In 1884, mathematician Edward Abbott Abbott wrote a satire about an imaginary world, Flatland, where everything had only two dimensions.
More than a century later, scientists are creating their own flatland -- or as close as we can get -- aboard Space Shuttle Columbia in a very serious attempt to understand electricity in very small structures.
"This is a special kind of flatland," said Dr. John Lipa, principal investigator for the Confined Helium Experiment (CHeX) on the U.S. Microgravity Payload (USMP-4) aboard the Space Shuttle Columbia. "The properties of the creatures are very different from what they are in three-dimensional land."
It's not quite Flatland, but as close as we three-dimensional creatures can get. Abbott's Flatland had only length and width. In Flatland, if you bumped into something, everything else was bumped, too. Nothing could flow "over the top" because up and down did not exist.
It turns out that matter behaves pretty much the same way under the right conditions thanks to a phenomenon called the finite size effect. It's on the horizon for the electronics industry, but they aren't sure if it's a roadblock on the way to smaller, faster chips, or if they can find a bypass around the problem.
Lipa, a professor or physics at Stanford University, explained that electrons travel in blobs or packets. Down to the scale of today's microelectronics, with connectors no smaller than 0.2 microns across, the blobs travel without any problem.
To make electronics faster and to put more components on a single chip, the size of the conductors and other devices eventually must approach the size of the electron packets.
"As you take these conductors and semiconductors and squeeze them down, the properties of the conduction electrons change," Lipa said.
Exactly how they change is uncertain. A circuit 1/100th the size of today's circuits won't necessarily conduct 1/100th as much current. The conductor might even prove to be an insulator.
"At some point the electron packets have to adjust to the fact that there are boundaries near them," he continued.
No one can make electronic circuits that small yet - Intel is investing $250 million in technologies to make circuits 1/10th the size of today's circuits. CHeX is providing a way to tell whether the circuits work at smaller scales.
CHeX is a sort of microscope in which liquid helium and its heat capacity stand in for the electron packets and their conductivity. The heart of CHeX is a stack of 400 silicon wafers, spaced 57 microns apart, a generous distance in microscopic terms. The stack sits in a bath of liquid helium.
At very low temperatures, liquid helium becomes a superfluid: it slides around without friction and conducts heat exceptionally well. Inside the superfluid are packets of helium where the properties of the liquid remain constant (these can vary a little from packet to packet). As the helium is warmed, the superfluid packets expand from about 2 Angstroms across until they form disks about a million Angstroms across.
The superfluid helium now has arrived in Flatland courtesy of the Finite Size Effect. An effect at one point in the helium will be felt throughout the entire blob. Producing a thick "2D" fluid eliminates interatomic forces that would obscure the results if the experiment was conducted at a truly small scale.
With special high-resolution thermometers that measure temperature differences to better than a billionth of a degree, Lipa and his colleagues will record changes in the helium's heat capacity - how much heat has to be added to change the temperature by a set amount.
"The change in heat capacity is analogous to a change in conductance," Lipa said. "The theorists have done a lot of work on heat capacity, so we have good predictions and this gives us a way to test the theory."
Once the theory is tested for heat capacity, Lipa continued, it can be extended to cover a wide range of materials.
"The theory is capable of explaining a number of effects in condensed matter," he said.
So far, CHeX has been returning great data.
"The experiment appears to be running very well," Lipa said. "We're able to get a temperature resolution of less than one ten-billionth of a degree Kelvin. We've already been able to see the finite-size effects. Our aim now is to get improved signal-to-noise ratios on the measurements."
And after USMP-4, Lipa is thinking about going out of Flatland to Lineland to push our understanding even farther.