LEVEL 39 BSIM2 Model

The BSIM2 (Berkeley Short-Channel IGFET Model 2) Jeng, M. C. Design and Modeling of Deep Submicrometer MOSFETs, Ph.D. Dissertation, University of California, Berkeley, 1989.,Duster, J.S., Jeng,M.C., Ko, P. K. and Hu, C. User's Guide for the BSIM2 Parameter Extraction Program and the SPICE3 with BSIM Implementation. Industrial Liaison Program, Software Distribution Office, University of California, Berkeley, May 1990. is available in Star-Hspice as LEVEL 39. Avant!'s implementation of this model is based on Berkeley SPICE 3E2.

Provide input to the model by assigning model parameters, as for other Star-Hspice models. Tabular model entry without model parameter names (as used for BSIM1) is not allowed for BSIM2.

LEVEL 39 Model Parameters

The following is a list of the BSIM2 parameters, their units, their Star-Hspice defaults (if any), and their descriptions. There are 47 BSIM2-specific parameters listed in the following table. Considering that three of the parameters (TEMP, DELL, DFW) are not used in Star-Hspice and, considering the width and length sensitivity parameters associated with all the remaining parameters except the first six (TOX, VDD, VGG, VBB, DL, DW), the total parameter count is 120. (Unlike Berkeley SPICE, Star-Hspice has L and W sensitivity for MU0). This count does not include the "generic" MOS parameters listed in a later table or the WL-product sensitivity parameters, which are Avant! enhancements.

BSIM2 Model Parameters

All BSIM2 parameters should be specified according to NMOS convention, even for a PMOS model. Examples: VDD=5, not -5, and VBB=-5, not 5, and ETA0=0.02, not -0.02.

Also see the notes following the last table in this section.

Other SPICE Parameters

The following generic SPICE MOS parameters are used with BSIM2 in Berkeley SPICE 3. All are also Star-Hspice parameters that can be used with Star-Hspice's BSIM2. See Gate Capacitance Modeling and Selecting MOSFET Model LEVELs for more information.

Generic SPICE MOS Parameters

Additionally, source/drain bulk diode sidewall reverse saturation current density, JSW[A/m], is available in Star-Hspice.

Other Star-Hspice Model Parameters Affecting BSIM2

The following Star-Hspice MOS model parameters are needed to use some Star-Hspice enhancements, such as LDD-compatible parasitics, model parameter geometry adjustment relative to a reference device, impact ionization modeling with bulk-source current partitioning, and element temperature adjustment of key model parameters.

This is a partial list. For complete information, see Calculating Effective Length and Width for AC Gate Capacitance, Using Drain and Source Resistance Model Parameters, Using Impact Ionization Model Parameters, and Temperature Parameters. See .MODEL VERSION Changes to BSIM2 Models for information about how the .MODEL statement VERSION parameter changes the BSIM2 model depending on the model version number.

Star-Hspice Model Parameters

LEVEL 39 Model Equations

In the following expressions, model parameters are in all upper case Roman. It is assumed that all model parameters have already been adjusted for geometry, and that those without a trailing "0" have already been adjusted for bias, as appropriate. The exceptions are U1 and N, whose bias dependences are given explicitly below.

Threshold voltage, V th :

where:

Strong inversion (V gs > V th + VGHIGH ):

Linear region ( V ds < V dsat ) drain-source current I DS :

where:

where ( x ) is the usual unit step function,

and:

Saturation ( V ds > V dsat ) drain-source current, I DS:

where the impact ionization term, f is

Weak Inversion (V gs <V th +VGLOW; [VGLOW<0]):

Subthreshold drain-source current, I ds :

where and

Strong inversion-to-weak inversion transition region ( Vth +VGLOW <= V gs <= th +VGHIGH):

replaces V gst = V gs - V th in the linear or saturation drain currents, based on V dsat ( V geff ). At the lower boundary V gs -V th =VGLOW, the saturation equation is assumed to be valid for all Vds (that is,
V dsat (V geff (VGLOW)) 0), to allow a match to the subthreshold equation given above. The coefficients Cj of the cubic spline V geff are internally determined by the conditions that I DS and dI ds /dV gs both be continuous at the boundaries V gs = V th + VGLOW and V gs = V th + VGHIGH.

Effective Length and Width

If DL is nonzero:

Otherwise,

If DW is nonzero:

Otherwise,

Geometry and Bias Adjustment of Model Parameters

Most of the BSIM2 parameters have associated width and length sensitivity parameters. Avant!-proprietary WL-product sensitivity parameters can also be specified. If P is a parameter, then its associated width, length, and WL-product sensitivity parameters are WP, LP, and PP, respectively. The value of the parameter P' adjusted for width, length, and WL-product is:

The WREF and LREF terms do not appear in Berkeley SPICE. They are effectively infinite, which is the Star-Hspice default.

