Homework #3
COE 3002
“Introduction to the Microelectronics and
Nanotechnology Revolution”
Dr. John D. Cressler
Due Date: Tuesday, October 27th
[1] Resolve all problems on Exam #1 that you had any points taken off on.
[2] Sit down, with no (serious) distractions, and carefully read Chapter 5 (pp. 98-135) and Chapter 6 (pp. 136-156) of Silicon Earth. Then fill out the following and sign it.
I, ______, the undersigned, do hereby attest, that the foresworn has carefully read Chapter 5 (pp. 98-135) and Chapter 6 (pp. 136-156) from Cressler’s Silicon Earth and am now ready for meaningful discussion of said material.
______
Signature Date
[3] Given that there are 8 atoms in the silicon (diamond) lattice unit cell (primitive building block – the yellow dental-flossed cube in my toy lattice), prove that the atomic density of silicon is 5x1022 atoms/cm3. Think chemistry. Show your work.
[4] a) Calculate the resistivity (in Ω-cm) of a slab of Si of cross-sectional area 1.5 μm2 and length 4.0 μm, if you know that it has a measured resistance of 20 kΩ. Show your work.
b) If one applies 20 V across the ends of the sample, what is the magnitude of the electric field present (in V/cm)? Show your work.
c) Would this value of electric field be considered “large” or “small” in the context of semiconductors? Hint: Think about what defines large vs. small in the context of electric field in semiconductors.
[5] Consider a sample of Si at 300 K which is doped with 2.0x1016 cm-3 of B. Show your work.
a) Which carrier is the majority carrier, and which is the minority carrier?
b) Calculate the majority carrier density (cm-3). Use correct notation for it.
c) Calculate the minority carrier density (cm-3). Use correct notation for it.
d) Calculate the resistivity of the sample (in Ω-cm). Show your work. You may assume the electron mobility is 1165 cm2/Vs and the hole mobility is 419 cm2/Vs.
e) Assuming that we apply a voltage of 0.5 V across a sample of this construction which is 10 μm long, what current density would flow in the sample (in mA/μm2)? Show your work.
[6] Consider an electron in Si at 300K. You have any means at your disposal to manipulate the electron without violating the laws of physics, but you need to move that electron from Atlanta to San Francisco and back again in the fastest possible time, assuming it travels that entire distance entirely within the Si (it’s a thought experiment!). Estimate the fastest possible time for the electron to travel from Atlanta to San Francisco and back (in sec). Show your work.
[7] Explain (using no less than 1/2 page of 12 point font, single spaced, Times Roman, with 1 inch margins) how SIMS, secondary ion mass spectroscopy, is used to actually measure the position-dependent doping density in a piece of semiconductor? Include 1) an illustration of a SIMS and 2) an example “doping profile” as addendums to the text. English counts.
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