📄 ch13.a.htm
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<P CLASS="Computer">
<A NAME="pgfId=108545">
</A>
+ U0=0.2, LU0=6E-2, WU0=-6E-2</P>
<P CLASS="Computer">
<A NAME="pgfId=108546">
</A>
+ U1=1E-2, LU1=1E-2, WU1=7E-4</P>
<P CLASS="Computer">
<A NAME="pgfId=108547">
</A>
+ X2MZ=7, LX2MZ=-2, WX2MZ=1</P>
<P CLASS="Computer">
<A NAME="pgfId=108548">
</A>
+ X2E= 5E-5, LX2E=-1E-3, WX2E=-2E-4</P>
<P CLASS="Computer">
<A NAME="pgfId=108549">
</A>
+ X3E=8E-4, LX3E=-2E-4, WX3E=-1E-3</P>
<P CLASS="Computer">
<A NAME="pgfId=108550">
</A>
+ X2U0=9E-3, LX2U0=-2E-3, WX2U0=2E-3</P>
<P CLASS="Computer">
<A NAME="pgfId=108551">
</A>
+ X2U1=6E-4, LX2U1=5E-4, WX2U1=3E-4</P>
<P CLASS="Computer">
<A NAME="pgfId=108552">
</A>
+ MUS=150, LMUS=10, WMUS=4</P>
<P CLASS="Computer">
<A NAME="pgfId=108553">
</A>
+ X2MS=6, LX2MS=-0.7, WX2MS=2</P>
<P CLASS="Computer">
<A NAME="pgfId=108554">
</A>
+ X3MS=-1E-2, LX3MS=2, WX3MS=1</P>
<P CLASS="Computer">
<A NAME="pgfId=108555">
</A>
+ X3U1=-1E-3, LX3U1=-5E-4, WX3U1=1E-3</P>
<P CLASS="Computer">
<A NAME="pgfId=108556">
</A>
+ TOX=1E-2, TEMP=25, VDD=5</P>
<P CLASS="Computer">
<A NAME="pgfId=108557">
</A>
+ CGDO=2.4E-10, CGSO=2.4E-10, CGBO=3.8E-10</P>
<P CLASS="Computer">
<A NAME="pgfId=108558">
</A>
+ XPART=1</P>
<P CLASS="Computer">
<A NAME="pgfId=108559">
</A>
+ N0=1, LN0=0, WN0=0</P>
<P CLASS="Computer">
<A NAME="pgfId=108560">
</A>
+ NB=0, LNB=0, WNB=0</P>
<P CLASS="Computer">
<A NAME="pgfId=108561">
</A>
+ ND=0, LND=0, WND=0</P>
<P CLASS="Computer">
<A NAME="pgfId=108562">
</A>
* p+ diffusion </P>
<P CLASS="Computer">
<A NAME="pgfId=108563">
</A>
+ RSH=2, CJ=9.5E-4, CJSW=2.5E-10</P>
<P CLASS="Computer">
<A NAME="pgfId=108564">
</A>
+ JS=1E-8, PB=0.85, PBSW=0.85</P>
<P CLASS="Computer">
<A NAME="pgfId=108565">
</A>
+ MJ=0.44, MJSW=0.24, WDF=0</P>
<P CLASS="Computer">
<A NAME="pgfId=108566">
</A>
*, DS=0</P>
</TD>
</TR>
</TABLE>
</OL>
<P CLASS="BodyAfterHead">
<A NAME="pgfId=108571">
</A>
<A HREF="CH13.a.htm#31851" CLASS="XRef">
Table 13.15</A>
shows the BSIM1 parameters (in the PSpice <SPAN CLASS="BodyComputer">
LEVEL = 4</SPAN>
format) for the G5 process. The <SPAN CLASS="Definition">
Berkeley short-channel IGFET model</SPAN>
<A NAME="marker=108878">
</A>
(<SPAN CLASS="Definition">
BSIM</SPAN>
<A NAME="marker=108880">
</A>
<A NAME="marker=108879">
</A>
) family models capacitance in terms of charge. In Sections 2.1 and 3.2 we treated the gate–drain capacitance, <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
GD</SUB>
, for example, as if it were a <SPAN CLASS="Definition">
reciprocal capacitance</SPAN>
<A NAME="marker=109075">
</A>
, and could be written assuming there was charge associated with the gate, <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
, and the drain, <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
, as follows: </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127420">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127422">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127424">
</A>
-∂<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127426">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=127428">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127570">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127688">
</A>
-∂<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=127574">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=127430">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127432">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
GD</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127434">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127436">
</A>
––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127438">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127440">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
DG</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127576">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127690">
</A>
––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=127580">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=127442">
</A>
<A NAME="12593">
</A>
(13.31)</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127444">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127446">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127448">
</A>
∂<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127450">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=127452">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127582">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=127692">
</A>
∂<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=127586">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=127454">
</A>
</P>
</TD>
</TR>
</TABLE>
<P CLASS="Body">
<A NAME="pgfId=108612">
</A>
Equation <A HREF="CH13.a.htm#12593" CLASS="XRef">
13.31</A>
(the <A NAME="marker=109068">
</A>
<SPAN CLASS="Definition">
Meyer model</SPAN>
) would be true if the gate and drain formed a parallel plate capacitor and <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
= –<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
