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I do understand that the wavelength of the lights depends on the energy gap of the semiconductor, but why does it consist of a narrow range instead of a fixed value? is it because during recombination the photons have random phases?

Also, how does the spectral linewidth change if I increase the temperature? If I increase the temperature, the electron distribution in the conduction band will increase as more electrons jump from VB to CB. How does that exactly change my spectral linewidth?

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  • \$\begingroup\$ For one thing, if it was a single well-defined wavelength, that would be an infinitely precise energy, and the Heisenberg uncertainty principle means that that would imply an infinitely imprecise momentum. \$\endgroup\$
    – Hearth
    Mar 26 at 15:49
  • \$\begingroup\$ The full-width half-max widens with increasing temperature. That should be rather obvious. Just as it should be fairly obvious that the band-filling effects would tend towards saturation with increasing current. Beyond that, a lot of particulars may vary with construction, intentional and unintentional impurities, and defects (vacancies, interstitial, and antisites, for example.) Look up "TSOP" (temperature sensitive optical parameters" for LEDs, for example, to help find research, \$\endgroup\$
    – jonk
    Mar 26 at 18:36
  • \$\begingroup\$ Maybe physics.stackexchange.com will be able to provide more helpful answers :) \$\endgroup\$ Mar 27 at 7:20
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Each photon emitted from an LED is the product of an electron-hole pair recombination. Charge carriers (electrons/holes) in a semiconductor have an energy distribution which is a function of dopant concentration, density of states of the semiconductor and the Fermi distribution. At elevated temperature the Fermi distribution is stretched out and results in a wider range of electron and hole energies. These are all still concentrated near the bandgap, but increases the probability of a slightly more energetic electron combining with a slightly more energetic hole to emit a photon of higher energy (shorter wavelength). At higher temperatures there are also more phonons available that enable transitions that would otherwise be forbidden. This also broadens the emitted spectrum and allow for slightly sub-bandgap emission.

But temperature also affects the bandgap energy. As the temperature increases, the bandgap energy decreases. This will shift your peak to longer wavelengths at higher temperature.

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