This section reviews the history, motivation, strengths and weaknesses of the most commonly used MOS models in Star-Hspice:
This section describes the history of and motivation for using MOS models in Star-Hspice.
Avant! modified the standard SPICE models to satisfy the needs of customers. The modifications are in the areas of:
The LEVEL 2 model is an enhanced Grove equation. It is the most common of MOS equations in all simulators.
The basic current equation with the 3/2-power terms was developed by Ihantola and Moll in 1964. Channel length modulation was added by Reddi and Sah in 1965. The vertical field reduction was added by Crawford in 1967. The ECRIT parameter was added by Klassen in 1978.
The LEVEL 3 model was developed by Liu in 1981. It is computationally more efficient, replacing the 3/2-power terms with a first-order Taylor expansion. The drain-induced barrier lowering effect (ETA parameter) was added.
The LEVEL 3 models is impressively physical, modeling two-dimensional effects based on junction depth and depletion depths.
The BSIM1 model was developed by Sheu, Scharfetter, Poon and Hu at Berkeley in 1984, for higher accuracy modeling of short-channel devices. The approach is empirical rather than physical. It uses polynomials frequently. This makes it easier to write a parameter extraction program, but the polynomials often behave badly. For example, a quadratic function of VDS is used for mobility. Parameters specify the values at VDS=0 and 5 and the slope at VDS=5; unfortunately, values that look reasonable can produce a quadratic that is non-monotonic, giving a GDS<0 problem.
The Star-Hspice implementation of BSIM1 as LEVEL 13 removed discontinuities in the current function, added temperature parameters, and added diode and capacitance models consistent with other models. The Berkeley version did not include temperature parameters.
LEVEL 28 is a proprietary Star-Hspice model for submicron devices, designed to fix the following problems in BSIM1:
LEVEL 28 is based on BSIM1, but some of the parameters are quite different. A BSIM1 parameter set cannot be used as a LEVEL 28 model. The LEVEL 28 model is designed for optimization; there is no simple extraction program. It has proven stable for automated model parameter generation.
Optimization of LEVEL 28 models to IDS, GDS, GM data is accomplished routinely by Avant!.
The BSIM2 model was developed by Duster, Jeng, Ko, and Hu, and released in SPICE3 in 1991. It is designed for deep submicron devices. It uses a cubic spline to give smooth weak inversion transition and has many additional parameters for improved accuracy. The GDS transition at VDSAT is markedly smoother than in BSIM1.
This sequence of models shows a trend towards empirical rather than physical models, and an ever- increasing number of parameters. It is unfortunate to lose contact with the physics, but it can be unavoidable, because the physics has become less universal. Short-channel devices are much more sensitive to the detail of the process. I-V curves from different manufacturers show qualitative differences in the shape of the curves. Therefore, the models need to be very flexible, requiring a large number of empirical parameters.
This section describes the following aspects of the model equations:
Some of these aspects depend on general Star-Hspice features that are the same for all levels. Others result in simple objective measures for comparing the levels. These measures are summarized in the Comparison of Star-Hspice Parameters with UCB SPICE 2 and 3.
Generally, the model with the largest number of parameters has the potential to give the best fit. For the purpose of comparing the models, the number of parameters are counted in two ways.
Only the drain current parameters are counted, not the diode or series resistance, nor gate capacitance and impact ionization parameters, since these are almost the same for all levels.
LEVEL 2: VTO, PHI, GAMMA, XJ, DELTA, UO, ECRIT, UCRIT, UTRA, UEXP, NSUB, LAMBDA, NFS (total=13).
LEVEL 3: VTO, PHI, GAMMA, XJ, DELTA, ETA, UO, THETA, VMAX, NSUB, KAPPA, NFS (total=12).
LEVEL 13: VFB0, PHI0, K1, K2, ETA0, X2E, X3E, MUZ, X2M, X3MS, MUS, X2MS, U00, X2U0, U1, X2U1, X3U1, N0, ND0, NB0, plus L- and W- variation parameters (total = 20*3 = 60).
LEVEL 28: similar to LEVEL 13, minus MUS, X2MS, plus X33M, WFAC, WFACU (total = 21*3 = 63).
LEVEL 39: VGHIGH, VGLOW, VFB, K1, K2, ETA0, ETAB, MU0, MU0B, MUS0, MUSB, MU20, MU2B, MU2G, MU30, MU3B, MU40, MU4B, MU4G, UA0, UAB, UB0, UBB, U10, U1B, U1D, N0, NB, ND, plus L- and W- parameters (total = 33*3=99).
The minimal number of parameters is defined as the subset of the above set of parameters that would normally be needed to fit a specific W/L device. For LEVEL 2, 3 DELTA is dropped, which is a W-effect parameter. For LEVEL 13 and 28, the L- and W- terms are dropped, as are X2E, X3E, ND0, which are second-order effects. For LEVEL 39, ETAB, MU40, MU4B, MU4G, ND are dropped.The resulting minimal parameter counts for the five models are LEVEL 2=12, LEVEL 3=11, LEVEL 13=17, LEVEL 28=18, and LEVEL 39=28.
