Library Characterization

The numbers in a library table were not made up and not measured on your chip. They come from circuit simulation of each cell, done once by the library vendor. This is called characterization. It also explains why a library exists in several versions called corners, and why the same cell has different delays in each one.

Think of the fuel consumption figure of a car. It is measured once, in a test laboratory, under fixed conditions, and the same car uses more or less fuel on a hot day or a steep road. A cell library is the same: the delays are measured once by simulation, and the chip is then checked under several different conditions.

7 min read | Intermediate

What You'll Learn

• Describe how a cell is characterized and where the table numbers come from
• Explain process, voltage and temperature, and what a corner is
• Read the nominal and operating conditions in a library header
• Compare the same cell at the slow, typical and fast corners

How a Cell Is Characterized

For every cell, the vendor starts with a transistor-level description of the circuit and the models of the transistors. A circuit simulator then runs the cell over and over, once for every grid point of every table:

For one arc and one table, that means one simulation for each combination of input slew and output load. A 7 x 7 table needs 49 simulations. Every arc of every cell needs its own tables, and the whole library has to be done again for every set of operating conditions. Characterizing a complete library for one set of conditions can take a long time, which is why vendors deliver it as finished files.

Each simulation is measured the same way. The delay is the time between the 50% point of the input edge and the 50% point of the output edge. The slew is the time the output takes to go from 20% to 80% of the supply voltage. These thresholds are written into the library header, so every tool reads the numbers the same way.

Process, Voltage and Temperature

A chip's speed is not a fixed property. Three things change it:

• Process: small manufacturing differences make some chips faster and some slower than the typical one.
• Voltage: a lower supply voltage makes the transistors switch more slowly.
• Temperature: transistors usually get slower as the chip gets hotter.

A combination of the three is called a PVT condition. A corner is a PVT condition chosen to represent an extreme or typical case. The sky130 library comes in three corners, which also appear in the library name:

Nominal and Operating Conditions

A library header states two things: the conditions the data was characterized at (nom_process, nom_temperature, nom_voltage), and the operating_conditions to use it at. In the sky130 files, both are the same. For the slow corner:

nom_temperature : 100;
nom_voltage     : 1.6;
operating_conditions ("ss_100C_1v60") {
  voltage     : 1.6;
  temperature : 100;
}

If they were different, the tool would adjust (derate) the numbers with correction factors. Such derating is only approximate, so vendors characterize the library at the conditions where it is used. The process value is just the number 1.0 in all three files. The slow or fast character is in the table values themselves.

The Same Cell at Three Corners

The effect is large. These are the delay of the AND gate and2_0 from A to X (rising output, input slew 0.05 ns, load 0.003 pF) and the setup time of the flip-flop dfxtp_1 for falling data:

The AND gate delay is about 1.9 times the typical value at the slow corner and about 0.66 times the typical value at the fast corner. The flip-flop setup time moves by a similar factor. That spread is why a design must be checked at more than one corner. The same demo design has these worst slacks with a 2.0 ns clock:

Setup is tightest at the slow corner, because the data is late. Hold is tightest at the fast corner, because the data is early. This is the reason that setup is signed off at the slow corner and hold at the fast corner, as explained in Setup and Hold: The Two Fundamental Checks. Later chapters show how a real project analyzes all corners together.

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