LEVEL 2 IDS: Grove-Frohman Model

This section describes the parameters and equations for the LEVEL 2 IDS: Grove-Frohman model.

LEVEL 2 Model Parameters

The LEVEL 2 model parameters follow.

Basic Model Parameters

Effective Width and Length Parameters

Threshold Voltage Parameters

Mobility Parameters

The mobility parameters are best determined by curve fitting. In most cases UTRA should be specified between 0.0 and 0.5. Nonzero values for UTRA can result in negative resistance regions at the onset of saturation.

LEVEL 2 Model Equations

The LEVEL 2 model equations follow.

IDS Equations

The following section describes the way the LEVEL 2 MOSFET model calculates the drain current of n-channel and p-channel MOSFETs.

Cutoff Region,

(see subthreshold current)

On Region, vgs>vth

where:

Effective Channel Length and Width

The model calculates effective channel length and width from the drawn length and width as follows:

Threshold Voltage, vth

The model parameter VTO is an extrapolated zero-bias threshold voltage of a large device. The effective threshold voltage, including the device size effects and the terminal voltages, is calculated by:

where:

The narrow width effect is included through vbi and . To include the narrow width effect, specify the model parameter DELTA. The short-channel effect is included through the effective . To include short-channel effects, the model parameter XJ must be greater than zero. Then:

The depletion widths, W s and W d , are determined by:

Star-Hspice calculates parameters such as VTO, GAMMA, and PHI unless you specify them. The model uses these parameters to calculate threshold voltage. (See Common Threshold Voltage Parameters).

Saturation Voltage, vdsat

If you do not specify the model parameter VMAX, the program computes the saturation voltage due to channel pinch off at the drain side. By including the corrections for small-size effects, vsat is:

If you specify ECRIT, the program modifies vsat to include carrier velocity saturation effect.

where:

Mobility Reduction, ueff

The mobility of carriers in the channel decreases as the carriers' speeds approach their scattering limited velocity. In Star-Hspice the mobility degradation for the LEVEL 2 MOS model uses two different equations, depending on the mobility equation selector value of MOB.

If MOB=0, (default):

Since ueff is less than UO, the program uses the above equation if the bracket term is less than one; otherwise the program uses ueff=UO.

If MOB=7, THETA 0

vgs<vth, ueff = UO

If MOB=7, THETA=0

If MOB=7, VMAX>0

Channel Length Modulation

The LEVEL 2 MOS model includes the channel length modulation effect by modifying the I ds current as follows:

The model calculates the value of if you do not specify the model parameter LAMBDA.

LAMBDA>0

VMAX>0, NSUB >0, and LAMBDA

VMAX=0, NSUB>0, and LAMBDA

If MOB=0

If MOB=7

where X d is defined by:

The above equations do not include the effect of the field between gate and drain and gate and pinch-off point, respectively. They tend to overestimate the output conductance in the saturation region.

The modification of I ds by factor (1 - · vds) is equivalent to replacing Leff with:

To prevent the channel length (Le) from becoming negative, Star-Hspice limits the value of Le.

If Le < xwb, then Le is replaced by:

where:

Subthreshold Current, I ds

This region of operation is characterized by the fast surface states model parameter, NFS. For NFS>0 the model determines the modified threshold voltage (von) as follows:

where:

and vt is the thermal voltage.

The I ds current for vgs<von is given by:

where:

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

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