LEVEL 55 EPFL-EKV MOSFET Model

The EPFL-EKV MOSFET model is a scalable and compact simulation model built on fundamental physical properties of the MOS structure. This model is dedicated to the design and simulation of low-voltage, low-current analog, and mixed analog-digital circuits using submicron CMOS technologies.

This section provides a description of the equations and parameters used for the computer simulation version of the EPFL-EKV MOSFET model. The description concentrates on the intrinsic part of the MOSFET, and is intended to give the model user information on parameter handling and the actual equations used in the computer simulation.

The extrinsic part of the MOSFET is handled as it is often made for other MOSFET models. The extrinsic model includes the series resistances of the source and drain diffusions, which are handled as external elements, as well as junction currents and capacitances.

Single Equation Model

The EPFL-EKV MOSFET model is in principle formulated as a `single expression', which preserves continuity of first- and higher-order derivatives with respect to any terminal voltage, in the entire range of validity of the model. The analytical expressions of first-order derivatives as transconductances and transcapacitances are not presented in this section but are also available for computer simulation.

Effects Modeled

The EPFL-EKV MOSFET model version 2.6 includes modeling of the following physical effects:

• Basic geometrical and process related aspects as oxide thickness, junction depth, effective channel length and width
• Effects of doping profile, substrate effect
• Modeling of weak, moderate, and strong inversion behavior
• Modeling of mobility effects due to vertical and lateral fields, velocity saturation
• Short-channel effects as channel-length modulation (CLM), source and drain charge-sharing (including for narrow channel widths), reverse short channel effect (RSCE)
• Modeling of substrate current due to impact ionization
• Quasi-static charge-based dynamic model
• Thermal and flicker noise modeling
• First-order non-quasi-static model for the transadmittances
• Short-distance geometry- and bias-dependent device matching.

Coherence of Static and Dynamic Models

All aspects regarding the static, the quasi-static and non-quasi-static dynamic and noise models are all derived in a coherent way from a single characteristic, the normalized transconductance-to-current ratio. Symmetric normalized forward and reverse currents are used throughout these expressions. For quasi-static dynamic operation, both a charge-based model for the node charges and trans-capacitances, and a simpler capacitances model are available. The dynamic model, including the time constant for the nonquasi-static model, is described in symmetrical terms of the forward and reverse normalized currents. The charge formulation is further used to express effective mobility dependence of local field.

Bulk Reference and Symmetry

Voltages are all referred to the local substrate:

V S and V D are the intrinsic source and drain voltages, which means that the voltage drop over extrinsic resistive elements is supposed to have already been accounted for externally. V D is the electrical drain voltage, and is chosen such that . Bulk reference allows the model to be handled symmetrically with respect to source and drain, a symmetry that is inherent in common MOS technologies (excluding non-symmetric source-drain layouts).

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NOTE: Intrinsic model equations are presented for an N-channel MOSFET. P-channel MOSFETs are dealt with as pseudo-N-channel, i.e. the polarity of the voltages ( , , , as well as VFB , VTO and TCV ) is reversed prior to computing the current for P-channel, which is given a negative sign. No other distinctions are made between N-channel and P-channel, with the exception of the factor for effective mobility calculation.

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Equivalent Circuit

This figure represents the intrinsic and extrinsic elements of the MOS transistor. For quasi-static dynamic operation, only the intrinsic capacitances from the simpler capacitances model are shown here. However, a charge-based transcapacitances model is also available for computer simulation.

Device Input Variables

EKV Intrinsic Model Parameters

Process Related Parameters

Basic Intrinsic Model Parameters

Optional Parameters

The following parameters are introduced, to accommodate scaling behavior of the process and basic intrinsic model parameters, as well as statistical circuit simulation. Note that the parameters TOX , NSUB , VFB , UO , and VMAX are only used if COX , GAMMA and/or PHI , VTO , KP and UCRIT are not specified, respectively. Further, a simpler mobility reduction model due to vertical field is accessible. The mobility reduction coefficient THETA is only used if E0 is not specified.

Channel Length Modulation and Charge Sharing Parameters

Reverse Short-channel Effect Parameters

Impact Ionization Related Parameters

Intrinsic Model Temperature Parameters

Matching Parameters

Flicker Noise Parameters

Setup Parameter s

Static Intrinsic Model Equations

Basic Definitions

Parameter Preprocessing

Handling of Model Parameters for P-channel MOSFETs

For P-channel devices, the sign of VFB , VTO and TCV is inversed before processing. Therefore, VTO and TCV are usually positive and VFB negative for N-channel, and vice versa for P-channel MOSFETs.

