📄 ch02.1c.htm
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<UL>
<LI><A NAME="pgfId=215136"></A>a. Do you think it is possible to make
an IC mask using a 600<SPAN CLASS="White"> </SPAN>dpi
(dots per inch) LaserWriter and a transparency?
<LI><A NAME="pgfId=215137"></A>b. What would <SPAN CLASS="Symbol">
l</SPAN> be?
<LI><A NAME="pgfId=215138"></A>c. (Harder) See if you can use a microscope
to look at the dot and the rectangular bars (serifs) of a letter 'i' from
the output of a LaserWriter on paper (most are 300<SPAN CLASS="White"> </SPAN>dpi
or 600<SPAN CLASS="White"> </SPAN>dpi). Estimate
<SPAN CLASS="Symbol"> l</SPAN> . What is causing the problem? Why is there
no rush to generate 1200<SPAN CLASS="White"> </SPAN>dpi
LaserWriters for paper? Put a page of this textbook under the microscope:
can you see the difference? What are the similar problems printing patterns
on a wafer?
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=179747"></A>2.17 (Lambda,
10<SPAN CLASS="White"> </SPAN>min.) Estimate <SPAN CLASS="Symbol"> l</SPAN></P>
<UL>
<LI><A NAME="pgfId=215139"></A>a. for your TV screen,
<LI><A NAME="pgfId=215140"></A>b. for your computer monitor,
<LI><A NAME="pgfId=215141"></A>c. (harder) a photograph.
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=107095"></A>2.18 (Pass-transistor
logic, 10<SPAN CLASS="White"> </SPAN>min.)</P>
<UL>
<LI><A NAME="pgfId=215143"></A>a. In Figure 2.36 suppose we set
A<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>B<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>C<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>D<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>'1',
what is the value of F?
<LI><A NAME="pgfId=215144"></A>b. What is the logic strength of the
signal at F?
<LI><A NAME="pgfId=215145"></A>c. If <SPAN CLASS="EquationVariables">
V</SPAN> <SUB CLASS="SubscriptVariable"> DD</SUB> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>5<SPAN CLASS="White"> </SPAN>V
and <SPAN CLASS="EquationVariables"> V</SPAN> <SUB CLASS="Subscript"> t</SUB>
<SUB CLASS="SubscriptVariable"> n</SUB> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>0.6<SPAN CLASS="White"> </SPAN>V,
what would the voltage at the source and drain terminals of M1, M2, and
M3 be?
<LI><A NAME="pgfId=215146"></A>d. Will this circuit still work if
<SPAN CLASS="EquationVariables"> V</SPAN> <SUB CLASS="SubscriptVariable">
DD</SUB> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>3<SPAN CLASS="White"> </SPAN>V?
<LI><A NAME="pgfId=215142"></A>e. At what point does it stop working?
<TABLE BORDER="0" CELLSPACING="2" CELLPADDING="0">
<TR>
<TD> <P><P CLASS="TableFigTitleSide"><A NAME="pgfId=107102"></A> </P>
<P><P CLASS="TableFigTitleSide"><A NAME="pgfId=215382"></A>FIGURE 2.36 A
pass transistor chain (Problem 2.18).</TD>
<TD> <P CLASS="TableFigure"><A NAME="pgfId=107110"></A><IMG SRC="CH02-121.gif"
ALIGN="BASELINE" WIDTH="115" HEIGHT="84" NATURALSIZEFLAG="3"> </TD></TR>
</TABLE>
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=107202"></A>2.19 (Transistor
parameters, 20<SPAN CLASS="White"> </SPAN>min.)
Calculate the <B>(a)</B> electron and <B>(b)</B> hole mobility
for the transistor parameters given in Section 2.1 if <IMG SRC="CH02-122.gif"
ALIGN="BASELINE" WIDTH="14" HEIGHT="20" NATURALSIZEFLAG="3"> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>80<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
mA</SPAN> V<SUP CLASS="Superscript"> 2</SUP> and <IMG SRC="CH02-123.gif"
ALIGN="BASELINE" WIDTH="15" HEIGHT="20" NATURALSIZEFLAG="3"> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>40<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
mA</SPAN> V<SUP CLASS="Superscript"> 2</SUP> .</P>
<P><P CLASS="Exercise"><A NAME="pgfId=190307"></A>Answer: (a) 0.023<SPAN CLASS="White"> </SPAN>m<SUP CLASS="Superscript">
2</SUP> V<SUP CLASS="Superscript"> 1</SUP> s<SUP CLASS="Superscript"> 1</SUP>
.</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=107221"></A>2.20 (Quantum
behavior, 10<SPAN CLASS="White"> </SPAN>min.)
