Band-gap Dependence of LED frequency

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The frequency of the light emitted by a Light Emitting Diode(LED) is proportional to the Band-gap of the semiconductor material. Band-gap is temperature dependent. Hence on immersing the LED in liquid nitrogen the material's band-gap changes. Due to this the frequency of light also changes.
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The low temperature causes the LED to contract (including the band gap), and the shorter distance in the gap causes frequency change? Is that correct? If so, (and assuming no change of input frequency) what allows resonance to still occur? I assumed input frequency would need to be tuned to match the LED's emission wavelength.

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