LEVEL 3 IDS: Empirical Model

This sections provides the LEVEL 3 IDS: Empirical model parameters and equations.

LEVEL 3 Model Parameters

The LEVEL 3 model parameters follow.

Basic Model Parameters

Effective Width and Length Parameters

Threshold Voltage Parameters

Mobility Parameters

LEVEL 3 Model Equations

The LEVEL 3 model equations follow.

IDS Equations

The following describes the way the LEVEL 3 MOSFET model calculates the drain current, I ds .

Cutoff Region,

(See subthreshold current)

On Region, vgs > vth

where:

and:

The narrow width effect is included through the f n parameter:

The term f s expresses the effect of the short channel and is determined as:

Effective Channel Length and Width

The model determines effective channel length and width in the LEVEL 3 model as follows:

Threshold Voltage, vth

The effective threshold voltage, including the device size and terminal voltage effects, is calculated by:

where:

or

The VTO is the extrapolated zero-bias threshold voltage of a large device. If VTO, GAMMA, and PHI are not specified, Star-Hspice computes them (see Common Threshold Voltage Parameters).

Saturation Voltage, vdsat

For the LEVEL 3 model, Star-Hspice determines saturation voltage due to channel pinch-off at the drain side. The model uses the parameter VMAX to include the reduction of the saturation voltage due to carrier velocity saturation effect.

where:

The surface mobility parameter "us" is defined in the next section. If the model parameter VMAX is not specified, then:

Effective Mobility, ueff

The model defines the carrier mobility reduction due to the normal field as the effective surface mobility (us).

vgs>vth

The model determines the degradation of mobility due to the lateral field and the carrier velocity saturation if you specify the VMAX model parameter.

VMAX>0

otherwise,

Channel Length Modulation

For vds>v dsat , the channel length modulation factor is computed. The model determines the channel length reduction differently, depending on the VMAX model parameter value.

VMAX = 0

VMAX>0

where E p is the lateral electric field at the pinch off point. Its value is approximated by:

The current I ds in the saturation region is computed as:

In order to prevent the denominator from going to zero, Star-Hspice limits the value as follows:

If

then

Subthreshold Current, I ds

This region of operation is characterized by the model parameter for fast surface state (NFS). The modified threshold voltage (von) is determined as follows:

NFS>0

where:

The current I ds is given by:

vgs<von

If WIC=3, the model calculates subthreshold current differently. In this case, the I ds current is:

Subthreshold current isub for LEVEL=3 is the same as for LEVEL=13 (see Subthreshold Current ids).

N0eff and NDeff are functions of effective device width and length.

Compatibility Notes

This section describes compatibility issues.

Star-Hspice versus SPICE3

Differences between Star-Hspice and Berkeley SPICE3 can arise in the following situations:

Small XJ

Star-Hspice and SPICE3 differ for small values of XJ, typically less than 0.05 microns. Such small values for XJ are physically unreasonable and should be avoided. XJ is used to calculate the short-channel reduction of the GAMMA effect,

f s is normally less than or equal to 1. For very small values of XJ, f s can be greater than one. Star-Hspice imposes the limit f s <= 1.0, while SPICE3 allows f s >1.0.

ETA

Star-Hspice uses 8.14 as the constant in the ETA equation, which provides the variation in threshold with v ds . Berkeley SPICE3 uses 8.15.

Solution: To convert a SPICE3 model to Star-Hspice, multiply ETA by 815/814.

NSUB Missing

When NSUB is missing in SPICE3, the KAPPA equation becomes inactive. In Star-Hspice, a default NSUB is generated from GAMMA, and the KAPPA equation is active.

Solution: If NSUB is missing in the SPICE3 model, set KAPPA=0 in the Star-Hspice model.

LD Missing

If LD is missing, Star-Hspice uses the default 0.75·XJ. SPICE3 defaults LD to zero.

Solution: If LD is missing in the SPICE3 model, set LD=0 in the HSPICE model.

Constants

Temperature Compensation

The example below verifies temperature dependence for LEVEL 3.

Input file

$ test of temp dependence for LEVEL=3 Tlevc=0 Tlev=1

.option ingold=2 numdgt=6

.temp 25 100

vd d 0 5

vg g 0 2

m1 d g 0 0 nch w=10u L=1u

.op

.print id=lx4(m1) vdsat=lv10(m1)

.model nch nmos LEVEL=3 tlev=1 tlevc=0 acm=3

+ uo=600 tox=172.6572

+ vto=0.8 gamma=0.8 phi=0.64

+ kappa=0 xj=0

+ nsub=1e16 rsh=0

+ tcv=1.5e-3 bex=-1.5

.end

This simple model, with XJ=0 and KAPPA=0, has a saturation current:

Using the model parameters in the input file and the equations from the previous page:

At room temperature:

At T=100:

Star-Hspice results:

T=25, id=6.91200e-04

T=100, id=5.72451e-04

These results are in agreement with the hand calculations.