Adrian Gonzalez - MTE 208 Assigment 9
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Transcript of Adrian Gonzalez - MTE 208 Assigment 9
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6. From this diagram, which has a larger effective mass, electrons or holes? Explain how you
can tell.
By theory, n = p in an intrinsic semiconductor. This means that both, electrons and holes will
have the same effective mass. This is can be proved by the final log of the simulation:
7. What is the energy that has the highest density of electrons? How far above the band edge is
this energy (in eV)?
We select "Electron 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+11eV/cm3 (which
is the largest density) the energy is 1.14eV. Which is around 1.14eV-1.12eV = 0.02eV above the
band edge.
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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
both electrons and holes (approximately).
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10. How do the maximum concentrations of electrons and holes compare? (give their values)
From what we learned so far of intrinsic semiconductors, we know that if the amount of
electrons and holes equal each other, then the maximum concentration of electrons and holes
must be the same. The maximum concentration for electrons and holes are the same at
1.62e+11 eV/cm3
11. If you were to integrate DOS for electrons and DOS for holes over all energies in each band,
what would be the relationship between these two values? Explain in terms of what is
physically happening in the material.
.
If we were to integrate the DOS for both, electrons and holes over all energies in each band,
then we would get the same area under the curve for each band, because as we stated earlier,
n=p, thus we would have the same area under the curve. This means that the electrical
conductivity is due to crystals defects since we are dealing with a pure silicon. Also because of
thermal excitation, an electron can jump into the Conduction Band, yet at the same moment it
jumps to this band it would leave behind a hole. Hence n=p for intrinsic semiconductors.
These are trends that you should investigate and try to understand:
12. In an intrinsic material, what happens to the occupation function as temperature is
changed? (hint: you can sweep the temperature)
As temperature is changed, we can see that when the temperature is cold we can see that the
occupation function looks like a step function (square wave), as we increase the temperature
the occupation function soon starts to curve.
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13. What happens to the Fermi energy under different doping levels? Run the simulation at
300K for several doping levels between 10 and 10E20. Compare these graphs and describe how
Ef changes.
At 10/cm3: At 10e12/cm
3
:
At 10e17/cm3: At 10e18/cm
3
:
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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
density must increases as well.