ch17.6.htm
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<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
b</SUB>
= fringe (two edges)</P>
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2.80</P>
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C<SUB CLASS="Subscript">
c</SUB>
= coupling (one neighbor)</P>
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0.19</P>
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<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
c</SUB>
/<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
a</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
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6%</P>
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<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
a </SUB>
/<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
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52%</P>
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</P>
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<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
b </SUB>
/<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15590">
</A>
42%</P>
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<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15592">
</A>
</P>
</TD>
</TR>
<TR>
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<P CLASS="TableLeftEnd">
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<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
c</SUB>
/<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
</P>
</TD>
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<P CLASS="TableLast">
<A NAME="pgfId=15596">
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3%</P>
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</P>
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</UL>
<P CLASS="Exercise">
<A NAME="pgfId=15196">
</A>
<A HREF="CH17.6.htm#15069" CLASS="XRef">
Table 17.4</A>
shows the predicted fringing and coupling capacitance for a <SPAN CLASS="Symbol">
l</SPAN>
= 0.5 <SPAN CLASS="Symbol">
m</SPAN>
m process expressed in pFcm<SUP CLASS="Superscript">
–1</SUP>
. </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="4">
<P CLASS="TableTitle">
<A NAME="pgfId=15733">
</A>
TABLE 17.4 <A NAME="15069">
</A>
Predicted line capacitance including fringing and coupling capacitance (pFcm<SUP CLASS="Superscript">
–1</SUP>
) for <SPAN CLASS="Symbol">
l</SPAN>
= 0.125 <SPAN CLASS="Symbol">
m</SPAN>
m and using quasi-ideal scaling and the Sakurai equations. Problem <A HREF="CH17.6.htm#13391" CLASS="XRef">
17.10</A>
completes this table.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
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Parameter</P>
</TD>
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<P CLASS="TableFirst">
<A NAME="pgfId=15743">
</A>
<SPAN CLASS="Symbol">
l</SPAN>
= 0.5 <SPAN CLASS="Symbol">
m</SPAN>
m</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=15745">
</A>
<SPAN CLASS="Symbol">
l</SPAN>
= 0.125 <SPAN CLASS="Symbol">
m</SPAN>
m</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=15747">
</A>
Comment</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15757">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
= <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
a</SUB>
+ <SPAN CLASS="EquationVariables">
C</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15759">
</A>
2.16</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15761">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15763">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
is capacitance of line to ground.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15765">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
= <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
+ <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
c</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15767">
</A>
2.22</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15769">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15771">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
is capacitance including one neighbor.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15773">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
= <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
+ 2<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
c</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15775">
</A>
2.29</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15777">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15779">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
is capacitance including two neighbors.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15781">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
a</SUB>
= plate</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15783">
</A>
1.19</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15785">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15787">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
a</SUB>
is parallel-plate capacitance.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15789">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
b</SUB>
= fringe</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15791">
</A>
0.97</P>
</TD>
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<P CLASS="Table">
<A NAME="pgfId=15793">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15795">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
b</SUB>
is fringe for both edges.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15797">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
c</SUB>
= coupling</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLast">
<A NAME="pgfId=15799">
</A>
0.07</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLast">
<A NAME="pgfId=15801">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeftEnd">
<A NAME="pgfId=15803">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
is coupling to one neighbor only.</P>
</TD>
</TR>
</TABLE>
<UL>
<LI CLASS="ExercisePart">
<A NAME="pgfId=21926">
</A>
b. Complete the corresponding values for <SPAN CLASS="Symbol">
l</SPAN>
= 0.125 <SPAN CLASS="Symbol">
m</SPAN>
m, again assuming quasi-ideal scaling.</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=21931">
</A>
c. Comment on the difference between <SPAN CLASS="Symbol">
l</SPAN>
= 0.5 <SPAN CLASS="Symbol">
m</SPAN>
m and <SPAN CLASS="Symbol">
l</SPAN>
= 0.125 <SPAN CLASS="Symbol">
m</SPAN>
m.</LI>
</UL>
<P CLASS="ExerciseHead">
<A NAME="pgfId=15141">
</A>
17.11 <SPAN CLASS="Emphasis">
</SPAN>
(**Routing algorithms, 60 min.) “The Lee algorithm is guaranteed to find a path if it exists, but not necessarily the shortest path.” Do you agree with this statement? Can you prove or disprove it? </P>
<P CLASS="ExerciseNoIndent">
<A NAME="pgfId=71089">
</A>
“The Hightower algorithm is not guaranteed to find a path, even if one exists.” Do you agree with this statement? Can you prove or disprove it? <SPAN CLASS="Emphasis">
Hint: </SPAN>
The problems occur not with routing any one net but with routing a sequence of nets.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=36732">
</A>
17.12 (Constraint graphs, 10 min.) Draw the horizontal and vertical constraint graphs for the channel shown in <A HREF="CH17.2.htm#31067" CLASS="XRef">
Figure 17.13</A>
(a). Explain how to handle the net that exits the channel and its pseudoterminal.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=9640">
</A>
17.13 <A NAME="31813">
</A>
(**Electromigration, 60 min.) You just received the first prototype of your new ASIC. The first thing you do is measure the resistance between VDD and VSS and find they are shorted. Horrified, you find that you added your initials on m1 instead of m2 and shorted the supplies, next to the power pads. Your initials are only 10 <SPAN CLASS="Symbol">
m</SPAN>
m wide, but about 200 <SPAN CLASS="Symbol">
m</SPAN>
m high! Fortunately only the first capital “I” is actually shorting the supplies. The power-supply rails are approximately 100 <SPAN CLASS="Symbol">
m</SPAN>
m wide at that point. A thought occurs to you—maybe you can electromigrate your initial away. You remember that electromigration obeys an equation of the form: </P>
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<P CLASS="TableEqnRight">
<A NAME="pgfId=85244">
</A>
MTTF</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=85246">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=85248">
</A>
<SPAN CLASS="EquationNumber">
A</SPAN>
<SPAN CLASS="EquationVariables">
J</SPAN>
<SUP CLASS="Superscript">
–2</SUP>
<SPAN CLASS="EquationNumber">
exp</SPAN>
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