LEVEL 6 and LEVEL 7 IDS: MOSFET Model

These models represent ASPEC, MSINC, and ISPICE MOSFET model equations. The only difference between LEVEL 6 and LEVEL 7 equations is the handling of the parasitic elements and the method of temperature compensation. See Mobility Parameters and Channel Length Modulation for those model parameters.

LEVEL 6 and LEVEL 7 Model Parameters

The LEVEL 6 and LEVEL 7 model parameters are listed in this section.

Basic Model Parameters

Effective Length and Width Parameters

Threshold Voltage Parameters

Alternate Saturation Model Parameters

UPDATE Parameter for LEVEL 6 and LEVEL 7

The general form of the I ds equation for LEVEL 6 is the same as the LEVEL 2 MOS model, but the small size effects, mobility reduction, and channel length modulation are included differently. Also, you can use LEVEL 6 models to model the MOS transistors with ion-implanted channels through the multi-level GAMMA capability.

The LEVEL 6 model represents the ASPEC, MSINC, and ISPICE programs MOSFET model. Use the enhanced model parameter UPDATE to invoke different versions of the LEVEL 6 model, as described next.

UPDATE=0

This is the original LEVEL 6 model in Star-Hspice which is not quite compatible with the ASPEC model. It has some discontinuities in weak inversion, mobility equations (MOB=3), and multi-level GAMMA equations.

UPDATE=1

This enhanced version of the LEVEL 6 model contains improved multi-level GAMMA equations. The saturation voltage, drain-source current, and conductances are continuous.

UPDATE=2

This version of the LEVEL 6 model is compatible with the ASPEC model. The multi-level GAMMA model is not continuous, which is the case in the ASPEC program. See ASPEC Compatibility.

Set UPDATE to 1.0 to implement changes to the device equations. Set UPDATE to 1.0 or 2 to implement the default handling of RS and RD are implemented. These values and changes provide a more accurate ASPEC model.

UPDATE=1 or 2 then,

UPDATE=0 then,

Calculation of RD and RS in the MOSFET changes as follows when LDIF is not specified:

UPDATE=1 or 2 and LDIF=0,

LDIF 0,

The vde in the mobility equations for alternate saturation model changes as follows:

, UPDATE = 1 or 2

, UPDATE = 0

The saturation voltage in the impact ionization equation is as follows:

, UPDATE= 1 or 2

, UPDATE= 0

Mobility equation MOB=3 changes as follows:

UPDATE= 1 or 2 and > VF1,

UPDATE= 0 and > VF1,

LEVEL 6 Model Equations, UPDATE=0,2

IDS Equations

where:

Include the narrow-width effect through , vbi, and values. For the narrow-width effect, specify model parameters NWE and/or NWM. Include the short-channel effect through parameters vbi and .

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 determines effective threshold voltage as follows:

The built-in voltage vbi and is computed differently depending on the specified model parameters.

Single-Gamma, VBO=0

When model parameter VBO is zero, the single-gamma model is used. In this case the model treats the parameter LGAMMA as a junction depth. It then modifies the GAMMA parameter for short-channel effect by the scf factor, which is computed using the Poon and Yau formulation. In this case LGAMMA is multiplied by the SCALM option.

Specify the model parameter XJ to modify the model parameter GAMMA by the short-channel factor (gl).

The gl factor generally replaces the scf factor for the multilevel GAMMA model.

The model also includes the narrow-width effect by modifying GAMMA with the gw factor, which is computed as:

where:

Finally, the effective , including short-channel and narrow width effects, is:

Effective Built-in Voltage, vbi

The model includes the narrow-width effect, which is the increase in threshold voltage due to extra bulk charge at the edge of the channel, by modifying vbi if you specify the model parameter NWE.

The short-channel effect, which is the decrease in threshold voltage due to the induced potential barrier- lowering effect, is included through vbi modification. To include this effect, you must specify the model parameter FDS and/or UFDS and VFDS.

The expressions for vbi, which sum up the above features, are:

, or VFDS=0

vds>VFDS

The above equations describe piecewise linear variations of vbi as a function of vds. If you do not specify VFDS, the first equation for vbi is used.

Multi-Level Gamma, VBO>0

Use Multi-Level Gamma to model MOS transistors with Ion-Implanted channels. The doping concentration under the gate is approximated as step functions. GAMMA and LGAMMA, respectively, represent the corresponding body effects coefficients for the implant layer and the substrate. Threshold Voltage Variation shows the variation of vth as a function of vsb for Multi-Level Gamma.

