellow).

As the graph clearly shows, the relative light outputs of the red, white and blue light changes at different rates as temperatures increase. This shows how the intensity of the light overall changes with the temperature of the LED system. However, does this mean that the colour composition of the emitted light changes with temperature as well?

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There is no such single LED. White is produced either with a mixing of color LEDs or by embedding an LED, typically UV, inside a "bulb" with a phosphor coating such that the coating absorbs the photons and re-emits a wide spectrum of light.

That said, if you are mixing tricolor LEDs and their power outputs change at different gains with temperature, then obviously the color mix will change.

A given LED's bandgap will change slightly with temperature as well, but this is probably not significant in the situations you are interested in.

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To add to Carl Witthoft's answer:

In diode-based lasers (similar concept to LEDs) temperature control is important for maintaining a precise, stable wavelength. This is related to the band edge moving slightly with temperature. However, as Carl Witthoft said, this is a small effect on the scale of "colors" -- my recollection is a degree Celsius corresponds to sub-nm changes in wavelength for a blue diode laser (405 nm).

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The answer is YES for monochromatic LEDs and "not really" for Phosphor-converted LEDs. Monochromatic LEDs can change a lot in color depending on the operating temperature, with probably the worst ones being the Amber LEDs (590~600nm) that shift from amber-yellow to red when heated.

Since you are talking about "white" LEDs, you are talking about Phosphor-converted LEDs that use a blue or violet pump and a fluorescent material to produce white light. The mechnaism behind fluorescence is not as sensitive to temperature as monochromatic LEDs are, so in this case the spectral output change will be of little signifiance.

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