## Foundation of PVT Variation, you always wanted to know

Keywords

OCV (On Chip Variation), AOCV (Advanced OCV), POCV (Parametric OCV), SOCV (Statistical OCV), LVF (Liberty Variation Format), CCS (Composite Current Source), NLDM (Non-Linear Delay Model), STA (Static Timing Analysis), VLSI characterization, timing variation model

## What is Variation, after all?

Put simply, variation is a measure of spread from mean value of a statistical group. In circuit characterization context, the statistical group refers to parameters (e.g. Leff, Weff, RSD etc.) of the circuit device like transistors, resistors, capacitors, diodes etc. along with environmental conditions (i.e. voltage and temperature). When it comes to analyzing a device, we’re interested in combination of device parameter limits within which it behaves in the expected manner without failure. This collection of device parameter limits is called a process corner. Every process corner is used with limits of environmental conditions (including voltage and temperature) to create an analysis corner used in sign off analysis.

## Where does Variations come from?

Integrated circuits exhibit 4 main sources of variations

1. Process Variations
1. Global Variations
2. Local Variations

2. Voltage Variations

3. Temperature Variations

4. Aging

1. Hot Carrier Injection (HCI)
2. Bias Temperature Instability (BTI)

Next picture shows this as hierarchy of variation for clarity:

Variation characterization only deals with the effects of local process variation on circuits. It is helpful to discuss process variation along with process corners, since cells are characterized under a specific process corner as part of operating condition.

## Global and Local, 2 types of Variation

Process parameters vary across all parameters dimensions. Analog and AMS simulation tend to care for the entire spectrum for this variation. On the other hand, digital implementation flows are built around making sure that designs are function well in the typical and extreme of these process conditions. These conditions are used to create digital corners. In other words, extreme (i.e. best, worst) corners and mean (i.e. typical) process parameter values of forms the basis of digital process corners. Variation around digital corners is what is important for modeling in digital implementation and analysis flows.

## So, what are Digital Corners?

To test robustness of fabricated integrated circuits (ICs) a semiconductor manufactures (like TSMC, GlobalFoundries etc.) will manufacture a group of wafers with process parameters set to extreme operating values. ICs, thus manufactured, are tested in varying environmental conditions (such as voltage, temperature, clock frequency etc.) to ensure normal operation. This is called corner-lot analysis. Corner lot analysis is used to determine combinations of process corners and environmental conditions essential for sign-off analysis including timing sign-off.

To enable sign-off analysis, VLSI cell libraries are needed at the same combination of process and environmental conditions including voltage and temperature. This condition is represented as ‘operating_condition’ group in liberty file.

## Summary

We reviewed the variation, its classes and sources thereof. We also learnt how global variation parameters are picked to create digital corner for digital implementation flows. This knowledge is essential to separate local process variation among plethora of variation terms and keywords, like systematic variation, random variation etc.

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