SPICE provides a wide variety of MOS transistor models with various tradeoffs between complexity and accuracy. Level 1 and Level 3 models were historically important, but they are no longer adequate to accurately model very small modern transistors.

BSIM models are more accurate and are presently the most widely used. Some companies use their own proprietary models. This section briefly describes the main feature of each of these models. It also describes how to model diffusion capacitance and how to run simulations in various process corners.

The model descriptions are intended only as an overview of the capabilities and limitations of the models; refer to a SPICE manual for a much more detailed description if one is necessary.

**Level 1 Models**

The SPICE Level 1, or Shichman-Hodges [Shichman68] is closely realted to the Shockley model described in EQ(2.10), enhanced with channel length modulation and the body effect. The basic current model is:

The parameters from the SPICE model are given in ALL CAPS. Notice that $\beta$ is written instead of $KP(W_{eff}/L_{eff})$, where KP is a model parameter playing the role of k’ from EQ (2.7). $W_{eff}$ and $L_{eff}$ are the effective width and length, as described in Section 2.4.8. The LAMBDA term models channel length modulation.

$V_t=VTO+GAMMA(\sqrt{PHI+V_{th}}-\sqrt{PHI})\hspace{3cm}$ -(5.2)

Notice that this is identical to EQ (2.30), where VTO is the "zero-bias" threshold voltage $V_{to}$, GAMMA is the body effect coefficient $\gamma$, and PHI is the surface potential $\phi$.

The gate capacitance is calculated from the oxide thickness TOX. The default gate capacitance model in HSPICE is adequate for finding the transient response of digital circuits. More elaborate models exist that capture nonreciprocal effects that are important for analog design.

Level 1 models are useful for teaching because they are easy to correlate with hand analysis, but are too simplistic for modern design.

**Level 2 and 3 Models**

The SPICE Level 2 and 3 models add effects of velocity saturation, mobility degradation, subthreshold conduction, and drain-induced barrier lowering. The Level 2 model is based on the Grove-Frohman equations (Frohman69), while the Level 3 model is based on empirical equations that provide similar accuracy and faster simulation times and better convergence. However, these models still do not provide good fits to the measured I-V characteristics of modern transistors.

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