Generally, the larger the "minimal number of parameters", the more time needs to be spent fitting the data. The systematic L and W effect parameters of LEVEL 13, 28, and 39 makes fitting easier because optimization can be done to individual W/L devices. Then the final model parameters, with L and W terms, can be calculated from the individual models. On the other hand, the more physical parameters of LEVEL 2 and 3 are helpful because it is easier to predict the value from a knowledge of the process, before fitting to I-V data. Examples of physical parameters are junction depths and doping concentrations.
Starting with the minimal set of parameters, the percentage that are physical are calculated. For LEVEL 2-- PHI, XJ, UO, ECRIT, NSUB, and NFS are physical, while VTO, GAMMA, UCRIT, UTRA, UEXP, LAMBDA are empirical, which gives 50% physical parameters. For LEVEL 3-- PHI, XJ, UO, VMAX, NSUB, NFS are physical, which gives 55%. For LEVELs 13, 28, and 39--only PHI0 and MUZ are physical, giving 12%, 11%, and 7% physical parameters, respectively.
A discontinuity in the derivatives GM, GDS, GMBS can cause convergence problems. Also, since real devices have continuous derivatives, a discontinuity leads to a large inaccuracy in the derivatives near that region. This can be annoying to an analog designer looking at a plot of gain versus bias, for example. The most common important discontinuities are GDS at vds=vdsat, and GM at vgs=vth. The LEVEL 2 and 3 models have these discontinuities, while the LEVEL 13, 28, and 39 models do not.
However, the LEVEL 13 model (BSIM1) often produces a negative GDS, which is obviously inaccurate, and causes oscillation, which can lead to convergence failure or a "timestep too small" error. It is possible for a LEVEL 13 model to avoid negative GDS, but it depends on complex relationships between the parameters MUZ, X2M, MUS, X2MS, X3MS, U1, X2U1, X3U1. Usually, a negative GDS can be removed by setting X3MS=0, but this lowers the accuracy of the model in the linear region. The LEVEL 39 (BSIM2) model also is capable of producing negative GDS unless you select parameters carefully. The LEVEL 28 model does not give negative GDS.
The BSIM1 model has a continuous GM at vgs=vth, but a plot of GM/IDS versus VGS shows a kink, while data from real devices is monotonic. This kink is annoying to analog designers working with devices in the weak and medium inversion region. LEVEL 28 and 39 have solved this problem, at the cost of additional parameters.
There are three more important measures, as follows:
LEVELs 2 and 3 fail. LEVELs 13, 28, and 39 pass.
LEVELs 13 and 39 fail. LEVELs 2, 3, and 28 pass.
LEVELs 2, 3, and 13 fail. LEVELs 28 and 39 pass.
A model can give a very good fit to IDS data in the normal operating region and still fail to be useful for simulating some circuits.
The first criterion of this type is that the model should have good temperature dependence. Star-Hspice provides temperature-dependence parameters for threshold voltage and mobility for all levels. The LEVEL 13, 28 and 39 models also have an FEX parameter that controls VDSAT variation with temperature.
The next most important criterion is that the model should have subthreshold current to provide accurate analog simulation. Even for digital circuits it aids in convergence. Fortunately, all of these models have subthreshold current.
Impact ionization causes a drain-to-bulk current that has a strong effect on cascode circuits. Star-Hspice provides parameters ALPHA and VCR for this current, which can be used for all levels.
The BSIM2 model has a more complex impact ionization model, with parameters AI0, AIB, BI0, BIB, but in the Berkeley SPICE3 release this current was all assigned to drain-to-source current, IDS. Using the Star-Hspice parameters ALPHA and VCR, the impact ionization current is assigned to IDB, which is essential for cascode simulation. The Star-Hspice parameter IIRAT allows the model to divide the current between IDS and IDB, if needed.
Usually, full model parameter extraction or optimization is only done on a small number of test wafers. Statistical data on process variation is gathered by in-fabrication measurements (for example, TOX) and simple electrical measurements (for example, VT), made on a large number of wafers. This statistical data gives variances that are used to simulate process variation, using a worst-case, Monte-Carlo, or Taguchi methodology.
In order to do this simulation, models must be modified to take into account variations in TOX, thresholds, line widths, and sheet resistance. In Star-Hspice, we have made the different levels similar in their use of these parameters. All of the models discussed here accept the following parameters: TOX, DELVTO, XL, XW, RSH. The DELVTO model parameter shifts the threshold.
