### A Fundamental Ampere

July 20, 2012

Standards are very important to science. When I want a mole of aluminum, I go to my pan balance and weigh out 26.9815 grams. The reason I'm able to do this is because the balance is calibrated against a set of mass standards, which, in turn, were referenced against some better mass standards.

One model of the universe has the world resting on the back of a huge turtle; or, in another form, elephants atop a turtle. The problem of where the turtle stands or swims is solved by having the turtle itself stand on the back of another turtle, ad infinitum. Mathematician, Augustus De Morgan, expressed it this way,
Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.

Our mass calibration is different, since our mass reference ends somewhere. That's the standard kilogram, maintained at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures) outside Paris.

It's turtles, all the way down.

Infinity is an entertaining concept. One of the more interesting thought experiments involving infinity is Hilbert's paradox of the Grand Hotel. If a hotel with an infinite number of rooms has a guest in every room, a new guest can be accommodated by having him take the first room, the first room's occupant taking the second room, the second room's occupant taking the third room, etc.

(Via Wikimedia Commons))

I reviewed the problems associated with maintaining a physical object as a standard in a previous article (Mass Standard, November 1, 2010). Although the fundamental standards of length and time can be derived from measurements of fundamental constants in any laboratory, mass is still derived from an object.

We define time as as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." Once we have a time standard, length can be defined with reference to the speed of light.

The advantage of such a fundamental approach is that references of great accuracy can be synthesized in nearly any laboratory. You can examine a physical process, find its most fundamental expression, and go from there. At its most fundamental level, an ampere is the movement of 6.241 x 1018 electrons past a point in one second; that is, a coulomb per second.

Dispensing electrons at a controlled rate to form a current reference is the approach developed by scientists at Cavendish Laboratory, Cambridge University , and the National Physical Laboratory, Teddington, UK.[1-2] Their electron dispensing devices use semiconductor quantum dots that store and eject single electrons at a given rate. The quantum dots are formed between metal control gates that are driven with an optimal waveform that allows this to happen (see figure).

Micrograph of a quantum dot electron pump device.

(Fig. 1(a) of ref. 1, via the arXiv Preprint Server, modified)[1]

Their device can pump nearly a billion electrons per second to generate a current of 150 picoamperes.[1-2] The research team demonstrated this with an accuracy better than 1.2 parts-per-million (ppm), and they project an accuracy approaching 0.01 ppm. That's ten parts in a billion. This is an improvement over the research team's previously reported 15 ppm at a maximum current of 50 pA.[3]

The electron pump devices were fabricated on GaAs/AlxGa1−xAs wafers using standard integrated circuit processing techniques. The only unfortunate, but necessary, requirement was that the devices work at 300 milliKelvin. The device functions as a two-dimensional electron gas, controlled by two metal gates with an isolated quantum dot between them. The quantum dot holds electrons, and with a proper voltage biasing, it holds just a single electron.

Although the device is built as a current source, it's interesting to think of other applications in which control of individual electrons might be useful. At this point, my mind is too addled by the summer's heat to think of any; but, as my textbooks used to say, the exercise is left to the reader.

### References:

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