Activity 23: Quantum Wells

In today's activity, you will use a shockwave routine to examine energy levels in Quantum Wells.

Before You Start:
Answer the following questions to the best of your ability before doing the experiment.

Think about the expression for allowed energies in an infinite well, E = p²/2m = h²n²/8ma² . What happens to the allowed energies as you increase the well's width?

Now consider a finite well. The energy expression is much more complicated, but it will have similar qualities to the expression for an infinite well. One of the major differences, however, is that energies above a certain amount are no longer in the well.

What do you think will happen to the spacing of energy levels as you increase the well's width?
What will happen to the number of energy levels in the well as you increase the width?
What will happen to the number of energy levels in the well as you increase the well's depth?

After you have thought about your answers, compare notes with your group members. Does everyone have the same predictions, or are there differing opinions?

Quantum Wells

Go to the web site http://phys.educ.ksu.edu/vqm/html/eband.html. You may need to download a Shockwave plugin to use this page.

1. Using the default settings of V = 100 eV and a = 0.100 nm, click on Find Energies. How many energy levels appear in the well?

2. Using the vertical energy scale on the graph, determine the energy of the lowest (n=1) energy level. How far above the bottom of the well is this?

3. Now increase the well depth to its maximum value of 400 eV, and click on Find Energies. How many energy levels appear in the well now? Is this what you expected?

4. Using the vertical energy scale on the graph, determine the energy of the lowest (n=1) energy level. How far above the bottom of the well is this?

5. Use the formula to calculate the n=1 energy level for an infinite well of width 0.100 nm. How does it compare with the distances from the bottom of the well you calculated in 2 and 4? Which is closer to the infinite well value? Does this make sense? Why or why not?

6. Now increase the width of the well to its maximum value of 0.200nm, and click on Find Energies. What happens to the energy levels? Is this what you expected? Why or why not?

Energy Bands

Set the well width back to a = 0.100 nm, but keep the depth at V = 400 eV. Now change the number of atoms to 10 and answer the following questions.

7. Click on Find Energies. How many distinct energy bands are formed? How does this compare with the case for one atom (question 3)?

8. Increase the atom spacing to 0.500 nm. What happens to the bands?

9. Go back to the default setting of 0.200 nm, then click on the Impurities tab. Increase the impurities concentration to 4 in 10. What happens to the energy bands? What if you increase it to 6?

You will be asked to complete an evaluation of today's activity and lecture before the start of next class.

1.	Using the default settings of V = 100 eV and a = 0.100 nm, click on Find Energies. How many energy levels appear in the well?
2.	Using the vertical energy scale on the graph, determine the energy of the lowest (n=1) energy level. How far above the bottom of the well is this?
3.	Now increase the well depth to its maximum value of 400 eV, and click on Find Energies. How many energy levels appear in the well now? Is this what you expected?
4.	Using the vertical energy scale on the graph, determine the energy of the lowest (n=1) energy level. How far above the bottom of the well is this?
5.	Use the formula to calculate the n=1 energy level for an infinite well of width 0.100 nm. How does it compare with the distances from the bottom of the well you calculated in 2 and 4? Which is closer to the infinite well value? Does this make sense? Why or why not?
6.	Now increase the width of the well to its maximum value of 0.200nm, and click on Find Energies. What happens to the energy levels? Is this what you expected? Why or why not?

7.	Click on Find Energies. How many distinct energy bands are formed? How does this compare with the case for one atom (question 3)?
8.	Increase the atom spacing to 0.500 nm. What happens to the bands?
9.	Go back to the default setting of 0.200 nm, then click on the Impurities tab. Increase the impurities concentration to 4 in 10. What happens to the energy bands? What if you increase it to 6?