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PrimeTime VX adds variation-aware analysis capabilities to PrimeTime. A variation-aware analysis increases the accuracy of timing analysis by considering the statistical distribution of characterized parameters. Running a variation-aware timing analysis requires one or more variation-aware libraries, which can be created by Liberty NCX.

To specify the functional dependence of delay or slew on a parameter, the library cells are characterized at the typical parameter value and at two nearby values. An example is shown in Figure 2-5.

Figure 2-5 Delay as a Function of Parameter P

Gate Delay D = f(P) Parameter P typ Distribution of P typ D higher lower Distribution of D

Given the distribution of the parameter P, PrimeTime VX calculates the distribution of delays continuously throughout the range of values, using linear interpolation and extrapolation of the library-defined functional operating points.

The surrounding data points should be close enough to the typical operating point to ensure good accuracy at the middle of the distribution, where the actual parameter value is most likely to occur, but also far enough away to get good accuracy at the more extreme parameter values, where timing violations are most likely to occur.

Chapter 2: Characterization Flows

Acquisition Types 2-26

For on-chip variation, characterization is recommended at one standard deviation (1s) away from the typical value to get the best probable average accuracy along the curve. For die-to-die variations, characterization is recommended at three standard deviations (3s) away from the typical value to get better accuracy at the tail ends of the distribution where violations are more likely to occur.

To generate the libraries that are to be used for variation-aware analysis in PrimeTime VX, you can generate a single CCS-based library that combines the nominal characterization data with the characterization data at each individual parameter value higher or lower than the nominal value. This type of library is called a merged library because it contains variation-aware characterization data at multiple sets of parameter values. Liberty NCX employs base curve technology to minimize the size of the merged library.

To create a single variation-aware CCS library at the same time as characterization (without using va_merge), you need to specify the parameter names, nominal values, and offset values in the template file. When you invoke Liberty NCX, set the variation option to true.

Liberty NCX then performs characterization at the specified parameter data points and merges all the characterization data into a single library.

These are the library template attributes that specify the variation-aware parameters and values:

• va_parameters: A list of variation parameter names.

• nominal_va_values: A list of absolute nominal values of the parameters, in order

corresponding to va_parameters. These are the values that represent the nominal conditions.

• va_variation_values: A list of variation offset values, in order corresponding to

va_parameters. These values are added to and subtracted from the nominal values to

generate the off-nominal conditions. The cells are characterized with each parameter’s nominal value changed by the specified amount while the other parameters are kept at their nominal values.

For example, the library template file could contain the following attribute settings:

va_parameters : len vt ;

nominal_va_values : 100.0 0.24 ; va_variation_values : 5.0 0.02 ;

In this example, there are two parameters, len and vt. Their nominal values are len=100 and vt=0.24. Their corresponding off-nominal values are len=105, len=95, vt=0.26, and vt=0.22. Liberty NCX characterizes the cells with all the parameters set to their nominal values and also at each of the off-nominal values (while the remaining parameter is set to its nominal value), and combines all the characterization data into a single variation-aware CCS library.

Chapter 2: Characterization Flows

Acquisition Types 2-27

Chapter 2: Characterization Flows

Acquisition Types 2-27

You can also control the usage of index values in the off-nominal delay and slew tables with the following library template parameters:

ncx_va_input_net_transition_index : ordinal_list

ncx_va_total_output_net_capacitance_index : ordinal_list

For details, see “Variation-Aware Index Values” on page 3-89.

Variation-aware characterization at multiple sets of parameter values requires more runtime than characterization of a single set of parameter values. Due to longer runtimes, you might consider running the characterization incrementally as described in the section,

“Incremental Characterization.”

An alternative to generating a single merged library is to generate a nominal library and one additional library for each individual parameter value higher or lower than the nominal value, resulting in a total of 2N+1 separate libraries, where N is the number of parameters. This method is not as convenient to use in PrimeTime VX because you must keep track of the individual libraries and specify the parameter values for each respective library in PrimeTime VX.

To use a set of 2N+1 separate libraries, you must create a separate library for each of the desired parameter characterization points. For example, for variation-aware analysis with two parameters, you would characterize the timing behavior at five operating points: the nominal data point, plus two surrounding data points for the first parameter (with the second parameter at its nominal value), plus two more surrounding data points for the second parameter (with the first parameter at its nominal value). For two parameters “len” and “vt,” you would characterize the behavior at the five data points shown in Figure 2-6 on

Chapter 2: Characterization Flows