📄 ch15.5.htm
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q<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
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<SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
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=</P>
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<SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="Subscript">
0</SUB>
exp</P>
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–––––</P>
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–</P>
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1</P>
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(15.9)</P>
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<SPAN CLASS="Symbol">
Ë</SPAN>
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nkT</P>
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</P>
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where <SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="Subscript">
0</SUB>
is a constant, and the constant, <SPAN CLASS="EquationNumber">
n,</SPAN>
<SPAN CLASS="EquationVariables">
</SPAN>
is normally between 1 and 2. </P>
<P CLASS="Body">
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The slope, <SPAN CLASS="EquationNumber">
S,</SPAN>
of the transistor current in the subthreshold region is </P>
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–nkT</P>
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nkT</P>
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S</P>
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=</P>
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––––</P>
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log<SUB CLASS="Subscript">
10</SUB>
e</P>
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=</P>
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2.3</P>
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––––</P>
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V/decade .</P>
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(15.10)</P>
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q</P>
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q</P>
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<P CLASS="Body">
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For example, at a junction temperature, <SPAN CLASS="EquationNumber">
T</SPAN>
= 125 °C ( <SPAN CLASS="Symbol">
ª</SPAN>
400 K) and assuming <SPAN CLASS="EquationNumber">
n</SPAN>
<SPAN CLASS="Symbol">
ª</SPAN>
1.5, <SPAN CLASS="EquationNumber">
S</SPAN>
= 120 mV/decade (<SPAN CLASS="EquationNumber">
q</SPAN>
= 1.6 <SPAN CLASS="Symbol">
¥</SPAN>
10<SUP CLASS="Superscript">
–19</SUP>
Fm<SUP CLASS="Superscript">
–1</SUP>
, <SPAN CLASS="EquationNumber">
k</SPAN>
= 1.38 <SPAN CLASS="Symbol">
¥</SPAN>
10<SUP CLASS="Superscript">
–23</SUP>
JK<SUP CLASS="Superscript">
–1</SUP>
), which does not scale. The constant value of <SPAN CLASS="EquationNumber">
S</SPAN>
= 120 mV/decade means it takes 120 mV to reduce the subthreshold current by a factor of 10 in any process. If we reduce the threshold voltages to 0.36 V in a deep-submicron process, for example, this means at <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
= 0 V we can only reduce <SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
to 0.001 times its value at <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
= <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
t</SUB>
. This problem can lead to large static currents.</P>
<P CLASS="Body">
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Transistor leakage is caused by the fact that a reverse-biased diode conducts a very small <A NAME="marker=161329">
</A>
leakage current. The sources and drains of every transistor, as well as the junctions between the wells and substrate, form <A NAME="marker=161330">
</A>
parasitic diodes. The parasitic-diode leakage currents are strongly dependent on the type and quality of the process as well as temperature. The parasitic diodes have two components in parallel: an area diode and a perimeter diode. The ideal parasitic diode currents are given by the following equation: </P>
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</P>
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<P CLASS="TableEqnCenter">
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q<SPAN CLASS="EquationVariables">
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</P>
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<SPAN CLASS="EquationVariables">
I</SPAN>
</P>
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=</P>
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<SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="Subscript">
s</SUB>
exp</P>
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–––––</P>
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–</P>
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1</P>
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(15.11)</P>
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nkT</P>
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<P CLASS="EquationNumbered">
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<IMG SRC="CH15-5.gif" ALIGN="BASELINE">
.(15.1)</P>
<P CLASS="Body">
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