EE 505 – Nanostructures: Fundamentals and Applications
Fall 2010
Prof. Carmen S. Menoni
Homework #2
Due Date: October 5, 2010
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1. Using the normalization condition, find the normalization constant for the problem
solved in HW 1 of a finite potential well for the case E<Vo.
2. Explain which are characteristics of the electron wavefunction in a crystal. Provide a
comparison for Schroedinger equation for a crystal compared with that for a
hydrogen atom. Contrast also the eigenfunctions.
3. A stream of particles of mass m and energy E encounters a potential step of height W
1−𝜇 2
𝑗
(<E). Show that the fraction reflected is 𝑅 = (1+𝜇) where 𝜇 = 𝑘 , 𝑘 2 =
2𝑚
ℏ2
𝐸 , 𝑗2 =
2𝑚
(𝐸 − 𝑉). B) Show that the sum of the fluxes of the reflected and transmitted
particles is equal to the flux of incident particles.
ℏ2
E
W
V=0
0
x=0
x
4. Explain band formation in a solid and provide main differences between a metal,
insulator and semiconductor in terms of the band picture.
5. What is a hole?
6. Calculate the density of states in the conduction band of Ge for an excess energy
E=60 meV about the conduction band minimum. Calculate the total number of
electrons at T=100K.
7. Explain how you would design a quantum well with a bandgap around 1.8 eV using
III-V semiconductor materials. Assume a 50/50 conduction/valence band split.
Calculate the number of confined eigenstates.
8. Explain the variation of the bandgap energy in a quantum dot material with dot size.
Then explain main features of the figure in page 74 of the notes.
9. How is the interaction between an electron in a crystal and a photon modeled? How
is Schroedinger equation modified?
10. Describe the differences between absorption and emission processes. What are
conservation laws. Explain this in the context of the band diagram for a direct
bandgap semiconductor material.
11. What is an exciton? What are the main signatures of exciton formation? What are
the main differences in the absorption in a semiconductor quantum well with and
without excitonic contributions?
12. Which type of materials do you expect have the largest excitonic binding energy?
13. Why is it important to know (E) in a low dimensional material system?
14. Explain what type of recombination processes are possible in quantum confined
semiconductor systems.
505hw2