# Peak wavelength and Spectral Bandwidth

• says
In summary, the peak wavelength and spectral bandwidth of both GaAs and silicon LEDs were calculated at liquid nitrogen temperature (77 K) and room temperature (300 K). The maximum wavelengths were found to be 0.867 μm for GaAs and 1.088 μm for Si. The spectral bandwidths were calculated to be 2.9*10-5m for GaAs and 7.6*10-6m for Si. The peak wavelength measures the maximum wavelength at which an electron-hole pair can be excited, while the spectral bandwidth measures the range of wavelengths emitted by the LED. In terms of which case would result in the best emitter, it is difficult to quantify as it depends on the specific application and desired
says

## 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

λg = hc/Eg
λg: maximum wavelength
λg [μm] = 1.24/Eg

Spectral bandwidth = (1.8kbT) / ħ

## The Attempt at a Solution

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

GaAs Eg: 1.43 eV
Si Eg: 1.14 eV

λg [μm] = 1.24/1.43 = 0.867 μm (maximum wavelength for GaAs)

λg [μm] = 1.24/1.14 = 1.088 μm (maximum wavelength for Si)

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Spectral bandwidth = (1.8kb*300k) / ħ = 3.928*1013Hz
Expressing this in units of wavelength, I've used the relation between frequency and wavelength:

λ=c/f = c / 3.928*1013Hz
=7.6*10-6m

Spectral bandwidth = (1.8kb*77k) / ħ = 1.008*1013Hz = 2.9*10-5m/s
Expressing this in units of wavelength, I've used the relation between frequency and wavelength:

λ=c/f = c / 1.008*1013Hz
= 2.9*10-5m

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!

I would interpret "better emitter" as "brighter", meaning more total energy is emitted. You do have relevant information here.

What does the peak wavelength measure? Peak of what?
What does the spectral bandwidth measure? Bandwidth of what?

I'm guessing greater energy = better emitter = lower wavelength

Question is asked in regards to LEDs

Are you saying that longer wavelengths always equal more energy? So the energy given off by a nuclear explosion in gamma rays is less than the energy given off by a glowing coal in the infrared? Are you sure?

Again, what does the peak wavelength measure? Peak of what? What does the spectral bandwidth measure? Bandwidth of what? How are those things defined?

I know it's about LEDs. I'm asking you to think through the meaning of those parameters. "It's the bandwidth" and "it's about LEDs" are not an explanation. What is it that has a width? What are the axes of the associated graph?

## 1. What is the peak wavelength?

The peak wavelength is the wavelength at which an object or substance emits or reflects the most energy. It is often referred to as the "color" of light and is determined by the frequency of the electromagnetic waves.

## 2. How is peak wavelength measured?

Peak wavelength is typically measured using a spectrophotometer, which measures the amount of light absorbed or emitted by a substance at various wavelengths. The wavelength at which the peak absorbance or emission occurs is the peak wavelength.

## 3. What is the relationship between peak wavelength and spectral bandwidth?

Spectral bandwidth refers to the range of wavelengths that a substance can absorb or emit light. The narrower the spectral bandwidth, the more specific the peak wavelength will be. Similarly, a wider spectral bandwidth means a broader range of wavelengths are being absorbed or emitted, resulting in a less defined peak wavelength.

## 4. How does peak wavelength affect the color of an object?

The peak wavelength of an object determines its color. Objects that reflect or emit light with a shorter peak wavelength (such as blue or violet) will appear blue or violet, while objects with a longer peak wavelength (such as red or orange) will appear red or orange. The peak wavelength also affects the intensity of the color, with higher peak wavelengths appearing brighter.

## 5. Can peak wavelength be changed?

The peak wavelength of an object is determined by its physical properties and cannot be changed. However, it can be manipulated by altering the composition or structure of the object. For example, adding a dye to a substance can change its peak wavelength, resulting in a different perceived color.

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