1 Gonzalez Adrian Gonzalez MTE 208 Dr. Faltens November 29, 2010 HW9 Carrier Statistics Lab Homework 1. What is the value for each doping level that you need to use? Explain. According to Wikipedia, an intrinsic semiconductor is one that is undoped, that is, is an i-type semiconductor, and is pure with no dopant present. Hence, we have to set N A and N D equal each other in order to obtain an intrinsic semiconductor. Notice that 10/cm 3 is the smallest possible test case. 2. Click on the Temperature tab, and deselect the box that sweeps the temperature. What is the default temperature for the simulation? The default temperatures is 300K, which is around room temperature: 300K - 273.15K = 26.85 0 C
8. What is the energy that has the highest density of holes? How far below the band edge is
this energy (in eV)?
We select "Hole density with energy" in the drop down menu, this will give us a plot with a
highest peak of density, by putting the mouse over we can see that @ 1.62e+11 eV/cm3 (which
is the largest density) the energy is -0.0127eV. Which is also represents the position below the
band edge.
9. What is the approximate width of the energy range where electrons are found? What is theapproximate width of the energy range where holes are found? How do these energies
compare to Eg ? How do these energies compare to kT (the thermal energy)?
An approximation for where the electrons and holes can be found can be anything that is
located under the cure of each plot. That is, for electrons the approximate width of the energy
range where they can be found could be between 1.12eV and 1.3eV (by looking at the graph).
Similarly, an approximate width of the energy range where holes are found can be between
0.0eV and 0.2eV. These energies are symmetrical, since the simulation results are from an
intrinsic semiconductor, thus the number of holes equal the number of electrons since Eg is
1.12eV. Now comparing these energies to the thermal energy:
= 8.62 ∙ 10−5
∙
= 300
= 0.02586
This means that Thermal Energy represents the energy above and below the band edges for
As you can see, when changing the doping levels between 10 and 10E20 the Fermi energy
slightly increases. This is because we no longer have an intrinsic semiconductor, and the
amount of electrons does not equal the amount of holes anymore.
14. What happens to the densities of electrons and holes as doping levels change?
By running the simulations above for different doping levels, I came to the conclusion that the
densities of electrons increase as doping levels increase. Yet as the doping levels increase the
densities of holes decrease.
15. What happens to the densities of electrons and holes as Temperature changes?
This is a really interesting part of the simulation, since we have to use temperature sweep.
After running the simulation for an intrinsic semiconductor, you can change the results to
"Electron density with energy" and then below the graph there is a play button where you cansee what happens to electron density as we change the temperature:
This means that as temperature increases, then the electron density increases. Similarly, since
we are dealing with an intrinsic semiconductor, then the number of electrons must equal the
number of holes, and since electron density increases as temperature increase, then hole