Figure 21-1: Threshold Voltage Variation

The threshold voltage equations for different regions are as follows:

Channel Depletion Region is in the Implant Layer,

Channel Depletion Region is Expanded into the Bulk, vsb> VBO

In order for the threshold voltage to be continuous at vsb=VBO, vtb must be:

The and are effective values of GAMMA and LGAMMA, respectively. The model computes them as in single-gamma models, except the scf factor is 1.0.

Effective Built-in Voltage, vbi for VBO>0

,

if vsb<=VBO,

if vsb>VBO,

For vds>VFDS,

if vsb<=VBO,

if vsb>VBO,

Saturation Voltage, vdsat (UPDATE=0,2)

The saturation voltage due to channel pinch-off at the drain side is determined by:

The reduction of saturation voltage due to the carrier velocity saturation effect is included as follows:

where vc is determined if model parameter ECRIT >0, or VMAX >0, and KU <= 1. If both ECRIT and VMAX are specified, then only the VMAX equation is used. However, the VMAX equation is not used if MOB=4 or MOB=5, since these mobility equations already contain a velocity saturation term.

or

Because vsb>VBO, is switched from to , the ids, vsat, and conductances are not continuous. This problem is demonstrated in the following example. To correct the discontinuity problem, specify model parameter UPDATE=1. The next section discusses this improvement.

Example

This is an example of a multi-level gamma model, UPDATE=0.

$ TGAM2.SP---MULTI-LEVEL GAMMA MODEL, UPDATE=0

* THIS DATA IS FOR THE COMPARISON OF MULTI-LEVEL GAMMA

* UPDATE=0 OR 2 AND THE IMPROVED MULTI-LEVEL GAMMA UPDATE=1.

*

.OPTIONS ASPEC NOMOD POST VNTOL=.1U RELI=.001 RELV=.0001

*

.MODEL NCH NMOS BULK=99 UPDATE=0

+ FDS=0.9 KU=1.6 MAL=0.5 MOB=1 CLM=1

+ LATD=0.2 PHI=0.3 VT=0.9 GAMMA=0.72 LGAMMA=0.14

+ VB0=1.2 F1=0.08 ESAT=8.6E+4 KL=0.05

+ LAMBDA=3.2U UB=638 F3=0.22

+ KA=0.97 MBL=0.76 NFS=1.0E+12 WIC=0

+ LDEL=0.084 WDEL=0.037 TOX=365 VSH=0.7

*

VD 1 0 5

VB 0 99 0

VG 2 0 1

MA 1 2 0 99 NCH 26.0 1.4

.DC VB 1.0 1.3 .01

.PRINT IDS=PAR(`I(MA)') VTH=PAR(`LV9(MA)') VDSAT=PAR(`LV10(MA)')

.PRINT GM=PAR(`LX7(MA)') GDS=PAR(`LX8(MA)') GMBS=PAR(`LX9(MA)')

.END

Figure 21-2: Variation of IDS, VTH and VDSAT for UPDATE=0

Figure 21-3: Variation of GM, GDS and GMBS for UPDATE=0

Each plot compares IDS, VTH, VDSAT, GM, GDS and GMBS as a function of vsb for UPDATE=0.

Improved Multi-Level Gamma, UPDATE=1

As demonstrated in previous sections, the regular Multi-Level Gamma displays some discontinuities in saturation voltage and drain current. This is because when vsb is less than VBO, is set to and used in ids and vsat calculation. This is not correct; if (vds + vsb) exceeds VBO, the depletion regions at drain side expands into the substrate region, which means must be used instead of in vsat computation. Since vsat = vgs - vth (drain), the threshold voltage at drain is computed using for vsb<VBO. As a result, the existing model overestimates the threshold voltage, ( ), and, in turn, underestimates the saturation voltage and the drain current in the saturation region.

This causes a discontinuous increase in the saturation drain current crossing from the region vsb<VBO to the region vsb>VBO.

There are two major differences between the improved Multi-Level model and the regular Multi-Level model: the saturation voltage equation and the drain current equations. To use the improved model, set the model parameter to UPDATE=1.

Example

This is an example of a multi-level gamma model, UPDATE=2.

$ TGAM2.SP---MULTI-LEVEL GAMMA MODEL, UPDATE=2

* THIS DATA IS FOR THE COMPARISON OF MULTI-LEVEL GAMMA

* UPDATE=0 OR 2 AND THE IMPROVED MULTI-LEVEL GAMMA UPDATE=1.

