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University of California at Berkeley College of Engineering Dept. of Electrical Engineering and Computer Sciences
EECS 40 Midterm II
Spring 1999 Prof. Roger T. Howe April 14, 1999
_Name: ______________________ Student ID ______________ last, first
Guidelines
- Closed book and notes; one 8.5” x 11” page (both sides) of your own notes is allowed.
- You may use a calculator.
- Do not unstaple the exam.
- Show all your work and reasoning on the exam in order to receive full or partial credit.
Score
Problem
Points Possible Score
Total 50
- Micromirror Structure [20 points]
Poly1 Mask (clear field)
Oxide1 Mask (clear field)
Oxide2 Mask (dark field)
Metal Mask (clear field)
y , [μm]
x , [μm]
B’
B
A A’
Poly2 Mask (clear field)
V 1
V 2
V 3
(c) [3 pts.] Find the numerical value of the capacitance between terminals 1 and 2 in femtoFarads (fF). Use the layout on p. 2 to estimate the area of the capacitor. Note that the substrate is grounded, so it has no contribution to the answer to this part. Hint: terminal 1 is connected to a poly2 structure, whereas terminal 2 is connected to a poly1 structure. The capacitance is between the two polysilicon structures.
(d) [3 pts.] Find the numerical value of the capacitance between terminal 3 and the substrate. Neglect the contribution from the metal layer. Hint: you are not expected to consider capacitors in series to find the answer.
- Integrated Circuit Resistor Structure [20 points]
A A’
V (^0) -
V (^2) -
V (^3) -
I 0
I 2 I^3
I 1
c
b
a
V 0 V 1 V 2 V 3 SiO 2
Doping concentrations and thicknesses of regions a , b , and c :
a 3 x 10^17 cm-3^ boron, 2.5 x 10^17 cm-3^ phosphorus (0.5 μm thick) b 1017 cm-3^ boron, 2.5 x 10^17 cm-3^ phosphorus (1 μm thick) c 1017 cm-3^ boron (substrate)
80 μm (^5) μm
Given Electron mobility: (^) μ n = 1000 cm^2 /(Vs) Hole mobility: (^) μ p = 400 cm^2 /(Vs) Unit charge: q = 1.6 x 10-19^ C
1 μm^ 0.5^ μm
(a) [2 pts.] What is the type (n or p) and the sheet resistance of layer a in the IC structure whose layout and cross section is shown in the figure?
- Switched capacitor circuit [10 points]
C C C
Vout
Vin
= 1 V
a
a
a
a
a a
b b b
Switch operation
t (μs)
a
b
a
b
HINT: This problem is MUCH SIMPLER than it looks!
(a) [3 pts.] Find the charge stored on each capacitor at the time t = 0.5 μs, given that C = 50 fF and Vin = 1 V. Hint: draw the circuit at that time, using the switch states given above.
(b) [3 pts.] Find the charge stored on each capacitor at the time t = 1.5 μs, given that C = 50 fF and Vin = 1 V. The same hint from part (a) applies.
(c) [4 pts.] Find the output voltage Vout at the time t = 1.5 μs, given that C = 50 fF and Vin = 1 V. The same hint from part (a) applies.
