3.18.2 Charge Deficit Model

The charge-deficit model from BSIM4 has been adopted here [10]. Based on a relaxation time approach, the deficient charge (equilibrium quasi-static charge minus the instantaneous channel charge) is kept track through a RC sub-circuit [17]. An extra node whose voltage is equal to the deficient charge is introduced for this purpose. The instantaneous channel charge that is obtained from the self-consistent solution of the MOSFET and RC sub-circuit is then split between the source and drain using a partition ratio ($X_{d,part}$) calculated from the quasi-static charges. A capacitance of 1 Farad is used for this purpose, while the resistance is given by the inverse of the relaxation time constant, $1/\tau$.

$X_{d,part} = \dfrac{q_d}{q_g} \qquad (3.542)$

$I_{dovVds} = \mu_0(T) \cdot C_{ox} \cdot \dfrac{W_{eff}}{L_{eff}} \cdot q_{ia} \cdot \dfrac{M_{oc}}{D_{vsat}} \qquad (3.543)$

$\dfrac{1}{R_{ii}} = NF \cdot NFIN \cdot XRCRG1_i \cdot \Bigg( I_{dovVds} + XRCRG2_i \cdot \dfrac{\mu_{eff} \cdot C_{oxe} \cdot W_{eff} \cdot kT}{q \cdot L_{eff}} \Bigg)$

$(3.544)$

$\dfrac{1}{\tau} = \dfrac{1}{R_{ii} \cdot C_{ox} \cdot W_{eff} \cdot L_{eff}} \qquad (3.545)$

Figure 10: RC network for calculating deficient charge $Q_{def}$ and the instantaneous charge, $Q_{def}/\tau$ is used in place of the quasi-static charges. [17]

References

[10] BSIM4 model. Department of Electrical Engineering and Computer Science, UC Berkeley.

[17] M. Chan, K. Y. Hui, C. Hu, and P. K. Ko, "A robust and physical BSIM3 non-quasi-static transient and AC small-signal model for circuit simulation," IEEE Transaction on Electron Devices, vol. 45, no. 4, pp. 834-841, April 1998.