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You can solve the following problems to help you understand the topics covered in the lectures.

From M.Shur's Book:

Chapter 1: 1-6-2, 1-6-5, 1-7-1, 1-7-2, 1-12-1, 1-12-2



From M.S. Tyagi's Book:

Chapter 3: 3.7,  3.8,  3.10,  3.11, 3.12,  3.16,  3.17, 3.20,  3.21,  3.22

Chapter 4: 4.5, 4.9, 4.11,  4.13, 4.14, 4.17, 4.18

Chapter 5: 5.2, 5.4, 5.5, 5.7, 5.12, 5.14,  5.15




Exercise 1: Go to Understanding Recombination via a Trap. Click on Applet tutorial on how to use it.  Go to Applet Worksheet and answer all the questions.

Exercise 2: Go to Drift and  diffusion Processes . Click on Applet tutorial on how to use it.  Go to Applet Worksheet and answer all the questions.

Frequently asked questions:(This list will increase as you keep asking me by email).

Q. I want to know exactly what is meant by  bound and unbound charges. How does the ionised donor  atom that has an associated +ve charge become a bound  charge.

Ans: If you diffuse, for example, a donor atom in silicon, it gets lodged inside the crystal lattice by forming covalent bonds with the surrounding silicon atoms. Therefore, like the other silicon atoms, this donor atom is not mobile. When it gives out the fifth electron, the donor atom becomes ionized or positively charged. The free electron can move around freely, therefore, it is an unbound or mobile charge. While the positively charged donor atom is a bound charge.

Q. In a heavily doped n-type semiconductor,  why do the donor atoms form a band of donor energy levels? What happens to the Fermi level now? Is it  in between valance band or conduction band OR  will it shift into the conduction band?

Ans: When the semiconductor is moderately doped, the donor atoms are far away from each other. Therefore, we can say that their probability density functions do not overlap or the donor atoms behave as if they are isolated entities. However, when the doping increases, the radial probability density function of each atom overlaps with the other resulting in the splitting of the donor energy levels. This leads to the formation of a band of donor energy levels resulting in a reduction in the bandgap. With increasing doping, the Fermi level moves into the conduction band. That means,  some of the donor levels which are below the Fermi level will not be ionized since the probability of finding an electron is now very high at these donor levels. As a result, the effective electron concentration will no longer  be equal to the donor atom concentration. Therefore, under bandgap narrowing conditions, the actual doping has to be replaced by an effective doping which is smaller than the actual doping.