3.17.1 Gate-to-Body Current

$I_{gbinv}$ and $I_{gbacc}$ are calculated only if $IGBMOD = 1$.

$A = 3.75956 \times 10^{-7} \qquad (3.512)$

$B = 9.82222 \times 10^{11} \qquad (3.513)$

$V_{aux,igbinv} = NIGBINV_i \cdot \dfrac{kT}{q} \cdot ln \Bigg[ 1 + exp \Bigg( \dfrac{q_{ia} - EIGBINV_i}{NIGBINV_i \cdot kT/q} \Bigg) \Bigg] \qquad (3.514)$

$\begin{aligned} I_{gb,inv} &= W_{eff0} \cdot L_{eff} \cdot A \cdot T_{ox,ratio} \cdot V_{ge} \cdot V_{aux,igbinv} \cdot I_{gtemp} \cdot NFIN_{total} \\ &\times exp \Big[ -B \cdot TOXG \cdot \Big( AIGBINV(T) - BIGBINV_i \cdot q_{ia} \Big) \\ &\times \Big( 1 + CIGBINV_i \cdot q_{ia} \Big) \Big] \end{aligned} \qquad (3.515)$

$A = 4.97232 \times 10^{-7} \qquad (3.516)$

$B = 7.45669 \times 10^{11} \qquad (3.517)$

$V_{fbzb} = \Delta \phi - E_g / 2 - \phi_B \qquad (3.518)$

$T_0 = V_{fbzb} - V_{ge} \qquad (3.519)$

$T_1 = T_0 - 0.02 \qquad (3.520)$

$V_{aux,igbacc} = NIGBACC_i \cdot \dfrac{kT}{q} \cdot ln \Bigg[ 1 + exp \Bigg( \dfrac{T_0}{NIGBACC_i \cdot kT/q} \Bigg) \Bigg] \qquad (3.521)$

$V_{oxacc} = \begin{cases} q_{i,acc} &\text{for } BULKMOD = 1 \\ 0.5 \cdot \Big[ T_1 + \sqrt{ {T_1}^2 - 0.08 \cdot V_{fbzb}} \Big] &\text{for } BULKMOD \ne 1 \text{ and } V_{fbzb} \le 0 \\ 0.5 \cdot \Big[ T_1 + \sqrt{ {T_1}^2 + 0.08 \cdot V_{fbzb}} \Big] &\text{for } BULKMOD \ne 1 \text{ and } V_{fbzb} > 0 \end{cases} \qquad (3.522)$

$\begin{aligned} I_{gb,acc} &= W_{eff0} \cdot L_{eff} \cdot A \cdot T_{ox,ratio} \cdot V_{ge} \cdot V_{aux,igbacc} \cdot I_{gtemp} \cdot NFIN_{total} \\ &\times exp \Big[ -B \cdot TOXG \cdot \Big( AIGBACC(T) - BIGBACC_i \cdot V_{oxacc} \Big) \\ &\times \Big( 1 + CIGBACC_i \cdot V_{oxacc} \Big) \Big] \end{aligned} \qquad (3.523)$

For $BULKMOD = 1$, $I_{gb}$ simply flows from the gate into the substrate. For $BULKMOD = 0$, $I_{gb}$ mostly flows into the source because the potential barrier for holes is lower at the source, which has a lower potential. To ensure continuity when Vds switches sign, $I_{gb}$ is partitioned into a source component, $I_{gbs}$ and a drain component, $I_{gbd}$ using a partition function:

$I_{gbs} = (I_{gb,inv} + I_{gb,acc}) \cdot W_f \qquad (3.524)$

$I_{gbd} = (I_{gb,inv} + I_{gb,acc}) \cdot W_r \qquad (3.525)$

$W_f$ and $W_r$ are defined in Equations (3.216) and (3.217), respectively.