Curiosities: What is the flattest thing in the world?

The answer depends on many factors, including how the measurement is made and the scale of interest. “A mountain can look very rough, but if you focus on a meadow from an airplane, it may look very flat,” says Max Lagally, a professor of materials science and engineering at the University of Wisconsin–Madison and an expert on roughness.

At the atomic scale, flatness depends on the geometry of the atomic bonds. In graphene (a single layer of carbon atoms whose discovery won the 2010 Nobel Prize in physics), “the bonds between the carbon atoms all lie in one plane, and so the atoms form an atomically flat sheet,” Lagally says.

In contrast, the bonds between silicon cause ripples on the atomic scale. 

But graphene will take the shape of whatever it rests on, and can only be made in tiny pieces, “so even if it is ‘flat’ over say 100 microns [roughly the diameter of a human hair], that is only over short dimensions,” Lagally says.

Crystals can be extremely flat, although they may have steps where one layer ends, exposing the layer below.  The steps in silicon are about 0.15 nanometers, or billionths of a meter, tall, Lagally says. “One can find “really flat” 12-inch silicon wafers that have steps totaling about 500 nanometers.”

That’s roughly 1/200 of a hair.

And so if we are concerned with flatness of a surface that’s visible to the naked eye, silicon wafers are the likely winner, Lagally says.