Homework 04

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Due Friday, 2014.10.03.

1) What techniques could be used to determine the thickness of a film of unknown composition? What techniques could not be used, and why?

2) What are the selection criteria for a dielectric material in semiconductor manufacturing when they are used e.g. as MOSFET gate dielectric? Why has SiO₂ dominated in many dielectric applications?

3) What is a high-K delectric, and why are these materials necessary in modern semiconductor manufacturing? What are some of the problems encountered with high-K materials in this context? (for more background, see the PDF "High-K Gate Dielectrics for Future CMOS Technology" and the Wikipedia article "High-K Dielectrics")

http://www.rcns.hiroshima-u.ac.jp/21coe/pdf/4th_WS/plenary-p08.pdf http://en.wikipedia.org/wiki/High-%CE%BA_dielectric

4) What assumptions and boundary conditions are used to derive the Deal-Grove SiO₂ oxidation model? How and why does the model fail to fit the data for the thinnest films?

5) Derive the Deal-Grove approximation for the SiO₂ growth rates for very thin films and for very thick films. What processes are rate-determining at these limits?

6) What is an 'activated process'? What functional dependence do activated processes have on temperature, and how is this related to the Maxwell-Boltzmann distribution of energies? Mathematically justify this relationship.

7) When is diffusion an activated process, and when is it not? Why?