The average thermal energy of an electron is approximately <SPAN CLASS="EquationNumber">
k</SPAN> T, where <SPAN CLASS="EquationNumber"> k</SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>1.38<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
¥</SPAN> <SPAN CLASS="White"> </SPAN>10<SUP CLASS="Superscript">
23</SUP> <SPAN CLASS="White"> </SPAN>JK<SUP CLASS="Superscript">
1</SUP> is Boltzmann's constant and T is the absolute temperature in kelvin.</P>
<UL>
<LI><A NAME="pgfId=122580"></A>a. The kinetic energy of an electron
is (1/2)<SPAN CLASS="EquationNumber"> m</SPAN> <SPAN CLASS="EquationVariables">
v</SPAN> <SUP CLASS="Superscript"> 2</SUP> , where <SPAN CLASS="EquationVariables">
v</SPAN> is due to random thermal motion, and <SPAN CLASS="EquationNumber">
m<SPAN CLASS="White"> </SPAN></SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>9.11<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
¥</SPAN> <SPAN CLASS="White"> </SPAN>10<SUP CLASS="Superscript">
31</SUP> <SPAN CLASS="White"> </SPAN>kg is
the rest mass. What is <SPAN CLASS="EquationVariables"> v</SPAN> at 300<SPAN CLASS="White"> </SPAN>K?
<LI><A NAME="pgfId=122581"></A>b. The electron wavelength <SPAN CLASS="EquationVariables">
l</SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN><SPAN CLASS="EquationNumber">
h</SPAN> /<SPAN CLASS="EquationVariables"> p</SPAN> , where <SPAN CLASS="EquationNumber">
h</SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>6.62
¥ 1034 <SPAN CLASS="White"> </SPAN>Js is
the Planck constant, and <SPAN CLASS="EquationVariables"> p</SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN><SPAN CLASS="EquationNumber">
m</SPAN> <SPAN CLASS="EquationVariables"> v</SPAN> is the electron momentum.
What is <SPAN CLASS="EquationVariables"> l</SPAN> at 25<SPAN CLASS="Symbol">
<SPAN CLASS="White"> </SPAN></SPAN> C?
<LI><A NAME="pgfId=122582"></A>c. Compare the thermal velocity with
the saturation velocity.
<LI><A NAME="pgfId=122583"></A>d. Compare the electron wavelength
with the MOS channel length and with the gate-oxide thickness in a 0.25<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
m</SPAN> m process and a 0.1<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
m</SPAN> m process.
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=30480"></A>2.21 (Gallium
arsenide, 5<SPAN CLASS="White"> </SPAN>min.)
The electron mobility in GaAs is about 8500<SPAN CLASS="White"> </SPAN>cm<SUP CLASS="Superscript">
2</SUP> V<SUP CLASS="Superscript"> 1</SUP> s<SUP CLASS="Superscript"> 1</SUP>
; the hole mobility is about 400<SPAN CLASS="White"> </SPAN>cm<SUP CLASS="Superscript">
2</SUP> V<SUP CLASS="Superscript"> 1</SUP> s<SUP CLASS="Superscript"> 1</SUP>
. If we could make complementary <SPAN CLASS="EmphasisPrefix"> n</SPAN>
-channel and <SPAN CLASS="EmphasisPrefix"> p</SPAN> -channel GaAs transistors
(the same way that we do in a CMOS process) what would the ratio of a GaAs
inverter be to equalize rise and fall times? About how much faster would
you expect GaAs transistors to be than silicon for the same transistor sizes?</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=147163"></A>2.22 (Margaret
of Anjou, 5<SPAN CLASS="White"> </SPAN>min.)</P>
<UL>
<LI><A NAME="pgfId=215149"></A>a. Why is it ones' complement but two's
complement?
<LI><A NAME="pgfId=215150"></A>b. Why Queen's University, Belfast
but Queens' College, Cambridge?
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=143289"></A>2.23 (Logic cell
equations, 5<SPAN CLASS="White"> </SPAN>min.)
Show that Eq. 2.31, 2.36, and 2.37 are correct.</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=143404"></A>2.24 (Carry-lookahead
equations, 10<SPAN CLASS="White"> </SPAN>min.)</P>
<UL>
<LI><A NAME="pgfId=215151"></A>a. Derive the carry-lookahead equations
for <SPAN CLASS="EquationVariables"> i</SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>8.
Write them in the same form as Eq. 2.56.