For the LEVEL 2 and 3 models, setting DELVTO=0.1 is equivalent to adding 0.1 to VTO; for the LEVEL 13, 28, 39 models, it is equivalent to adding 0.1 to VFB0. The parameters XL and XW represent line width variation. The equation for effective channel length is:
The Berkeley BSIM1 and BSIM2 models use Leff = L - DL. The DL and DW parameters (DL0, DW0 for BSIM1) are supported in Star-Hspice for compatibility, using XL, LD, XW, WD is recommended instead. In Star-Hspice, the geometry parameters (XL, LD, XW, WD) and the parasitic parameters (CJ, MJ, CJSW, MJSW, RSH) are kept simple and level-independent to use process variation information consistently.
LEVEL 2 and 3 were released in Berkeley SPICE with the Meyer model for gate capacitance. This model is non-charge-conserving and sets dQG/dVD = dQD/dVG, which is not valid in a real device, although provides an adequate response for most digital simulations. The BSIM1 and BSIM2 models were released from Berkeley with charge-conserving, non-symmetric capacitance models.
In Star-Hspice, several choices of capacitance models are available; the range of choices and the default varies with the model chosen. The default for LEVELs 2 and 3 is still the Meyer model, but you can also select a charge-conserving Ward-Dutton model.
1. Extract XL, LD, XW, WD, TOX, RSH, CGSO, CGDO, CGBO, CJ, MJ, CJSW, MJSW from resistor and capacitor data, and plots of Beta vs. W, L.
a. Extract VT versus VBS from IDS vs. VGS data.
b. Calculate ETA from log(IDS) vs. VGS plots at VDS=0.1, 5.0.
c. Fit VT parameters to the VT vs. VBS data.
d. Optimize the rest of the parameters, except L and W sensitivity parameters, to IDS, GDS, GM vs. VGS, VDS, VBS data.
3. For each W/L device, calculate L and W sensitivity parameters from the optimized parameters of nearby devices.
4. Fit the models together into one model using the Star-Hspice Lmin, Lmax, Wmin, Wmax feature.
The following plots show fits of LEVELs 2, 3, 13, 28, 39 to data from a submicron device, fabricated by a modern CMOS process. All of the models were optimized to the same data. Similar optimization files were used, optimizing different parameters. The Star-Hspice impact ionization model, with parameters ALPHA, VCR, was used in all models except LEVEL 39, which has its own impact ionization parameters.
The problem of negative GDS in LEVEL 13 was avoided by improved optimization of parameter values, but the GDS discontinuity in LEVEL 3 and the GM discontinuity in LEVEL 2 could not be avoided.
Model versus data plots are presented for drain and gate sweeps. These are followed by close-up plots of the models with small step size to show GM and GDS problems with the individual levels.
Ids vs. Vds at Vgs= 1, 2, 3, 4, 5, Vbs=0
Ids -vs.- Vgs at Vds=0.1, Vgs =0, -1, -2, -3, -4
Ids -vs.- Vgs at Vds=0.1, Vbs =0, -1, -2, -3, -4
This plot shows the behavior of gds at the linear to saturation transition. The LEVEL 3 model has a gds discontinuity.
This plot shows a gm discontinuity in the LEVEL 2 model, related to parameters UCRIT and UEXP.
This plot shows the ratio gm/Ids in the weak inversion transition region. The LEVEL 2, 3, and 13 models have kinks near threshold, while LEVELs 28 and 39 are monotonic.
1. Vladimirescu, Andrei and Liu, Sally. "Simulation of MOS Integrated Circuits Using SPICE2." University of California at Berkeley: Memorandum No. UCB/ERL M80/7, February 1980.
2. Huang, J.S., and Taylor, G.W. "Modeling of an Ion-Implanted Silicon Gate Depletion-Mode IGFET." IEEE Trans. Elec. Dev., Vol. ED-22, pp. 995-1000, Nov. 1975.
3. Frohman-Bentchkowski, D. and Grove, A. S. "On the Effect of Mobility Variation on MOS Device Characteristics," Proc. IEEE, 56, 1968.
4. Fargher, H. E. and Mole, P. J. The Implementation Of A 3 Terminal SOSFET Model In SPICE For Circuit Simulation. GEC VLSI Research Laboratory, MOS1 Division.
5. Marciniak, W. et. al., "Comments on the Huang and Taylor Model of Ion-Implanted Silicon-gate Depletion-Mode IGFET," Solid State Electron., Vol. 28, No.3, pp. 313-315, 1985.
6. Ballay, N. et. al., "Analytic Modeling of Depletion-Mode MOSFET with Short- and Narrow-Channel Effects," IEEE PROC, Vol. 128, Pt.I, No.6 (1981).
7. Tsividis, Y. Operations and Modeling of the MOS Transistor, McGraw-Hill, New York, 1987 p. 145; p. 241f. BFRC's counterpart in BSIM is x2u0.
8. Jeng, M. C. Design and Modeling of Deep Submicrometer MOSFETs , Ph.D. Dissertation, University of California, Berkeley, 1989.
9. 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.
10. 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.
Star-Hspice Manual - Release 2001.2 - June 2001
