Slide 1
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Problem XXXXXXXXXXpoints)
Demonstrate the fcc and bcc crystal systems are reciprocals of each other by:
Â
Start from fcc real space lattice vectors and show that the fcc reciprocal space lattice vectors are equivalent to a bcc real space system.
Start from bcc real space lattice vectors and show that the bcc reciprocal space lattice vectors are equivalent to an fcc real space system.
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Problem XXXXXXXXXXpoints)
A Silicon substrate (wafer) is doped n-type with neutral phosphorous atoms. The device it will be part of must operate at 253K.
Evaluate by reading it from the standard chart reproduced in Sze/Ng as Fig. 10. Make an assumption: that will not change significantly at 253K although will.
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Problem 2. continued (40 points)
A Silicon substrate (wafer) is doped n-type with neutral phosphorous atoms. The device it will be part of must operate at 253K
Evaluate by googling Ioffe Semiconductor:
Si/ Band structure and ca
ier concentration / Temperature dependences
Evaluate graphically from Sze/Ng Fig. 9
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Problem 2. continued (40 points)
A Silicon substrate (wafer) is doped n-type with neutral phosphorous atoms. The device it will be part of must operate at 253K
Find the ratio of neutral to ionized donors at 253K
Boltzman constant
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Problem XXXXXXXXXXpoints)
You will build a a p+n junction by depositing a silicon plus boron epitaxial layer on your (plasma cleaned) Problem 2 silicon wafer surface using molecular beam epitaxy. This is expensive and used when precise device fa
ication matters.
Since precision matters for your device, first check that your silicon wafer is in fact doped by running (several) C-V experiments that consistently produce the following result at room temperature:
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Problem 3 continued. (35 points)
You will build a a p+n junction by depositing a silicon plus boron epitaxial layer on your (plasma cleaned) Problem 2 silicon wafer surface using molecular beam epitaxy. This is expensive and used when precise device fa
ication matters.
What is the value for based on the C-V results? You may assume that you have full ionization during the room temperature measurement:
YES or NO: Is your wafer doped
Since you also need precise wiring, you want to order a custom n-type silicon wafer that provides an minimal neutral region but enough material to avoid punch-through during operation of your p+n device (punch-through: when maximum > n-side).
Assume device operation range. Evaluate the maximum value of on the n-side of the p+n silicon wafer.
Should you order the thickness wafer or the thickness wafer? State your logic.
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Problem XXXXXXXXXXpoints)
Your p+n junction in silicon is now being initially tested at room temperature for ON/OFF operation, with emphasis on achieving a good OFF. Unfortunately, the oxygen donor defect closest to midgap is causing problems.
What is the value of for the oxygen donor defect closest to midgap?
(Note: and  both defects. Use is: for useful dopants and for un-useful traps)
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Problem 4 continued. (40 points)
Your p+n junction in silicon is now being initially tested at room temperature for ON/OFF operation, with emphasis on achieving a good OFF. Unfortunately, the oxygen donor defect closest to midgap is causing problems.
Suppose an oxygen donor defect is located physically close to a phosphorus dopant.
Plot the energy levels for both the oxygen defect and phosphorus dopant on the graph below, similar to HW02, Pr. 4 Solutions, slide 21:
Do you expect the donor function of the phosphorus to be adversely impacted by a nea
y oxygen defect or not?
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Problem 4 continued. (40 points)
Your p+n junction in silicon is now being initially tested at room temperature for ON/OFF operation, with emphasis on achieving a good OFF. Unfortunately, the oxygen donor defect closest to midgap is causing problems.
Evaluate the maximum depletion region width for your device operation bias:
Evaluate the generation cu
ent density using standard assumptions for the oxygen defect as a single-level trap in silicon at room temperature:
Evaluate the diode (Sze: ideal) cu
ent density expected for this p+n junction
Evaluate the total cu
ent density
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Problem 4 continued. (40 points)
Your p+n junction in silicon is now being initially tested at room temperature for ON/OFF operation, with emphasis on achieving a good OFF. Unfortunately, the oxygen donor defect closest to midgap is causing problems.
YES or NO: is total cu
ent density in the range?
Look for a way to reduce from the oxygen traps:
In the depletion region during OFF for the standard assumptions given:
Evaluate the trap concentration for
What does the trap concentration have to be to make
?
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