Quantum Wells

Question 1

What is Schrodinger’s equation?

Answer 1

Where psi represents the wave equation and it is assumed that potential is 0 within the box.

Question 2

How does the Schrodinger equation relate to quantum well lasers?

Answer 2

By taking the 1-D form of the SE, we can obtain the discrete energy of a particle in the box as electrons in the semiconductor propagate with the wave function

Question 3

What is the quantum limit?

Answer 3

10nm and less

Question 4

How do the radiation properties change at the quantum limit?

Answer 4

The function of devices changes as rather than modeling a flow of current, it is more accurate to describe single particles moving.

As the length is close to the de Broglie wavelength the charges are confined to a finite quantum well in the y-direction.

Rather than being divided into the conduction and valence band, the energy levels are described as a density of states

As the density of states is practically constant there are more electrons able to recombine with more holes with the same energy.

Question 5

What are the quantum well assumptions

Answer 5

• Steady State Schrodinger’s Equation(SE) i.e. potential doesn’t change with time
• SE is simplified to one dimension
• Particle in a box perspective
• Assumed Sinusodial function for particle
• Potential is assumed to be 0 within the box of length L

Question 6

Why is GaAs used in semiconductors for high-speed processing?

Answer 6

The effective mass of an electron is 0.07 m_e

and the effective mass of a hole is 0.5 m_e

This means that processes such as the emission of electrons and the switching of transistors can occur far faster in the material.

Question 7

What is the discrete energy for a particle in a QW?

Answer 7

Using Fourier series derivations, we can find energy to be:

E = (n²h²)/8mL²

L is similar to the deBroglie Wavelength

Question 8

What happens to the energy as n increases?

Answer 8

As n grows, so does the Energy i.e. the gap between levels increases.

Question 9

Describe Energy Levels of Single Quantum Well

Answer 9

• ΔEC is greater than ΔEV
• Eg1 is usually proportioned between 50% to 60% to ΔEC and 50% to 40% to ΔEv
• The quantum well thickness of L is very small that we can treat it like a single potential energy well
• Usual design thickness is 5nm to 10nm

Question 10

What