# A Family Portrait of the BSIM Models

1. Introduction

BSIM1, the first model of the BSIM series was released about ten years ago. Some major improvements have been made since that time, making the BSIM3v3 and BSIM4 models become worldwide standards. This article presents the evolutions brought to BSIM models from BSIM3v3 to BSIM5 and BSIMDG, as well as their applications and differences.

2. Models Technologies : Threshold Voltage or Surface Potentials?

The first MOSFET models computations were based on Threshold voltage. It was the case until BSIM4. This technique divides the whole operating region of a MOSFET into pieces, each one described with its own set of equations. To provide a correct transition between these different equations, some smoothing functions are used.

Even when all regions are unified into one equation, smoothing functions are used. These functions are pure mathematics, and are not related to physics.

 Figure 1. Illustration of smoothing functions between two operating regions

This is a key point especially at moderate inversion since MOSFET devices keep shrinking ever and ever, supply voltages are down-scaled accordingly. Therefore, devices are now operated in the region near threshold voltage. At this precise point, equations rely on smoothing functions, which are not physical.

The release of BSIM5 brought a totally different approach in the BSIM models. It is based on a new core (Surface Potential Plus), which contains equations for surface potential along the channel, instead of threshold voltage. The major advantage is to get only one equation valid over the whole operating range. Transition issues disappear, as well as empirical parameters needed to fine-tune smoothing functions.

When other models (for example MOS11 or HiSIM) compute surface potentials either iteratively or directly (using an approximation), BSIM5 was designed to simply avoid the question. Instead of computing surface potential at source and drain sides (S, D), it computes charges (QS, QD). Another improvement is that solving charge equations does not require precision up to microvolts, which are needed by regular surface potential formulations.

The equations for channel currents are following, for both formulations :

Equations for Ids using surface potentials.

BSIM5 IDS equation

This new SPP core is now used in recent BSIM models : BSIMDG shares the same core as BSIM5. Presumably, it will be used in next models.

3. Geometry and Temperature Scalability

It is of great importance for a compact model to be valid over different device sizes. The first feature trying to fulfill this requirement is binning. It involves several model cards, each one being valid for a given range of sizes. This is completed by a set of model parameters describing the dependence of core parameters with regard to length (L), width (W) and product (LW).

Several model parameters are now binnable. The number of binnable parameters is increasing, while in the meantime the model card is kept as small as possible. The temperature dependence was also improved with a number of parameters dedicated to temperature variations. Extracting a whole model card becomes a tough task as the number of parameters increases, but it assures good accuracy with regard to device size and operating temperatures.

4. Models’ Complexity and its Influence on Simulation Time

The increasing complexity of models through the years should have logically lead to models more and more time-consuming. This is not totally the case, because in the meantime some major improvements were made to modeling techniques.

For example, the introduction of unified equations to describe all operating regions of a device improved convergence. The removal of smoothing functions helped with difficult convergence cases, since they could contain discontinuities and such mathematical issues. Removing purely mathematical formulations helps to concentrate on physics.

When changing from threshold-voltage to surface potentials (i.e. from BSIM3v3- BSIM4 to BSIM5 and BSIMDG), the main concern is to use an iterative algorithm to solve surface potential equations or not. Since the SPP core is not based on surface potentials but on charges, Berkeley simply did not need to question about this. The equation solved in this core brings the same performances as other models using surface potentials, without the issues raised by iterative solvers or approximations. Questions such as “what to do if the iterative process fails ?” or “is the approximation still valid for this bias ?” are not to be asked.

The simulation of a circuit containing 60 BSIM devices gives the results shown in Figure 2.

 Figure 2. Simulation time and iterations number for a circuit containing 60 BSIM devices.

These results show that :

• The iteration number for BSIM4 and BSIM5 is lower than the one for BSIM3v3. Convergence is improved in the recents models, with the help of better equations formulation and continuity.
• Simulation time keeps increasing, due to the fact that models are more and more complex and use highly physical equations, whereas old models are assembled with simple equations.

