# How does Band Gap and Refractive index relate to Wavelength?

• Nyfinscyf
In summary, the Nobel Prize for Physics was awarded for the development of a blue laser diode using Gallium Nitride with a band gap of 3.4 eV and a refractive index of 2.429. The energy band gap equation, E=hc/λ, can be used to determine the wavelength of the laser. However, the refractive index also plays a role in determining the velocity of light in the medium, which affects the wavelength. Using the equation λ=hc/(nE), a wavelength of approximately 150 nm is calculated, which does not match the observed blue wavelength of 445 nm. Further research is needed to understand the relationship between band gap, refractive index, and the resulting wavelength.
Nyfinscyf

## Homework Statement

Nobel prize for physics for blue laser diode using Gallium Nitride with band gap of 3.4 eV and a refractive index of 2.429.
Explain how these parameters determine at what wavelength a Gallium Nitride semiconductor will laser at.

## Homework Equations

$E=\frac{hc}{\lambda}$
Blue wavelength ## \approx 445 nm ##

## The Attempt at a Solution

This equation will give the energy band gap wavelength. But how does the refractive index factor into this? I know it changes the velocity that the light moves through the medium.
I found this article: https://www.quora.com/Whats-the-relation-between-bandgap-the-extinction-coefficient-and-the-index-of-refraction
But I'm still not sure how to answer the question.

Last edited by a moderator:
When light goes from one medium to another, it's wavelength changes.

Using the equations I can get:
$E=\frac{hc}{\lambda}$
$\lambda=\frac{hc}{E}=\frac{1240~eV~nm}{3.4~eV} \approx 365~nm$
The velocity of the light changes in the medium by $v=\frac{c}{n}$ replacing c in the above by the velocity in the medium gives
$\lambda=\frac{hv}{E}=\frac{hc}{nE}=\frac{1240~eV~nm}{(2.429)(3.4)~eV} \approx 150~nm$

I don't see how this gives blue light of 445 nm.

## 1. How does band gap affect the wavelength of light?

The band gap of a material refers to the energy difference between the valence band and the conduction band. This energy difference determines the wavelength of light that can be absorbed by the material. A wider band gap means that the material can only absorb shorter wavelengths, while a narrower band gap allows for the absorption of longer wavelengths.

## 2. How does refractive index impact the wavelength of light?

The refractive index of a material is a measure of how much the speed of light is reduced when passing through the material. This reduction in speed is what causes the bending of light when it enters a material. The refractive index also affects the wavelength of light, as it determines how much the light will be slowed down, and therefore, the wavelength of the light.

## 3. How does the band gap and refractive index of a material relate to each other?

The band gap and refractive index of a material are related in that they both affect the wavelength of light that can be absorbed or transmitted by the material. A material with a wider band gap will have a higher refractive index, meaning it will slow down light more and have a shorter wavelength for absorption. On the other hand, a material with a narrower band gap will have a lower refractive index and allow for the transmission of longer wavelengths of light.

## 4. Can the band gap and refractive index of a material be manipulated to control the wavelength of light?

Yes, the band gap and refractive index of a material can be engineered and manipulated to control the wavelength of light. This is often done through the use of doping, where impurities are intentionally added to a material to change its properties and alter the band gap and refractive index. This manipulation is crucial in the development of technologies such as solar cells, LEDs, and optical fibers.

## 5. How does the relation between band gap, refractive index, and wavelength impact the functionality of electronic and optical devices?

The relationship between band gap, refractive index, and wavelength plays a significant role in the functionality of electronic and optical devices. For example, a wider band gap material is used in solar cells to efficiently absorb higher energy photons, while a narrower band gap material is used in LEDs to emit specific wavelengths of light. The refractive index also allows for the manipulation of light in optical devices, such as lenses and fibers. Understanding and controlling these relationships is crucial in the design and development of electronic and optical technologies.

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