<LI><A NAME="pgfId=215152"></A>b. Derive the equations for the BrentKung
structure for <SPAN CLASS="EquationVariables"> i</SPAN> <SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>8.
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=40795"></A>2.25 (OAI cells,
20<SPAN CLASS="White"> </SPAN>min.) Draw a circuit
schematic, including transistor sizes, for <B>(a)</B> an OAI321 cell,
<B>(b)</B> an AOI321 cell. <B>(c)</B> Which do you think will
be larger?</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=107530"></A>2.26 (**Making
stipple patterns) Construct a set of black-and-white, transparent, 8-by-8
stipple patterns for a CMOS process in which we draw both well layers, the
active layer, poly, and both diffusion implant layers separately. Consider
only the layers up to m1 (but include m1 and the contact layer). One useful
tool is the Apple Macintosh Control Panel, 'General Controls,' that changes
the Mac desktop pattern.</P>
<UL>
<LI><A NAME="pgfId=122578"></A>a. (60<SPAN CLASS="White"> </SPAN>min.)
Create a set of patterns with which you can detect any errors (for example,
<SPAN CLASS="EmphasisPrefix"> n</SPAN> -well and <SPAN CLASS="EmphasisPrefix">
p</SPAN> -well overlap, or <SPAN CLASS="EmphasisPrefix"> n</SPAN> -implant
and <SPAN CLASS="EmphasisPrefix"> p</SPAN> -implant overlap).
<LI><A NAME="pgfId=122579"></A>b. (60<SPAN CLASS="White"> </SPAN>min.+)
Using a layout of an inverter as an example, find a set of patterns that
allows you to trace transistors and connections (a very qualitative goal).
<LI><A NAME="pgfId=123116"></A>c. (Days+) Find a set of grayscale
stipple patterns that allow you to produce layouts that "look nice"
in a report (much, much harder than it sounds).
</UL>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=16014"></A>2.27 (AOI and
OAI cells, 10<SPAN CLASS="White"> </SPAN>min.).
Draw the circuit schematics for an AOI22 and an OAI22 cell. Clearly label
each transistor as on or off for each cell for an input vector of (A1, A2, B1, B2)<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>(0101).</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=136792"></A>2.28 (Flip-flops
and latches, 10<SPAN CLASS="White"> </SPAN>min.)
In no more than 20 words describe the difference between a flip-flop and
a latch.</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=177680"></A>2.29 (**An old
argument) Should setup and hold times appear under maximum, minimum, or
typical in a data sheet? (From Peter Alfke.)</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=177674"></A>2.30 (***Setup,
20 min.) "There is no such thing as a setup and hold time, just two
setup timesfor a '1' and for a '0'." Comment. (From Clemenz Portmann.)</P>
<P><P CLASS="ExerciseHead"><A NAME="pgfId=136795"></A>2.31 (Subtracter,
20<SPAN CLASS="White"> </SPAN>min.) Show that
you can rewrite the equations for a full subtracter (Eqs. 2.652.66)
to be the same as a full adderexcept that A is inverted in the borrow out
equation, as follows:</P>
<P><P CLASS="EqnNmbrdAlign"><A NAME="pgfId=123008"></A> DIFF<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>A<SPAN CLASS="White"> </SPAN><SPAN CLASS="Symbol">
</SPAN> <SPAN CLASS="White"> </SPAN>B<SPAN CLASS="Symbol">
<SPAN CLASS="White"> </SPAN><SPAN CLASS="White"> </SPAN></SPAN>
BIN<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>SUM(A,
B, BIN)(2.70)</P>
<P><P CLASS="EqnNmbrdAlign"><A NAME="pgfId=123009"></A> BOUT<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>NOT(A)<SPAN CLASS="White"> </SPAN>·<SPAN CLASS="White"> </SPAN>B<SPAN CLASS="White"> </SPAN>+<SPAN CLASS="White"> </SPAN>NOT(A)<SPAN CLASS="White"> </SPAN>·<SPAN CLASS="White"> </SPAN>BIN<SPAN CLASS="White"> </SPAN>+<SPAN CLASS="White"> </SPAN>B<SPAN CLASS="White"> </SPAN>·<SPAN CLASS="White"> </SPAN>BIN<SPAN CLASS="White"> </SPAN>=<SPAN CLASS="White"> </SPAN>MAJ(NOT(A),
B, CIN)(2.71)</P>
<P><P CLASS="Exercise"><A NAME="pgfId=123010"></A>Explain very carefully
why we need to con⌨️ 快捷键说明
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