- #1

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## Homework Statement

Calculate the expected peak wavelength and spectral bandwidth (in units of wavelength) of the

emission for both a GaAs and silicon LED at liquid nitrogen temperature (77 K) and room temperature (300 K). Which of these cases would you expect to result in the best emitter and why?

## Homework Equations

λ

_{g}= hc/E

_{g}

λ

_{g}: maximum wavelength

λ

_{g}[μm] = 1.24/E

_{g}

Spectral bandwidth = (1.8k

_{b}T) / ħ

## The Attempt at a Solution

λ

_{g}: band gap represents minimum energy, or maximum wavelength for which an electron-hole pair can be excited

GaAs E

_{g}: 1.43 eV

Si E

_{g}: 1.14 eV

λ

_{g}[μm] = 1.24/1.43 = 0.867 μm (maximum wavelength for GaAs)

λ

_{g}[μm] = 1.24/1.14 = 1.088 μm (maximum wavelength for Si)

---

Spectral bandwidth = (1.8k

_{b}*300k) / ħ = 3.928*10

^{13}Hz

Expressing this in units of wavelength, I've used the relation between frequency and wavelength:

λ=c/f = c / 3.928*10

^{13}Hz

=7.6*10

^{-6}m

Spectral bandwidth = (1.8k

_{b}*77k) / ħ = 1.008*10

^{13}Hz = 2.9*10

^{-5}m/s

Expressing this in units of wavelength, I've used the relation between frequency and wavelength:

λ=c/f = c / 1.008*10

^{13}Hz

= 2.9*10

^{-5}m

So I think I've got the correct peak wavelength and spectral bandwidth, I'm not sure about the last question though or how I can quantify if one is a better emitter than the other. Any help would be much appreciated!