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HW 01

The document outlines Exercise #1 for the ELEC 3500 course, focusing on semiconductor physics and Fermi-Dirac statistics. It includes problems related to energy levels, electron states, and calculations involving intrinsic and doped silicon. The exercise requires students to apply concepts such as the Fermi level, holes, and the Boltzmann approximation in various scenarios.

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23 views2 pages

HW 01

The document outlines Exercise #1 for the ELEC 3500 course, focusing on semiconductor physics and Fermi-Dirac statistics. It includes problems related to energy levels, electron states, and calculations involving intrinsic and doped silicon. The exercise requires students to apply concepts such as the Fermi level, holes, and the Boltzmann approximation in various scenarios.

Uploaded by

cheukkiutsang
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Hong Kong University of Science & Technology

Department of Electronic & Computer Engineering

Fall 2020 ELEC 3500: Semiconductor Device and Technology Mansun Chan

Name: ________________________ E-mail: ___________________________

Exercise #1 (September 25)


1) Suppose there is an unknown atom with 2 states at the first energy level (E1), 8 states at the 2-4 energy levels (E2, E3, E4)
as shown in the figure. Assume the temperature is low enough that electrons will stay at the lowest possible states. Sketch
the location of the Fermi level on the given figure when

a) Sketch the location of the Fermi level when there are 12 electrons in the atom.

b) How many holes are there at E2 in problem (a)?

c) If f(E) is the Fermi-Dirac function, what is the value of f(E3)?

d) You try to calculate the number of electrons in problem (a) at an energy level by using the number of states multiply
by the probably of the states to be filled at that level. Instead of using the Fermi-Dirac function, you want to use
Boltzmann approximation. At which energy level(s) (E1, E2, E3 or E4) you will get the least error?

2) Suppose the system now has 6 states at each energy level and the Fermi-Dirac statistics is given in the figure.
Assume the energy difference between E2-E1, E3-E2 and E4-E3 are 0.8eV, 0.7eV and 0.6eV respective. The
Fermi-Dirac function of the system is also given:

a) What is the number of electrons at the energy level E4 at a given


temperature K?

b) How many electrons are there in the system?

3) Consider a silicon with intrinsic carrier concentration ni equal to 1010 cm-3 at room temperature. It is then
doped to p-type with a doping concentration of NA=1 x1017cm-3. What is the location of the Fermi-level relative
to the conduction band? (Hint: NC=2.8x1019cm-3)
4) A silicon is doped with n-type dopant with concentration of 1.5x1016cm-3. What is the number of electrons in
the conduction band and where is the Fermi-level at 800K? The following steps will guide you through the
process to answer this question.

a) What is the intrinsic carrier concentration ni at 800K?

i) Which equation can be used to answer the above question?

ii) What are the value of NC and NV at 800K?

NC = ____________________ NV = ____________________

iii) What is the value of EG/kT at 800K?

______________________

iv) What is the intrinsic carrier concentration ni at 800K?

b) What is the number of electrons in the conduction band?

c) Where is the Fermi-level at 800K?

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