The following BSIM2 parameters have no associated geometry sensitivity parameters:

TOX, TEMP (not used), VDD, VGG, VBB, DL, and DW.

The BSIM2 parameters ending in "0" are assumed to be valid at zero bias, and they have associated bias sensitivities, as given in the BSIM2 parameter table.

If PB, PD, and PG are the geometry-adjusted v bs -, v ds -, and v gs - sensitivity parameters, respectively, associated with the geometry-adjusted zero-bias parameter P0, then in general the bias-dependent parameter P is given by

The exceptions are the velocity saturation factor U1 and the subthreshold swing coefficient N. Expressions for their bias dependences is given later.

Compatibility Notes

SPICE3 Flag

If model parameter SPICE3=0 (default), certain Avant! corrections to the BSIM2 equations are effective. If SPICE3 is set to 1, the equations used are as faithful as possible to the BSIM2 equations for SPICE3E2. Even in this mode, certain numerical problems have been addressed and should not be noticeable under normal circumstances.

Temperature

The model reference temperature TNOM's default is 25°C in Star-Hspice unless .OPTION SPICE is set. In this case TNOM defaults to 27° C. This option also sets some other SPICE compatibility parameters. Star-Hspice's TNOM is set in an .OPTION line in the netlist and can be overridden locally (that is, for a model) with model parameter TREF. ("Reference temperature" means that the model parameters were extracted at, and are therefore valid at, that temperature.)

In UCB SPICE 3, TNOM (default 27° C) is not effective for the BSIM models, and model parameter TEMP is used (and must be specified) as both the model reference temperature and analysis temperature. The analysis at TEMP only applies to thermally activated exponentials in the model equations. There is no adjustment of model parameter values with TEMP. It is assumed that the model parameters were extracted at TEMP, TEMP being both the reference and analysis temperature.

For model levels other than 4 (BSIM1) and 5 (BSIM2) in UCB SPICE3, key model parameters are adjusted for the difference between TEMP (default 27°C) and TNOM, and TEMP is specified in the netlist with .TEMP #, just as in Star-Hspice.

In contrast to UCB SPICE's BSIM models, Star-Hspice LEVEL 39 does provide for temperature analysis. The default analysis temperature is 25°C in Star-Hspice. Set .TEMP # in the Star-Hspice netlist to change the Star-Hspice analysis temperature (TEMP as a model parameter is NOT USED). Star-Hspice provides temperature adjustment of key model parameters, as explained later.

Parasitics

ACM > 0 invokes Star-Hspice MOS source-drain parasitics. ACM=0 (default) is SPICE style. See Star-Hspice Enhancements.

Gate Capacitance Selection

CAPOP=39 selects the BSIM2 charge-conserving capacitance model as shipped with Berkeley SPICE 3E2. This is the default selection if SPICE3=1 is set. Please note that XPART (charge-sharing flag) is currently not a BSIM2 model parameter, despite its specification in the sample BSIM2 input decks shipped with Berkeley SPICE 3E. It appears that its use in SPICE 3E was as a printback debug aid. Saturation charge sharing appears to be fixed at 60/40 (S/D) in the BSIM2 capacitance model. Charge equations are given later under Charge-based Gate Capacitance Model (CAPOP=39). See also Modeling Guidelines and Removal of Mathematical Anomalies.

Other CAPOPs can be chosen. CAPOP=13 (recommended) selects Avant!'s BSIM1-based charge-conserving capacitance model that is in common usage with Star-Hspice MOS LEVELs 13 (BSIM1) and LEVEL 28 (modified BSIM1). This option is the default selection if SPICE3=0. With this capacitance model, charge sharing can be adjusted using model parameters XPART or XQC. See LEVEL 13 BSIM Model for more information.

Unused Parameters

SPICE model parameters DELL (S/D diode length reduction) and WDF (default device width) are not used in Star-Hspice. The function of DELL in SPICE 3E cannot be determined. A default width can be specified in Star-Hspice on the .OPTION line as DEFW (which defaults to 100µ).

