3.20.4 Two-Step Source Side Junction Capacitance

In some cases, the depletion edge in the channel/ substrate edge might transition into a region with a different doping (for example in a NMOS device: [$n^{+}$ (source), $p_1$ (channel/substrate), $p_2$ (substrate)], where $p_1$ and $p_2$ are regions with different doping levels). The following could be used to capture such a situation. In what follows, $V_{escn} < 0$ can be interpreted as the transition voltage at which the depletion region switches from $p_1$ to $p_2$ region. It is calculated assuming parameters SJxxx (proportionality constant for second region) and MJxxx2 (gradient of second region's doping) are given, to give a continuous charge and capacitance.

For $V_{es} < V_{esc1}$,

$\begin{aligned} Q_{es1} = C_{zbs} \cdot &\Bigg[ PBS(T) \cdot \dfrac{1 - \Big( 1 - \dfrac{V_{esc1}}{PBS(T)} \Big)^{1 - MJS} }{1 - MJS} + \\ & SJS \cdot P_{bs2} \cdot \dfrac{1 - \Big( 1 - \dfrac{V_{es} - V_{esc1}}{P_{bs2}} \Big)^{1 - MJS2}}{1 - MJS2} \Bigg] \end{aligned} \qquad (3.593)$

Else use the $Q_{es1}$ of single junction above for $V_{es} > V_{esc1}$, where

$V_{esc1} = PBS(T) \cdot \Big[ 1 - \Big( \dfrac{1}{SJS} \Big)^{\frac{1}{MJS}} \Big] \qquad (3.594)$

$P_{bs2} = \dfrac{PBS(T) \cdot SJS \cdot MJS2}{MJS \cdot \Big( 1 - \dfrac{V_{esc1}}{PBS(T)} \Big)^{-1 - MJS}} \qquad (3.595)$

For $V_{es} < V_{esc2}$,

$\begin{aligned} Q_{es2} = C_{zbssw} \cdot &\Bigg[ PBSWS(T) \cdot \dfrac{1 - \Big( 1 - \dfrac{V_{esc2}}{PBSWS(T)} \Big)^{1 - MJSWS} }{1 - MJSWS} + \\ & SJSWS \cdot P_{bsws2} \cdot \dfrac{1 - \Big( 1 - \dfrac{V_{es} - V_{esc2}}{P_{bsws2}} \Big)^{1 - MJSWS2}}{1 - MJSWS2} \Bigg] \end{aligned} \qquad (3.596)$

Else use the $Q_{es2}$ of single junction above for $V_{es} > V_{esc2}$, where

$V_{esc2} = PBSWS(T) \cdot \Big[ 1 - \Big( \dfrac{1}{SJSWS} \Big)^{\frac{1}{MJSWS}} \Big] \qquad (3.597)$

$P_{bsws2} = \dfrac{PBSWS(T) \cdot SJSWS \cdot MJSWS2}{MJSWS \cdot \Big( 1 - \dfrac{V_{esc2}}{PBSWS(T)} \Big)^{-1 - MJSWS}} \qquad (3.598)$

For $V_{es} < V_{esc3}$,

$\begin{aligned} Q_{es3} = C_{zbsswg} \cdot &\Bigg[ PBSWGS(T) \cdot \dfrac{1 - \Big( 1 - \dfrac{V_{esc3}}{PBSWGS(T)} \Big)^{1 - MJSWGS} }{1 - MJSWGS} + \\ & SJSWGS \cdot P_{bswgs2} \cdot \dfrac{1 - \Big( 1 - \dfrac{V_{es} - V_{esc3}}{P_{bswgs2}} \Big)^{1 - MJSWGS2}}{1 - MJSWGS2} \Bigg] \end{aligned} \qquad (3.599)$

Else use the $Q_{es3}$ of single junction above for $V_{es} > V_{esc3}$, where

$V_{esc3} = PBSWGS(T) \cdot \Big[ 1 - \Big( \dfrac{1}{SJSWGS} \Big)^{\frac{1}{MJSWGS}} \Big] \qquad (3.600)$

$P_{bswgs2} = \dfrac{PBSWGS(T) \cdot SJSWGS \cdot MJSWGS2}{MJSWGS \cdot \Big( 1 - \dfrac{V_{esc3}}{PBSWGS(T)} \Big)^{-1 - MJSWGS}} \qquad (3.601)$