Download ECE3030 Physical Foundations of Computer Engineering, Fall 2015

ECE3030 Physical Foundations of Computer Engineering, Fall 2015
Assigned Oct. 30
Homework 9
60 pts.
Due prior to 4:25pm on Friday Nov. 6
1) (10 pts.) You need to drive a load of 1 pF. Your first stage gate has a capacitance of 7
fF. How many stages do you need to minimize the total delay?
2) (10 pts.) Define the following terms:
a) Noise Margin
b) Dynamic Power
c) Static Power
d) Leakage Current
3) (10 pts.) Consider an inverter in a Silicon technology with supply voltage VDD = 1.3V.
Given nFET threshold voltage Vtn and pFET threshold voltage Vtp for the transistors
used in the inverter, and given symmetric threshold voltages (i.e., Vtn = |Vtp| ), what
range of values for the symmetric threshold voltages result in no short circuit current?
Please note that, for example, < is different than ≤; e.g., if x ≤ 5 and y ≥ 5, then it is
possible that x = 5 = y. On the other hand, if x < 5 and y > 5, then x and y never have
the same value. You must use proper versions of <, ≤, ≥ or > in your answer to receive
full credit for this problem.
4) (30 pts.) Consider subthreshold drain current as described by the equation given in
lecture: = µ ε ||
Φ
|| (1 − ||
)
Describe how the subthreshold drain current varies as each of the following varies
linearly: transistor channel width Z, doping concentration Na, temperature T, and
technology generation where a new technology generation is defined by both a new
transistor channel length L and a new transistor channel width Z. To describe how
subthreshold drain current varies, please choose between the following seven options:
constant (or zero), increases linearly, increases polynomially, increases exponentially,
decreases linearly, decreases polynomially and decreases exponentially. For example, as
increases linearly, it is clearly the case that also increases linearly. Please give
your answers labelled (a) through (d) for each of the following cases:
(a) Describe how varies as Z increases linearly (NOTE: L does not
change!).
(b) Describe how varies as Na increases linearly. (NOTE: you will need to
substitute ϕF = ln in order to properly account for Na.; further
more, please assume Na >> ni and assume a fixed value for ni.)
(c) Describe how varies as T (in Kelvin) increases linearly. Please assume
that = 0 V (do not worry about the case where ≠ 0 V).
(d) Describe how varies as Silicon technology generations improve, i.e.,
new transistor channel length L and new transistor channel width Z
decrease linearly at the same rate.
EXTRA CREDIT: (5 pts.)
Consider subthreshold drain current as described by the equation given in lecture:
= µ ε ||
Φ
|| (1 − ||
)
Describe how the subthreshold drain current varies as each of the following varies linearly:
transistor channel width Z, doping concentration Na, temperature T, and technology
generation where a new technology generation is defined by both a new transistor channel
length L and a new transistor channel width Z. To describe how subthreshold drain current
varies, please choose between the following six options: increases linearly, increases
polynomially, increases exponentially, decreases linearly, decreases polynomially and
decreases exponentially. For example, as increases linearly, it is clearly the case that
also increases linearly.
Describe how varies as T (in Kelvin) increases linearly. Please assume that ≠ 0 V (do
not worry about the case where = 0 V). You should also assume the following for the
range of voltages which are possible: || ≫ (1 − ||
).
YOU MAY NOT CONSULT HOMEWORK SOLUTIONS OF THESE EXACT
PROBLEMS FROM OTHER COURSES, INCLUDING OTHER/PREVIOUS
SECTIONS OF ECE 3030. ALL HOMEWORK SUBMISSIONS MUST INCLUDE
YOUR NAME, COURSE NUMBER, SECTION, AND THE HOMEWORK SET
NUMBER. ALL SHEETS MUST BE STAPLED TOGETHER. ALL WRITING
MUST BE EASY TO READ (FOR EXAMPLE, YOU MAY HAVE TO WRITE
ONLY ON ONE SIDE OF EACH SHEET OF PAPER THAT YOU SUBMIT AND
MAY NOT BE ABLE TO USE RECYCLED PAPER). FAILURE TO FOLLOW
INSTRUCTIONS MAY RESULT IN ZERO POINTS. ALL WORK MUST BE
YOUR OWN. NO PLAGIARISM IS ALLOWED, AND YOU MUST PROPERLY
REFERENCE ALL SOURCES OF YOUR INFORMATION – ALTHOUGH YOU
SHOULD NOT LOOK FOR AND MAY NOT CONSULT “SOLUTIONS”
AVAILABLE FROM OTHER SOURCES (TO REPEAT, YOU MAY NOT
CONSULT HOMEWORK SOLUTIONS OF THESE EXACT PROBLEMS FROM
OTHER COURSES!).