.MODEL VERSION Changes to BSIM2 Models

Star-Hspice provides a VERSION parameter to the .MODEL statement, which allows portability of LEVEL 13 BSIM and LEVEL 39 BSIM2 models between Star-Hspice versions. Using the VERSION parameter in a LEVEL 13 .MODEL statement results in the following changes to the BSIM model:

Prevention of Negative Output Conductance

Star-Hspice internally protects against conditions in the LEVEL 13 model that cause convergence problems due to negative output conductance. The constraints imposed are:

These constraints are imposed after length and width adjustment and VBS dependence. This feature is gained at the expense of some accuracy in the saturation region, particularly at high Vgs. Consequently, BSIM2 models might need to be requalified in the following situations:

1. Devices exhibit self-heating during characterization, which causes declining I ds at high V ds . This would not occur if the device characterization measurement sweeps V ds .

2. The extraction technique produces parameters that result in negative conductance.

3. Voltage simulation is attempted outside the characterized range of the device.

Charge-based Gate Capacitance Model (CAPOP=39)

The BSIM2 gate capacitance model conserves charge and has non-reciprocal attributes. The use of charges as state variables guarantees charge conservation. Charge partitioning is fixed at 60/40 (S/D) in saturation and is 50/50 in the linear region. Q s = -(Q g +Q d +Q b ) in all regions.

Accumulation region ( V gs < V bs +VFB):

Subthreshold region ( V bs + VFB< V gs <V th + VGLOW):

Saturation region ( V ds > V dsat ):

where:

Linear region :

Star-Hspice Enhancements

In the following expressions, model parameters are in all upper case Roman. It is assumed that all model parameters without a trailing "0" have already been adjusted for both geometry and bias, as appropriate.

Temperature Effects

TLEV=1 is enforced for LEVEL=39. No other TLEV value is currently allowed.

Threshold voltage for LEVEL 39 TLEV=1 is adjusted according to:

where:

,

,

and the nominal-temperature, zero-bias threshold voltage is given by

and (T) is calculated according to the value of TLEVC as specified.

Mobility is adjusted according to

Velocity saturation is adjusted through UIS according to

In addition, all of the usual Star-Hspice adjustments to capacitances and parasitic diodes and resistors are effective.

Alternate Gate Capacitance Model

Select CAPOP=13 for Avant!'s Star-Hspice's charge-conserving capacitance model, widely used with LEVEL=13 (BSIM1) and LEVEL=28 (improved BSIM1). See LEVEL 13 BSIM Model for more details.

Impact Ionization

You can select Star-Hspice impact ionization modeling (instead of BSIM2's) by leaving AI0=0 and specifying model parameters ALPHA [ALPHA · ( Vds - V dsat ) replaces AI in equation for f in the BSIM2 equations section above], VCR (replaces BI), and IIRAT (multiplies f ).

Star-Hspice impact ionization modeling differs from BSIM2's in two ways:

1. There is a bias term, V ds - V dsat , multiplying the exponential, as well as ALPHA.

2. The impact ionization component of the drain current can be partitioned between the source and the bulk with model parameter IIRAT. IIRAT multiplies f in the saturation I ds equation. Thus, the fraction IIRAT of the impact ionization current goes to the source, and the fraction 1-IIRAT goes to the bulk, adding to IDB . IIRAT defaults to zero (that is, 100% of impact ionization current goes to the bulk).

BSIM2's impact ionization assumes that all of the impact ionization current is part of I ds . In other words, it flows to the source. This assumption can lead to inaccuracies in, for example, cascode circuits. See Calculating the Impact Ionization Equations for more details.

Parasitic Diode for Proper LDD Modeling

Star-Hspice has alternative MOS parasitic diodes to replace SPICE-style MOS parasitic diodes. These alternatives allow for geometric scaling of the parasitics with MOS device dimension, proper modeling of LDD parasitic resistances, allowance for shared sources and drains, and allowance for different diode sidewall capacitances along the gate edge and field edge.

The MOS parasitic diode is selected with model parameter ACM. ACM=0 (default) chooses SPICE style. The alternatives likely to be of most interest to the BSIM2 user are ACM=2 and 3.

ACM=2 allows for diode area calculation based on W, XW, and HDIF (contact to gate spacing). The calculation can be overridden from the element line. It further allows specification of LDIF (spacer dimension) and RS, RD (source and drain sheet resistance under the spacer) for LDD devices, as well as RSH (sheet resistance of heavily doped diffusion). Thus, total parasitic resistance of LDD devices is properly calculated.

ACM=3 uses all the features of ACM=2 and, in addition, its calculations of diode parasitics takes into account the sharing of source/drains, and different junction sidewall capacitances along the gate and field edges. Specify source/drain sharing from the element line with parameter GEO.

See Selecting MOSFET Diode Models for more details.

