1. Design a silicon semiconductor resistor, with resistance between 6-10 kΩ, in the shape of a rectangular bar. Assume this resistor will be used in an integrated circuit and therefore a small size is necessary as well as operation in at least the 250K - 450K temperature range.
Your resistor is not allowed to be doped at a degenerate level. You need to specify the length, cross-sectional area, doping atom, and doping concentration. State any assumptions you are making and support your design choices. Determine the at least the following about your design:
(a) Linear range of the device (voltage and current limits)
(b) What are the temperature considerations?
(c) Show the exact band diagram of your device under no bias.
(d) Show the band diagram under bias (choose the bias).
(e) Under the same bias you chose for the last part, what is the current through the device.
2. Somehow in production of your semiconductor resistor designed in the last question the doping of the device got messed up. You discover that the doping was non-uniform and varies linearly across the length of the device. The doping on the 'left' side of the device is your desired doping level, but on the right it is only half of your desired level. Find the new current through the device at the test bias voltage you chose for parts (d) and (e) in the last problem. How has the band diagram changed under no bias?
3. Design a GaAs based photo-conductor (photo-resistor) for operation at T = 300 K. Assume carrier lifetimes of τn0 = 10-7 s and, τp0 = 5 x 10-8 s.
NOTE: carrier lifetimes are only constant for low-injection. Uniform doping is achieved by adding Si atoms: 90, of the Si atoms replace Ga atoms and 10%, replace As atoms. When light is shining on the photo-conductor it produces a uniform excitation of g' = 1021cm-3s-1. The applied voltage is 2V and the resistance of the device must between 8-10 kΩ without the light shining. You need to specify the length, cross-sectional area, and doping concentration. State any assumptions and support your design choices.
Determine at least the following about your design:
(a) How does the resistance change with the light?
(b) How quickly can the light be pulsed such that the output current represents the input pulse?
(c) Show the band diagram of your device under no bias. (quasi fermi levels included)