FX is a trusted model, circuit simulator and variance solver that sits at the heart of CLKDA’s margin analysis applications. FX enables comprehensive, SPICE accurate analysis of the delay and varianceof entire libraries, hundreds of thousands of critical paths, clock tree insertion delay/skew/jitter, memory variance, and custom logic optimization - all in hours instead of weeks.

FX has been validated at all of the major foundries, at 28nm, 20nm, 16nm, 14nm, and 10nm on all of the major models (BSIM4, BSIMSOI, PSP, BSIMCMG, etc.), and on multiple proprietary and all third party libraries. It is currently in production at the most advanced process nodes in use today.

**FX: Circuit Simulator, Variance Solver, Transistor Model**

FX has three key components: the FX transistor model, FX circuit simulator, and FX variance solver. Taken together, they provide a SPICE accurate solution that can be used for multiple time domain applications during cell design, library variance characterization, path, or memory timing analysis.

**The FX Circuit Simulator**

The FX Circuit Simulator is a time domain (transient) transistor level simulator for the FX Model. The FX Circuit Simulator is neither SPICE nor a Fast SPICE. It is a novel simulator with unique algorithms and data structures. Typical accuracy for the FX Simulator is ±2% of SPICE for delay at the cell or path level, and similar correlation for nominal ±3σ (sigma).

The FX Circuit Simulator is only accessible through the FX Platform Applications, such as Variance FX, Path FX, etc. The applications combine the circuit and any other information (side inputs, voltages, input waveforms, etc.) to drive the analysis. The output is also controlled by the application: the variance database and derate tables in the case of Variance FX, and timing reports in the case of Path FX.

The FX Circuit Simulator is fully thread safe. This enables all of the FX applications to be both threaded and distributed for efficient and expandable use of all available computing resources.

**The FX Variance Solver**

The FX Variance Solver is tightly integrated into the FX Circuit Simulator. It enables the FX Circuit Simulator to simultaneously solve for both delay and statistical variance, without the use of any sampling. FX variance results are typically within 2% of mean ±3σ of the leading commercial SPICE results. *The FX Variance Solver provides 3σ statistical accuracy 300,000 to 500,000 times faster than Monte Carlo SPICE.*

**The FX Transistor Model**

FX is a transistor level model that can be used at the cell, macro or block level. The model itself is a four terminal, small signal transistor representation for transient analysis. This model consists of nonlinear current sources and capacitances. Statistical FX models have been qualified at 65nm, 40nm and 28nm BSIM4 models, as well as 28nm and 22nm PSP models, with many tape outs at these process nodes. FX has been qualified for bulk, SOI, metal gate and FinFET processes. Multiple advanced geometry nodes (<20nm) have also been qualified.

The characteristics for each transistor in a netlist are directly extracted from the foundry SPICE model (BSIM4, BSIMSOI, PSP, BSIMCMG, etc.). These characteristics include both the DC behavior for the transistor, capacitances and variance with respect to parameterized SPICE model values. The parameters can be singular values (e.g. length or width), principal component based (aggregated parameters), independent or correlated, systematic (die-die) and on-chip (intra-die) variations.

The figure to the right shows the FX model for a MOSFET transistor. The current is a function of terminal voltages, process parameters and temperature. The device capacitance are functions of terminal voltage. The device current and capacitances are characterized for voltage ranges, which are larger than the maximum allowable value. The negative voltage and higher than MAX supply voltage range is needed to handle transient effects due to coupling noise, charge sharing noise, Miller-capacitance effects and supply variation effects. Please note that characteristics for each device must be generated for each process or major temperature corner, but NOT for voltage. One process/temperature model works for all voltages.

**FX Model Extraction**

Unlike traditional CCS or ECSM models that take days or weeks to characterize, FX models take an hour or less to extract. FX Models are directly extracted from a customer provided SPICE netlist (LPE or LVS), and the Foundry SPICE model. The extraction process is very fast – seconds per cell to minutes per block. A 1000 cell library can be extracted in less than an hour for a given process corner. The inputs can also include a Liberty File for specific applications such as Variance FX, which generates derates for cell libraries.

The output from the extraction is an FX Model Library, in the Liberty format. The FX Model library can be combined with a standard cell library (.lib) to generate an equivalent library file to be used with the FX circuit simulator applications. Each cell will contain FX representations of each of the transistors (uniquely extracted with respect to SPICE parameters) connected together with same R/C network from the LPE netlist. Similarly, if the input is a custom block or memory, the output will be an FX Model Library for the block.