Introduction to Matching

For Analog Integrated Circuit Layout

Matching devices is a key concept in analog circuit design, but at its core it’s not about circuits. It’s about robustness.

This post aims to give a first introduction to the subject for engineers that do not have vast experience on analog layout.

I will start with a high level description of a seemingly unrelated example to illustrate the problem, then I will describe how these concepts relate to circuits and finalize with some best practices.

Hope you enjoy it!

Table of Contents

Introduction

Imagine you have been tasked with designing a dining table.

You are not very experienced, but you do some research and find out that the standard table height is about 76 cm or 30 inches. You reach out to your local carpenter and ask them for four table legs. So far, so good.

Dining table design.

Now the carpenter tells you they can do it, but there’s a catch. Their tools are not that precise. Sometimes the legs are 75.5 cm, sometimes 76.5 cm.

Small variations in leg height are manageable as long as the legs are even.

Well, as long as they variations are small and all the legs are even your table is fully functional. Not such a big deal, right?

Truth is, you probably care a lot more about the table not wobbling than its actual height.

You go to the carpenter and tell them you’re in for business. But please, make sure that the table legs match!

Tables on the sides are different but both acceptable, whereas the one in the middle will wobble and give a very bad experience.

Believe it or not, analog integrated circuits are very similar. Semiconductor manufacturing processes are not perfect, and small variations in the devices need to be accounted for if you want a functional design.

Matching in Analog Design

One way in which analog designers work around this limitation is by basing their design on ratios between components rather than on their absolute values (like the four legs of a table).

Say the mobility of electrons is off by a few percent points from the ideal. Well, your current mirrors will still work almost the same.

A cool thing about electronics is that for most basic components you can find an equivalent set of smaller devices connected in series/parallel to replace them.

Breaking device A apart.

It turns out that a clever placement of said smaller devices can be made far more robust to variations.

Breaking devices A and B apart.

Why is this? One example that is often brought in classrooms is etching.

Etching is a part of of the fabrication process in which a corrosive substance is applied on top of a silicon wafer to chemically “eat away” certain materials. Some parts of the wafer are protected from the substance with “masking” materials, and thus the devices we designed are created.

But there are not guarantees that the etchant will affect every single part of the wafer equally, and thus variations will arise.

For example, in an array of devices, those on the periphery are more exposed to the etchant and may be subject to larger deformation than those in the middle. A good layout designer is aware of this, and will place their devices strategically so critical devices are affected equally.

Clever placement brings robustness to process variations.

Other causes of mismatch in integrated circuits include variations in dopant concentrations, temperature gradients, or mechanical stress.

Best Practices

There are many established best practices for analog layout matching, but none is a silver bullet. A good engineer should be aware of the trade-offs and choose the best option for each design.

Often times you will be able to combine more than one technique.

The following are some of the most common.

Common Centroid

A common approach to matching is to have all your devices share a common centroid.

This is great for guarding against variations with strong first order gradients. For example, if the concentration of a dopant is stronger on the left and weaker on the right. However, it may not be the best suited against variations like etching that mostly affect the edges.

Common centroid before and after fabrication.

Interdigitation

Another useful approach is to place the devices in alternated fashion.

This will give best results against variations affecting the edges, but may not be as good against more linear variations.

Interdigitation before and after fabrication.

Use dummies

No matter what strategy you choose, it is almost always a good idea to add extra “dummy” devices on the edges.

As the name implies, dummies are devices that do not serve any function at circuit level, but are useful for fabrication. Strategical placement at the edges means that the active devices will be more protected against edge effects.

Adding dummy devices before and after fabrication.

Warning: dummies typically add (small) load capacitance to the nodes they are connected to, so they may not be suitable for very high-speed applications.

Conclusion

Matching is a very important concept in analog layout that doesn’t require deep mathematical, but awareness of it has a direct impact on the quality of your results.

If you want to dive deeper into the subject, The Art of Analog Layout by Alan Hastings is a great read.

So this is it. Hope you enjoyed it!

Fabián Torres
Fabián Torres
ECE Master’s student

My interests include integrated circuits, machine learning, and hardware acceleration.

Related