Problem 1: Silicon is doped with 5x10¹⁷ phosphorous dopants per cm³. What is the Fermi level (Ef-Ei) for this material?  If we assume all of the dopants are ionized, and the electron mobility is 500 cm²/V.sec, what is the conductivity of this material? If we have a 1mm long and 1micron wide wire with 100nm thickness, what is the resistance of that wire?

Problem 2: If 5x10¹⁸ dopant/cm³ Boron dopants are implanted into the material from Problem 1 to form a PN junction, what is the built-in potential of the resulting diode?  What will be the zero-bias depletion width of that device, if we assume a step-junction? What would you expect the reverse-bias break-down effect to be?

Problem 3: The silicon from problem 1 is patterned into a 5nm nanowire, which is 100nm long, and we would like to build a junction FET with a wrap-around gate. How many dopant atoms will be in the conducting channel of that transistor? What is the Fermi level of the conducting channel?

Problem 4: Why is silicon not a good light emitter? Why would silicon nano wires start emitting light when very narrow dimensions are used? Describe the concept of geometric bandgap engineering.

Problem 5: The transistor from problem 5 is constructed by using a 5x1018 doped n-layer implanted into a 1016 doped p-type substrate. If the area of the source and drain contacts are 1x1micron, what is the current in the transistor when the gate is turned off? Describe the concept of inversion? What will be the threshold voltage if a poly-silicon gate is used? List assumptions you had to make.

Problem 6: A N-MOSFET transistor is formed with a planar silicon geometry, with a source, drain and polysilicon gate. The gate length is 0.13 microns, and a source-drain voltage of 2V is applied. What is the electric field? What is the saturation velocity? What is the carrier transit time? Repeat the calculations for 60nm, 45nm and 22nm gate lengths. How does the carrier transit time relate to the maximum frequency of the transistor?

Problem 7: Why is a bipolar junction transistor called a minority carrier device? What design parameters determine the gain of a BJT?

Problem 8: If a 10mW red laser with wavelength of 650nm is used to irradiate a GaAs thin film that is 220nm thick, how much of that light is absorbed? How many electron-hole pairs are generated? If the optical quantum efficiency of the GaAs is 50%, how much power is emitted from the GaAs? How much heat is dissipated in the film?

Problem 9: Describe the geometries of (a) a typical double-hetero structure edge-emitting laser, (b) a distributed feedback (DFB) laser and (c) a vertical cavity surface emitting laser, indicating where the gain, the reflectors and the light emission direction will be. Plot the expected spectra of these three types of semiconductor lasers. Describe the fabrication necessary for these lasers to be made.

Problem 10: Magnetic media can be used for high-density hard-disk drive storage. What are the critical dimensions that need to be controlled for reading and writing the highest possible storage densities? What does the giant magneto resistive material do? What determines that minimum size of the individual bits of media? What is HAMR? Why does perpendicular magnetic recording provide higher areal densities (up to several hundred Gb/in²)? Why would you back-fill your hard drive with Helium?

Problem 11: What is the difference between a single-mode and a multi-mode optical fiber? Why would you use a single-mode fiber for longer distances? What are the common reasons for fiber dispersion? Why is the bandwidth-distance product for single mode fibers so much higher than that of multi-mode fibers?

Problem 12: Why is the wall plug efficiency of a laser typically higher than that of a light-emitting diode? Why can you not use a LED for a 10Gb/s data-link?

Problem 13: Why are surface plasmons useful in concentrating light into small volumes? Why are surface plasmon waveguides lossy? How can you create a plasmon cavity?

Problem 14: What is surface-enhanced Raman spectroscopy, and why is it useful?

Problem 15: What is a field ion microscope and how does it enable such a high magnification? How does atomic force microscopy work? How does scanning tunneling microscopy work?

Problem 16: What determines the ultimate resolution of an (a) optical microscope, (b) scanning electron microscope, (c) transmission electron microscope, (d) scanning near-field optical microscope, (e) two-photon microscope and (f) field ion microscope.

Problem 17: What is a TEM lattice image? Do you see individual atoms in such an image?

Problem 18: Compare contact lithography with projection lithography. Why is projection lithography used in most commercial microelectronics applications? Why has it been difficult to create lenses for 157nm laser sources?

Problem 19: What is the difference between projection photolithography and extreme-UV lithography? Describe projection systems for both cases. Why is mask repair difficult in EUV lithography?

Problem 20: Vector-scanning electron beam lithography is used for high-resolution mask-making and research, but not for many production applications. Why? Describe shaped electron beam lithography, electron projection lithography, and describe the challenges and advantages of these techniques.