*

.OPTIONS ASPEC NOMOD POST VNTOL=.1U RELI=.001 RELV=.0001

*

.MODEL NCH NMOS BULK=99 UPDATE=1

+ FDS=0.9 KU=1.6 MAL=0.5 MOB=1 CLM=1

+ LATD=0.2 PHI=0.3 VT=0.9 GAMMA=0.72 LGAMMA=0.14

+ VB0=1.2 F1=0.08 ESAT=8.6E+4 KL=0.05

+ LAMBDA=3.2U UB=638 F3=0.22

+ KA=0.97 MBL=0.76 NFS=1.0E+12 WIC=0

+ LDEL=0.084 WDEL=0.037 TOX=365 VSH=0.7

*

VD 1 0 5

VB 0 99 0

VG 2 0 1

MA 1 2 0 99 NCH 26.0 1.4

.DC VB 1.0 1.3 .01

.PRINT IDS=PAR(`I(MA)') VTH=PAR(`LV9(MA)') VDSAT=PAR(`LV10(MA)')

.PRINT GM=PAR(`LX7(MA)') GDS=PAR(`LX8(MA)') GMBS=PAR(`LX9(MA)')

.END

Figure 21-4: Variation of IDS, VTH and VDSAT for UPDATE=2

Figure 21-5: Variation of GM, GDS and GMBS for UPDATE=2

Each plot compares IDS, VTH, VDSAT, GM, GDS and GMBS as a function of vsb for UPDATE=1.

Saturation Voltage, vsat

To get the right value for vsat, two trial values of vsat corresponding to and are calculated:

vbi1 and vbi2 are built in potentials corresponding to and , respectively.

If (vdsat1 + vsb) <= VBO, then vdsat = vdsat1
If (vdsat2 + vsb) > VBO, then vdsat = vdsat2

LEVEL 6 IDS Equations, UPDATE=1

There are three equations for ids depending upon the region of operation. The model derives these equations by integrating the bulk charge (vgs - vth (v) - v) from the source to the drain.

For vsb<VBO-vde, the model forms an entire gate depletion region in the implant layer.

where vbi1 is the same as vbi for vsb<=VBO.

For vsb >= VBO, the entire gate depletion region expands into the bulk area.

where vbi2 is the same as vbi for vsb>VBO.

For VBO-vde<vsb<VBO, the source side gate depletion region is in the implant layer, but the drain side gate depletion region is expanded into the bulk area.

Alternate DC Model, (ISPICE model)

If model parameter KU>1, this model is invoked. Then, the model computes vfu and vfa scale factors to scale both the vds voltage and the ids current. These scale factors are functions of ECRIT and vgs voltage. The vfa and vfu factors are defined as follows:

where:

The current ids is modified as follows:

NU=1

For NU=0, the factor is set to one.

The current ids is a function of effective drain to source voltage, vde, which is determined as:

and:

This alternate model is generally coupled with the mobility normal field equations (MOB=3) and the channel length modulation drain field equation (CLM=3). The vde value used in the mobility equations is:

, UPDATE=0

, UPDATE=1,2

Subthreshold Current, ids

This region of operation is characterized by the choice of two different equations, selected through the model parameter WIC (Weak Inversion Choice). WIC can be designated as follows:

In addition to WIC, set the parameter NFS. NFS represents the number of fast states per centimeter squared. Reasonable values for NFS range from 1e10 to 1e12.

WIC=0, no weak inversion.

WIC=1, the threshold voltage vth is increased by the term fast.

where:

and vt is the thermal voltage.

The current ids for vgs<von is given by:

if vgs von, then

WIC=2

The subthreshold region is limited between cutoff and strong inversion regions. Although it appears that, if the gate voltage is less than vth-PHI, there can be no weak inversion conduction, there still can be diffusion conduction from the drain-to-bulk rather than drain-to-source.

where:

Cutoff Region, vgs <= vth - PHI

Weak Inversion, vth - PHI < vgs <= von

Strong Inversion, vgs > von

If WIC=3, the subthreshold current is calculated differently. In this case, the ids current is:

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

Effective Mobility, ueff

All mobility equations have the general form:

Use model parameter MOB to select the mobility modulation equation used by Star-Hspice as follows:

These equations are described in the following sections.

MOB=0 Default, No Mobility

factor = 1.0 No mobility reduction

MOB=1 Gm Equation

The MOB=1 equation is useful for transistors with constant source-to-bulk voltage, since the factor does not contain a vsb term. Use of this equation can result in over-estimation of mobility for small gate voltages and large back-bias such as depletion pull-ups.

