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U.C Berkeley
EECS 140 Midterm 1: October 8, 1990 Fall 1990 Professor R.T. Howe
Ground Rules:
Closed Book and Notes Do all work on exam pages You have 50 minutes; use your time wisely
QUESTION 1. MOS Inverter [15 points]
(picture 1)
Non-linear iL versus vl characteristics of load device.
iL = kL* squareroot ( vL ) where kL = 800 micro * A * V -1/
(picture 2)
Output characteristics of the MOSFET. The constant mu sub n * Cox (W / L ) = 500 micro * A * V -1/
a.) [5 points] Find an equation relating vo to vI which is valid when the MOSFET is in the triode region.
b.) [5 points] Find an equation relating vo to vI which is valid when the MOSFET is saturated.
c.) [5 points] Using the graphical load line technique, plot the transfer curve vo versus vI on the graph below, using the given current-voltage characteristics of the MOSFET. Label on your plot the points on the transfer curve which mark the boundaries between the cutoff, saturation, and triode regions of operation.
picture 4
QUESTION 2 [17 points]
Potential in Thermal Equilibrium
a.) 6 points Consider an n-type sample with the donor concentration varying as shown in the log-linear plot below. In thermal equilibrium, plot the variation in potential phi (x) for 0 < x < 3 micro metres on the plot below.
c.) [5 points]
Consider a sample which is doped with the superposition of the donor and acceptor concentrations from part a and part b, as shown in the log-linear plot below. In thermal equilibrium, sketch the variation potential phi (x) for 0 < x < 3 micro metres on the plot below. Hint: the width of the deletion region is 1 micro meter
picture 7
picture 5
QUESTION 3 [18 POINTS]
pn junction diode
Given : pn junction diode with cross sectional area of 10 * 10 -6^ cm 2
p side doping: Na = 2 * 10^16 cm - Nd = 0
n side doping: Na = 1 * 10^16 cm - Nd = 0
minority carrier properties:
Dn = 25 cm 2 s- Taun = 400 ns = .4 micro seconds
Dp = 25 cm 2 s- Taun = 10 microseconds (translators note: Yes the exam redefines tau???)
miscellaneous
kT/q = 26mV ni = 1 * 10^10 cm -
a.) [7 points] Plot the minority carrier concentrations on the linear graphs below for the case of forward bias VD = 0.6 V
picture 8
