Homework on Tunneling (solutions)

Feel free to work on the homework in groups. The work you hand in, however, should reflect your understanding of the material and be in your own words.  Students who turn in identical (or close to identical) homework assignments will be asked to explain their answers orally to the TA or prof.  A student who cannot explain how he or she arrived at a given answer will be charged with academic dishonesty.

You should  justify all of your answers for full credit.

Tunneling

	Energy diagrams for a p-n junction with different applied voltages are shown below.  For each diagram, indicate whether current will flow due to (a) classical (non-quantum) sources, through (b) tunneling, or (c) both, or (d) current will not flow.  Also indicate in which direction the current will flow.  Explain how you arrived at your answer.
1.	A p-n junction with no bias applied No current - you can't get something for nothing.
2.	A p-n junction with a moderate reverse bias applied No classical current - diodes only permit current in one direction. However, a very small reverse tunneling current will exist - generally this is considered negligible.
3.	A p-n junction with a small forward bias applied Small forward current due to tunneling - the free electrons on the n-side are at the same energy as the available holes on the p-side.
4.	A p-n junction with a moderate forward bias applied No current - too small a bias for classical current, too large for tunnelling.
5.	A p-n junction with a large forward bias applied Forward current due to classical reasons - the electrons can move normally.
6.	Explain how your answers to the previous questions illustrate the concept of negative resistance.  How and when does negative resistance occur in a diode? Increasing the voltage from case 3 to case 4 resulted in a decrease in current. Resistance is the ratio of voltage to current, so in the voltage region just above where tunneling occurs, resistance can be said to be negative.