Skewing of Model Parameters

The BSIM2 model file, like any other Star-Hspice model, can be set up for skewing to reflect process variation. Worst-case or Monte-Carlo analysis can be performed, based on fab statistics. For more information, see Performing Worst Case Analysisand Performing Monte Carlo Analysis.

Star-Hspice Optimizer

The BSIM2 model, like any other Star-Hspice model, can be tied into the Star-Hspice optimizer for fitting to actual device data.

For more information, see Optimization. An example fit appears at the end of this section.

Modeling Guidelines and Removal of Mathematical Anomalies

Because of the somewhat arbitrary geometric and bias adjustments given to BSIM2 parameters, they can take on non-physical or mathematically unallowed values in Berkeley SPICE 3. This can lead to illegal function arguments, program crashes, and unexpected model behavior (for example, negative conductance). The following guidelines and corrections must be satisfied at all geometries of interest and at biases, up to double the supply voltages (that is, to Vds = 2 · VDD, Vgs = 2 · VGG, and Vbs = 2 · VBB).

To avoid drain current discontinuity at Vds = Vdsat, be sure that BI if AI0 0.

To prevent negative g ds , be sure that ETA > 0 and that MU3 > 0 and MU4 < MU3 / (4 * VDD). This should ensure positive g ds at biases up to double the supply voltages. To simplify matters, set all MU4 parameters to zero. You can obtain reasonably good fits to submicron devices without using MU4 Duster, J.S., Jeng, M.C., Ko, P. K., and Hu, C. User's Guide for the BSIM2 Parameter Extraction Program and the SPICE3 with BSIM Implementation. Industrial Liaison Program, Software Distribution Office, University of California, Berkeley, May 1990. .

In Star-Hspice, U1S is prevented from becoming negative. A negative U1S is physically meaningless and causes negative arguments in a square root function in one of the BSIM2 equations. It is also recommended that U1D be kept less than unity (between 0 and 1).

For reasonable V th behavior, make sure that .

For the equations to make sense, the following must hold: N > 0, VGLOW <= 0, and VGHIGH >= 0.

The BSIM2 gate capacitance model of SPICE 3E tends to display negative C gs in subthreshold. This appears to be due to C gg → 0 as V gs → V th by construction of the gate charge equation, so that C gs = C gg - C gd - C gb → - C gd - C gb - C gb . Therefore the use of CAPOP=13 (default) is recommend until an improved BSIM2 gate capacitance model is released by Berkeley.

Modeling Example

The following is the result of fitting data from a submicron channel-length NMOS device to BSIM2. The fitting was performed with Avant!'s ATEM characterization software and the Star-Hspice optimizer.

Figure 21-8: I DS vs.V ds for V gs = 1, 2, 3, 4, 5V; BSIM2 Model vs. Data

Figure 21-9: g ds vs. V ds for V gs = 2, 3, 4, 5V; BSIM2 Model vs. Data, LOG scale

Figure 21-10: I DS vs. V gs for V ds = 0.1V, V bs = 0, -1, -2, -3, -4V, Showing Subthreshold Region; Model vs. Data

Figure 21-11: gm /I DS vs. V gs for V ds = 0.1V, V bs = 0, -2V; BSIM2 Model vs. Data

Typical BSIM2 Model Listing

In this example, geometry sensitivities are set to zero because a fit at only one geometry has been performed. Note the extra HSPICE parameters for LDD, temperature, and geometry.