MOB=2 Frohman-Bentchkowski Equation

Mobility reduction equation (MOB=2 Frohman-Bentchkowski, D. and Grove, A. S. "On the Effect of Mobility Variation on MOS Device Characteristics," Proc. IEEE, 56, 1968. produces good results for high gate voltages and drain fields with constant back-bias. This equation is typically used for p-channel pull-ups and n-channel pull-downs. Specify a value for VMAX to cause the proper calculation scheme to be used for vdsat. MOB=2 corresponds to MSINC UN=2 and is the SPICE default.

where vde is defined the same as for MOB=1 equation.

MOB=3 Normal Field Equation

This equation is the same as MSINC UN=1.

<= VF1,

If UPDATE=0, and (vgs-vth) F2 > VF1,

If UPDATE=1, 2 and (vgs-vth) F2 > VF1,

MOB=4 and MOB=5 Universal Field Mobility Reduction

The MOB=4 equation is the same as the MSINC UN=3 equation. The MOB=5 equation is the same as MOB=4 except that F3 substitutes for ECRIT in the expression for vc.

The MOB=5 equation provides a better fit for CMOS devices in the saturation region. Do not specify a value for VMAX since velocity saturation is handled in the mobility equation.

If MOB=4,

If MOB=5,

MOB=6, 7 Modified MOB=3

This mobility equation is the same as MOB=3, except the equation uses VTO instead of vth. When MOB=6 is used, the current ids also is modified as follows:

Channel Length Modulation

The basic MOSFET current equation for ids describes a parabola, where the peak corresponds to the drain-to-source saturation voltage (vdsat). Long-channel MOSFETs generally demonstrate ideal behavior. For vds voltages greater than vdsat, there is no increase in the ids current. As the channel length decreases, the current in the saturation region continues to increase. This increase in current is modeled as a decrease in the effective channel length. Except for CLM=5 and 6, the channel length modulation equations are only calculated when the device is in the saturation region. Star-Hspice provides several channel length modulation equations; all (except for CLM=5) modify the ids equation as follows:

L is the change in channel length due to MOSFET electric fields.

Use model parameter CLM to designate the channel length modulation equation Star-Hspice uses as follows:

These equations and the associated model parameters are discussed in the following sections.

CLM=0 No Channel Modulation - Default

This is the default channel length equation, representing no channel length modulation; it corresponds to MSINC GDS=0.0

CLM=1 Step Depletion Equation

If not user-specified, LAMBDA is calculated as:

This is a one-sided step depletion region formulation by Grove: L varies with the depletion layer width, which is a function of the difference between the effective saturation voltage (vdsat) and the drain-to-source channel voltage (vds). This equation is typically used for long channels and high dopant concentrations. This corresponds to GDS=1 in MSINC.

CLM=2 Electrostatic Fringing Field

The fringing field equation, or electrostatic channel length reduction, developed by Frohman-Bentchkowski, is most often used for modeling short-channel enhancement transistors. In MSINC, the equivalent equation is GDS=2.

CLM=3 Carrier Velocity Saturation

This equation is an extension of the first depletion layer equation, CLM=1, and includes the effects of carrier velocity saturation and the source-to-bulk voltage (vsb) depletion layer width. It represents the basic ISPICE equation. See Alternate DC Model, (ISPICE model) for definitions of vfa and vfu.

CLM=4, Wang's Equation

Linearly Graded Depletion Layer

Wang's equation allows the inclusion of junction characteristics in the calculation of channel length modulation. The equation assumes that the junction approximated a linearly-graded junction and provides a value of 0.33 for the exponent. This equation is similar to MSINC GDS=3.

CLM=5, Star-Hspice Channel Length Modulation

When CLM=5, the current ids is increased by idssat, given as:

CLM=6, Star-Hspice L Equation

Unlike the other CLMs, this equation calculates the channel length modulation ( L) in all regions of operations and uses it to modify current ids.

and:

ASPEC Compatibility

Make MOSFET models compatible with ASPEC by specifying ASPEC=1 in the .OPTION statement and LEVEL=6 in the associated MOSFET model statement.

If you assign the element parameters without keynames, you must use the parameter sequence given in the general format. Star-Hspice assigns parameters in the order they are listed in the element statement. Errors occur if parameter names are also element keynames.

When Option ASPEC is in effect, a number of program variations occur. The MOSFET model parameter LEVEL is set to 6.

ASPEC sets the following options:

Since the ASPEC option sets the SCALE and SCALM options, it effectively changes the default units of any parameters affected by these options; use parameter values consistent with these scaling factors.

ASPEC sets the following model parameter defaults:

TLEV (TLEVC in turn, selects the ASPEC method of temperature update for the parameters CJ, CJSW, PB, PHP, VTO, and PHI.