 # Accurate Extraction of Interconnect Parasitics Based on 3D Back-End Process Simulation

Introduction

Modern integrated circuit technology has arrived at a point where parasitic effects are simply no longer negligible. IC designers start spending more time on parasitics modeling than on the actual circuit design. Among the most important parasitic effects limiting the chip performance are interconnect related problems like extensive signal delays and crosstalk.

In order to model interconnect layout information is absolutely necessary. Resistances can be extracted fairly accurately by "counting squares", i.e. summing up the total mask area of a conductor and multiplying this with a specific resistance. For capacitance extraction a model of the 3D geometry has to be derived. After the extraction of the interconnect parameters the original netlist has to be back-annotated in order to allow SPICE modeling under the influence of the interconnect parasitics.

The simplest model for an approximation of the 3D structure is shown in Figure 1. It splits the layout in very small pieces that can be approximated with fast empirical formulas [1,2,3]. These simple pieces are then patched together using heuristic algorithms. The advantage of methods like the one described is that they can handle complete IC's in a reasonable amount of time. The main disadvantage becomes obvious when shrinking device dimensions are considered. While the patching error stays constant, the range of validity of the formulas is shrinking. For today's 0.35 mm technologies the error can easily be in the order of 100%. Figure 1. Approximation of true capacitances by empirical formulas for C1-C5. Formulas are parameterized only by geometrical constants like w1, w2, w3 and h1, h2.

Another approach is based on an explicit discretization of the 3D geometries. Such as the simple cubic structures such as those shown in Figure 2a. The capacitance between these structures is then typically modeled using approximate boundary element methods. Obviously, this is not an accurate description of the true 3D geometries.   Figure 2. Different order approximation of 3D interconnect structures. a) is a first order cubic approach, b) more rigorous, but only c) is correct.

A more accurate approximation is shown in Figure 2b. The Figure has been generated by using a solid modeling approach. In  the approximations shown in Figure 2a and 2b were compared and a capacitance error of 30% was reported. The structure used here is assuming a 0.35 mm technology.

However none of the traditional approaches is able to model geometries such as the one shown in Figure 2c with a vertical variation of the metalization. This figure was generated with SILVACO's 3D Back-End Process Simulation approach.

3D Back-End Process Simulation

The conclusion has to be that for accurate interconnect parasitics modeling true 3D process simulation is mandatory. SILVACO's 3D Back-End Process Simulator, HIPEX, generates fully automatically 3D structures from arbitrary layout information. For a given layout it models lithography, deposition and etching process steps with precise physical models. The discretization is done by tetrahedra to enable the generation of arbitrary 3D structures.

As a next step HIPEX provides a 3D field solver for extracting the parasitic information. This field solver is based on finite element techniques. Experiments with boundary element methods for the resulting triangular surface grids have been disappointingly slow. In order to speed up the simulation further, SILVACO is currently parallelizing the field solver using domain decomposition methods.

As output HIPEX provides an equivalent SPICE netlist of the interconnect parasitics. If a netlist of the active devices is provided, it is also back-annotated.

Figures 3a-3f show an example of a HIPEX 3D Back-End Process Simulation. Figure 3a shows the layout of a sample cell. Oxide and Polysilicon are deposited and the photoresist is structured (Figure 3b). Figure 3c shows the structure after etching of the polysilicon. After oxide and aluminum deposit (Figures 3d and 3e) the next layer of photoresist is defined (Figure 3f).

Cell Level Parasitics Extraction

Based on this 3D Back-End Process Simulation SILVACO has developed a new parasitic extraction methodology. This new methodology characterizes the interconnect parasitics at the cell level by solving the complete cell numerically. This way all patching is avoided and the most accurate solution obtained. The cell characterization can be performed by cell library vendors as well as internal cell characterization groups. This characterization will be based on technology files provided by the Wafer Fab. The chip level integration of these accurate cell parasitics is done with major EDA vendors.

An example of the cell level parasitics approach is shown in Figures 4a-4d. The schematics of this XNOR cell is shown in Figure 4a and the layout in Figure 4b. Figure 4c shows the complete 3D process simulation result. The oxide has been removed for better visibility. Color coding has been done by conductor. In Figure 4d some of the equivalent RC models for the ground coupling networks are presented.      Figure 3. 3D Back-End Process simulation example.

The user specifies an error tolerance for the final capacitance. HIPEX then adaptively meshes the structure to ensure consistent results. For a 5% tolerance the structure in Figure 4c uses only 1500 tetrahedra. The complete simulation takes approximately 10 minutes on a SPARC20. Figure 4. Cell level parasitics extraction for an XNOR cell.

Conclusion

As shown above an accurate solution to the Interconnect problem must be technology based. SILVACO has developed a novel 3D Back-End Process Simulation based parasitics extraction methodology. This method supports all common layout and schematics formats through an interface to MaskViews. The first release of HIPEX is planned for Q1 1997.

References:

 T. Sakurai and K. Tamaru, "Simple formulas for two- and three-dimensional capacitances," IEEE Trans. Electron Devices, vol. ED-40, pp. 183-185, 1983.

 U. Choudry and A. Sangiovanni-Vincentelli, "Automatic generation of analytical models for interconnect capacitances," IEEE Trans. Computer-Aided Design, vol. 14, pp. 470-480, 1995.

 N. Arora, K. Raol, R. Schumann and L. Richardson, "Modeling and Extraction of Interconnect Capacitances for Multilayer VLSI Circuits," IEEE Trans. Computer-Aided Design, vol. 15, pp. 58-67, 1996.

 K. Nabors and J. White, "A new multiple algorithm for capacitance extraction of complex 3D geometries," presentation at the IEEE 1989 Custom Integrated Circuits Conference.

 J. Sefler and A. Neureuther, "BTU: Surface Triangularization Algorithms & Solid Extraction for Interconnect Analysis," Hierarchical Technology CAD workshop, Stanford, August 1995.