.MODEL NCH NMOS LEVEL = 39

+ TOX = 2.000000E-02 TEMP = 2.500000E+01

+ VDD = 5.000000E+00 VGG = 5.000000E+00 VBB =-5.000000E+00

+ DL = 0.000000E+00 DW = 0.000000E+00

+ VGHIGH = 1.270000E-01 LVGHIGH= 0.000000E+00
+ WVGHIGH= 0.000000E+00

+ VGLOW =-7.820000E-02 LVGLOW = 0.000000E+00
+ WVGLOW = 0.000000E+00

+ VFB =-5.760000E-01 LVFB = 0.000000E+00
+ WVFB = 0.000000E+00

+ PHI = 6.500000E-01 LPHI = 0.000000E+00
+ WPHI = 0.000000E+00

+ K1 = 9.900000E-01 LK1 = 0.000000E+00 WK1 = 0.000000E+00

+ K2 = 1.290000E-01 LK2 = 0.000000E+00 WK2 = 0.000000E+00

+ ETA0 = 4.840000E-03 LETA0 = 0.000000E+00
+ WETA0 = 0.000000E+00

+ ETAB =-5.560000E-03 LETAB = 0.000000E+00
+ WETAB = 0.000000E+00

+ MU0 = 3.000000E+02

+ MU0B = 0.000000E+00 LMU0B = 0.000000E+00
+ WMU0B = 0.000000E+00

+ MUS0 = 7.050000E+02 LMUS0 = 0.000000E+00
+ WMUS0 = 0.000000E+00

+ MUSB = 0.000000E+00 LMUSB = 0.000000E+00
+ WMUSB = 0.000000E+00

+ MU20 = 1.170000E+00 LMU20 = 0.000000E+00
+ WMU20 = 0.000000E+00

+ MU2B = 0.000000E+00 LMU2B = 0.000000E+00
+ WMU2B = 0.000000E+00

+ MU2G = 0.000000E+00 LMU2G = 0.000000E+00
+ WMU2G = 0.000000E+00

+ MU30 = 3.000000E+01 LMU30 = 0.000000E+00
+ WMU30 = 0.000000E+00

+ MU3B = 0.000000E+00 LMU3B = 0.000000E+00
+ WMU3B = 0.000000E+00

+ MU3G =-2.970000E+00 LMU3G = 0.000000E+00
+ WMU3G = 0.000000E+00

+ MU40 = 0.000000E+00 LMU40 = 0.000000E+00
+ WMU40 = 0.000000E+00

+ MU4B = 0.000000E+00 LMU4B = 0.000000E+00
+ WMU4B = 0.000000E+00

+ MU4G = 0.000000E+00 LMU4G = 0.000000E+00
+ WMU4G = 0.000000E+00

+ UA0 = 0.000000E+00 LUA0 = 0.000000E+00
+ WUA0 = 0.000000E+00

+ UAB = 0.000000E+00 LUAB = 0.000000E+00
+ WUAB = 0.000000E+00

+ UB0 = 7.450000E-03 LUB0 = 0.000000E+00
+ WUB0 = 0.000000E+00

+ UBB = 0.000000E+00 LUBB = 0.000000E+00
+ WUBB = 0.000000E+00

+ U10 = 0.000000E+00 LU10 = 7.900000E-01
+ WU10 = 0.000000E+00

+ U1B = 0.000000E+00 LU1B = 0.000000E+00
+ WU1B = 0.000000E+00

+ U1D = 0.000000E+00 LU1D = 0.000000E+00
+ WU1D = 0.000000E+00

+ N0 = 8.370000E-01 LN0 = 0.000000E+00 WN0 = 0.000000E+00

+ NB = 6.660000E-01 LNB = 0.000000E+00 WNB = 0.000000E+00

+ ND = 0.000000E+00 LND = 0.000000E+00 WND = 0.000000E+00

+ VOF0 = 4.770000E-01 LVOF0 = 0.000000E+00
+ WVOF0 = 0.000000E+00

+ VOFB =-3.400000E-02 LVOFB = 0.000000E+00
+ WVOFB = 0.000000E+00

+ VOFD =-6.900000E-02 LVOFD = 0.000000E+00
+ WVOFD = 0.000000E+00

+ AI0 = 1.840000E+00 LAI0 = 0.000000E+00
+ WAI0 = 0.000000E+00

+ AIB = 0.000000E+00 LAIB = 0.000000E+00
+ WAIB = 0.000000E+00

+ BI0 = 2.000000E+01 LBI0 = 0.000000E+00
+ WBI0 = 0.000000E+00

+ BIB = 0.000000E+00 LBIB = 0.000000E+00
+ WBIB = 0.000000E+00

+ DELL = 0.000000E+00 WDF = 0.000000E+00

Common SPICE Parameters

+ CGDO = 1.000000E-09 CGSO = 1.000000E-09
+ CGBO = 2.500000E-11

+ RSH = 3.640000E+01 JS = 1.380000E-06

+ PB = 8.000000E-01 PBSW = 8.000000E-01

+ CJ = 4.310000E-04 CJSW = 3.960000E-10

+ MJ = 4.560000E-01 MJSW = 3.020000E-01

Avant! Parameters

+ ACM = 3 LMLT = 8.500000E-01
+ WMLT = 8.500000E-01

+ XL =-5.000000E-08 LD = 5.000000E-08

+ XW = 3.000000E-07 WD = 5.000000E-07

+ CJGATE = 2.000000E-10 HDIF = 2.000000E-06
+ LDIF = 2.000000E-07

+ RS = 2.000000E+03 TRS = 2.420000E-03

+ RD = 2.000000E+03 TRD = 2.420000E-03

+ TCV = 1.420000E-03 BEX =-1.720000E+00 FEX =-2.820000E+00

+ LMU0 = 0.000000E+00 WMU0 = 0.000000E+00 JSW=2.400000E-12