Intrinsic Parameters Initialization

The basic intrinsic model parameters COX , GAMMA , PHI , VTO , KP and UCRIT are related to the fundamental process parameters TOX , NSUB , VFB , UO , VMAX , respectively, similarly as in early SPICE models. For the purpose of statistical circuit simulation, it is desirable to introduce parameter variations on the level of the latter parameters. These dependencies are also of interest if device scaling is to be analyzed, and are useful when parameter sets should be obtained from other MOSFET models. Therefore, the possibility is introduced to use the following relations:

If COX is not specified, then it is initialized as:

If GAMMA is not specified, then it is initialized as:

If PHI is not specified, then it is initialized as:

If VTO is not specified, then it is initialized as:

If DP is not specified, then it is initialized as:

If UCRIT is not specified, then it is initialized as:

If E0 is not specified, then a simplified mobility model is used with the parameter THETA:

Note that optional parameters may not be available in all implementations.

Default Values and Parameter Ranges

Model parameters that are not defined in the model parameter sets are either initialized according to the above relations, or set to their default values. For certain parameters, their numerical range has to be restricted to avoid numerical problems such as divisions by zero. If a parameter given in a parameter set falls outside the specified range (see range column in the parameter tables) then its value is set to the closest acceptable value.

Intrinsic Parameters Temperature Dependence

Bulk Referenced Intrinsic Voltages

Voltages are all referred to the local substrate (Bulk Reference and Symmetry):

For P-channel devices, all signs of the above voltages are inverted prior to processing.

Effective Channel Length and Width

Short Distance Matching

Random mismatch between two transistors with identical layout and close to each other is in most cases suitably described by a law following the inverse of the square root of the transistors' area. The following relationships have been adopted:

These model equations are only applicable in Monte-Carlo and sensitivity simulations.

Note that since negative values for both KP a and GAMMA a are not physically meaningful, these are clipped at zero.

Reverse Short-channel Effect (RSCE)

Effective Gate Voltage Including RSCE

Effective substrate factor including charge-sharing for short and narrow channels

Pinch-off voltage for narrow-channel effect:

Effective substrate factor accounting for charge-sharing:

Pinch-off Voltage Including Short- and Narrow-channel Effects

Note that the pinch-off voltage accounts for channel doping effects such as threshold voltage and substrate effect. For long-channel devices, V p is a function of gate voltage; for short-channel devices, it becomes also a function of source and drain voltage due to the charge-sharing effect.

Slope Factor

Note that the slope factor (or body effect factor), which is primarily a function of the gate voltage, is linked to the weak inversion slope.

Large Signal Interpolation Function

F(v) is the large-signal interpolation function relating the normalized currents to the normalized voltages. A simple and accurate expression for the transconductance-to-current ratio allows a consistent formulation of the static large-signal interpolation function, the dynamic model for the intrinsic charges (and capacitances) as well as the intrinsic time constant and the thermal noise model for the whole range of current from weak to strong inversion:

Large-signal interpolation function:

Unfortunately, cannot be inverted analytically. However, it can be inverted using a Newton-Raphson iterative scheme. Currently, a simplification of this algorithm that avoids iteration is used, leading to a continuous expression for the large signal interpolation function. The (inverted) large signal interpolation function has the following asymptotes in strong and weak inversion respectively:

Forward Normalized Current

Velocity Saturation Voltage

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NOTE:  accounts for multiple series device number .

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NOTE: The variable in this formulation for computer simulation is half the value of the actual saturation voltage.

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Drain-to-source Saturation Voltage for Reverse Normalized Current

Channel-length Modulation

Equivalent Channel Length Including Channel-length Modulation and Velocity Saturation

Reverse Normalized Current

Reverse normalized current:

Reverse normalized current for mobility model, intrinsic charges/capacitances, thermal noise model and NQS time-constant:

Transconductance Factor and Mobility Reduction Due to Vertical Field

Note that the use of the device parameter NP (or M) gives accurate results for simulation of parallel devices, whereas the use of NS (or N) for series devices is only approximate. Note that L eq accounts for multiple series device number NS.

