ch07.1.htm

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For example, suppose we have the four-antifuse connection shown in <A HREF="CH07.1.htm#11501" CLASS="XRef">
Figure&nbsp;7.4</A>
. Then, from Eq.&nbsp;<A HREF="CH07.1.htm#34895" CLASS="XRef">
7.6</A>
,  </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=47276">
 </A>
<SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
<SUB CLASS="Subscript">
4</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=47278">
 </A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=47280">
 </A>
<SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
14</SUB>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 + <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
24</SUB>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
 + <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
14</SUB>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 + <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
44</SUB>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
4</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=47282">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=47284">
 </A>
&nbsp;</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=47286">
 </A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=47288">
 </A>
<SPAN CLASS="EquationVariables">
(R</SPAN>
<SUB CLASS="Subscript">
1</SUB>
+ <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
2</SUB>
+ <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
3</SUB>
+ <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
4</SUB>
)<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
4</SUB>
 + <SPAN CLASS="EquationVariables">
(R</SPAN>
<SUB CLASS="Subscript">
1</SUB>
+ <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
2</SUB>
+ <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
3</SUB>
)<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
 + <SPAN CLASS="EquationVariables">
(R</SPAN>
<SUB CLASS="Subscript">
1</SUB>
+ <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
2</SUB>
)<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
 + <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
1</SUB>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=47290">
 </A>
&nbsp;</P>
</TD>
</TR>
</TABLE>
<P CLASS="Body">
<A NAME="pgfId=11310">
 </A>
If all the antifuse resistances are approximately equal (a reasonably good assumption) and the antifuse resistance is much larger than the resistance of any of the metal lines, L1&#8211;L5, shown in <A HREF="CH07.1.htm#11501" CLASS="XRef">
Figure&nbsp;7.4</A>
 (a very good assumption) then <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 = <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
2</SUB>
 = <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
3</SUB>
 = <SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="Subscript">
4</SUB>
 = <SPAN CLASS="Emphasis">
R</SPAN>
, and the Elmore time constant is  </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=47373">
 </A>
<SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
<SUB CLASS="Subscript">
4</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=47375">
 </A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=47377">
 </A>
4<SPAN CLASS="EquationVariables">
RC</SPAN>
<SUB CLASS="Subscript">
4</SUB>
 + 3<SPAN CLASS="EquationVariables">
RC</SPAN>
<SUB CLASS="Subscript">
3</SUB>
 + 2<SPAN CLASS="EquationVariables">
RC</SPAN>
<SUB CLASS="Subscript">
2</SUB>
 + <SPAN CLASS="EquationVariables">
RC</SPAN>
<SUB CLASS="Subscript">
1</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=47379">
 </A>
<A NAME="36693">
 </A>
(7.7)</P>
</TD>
</TR>
</TABLE>
<P CLASS="Body">
<A NAME="pgfId=11490">
 </A>
Suppose now that the capacitance of each interconnect segment (including all the antifuses and programming transistors that may be attached) is approximately constant, and equal to <SPAN CLASS="EquationVariables">
C</SPAN>
. A connection with two antifuses will generate a 3<SPAN CLASS="EquationVariables">
RC</SPAN>
 time constant, a connection with three antifuses a 6<SPAN CLASS="EquationVariables">
RC</SPAN>
 time constant, and a connection with four antifuses gives a 10<SPAN CLASS="EquationVariables">
RC</SPAN>
 time constant. This analysis is disturbing&#8212;it says that the interconnect delay grows quadratically (<SPAN CLASS="Symbol">
&#8733;  </SPAN>
<SPAN CLASS="EquationVariables">
n</SPAN>
<SUP CLASS="Superscript">
2</SUP>
) as we increase the interconnect length and the number of antifuses, <SPAN CLASS="EquationVariables">
n</SPAN>
. The situation is worse when the intermediate wire segments have larger capacitance than that of the short input stubs and output stubs. Unfortunately, this is the situation in an Actel FPGA where the horizontal and vertical segments in a connection may be quite long.</P>
</DIV>
<DIV>
<H2 CLASS="Heading2">
<A NAME="pgfId=11346">
 </A>
7.1.4&nbsp;Antifuse Parasitic Capacitance</H2>
<P CLASS="BodyAfterHead">
<A NAME="pgfId=1501">
 </A>
We can determine the number of antifuses connected to the horizontal and vertical lines for the Actel architecture. Each column contains 13 vertical signal tracks and each channel contains 25 horizontal tracks (22 of these are used for signals). Thus, assuming the channels are fully populated with antifuses, </P>
<UL>
<LI CLASS="BulletFirst">
