# EKV MOSFET Model Version 2.6 Now Available in SmartSpice and UTMOST III

**Introduction**

Silvaco now offers the EKV (ENZ, KRUMMENACHER,
VITTOZ) MOSFET model version 2.6 originally developed in EPFL ("Ecole
Polytechnique Federale de Lausanne" - Switzerland), as part
of the **SmartLib** product-independent model library. This model
is available within **SmartSpice** and **UTMOST** as level
44.

The EKV MOSFET model is dedicated to low-power and low-voltage for analog design. This model presents a unique solution to model static, quasi-static and non-quasi-static dynamic behavior as well as noise, based on a proper normalization and interpolation. The EKV model equation is based on a "single expression", which preserves continuity of first and higher order derivatives.

Physical Effects

The main effects modeled in this EKV model, as excerpted from the EPFL-EKV Model Manual [1], are described below:

- Basic geometrical and process related aspects
such as oxide thickness, junction depth, effective channel length
and width

- Effects of doping profile, substrate effect

- Modeling of weak, moderate and strong inversion
behavior

- Short-Channel effect such as channel-length
modulation (CLM), source and drain charge-sharing (including for
narrow channel width), reverse short channel effect (RSCE)

- Modeling of substrate current due to impact
ionization

- Quasi-static charge-based dynamic model

- Thermal and flicker noise modeling

- A first-order non-quasi-static model for the
transadmittances

- Short-distance geometry and bias dependent device matching

Simulation Model

Voltage bulk reference allows the model to be handled symmetrically with respect to drain and source. The "single expression" principle model equation implies the continuity of the large and small signal characteristics in all modes of operation, including the moderate inversion region.

The EKV model has only 10 physical parameters (COX, XJ, DW, DL, VTO, GAMMA, PHI, KP, E0, UCRIT), 3 fine tuning parameters (LAMBDA, LETA, WETA), 2 parameters for reverse short channel effects (Q0, LK), 3 parameters for impact ionization current (IBA, IBB, IBN), 4 temperature effect parameters (TCV, BEX, UCEX, IBBT), and 2 flicker noise parameters (KF, AF).

DC Static Model

New and prior versions can be selected through the UPDATE model parameter: UPDATE=2.6 (default) selects version 2.6.

The pinch-off voltage VP (referred to the bulk) is one of the basic concepts of EKV and corresponds to the channel potential for which inversion charge becomes zero in a non-equilibrium situation. The various modes of operation depend on the degree of inversion at each end of the channel, and therefore on VP-VD and VP-VS (VD and VS are drain and source potentials relative to the bulk).

The large signal interpolation function selector EKVINT (or INT) can be used: EKVINT=0 (default) invokes a precise interpolation function, EKVINT=1 a simpler interpolation function.

Substrate current is modeled as a current from the (intrinsic) drain to the substrate, in parallel with the extrinsic junction current.

Temperature effects are modeled for threshold voltage, mobility, critical field, and impact ionization current. Energy gap temperature dependency is also accounted for.

For Monte-Carlo and sensitivity simulation short distance mismatch rules have been introduced with the AVTO, AKP and AGAMMA parameters.

Figure 1: EKV simulation using Utmost ALL_DC routine.

Figure 2: EKV simulation of substrate current for different temperatures.

Dynamic Model

Two quasi-static dynamic models are available: a charge based model for transcapacitances, allowing charge-conservation during transient analysis, and a simpler capacitance based model more suitable for high-frequency operations (typically above 109 Hz).

Appropriate model can be selected through XQC parameter: XQC<0.5 (default) selects the charge transcapacitance model and XQC > 0.5, the capacitance only model.

Short-channel and reverse short-channel effects, as charge-sharing effects, are included in the dynamic model through the pinch-off voltage VP.

The EKV model includes a first-order Non-Quasi-Static (NQS) model for small-signal (.AC) simulations. This feature can be activated using the NQS flag (model parameter): the Non-Quasi-Static equation set is selected by NQS=1 (default is 0).

Noise Model

Previous equations from EPFL have been implemented for both thermal and flicker noise, using AF and KF model parameters. SmartSpice Common Equations for 1/f noise are also available using NLEV flag.

Output Device Variables

Usual device output variables for MOS models like node currents, conductances, various charges and capacitances, can be printed, stored and/or measured.

Saturation drain voltage (vdsat) and Threshold voltage (vth) values are not needed in EKV internal equations. However, specific equations have been introduced recently to evaluate these interesting device output variables.

Furthermore, according to the EPFL-EKV Model Manual [1], the following model internal variables are available for the user's output information: VP, VM, N, IF, IR, IRSAT, TEF, SAT, TAU and TAU0.

Extrinsic Model

The EKV model describes only the intrinsic part of a MOS transistor. The extrinsic part (i. e. parasitic elements) are evaluated using SmartSpice Common Equations. SmartSpice Area Calculation Method is also supported. Please refer to Silvaco documentation for a complete description [2].

Figure 3: EKV Intrinsic transcapacitances calculated with the charge conservation model

Acknowledgments

Silvaco would like to thank Matthias Bucher from the EPFL, Switzerland, for his invaluable help and support during the implementation of the model.

**References**

- M Bucher, et al "The EPFL-EKV MOSFET Model Equations for Simulation" EPFL Lausanne Switzerland, Technical Report, July 1998
- SmartSpice/UTMOST III Modeling Manual Volume 1 (Silvaco International)

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