For the definition of the normalized depletion and inversion charges and refer to the section on the node charges. The use of ensures that when . The formulation of arises from the integration of the local effective field as a function of depletion and inversion charge densities along the channel. No substrate bias dependency is needed due to the inclusion of depletion charge. Note that the resulting mobility expression also depends on .

Simple Mobility Reduction Model

For reasons of compatibility with the former EKV model versions (EKV model versions prior to v2.6), a possibility is introduced to choose the simpler mobility reduction model that uses the parameter THETA . In case the model parameter E0 is not specified (see parameter preprocessing), the simpler mobility model is taken into account according to:

Specific Current

Drain-to-source Current

For P-channel devices, is given a negative sign.

Transconductances

The transconductances are obtained through derivation of the drain current:

Note the following relationships with the derivatives where the source is taken as reference:

The analytic derivatives are available with the model code.

Impact Ionization Current

Note that the factor 2 in the expression for accounts for the fact that the numerical value of is half the actual saturation voltage. Further note that the substrate current is intended to be treated as a component of the total extrinsic drain current, flowing from the drain to the bulk. The total drain current is therefore expressed as .

The substrate current therefore also affects the total extrinsic conductances, in particular the drain conductance.

Quasi-static Model Equations

Both a charge-based model for transcapacitances, allowing charge-conservation during transient analysis, and a simpler capacitances-based model are available. Note that the charges model is formulated in symmetric terms of the forward and reverse normalized currents, that is, symmetrical for both drain and source sides.

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

Dynamic Model for the Intrinsic Node Charges

Normalized Intrinsic Node Charges:

is a fixed oxide charge assumed to be zero. The above equation expresses the charge conservation among the four nodes of the transistor.

Total Charges:

Intrinsic Capacitances

Transcapacitances

The intrinsic capacitances are obtained through derivation of the node charges with respect to the terminal voltages:

where the positive sign is chosen when and the negative sign otherwise. This results in simple and continuous analytical expressions for all the transcapacitances in terms of , , the pinch-off voltage and the slope factor, and derivatives thereof, from weak to strong inversion and non-saturation to saturation.

Normalized Intrinsic Capacitances

A simplified capacitive dynamic model, using the five intrinsic capacitances corresponding to the Equivalent Circuit, can be obtained when neglecting the slight bias dependence of the slope factor , resulting in the following simple functions:

Note that this simplified capacitances model can be chosen by setting XQC =1.

Total Intrinsic Capacitances

Non-Quasi-Static (NQS) Model Equations

The EKV model includes a first order NQS model for small-signal (.AC) simulations. The expression of the NQS drain current is obtained from the quasi-static value of the drain current which is then 1st-order low-pass filtered. NQS is a flag (model parameter) allowing to disable the NQS model and is the bias dependent characteristic time constant.

0 is the intrinsic time constant defined as:

The corresponding small-signal (.AC) transadmittances are then given by:

Note that the availability of the NQS model is simulator-dependent.

Intrinsic Noise Model Equations

The noise is modeled by a current source INDS between intrinsic source and drain. It is composed of a thermal noise component and a flicker noise component and has the following Power Spectral Density (PSD):

Thermal Noise

The thermal noise component PSD is given by:

Note that the above thermal noise expression is valid in all regions of operation, including for small .

Flicker Noise

The flicker noise component PSD is given by:

Note that in some implementations, different expressions are accessible.

Operating Point Information

At operating points, the following information should be displayed as a help for circuit design:

Numerical values of model internal variables:

VG , VS , VD , IDS , IDB , gmg , gms , gmbs, gmd , VP , n, ,

intrinsic charges/capacitances

Transconductance efficiency factor:

`Early voltage':

`Overdrive voltage':

For P-channel devices, is given a negative sign.

`SPICE-like' threshold voltage:

For P-channel devices, is given a negative sign.

Saturation voltage:

For P-channel devices, is given a negative sign.

Saturation / non-saturation flag:

Estimation and Limits of Static Intrinsic Model Parameters

The EKV intrinsic model parameters can roughly be estimated from SPICE level 2/3 parameters as indicated in the table below, if no parameter extraction facility is available. Attention has to be paid to units of the parameters. This estimation method can be helpful and generally gives reasonable results. Nevertheless, be aware that the underlying modeling in SPICE LEVEL 2/3 and in the EKV model is not the same, even if the names and the function of several parameters are similar. Therefore, it is preferred if parameter extraction is made directly from measurements.

