LEVEL 28 Modified BSIM Model

This section lists the LEVEL 28 parameters and equations for the modified BSIM model.

LEVEL 28 Features

The following are the significant features of the LEVEL 28 model.

• Vertical field dependence of carrier mobility
• Carrier velocity saturation
• Drain-induced barrier lowering
• Depletion charge sharing by source and drain
• Nonuniform doping profile for ion-implanted devices
• Channel length modulation
• Subthreshold conduction
• Geometric dependence of electrical parameters

LEVEL 28 Model Parameters

The LEVEL 28 model parameters follow.

Transistor Process Parameters

Notes:

1. When reading parameter names, be aware of the difference in appearance between the capital letter O, and the number zero 0.

2. All LEVEL 28 parameters should be specified using NMOS conventions, even for PMOS--for example, ETA0 = 0.02, not ETA0 = -0.02.

3. The WL-product sensitivity parameter is available for any parameter with an L and W sensitivity. Replace the leading "L" of the L sensitivity parameter name with a "P".

Basic Model Parameters

Temperature Parameters

Sensitivity Factors of Model Parameters

For transistors, the L (channel length), W (channel width), and WL-product sensitivity factors of a basic electrical parameter are denoted by adding the characters L, W, and P, respectively, at the start of the name, and often dropping any ending "0". For example, VFB0 sensitivity factors are LVFB, WVFB, and PVFB. If A0 is a basic parameter, LA, WA and PA are the corresponding sensitivity factors of this parameter (note that LA, WA and PA cannot be scaled using option SCALM in Star-Hspice). Then the model uses the following general formula to obtain the parameter value.

The left side of the equation represents the effective model parameter value after device size adjustment. All the effective model parameters are in lower case and start with the character z, followed by the parameter name.

LA and WA are specified in units of microns times the units of A0. PA is specified in units of square microns times the units of A0.

If you set LREF or WREF=0, you effectively set the parameter to infinity. This is the default.

Example

LEVEL 28 Model Equations

The LEVEL 28 model equations follow.

Effective Channel Length and Width

The effective channel length and width for LEVEL 28 is determined to be consistent with the LEVEL 3 model. L, W and the multiplier M are from the .MODEL statement in the netlist. SCALE and SCALM are options. When no scaling options or multipliers are used,

Leff = L+XL-2·LD Weff = W+XW-2·WD

Syntax

Lscaled = L·SCALE

Wscaled = W·SCALE

XLscaled = XL·SCALM

LDscaled = LD·SCALM

XWscaled = XW·SCALM

WDscaled = WD·SCALM

Leff = Lscaled·LMLT+XLscaled-2·LDscaled

LREFeff = LREFscaled·LMLT+XLREFscaled-2·LDscaled

Weff = M·(Wscaled·WMLT+XWREFscaled-2·WDscaled)

WREFeff = M·(WREFscaled·WMLT+XWscaled-2·WDscaled)

Threshold Voltage

Effective model parameter values for threshold voltage after device size adjustment are zphi, zvfb, zk1, zk2, zeta, zx2e, zx3e, zgammn, and zetamn. They are calculated from the model parameters PHI0, VFB0, K1, K2, ETA0, X2E, X3E, GAMMN, ETAMN, and their respective length and width sensitivity parameters.

xbs=(zphi-vbs) 1/2

xeta=zeta+zx2e·vbs+zx3e·vds

vth=zvfb + zphi + zk1·xbs - zk2·xbs 2 -xeta·vds

This equation is quadratic in xbs and vds. It is joined to linear equations at d(vth)/d(xbs) = zgammn and at d(vth)/d(vds) = -zetamn, which prevents the quadratics from going in the wrong direction.

Both gammn and etamn default to zero and typically do not affect behavior in the normal operating region.

Effective Mobility

The effective model parameter values for mobility after device size adjustment are zmuz, zx2m, zx3m, zx33m, zu0, and zx2u0. They are calculated from the model parameters MUZ, X2M, X3m, X33M, U00, X2U0, and their respective length and width sensitivity parameters.

Saturation Voltage (vdsat)

The effective model parameter values for saturation voltage after device size adjustment are zu1, zx2u1, and zx3u1. They are calculated from the model parameters U1, X2U1, X3U1 and their respective length and width sensitivity parameters.

This is the value of vds that makes the partial derivative of

with respect to vds equal to zero.

Transition Points

The effective model parameter values for transition points after device size adjustment are zb1 and zb2. They are calculated from the model parameters B1, B2, and their respective length and width sensitivity parameters.

Strong Inversion Current

For vds < v1,

The vds derivative varies approximately linearly between v1 and v2.

For vds>v2, ids is a function of beta and vgst only. If zb1 and zb2 are both positive, their main effect is to increase the current in saturation.

Weak Inversion Current

The effective model parameter values for weak inversion current after device size adjustment are zn0, znb, znd, zwfac and zwfacu. They are calculated from the model parameters N0, ND0, NB0, WFAC, WFACU, and their respective length and width sensitivity parameters.

The weak inversion current is calculated when zn0 is less than 200. It is added to the strong inversion current,

In deep subthreshold,

The modification of this formula near threshold is controlled by zwfac and zwfacu. Just above threshold, the device is in saturation:

so Iweak needs an xweak 2 term to cancel the kink in gm at threshold. Then Iweak goes to zero for xweak>A0, which is at a small voltage above threshold. Iweak has four regions:

(1) xweak < -zwfac+A0

(2) -zwfac+A0 < xweak < 0

where wf is the integral with respect to xweak of

(3) 0 < xweak < A0

(4) A0 < xweak

A0 and the constants in the formulas above are not model parameters, but are uniquely determined by continuity conditions at the boundaries between regions.