The conclusion of this measure is that a model is a trade-off between the complexity of physics to be solved, and an improved formulation to make convergence easy. The experience of Berkeley University certainly played a role to make the latests models powerfull with regard to earlier ones.

5. Specific Applications

5.1 Double-Gate Devices

If BSIM3v3, BSIM4 and BSIM5 have been designed to adress the requirements of general-purpose devices, it is not the case of BSIMDG. Because the scaling limit for bulk CMOS devices is reaching its limit, it is important to search for new structures fulfilling the need for small devices. Double-Gate MOSFET is considered a good candidate, but the physics involved are more difficult to describe because of its very small dimensions.

The double-gate technology has the advantage to suppress short-channel effects (at a given equivalent oxide thickness), and to remain scalable. BSIMDG has been created to provide answers to designers willing to explore this area.

BSIMDG has been developed to be used with various devices geometries, making a compromise to provide both flexibility and accuracy. The different device geometries accounted in BSIMDG model shown in Figures 3, 4 and 5.

 Figure 3. Planar double-gate MOSFET.

 Figure 4. FinFET structure.

 Figure 5. Vertical double-gate MOSFET.

5.2 High frequencies
It is not a surprise to see radio-frequencies modeling as part of today’s compact models requirements. BSIM3v3 was the first model of the BSIM-series to provide a Non- Quasi-Static (NQS) mode to account for phenomenons occurring during simulation involving high frequencies. This is important because the need for accurate device description is acute near cut-off frequency, which is critical for designers.

The purpose of this NQS mode is to account for the fact that carriers take a finite time to build up in the channel. Neglecting this time has no or little consequence when frequencies are low, but it becomes important for RF simulations. This special NQS mode is implemented for transient analyses. It extends the capabilities of these models, since it is not a problem anymore to run transient simulation containing high-frequency sources or signals. In the BSIM models, the NQS mode is implemented using a companion-sub circuit, as shown on Figure 6. In this sub circuit, the node Qdef(t) represents the deficit or surplus of channel charge needed to reach equilibrium. The current icheq(t) represents the equilibrium channel charging effect. The value for passive components is determined by relaxation time t for R, and is fixed for C to get the best simulation accuracy.

 Figure 6. Sub circuit used for NQS mode.

In addition to this simulation mode dedicated to RF, the models contain some elements designed for high frequencies, a network for substrate resistance, a model for intrinsic input resistance (IIR) as well as current models for the gate electrode. These features can be combined or used separately thanks to dedicated selectors. These features were improved in BSIM4, making the BSIM family of models suitable for this kind of simulations, which demands high performance.

6. Status in SmartSpice

The versions available in SmartSpice are :

 BSIM3v3 BSIM3v3.2.4 - 3.2.3 - 3.2.2 - 3.2.1 - 3.2.0 - 3.1.0 - 3.0.0 BSIM4 BSIM4.5.0 b - 4.4.0 - 4.3.0 - 4.2.1 - 4.2.0 - 4.1.0 - 4.0.0 BSIM5 BSIM5.0.0 BSIMDG Implementation in progress (v1.0)

All implementations benefit from :

• Full compliance with Berkeley original code. All Silvaco improvements can be disabled (specifying SMART=0 restores Berkeley compatibility). Before an error is fixed or an improvement is made, it is first submitted to Berkeley Labs. This way, always the best improvements are made to the model.
• Alternative geometries and extrinsic elements (such as bulk diodes), using dedicated selectors (ACM, DIOLEV, ...)
• SmartSpice improvements and options (VZERO option, convergence aids, enhanced parameter checking...)

Conclusion

Berkeley models have been improved through the years and now provide a full set of models suitable to different technologies and purposes. Older models can deal with well-proven technologies while models such as BSIM5 or BSIMDG allow to explore new devices capabilities. Even if the research is concentrated on innovating models, the old models such as BSIM3v3 still continue to be maintained. This way, the user can choose either very mature and reliable models, or new models for emerging technologies.