Lower and upper limits indicated in the table should give an idea on the order of magnitude of the parameters but do not necessarily correspond to physically meaningful limits, nor to the range specified in the parameter tables. These limits may be helpful for obtaining physically meaningful parameter sets when using nonlinear optimization techniques to extract EKV model parameters.

= 0.0345E-9 F/m q = 1.609E-19 C k = 1.381E-23 J/K

= 0.104E-9 F/m ni = 1.45E16 m-3 Vt = kT/q = 0.0259 V (at room temperature)

Model Updates Description

Throughout the use of the EKV v2.6 MOSFET model by many designers, several enhancements have appeared to be necessary from the model formulation point of view, or desirable from the point of view of the application of the model. This paragraph provides a summary of the updates to the EKV v2.6 model formulation and documentation since its first release. Wherever possible, backward compatibility with former formulations is maintained.

Revision I, September 1997

Description: Narrow channel effect on the substrate factor is revised to improve the transcapacitances behavior. The narrow channel effect is not anymore a function of the source voltage , but of the pinch-off voltage .

Consequence: the narrow channel effect parameters WETA , DW require different numerical values to achieve the same effect.

Revision II, July 1998

I ntrinsic time constant

Description: Intrinsic time constant is calculated as a function of the effective factor (including vertical field dependent mobility and short-channel effects) instead of maximum mobility according to the KP parameter.

Consequence: the NQS time constant has an additional gate voltage dependence, resulting in more conservative (lower) estimation of the NQS time constant at high , and additional dependence on short-channel effects.

Thermal noise

Description: Thermal noise power spectral density is calculated as a function of the effective factor (including vertical field dependent mobility and short-channel effects) instead of maximum mobility according to the KP parameter.

Consequence: has an additional gate voltage and short-channel effect dependence.

Optional process parameters for calculation of electrical intrinsic parameters

Description: The option is introduced to calculate the electrical parameters COX , GAMMA and/or PHI , VTO , KP and UCRIT as a function of the optional parameters TOX , NSUB , VFB , UO , and VMAX , respectively. NSUB and UO have cm as length units.

Consequence: This accommodates scaling behavior and allows more meaningful statistical circuit simulation due to decorrelation of physical effects. Compatible with former revisions except for default calculation of the parameters mentioned, if the optional parameters are specified.

Optional simplified mobility model

Description: The simple mobility model of former model versions, using the parameter THETA , is reinstated as an option.

Consequence: Simplifies adaptation from earlier model versions to the current version.

Parameter synonyms

Description: The parameters E0 and Q0 can be called by their synonyms EO and QO , respectively.

Consequence: Accommodates certain simulators where only alphabetic characters are allowed.

Operating point information

Description: The analytical expression for the `SPICE'-like threshold voltage in the operating point information is modified to include charge-sharing and reverse short-channel effects. The analytical expression for the saturation voltage in the operating point information is modified such that its value is non-zero in weak inversion.

Consequence: Improved information for the designer.

Corrections from EPFL R11, March, 1999

Equation 45, Equation 53, Equation 54, and Equation 58 have been corrected for multiple series device behavior with the parameter .

Corrections from EPFL R12, July 30, 1999

The following corrections were released by EPFL.

Correction 1- 99/07/30 mb (r12) corrected dGAMMAprime_dVG (narrow channel). An error has been detected in the analytical model derivatives. It is in the derivatives of GAMMAprime variable, affecting the transconductances and transcapacitances.

Correction 2- 99/07/30 mb (r12) preventing PHI from being smaller than 0.2 at init and after temperature update. For certain CMOS technologies, parameter values for the parameter PHI turn out to be as low as 400mV required to account for particular process details. When increasing the temperature from room temperature, PHI decreases due to its built-in temperature dependence, thus making PHI attain very low values, or even be negative, when reaching 100degC. To allow the model to function at these temperatures, a lower limit for PHI is introduced (200mV). Note: the usual range for this parameter is well above this value (600mV to 1V).

Correction 3- 99/06/28 mb (r12) corrected COX and KP initialization (rg).

Correction 4- 99/05/04 mb (r12) completed parameters init for XQC, DL, DW, removed IBC, ibc (cd).