<A NAME="pgfId=1505">
 </A>
An input stub (1 channel) connects to 25 antifuses.</LI>
<LI CLASS="BulletList">
<A NAME="pgfId=1507">
 </A>
An output stub (4 channels) connects to 100 (25 <SPAN CLASS="Symbol">
&#165;</SPAN>
 4) antifuses.</LI>
<LI CLASS="BulletList">
<A NAME="pgfId=1509">
 </A>
An LVT (1010, 8 channels) connects to 200 (25 <SPAN CLASS="Symbol">
&#165;</SPAN>
 8) antifuses.</LI>
<LI CLASS="BulletList">
<A NAME="pgfId=1511">
 </A>
An LVT (1020, 14 channels) connects to 350 (25 <SPAN CLASS="Symbol">
&#165;</SPAN>
 14) antifuses.</LI>
<LI CLASS="BulletList">
<A NAME="pgfId=1513">
 </A>
A four-column horizontal track connects to 52 (13 <SPAN CLASS="Symbol">
&#165;</SPAN>
 4) antifuses.</LI>
<LI CLASS="BulletLast">
<A NAME="pgfId=1515">
 </A>
A 44-column horizontal track connects to 572 (13 <SPAN CLASS="Symbol">
&#165;</SPAN>
 44) antifuses.</LI>
</UL>
<P CLASS="Body">
<A NAME="pgfId=11988">
 </A>
A connection to the diffusion of an Actel antifuse has a parasitic capacitance due to the diffusion junction. The polysilicon of the antifuse has a parasitic capacitance due to the thin oxide. These capacitances are approximately equal. For a 2 <SPAN CLASS="Symbol">
m</SPAN>
m CMOS process the capacitance to ground of the diffusion is 200 to 300 aF<SPAN CLASS="Symbol">
m</SPAN>
m<SUP CLASS="Superscript">
&#8211;2</SUP>
 (area component) and 400 to 550 aF<SPAN CLASS="Symbol">
m</SPAN>
m<SUP CLASS="Superscript">
&#8211;1</SUP>
 (perimeter component). Thus, including both area and perimeter effects, a 16 <SPAN CLASS="Symbol">
m</SPAN>
m<SUP CLASS="Superscript">
2</SUP>
 diffusion contact (consisting of a 2 <SPAN CLASS="Symbol">
m</SPAN>
m by 2 <SPAN CLASS="Symbol">
m</SPAN>
m opening plus the required overlap) has a parasitic capacitance of 10&#8211;14 f F. If we assume an antifuse has a parasitic capacitance of approximately 10 fF in a 1.0 or 1.2 <SPAN CLASS="Symbol">
m</SPAN>
m process, we can calculate the parasitic capacitances shown in <A HREF="CH07.1.htm#28701" CLASS="XRef">
Table&nbsp;7.2</A>
.</P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="3">
<P CLASS="TableTitle">
<A NAME="pgfId=9796">
 </A>
TABLE&nbsp;7.2&nbsp;<A NAME="28701">
 </A>
Actel interconnect parameters.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=9802">
 </A>
<SPAN CLASS="TableHeads">
Parameter</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=9804">
 </A>
<SPAN CLASS="TableHeads">
A1010/A1020</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=9806">
 </A>
<SPAN CLASS="TableHeads">
A1010B/A1020B</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9808">
 </A>
Technology</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=13058">
 </A>
2.0 <SPAN CLASS="Symbol">
m</SPAN>
m, <SPAN CLASS="Symbol">
l</SPAN>
 = 1.0 <SPAN CLASS="Symbol">
m</SPAN>
m</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9812">
 </A>
1.2 <SPAN CLASS="Symbol">
m</SPAN>
m, <SPAN CLASS="Symbol">
l</SPAN>
 = 0.6 <SPAN CLASS="Symbol">
m</SPAN>
m</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9814">
 </A>
Die height (A1010)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9816">
 </A>
240 mil </P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9818">
 </A>
144 mil </P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9820">
 </A>
Die width (A1010)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9822">
 </A>
360 mil </P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9824">
 </A>
216 mil </P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9826">
 </A>
Die area (A1010)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9828">
 </A>
86,400 mil <SUP CLASS="Superscript">
2</SUP>
 = 56 M <SPAN CLASS="Symbol">
l</SPAN>
<SUP CLASS="Superscript">
2</SUP>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9830">
 </A>
31,104 mil <SUP CLASS="Superscript">
2</SUP>
 = 56 M <SPAN CLASS="Symbol">
l</SPAN>
<SUP CLASS="Superscript">
2</SUP>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9832">
 </A>
Logic Module (LM) height (Y1)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9834">
 </A>
180 <SPAN CLASS="Symbol">
m</SPAN>
m = 180 <SPAN CLASS="Symbol">
l</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9836">
 </A>
108 <SPAN CLASS="Symbol">
m</SPAN>
m = 180 <SPAN CLASS="Symbol">
l</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9838">
 </A>
LM width (X)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9840">
 </A>
150 <SPAN CLASS="Symbol">
m</SPAN>
m = 150 <SPAN CLASS="Symbol">
l</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9842">
 </A>
90 <SPAN CLASS="Symbol">
m</SPAN>
m = 150 <SPAN CLASS="Symbol">
l</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9844">
 </A>
LM area (X <SPAN CLASS="Symbol">
&#165;</SPAN>
 Y1)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=12525">
 </A>
27,000 <SPAN CLASS="Symbol">
m</SPAN>
m<SUP CLASS="Superscript">
2</SUP>
 = 27 k <SPAN CLASS="Symbol">
l</SPAN>
<SUP CLASS="Superscript">
2</SUP>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=12531">
 </A>
9,720 <SPAN CLASS="Symbol">
m</SPAN>
m<SUP CLASS="Superscript">
2</SUP>
 = 27 k <SPAN CLASS="Symbol">
l</SPAN>
<SUP CLASS="Superscript">
2</SUP>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=9850">
 </A>
Channel height (Y2)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=9852">
 </A>
25 tracks = 287 <SPAN CLASS="Symbol">
m</SPAN>