What Is the Emission Wavelength of a 10nm GaAs Quantum Well Laser?

[Cheetox]

Homework Statement

Assuming and infinitely deep potential well, estimate the emission wavelength of a 10nm GaAs quantum well laser. The electron density at the normal operating point of the laser is 10¹⁶m^-2: what is the electron quasi-Fermi level (chemical potential) and how many levels are occupied? (The effective masses are me* = 0.07me, mh* =0.35me)

Homework Equations

The Attempt at a Solution

I don't really know how to start this one, I assume i'll need to use the quantised energy levels of a 2-d infinite potential well...will it be something to do with the difference in band gap energies between Ga and As? If anyone could link me some good internet resources on heterojunction lasers that would also be much appreciated as I have struggled to find any...cheers

 

[mark726]

!

Thank you for your question. To estimate the emission wavelength of a 10nm GaAs quantum well laser, we need to first understand the energy levels and band structure of the material. GaAs is a semiconductor material with a band gap energy of approximately 1.4 eV. In a quantum well structure, the electrons and holes are confined in a narrow region, creating discrete energy levels.

In an infinitely deep potential well, the energy levels are given by:

E_n = (n^2 * h^2)/(8mL^2)

Where n is the quantum number, h is Planck's constant, m is the effective mass of the electron or hole, and L is the width of the quantum well. For GaAs, the effective masses are me* = 0.07me and mh* = 0.35me.

To find the emission wavelength, we need to consider the energy difference between the highest occupied level (valence band) and the lowest unoccupied level (conduction band). This energy difference, also known as the band gap, determines the energy and therefore the wavelength of the emitted light.

The electron quasi-Fermi level, or chemical potential, is the energy level at which electrons are thermally excited to occupy higher levels. In a normal operating point of the laser, the electron density is 1016m-2. This corresponds to a Fermi level of approximately 0.1 eV above the conduction band minimum.

To determine the number of levels occupied, we can use the Fermi-Dirac distribution function, which gives the probability of a state being occupied at a given energy level. The number of occupied levels can be calculated by integrating this function from the conduction band minimum to the Fermi level.

As for resources on heterojunction lasers, I would recommend looking into textbooks on semiconductor physics or optoelectronics. You can also find some helpful information on reputable scientific websites such as IEEE or SPIE.

I hope this helps and please let me know if you have any further questions.
Scientist