, but they do not. In general, <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
≠ –<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
and Eq. <A HREF="CH13.a.htm#12593" CLASS="XRef">
13.31</A>
is not true. In an MOS transistor we have four regions of charge: <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
(gate), <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
(channel charge associated with the drain), <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
S</SUB>
(channel charge associated with the drain), and <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
B</SUB>
(charge in the bulk depletion region). These charges are not independent, since </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=128078">
</A>
<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G </SUB>
+ <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
D </SUB>
+ <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
S </SUB>
+ <SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
B</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=128080">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=128082">
</A>
0</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=128096">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=128084">
</A>
<A NAME="19634">
</A>
(13.32)</P>
</TD>
</TR>
</TABLE>
<P CLASS="Body">
<A NAME="pgfId=112798">
</A>
We can form a 4 <SPAN CLASS="Symbol">
¥</SPAN>
4 matrix, <SPAN CLASS="Vector">
M</SPAN>
, whose entries are ∂<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
i</SUB>
/∂<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
j</SUB>
, where <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
j</SUB>
= <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
, <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
S</SUB>
, <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
D</SUB>
, and <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
B</SUB>
. Then <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
ii</SUB>
= <SPAN CLASS="EquationVariables">
M</SPAN>
<SUB CLASS="SubscriptVariable">
ii</SUB>
are the terminal capacitances; and <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
ij</SUB>
= –<SPAN CLASS="EquationVariables">
M</SPAN>
<SUB CLASS="SubscriptVariable">
ij</SUB>
, where <SPAN CLASS="EquationVariables">
i</SPAN>
≠ <SPAN CLASS="EquationVariables">
j</SPAN>
, is a <SPAN CLASS="Definition">
transcapacitance</SPAN>
<A NAME="marker=112799">
</A>
. Equation <A HREF="CH13.a.htm#19634" CLASS="XRef">
13.32</A>
forces the sum of each column of <SPAN CLASS="URL">
M</SPAN>
to be zero. Since the charges depend on voltage differences, there are only three independent voltages (<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GB</SUB>
, <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DB</SUB>
, and <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
SB</SUB>
, for example) and each row of <SPAN CLASS="Vector">
M</SPAN>
must sum to zero. Thus, we have nine (= 16 – 7) independent entries in the matrix <SPAN CLASS="Vector">
M</SPAN>
. In general, <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
ij</SUB>
is not necessarily equal to <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
ji</SUB>
. For example, using PSpice and a <SPAN CLASS="BodyComputer">
LEVEL = 4</SPAN>
BSIM model, there are nine independent partial derivatives, printed as follows:</P>
<P CLASS="ComputerFirst">
<A NAME="pgfId=108750">
</A>
Derivatives of gate (dQg/dVxy) and bulk (dQb/dVxy) charges</P>
<P CLASS="Computer">
<A NAME="pgfId=108844">
</A>
DQGDVGB 1.04E-14</P>
<P CLASS="Computer">
<A NAME="pgfId=108845">
</A>
DQGDVDB -1.99E-15</P>
<P CLASS="Computer">
<A NAME="pgfId=108846">
</A>
DQGDVSB -7.33E-15</P>
<P CLASS="Computer">
<A NAME="pgfId=108847">
</A>
DQDDVGB -1.99E-15</P>
<P CLASS="Computer">
<A NAME="pgfId=108848">
</A>
DQDDVDB 1.99E-15</P>
<P CLASS="Computer">
<A NAME="pgfId=108849">
</A>
DQDDVSB 0.00E+00</P>
<P CLASS="Computer">
<A NAME="pgfId=108850">
</A>
DQBDVGB -7.51E-16</P>
<P CLASS="Computer">
<A NAME="pgfId=108851">
</A>
DQBDVDB 0.00E+00</P>
<P CLASS="ComputerLast">
<A NAME="pgfId=108852">
</A>
DQBDVSB -2.72E-15</P>
<P CLASS="Body">
<A NAME="pgfId=108905">
</A>
From these derivatives we may compute six <SPAN CLASS="Definition">
nonreciprocal capacitances</SPAN>
<A NAME="marker=108960">
</A>
: </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=128311">
</A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
GB</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=128313">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=128315">
</A>
∂<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
/∂<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GB</SUB>
+ ∂<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
/∂<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DB</SUB>
+ ∂<SPAN CLASS="EquationVariables">
Q</SPAN>
<SUB CLASS="SubscriptVariable">
G</SUB>
/∂<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
SB</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=128317">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
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