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Phonon Noise

December 17, 2014

I had an early buy-in to personal computing. A few years before the Apple Computer and the IBM PC, whose introduction most people identify with the start of personal computing, there was S-100 bus hardware and CP/M software. My computers at home and at the laboratory were built from component cards plugged into an S-100 backplane, named for the simple reason that there were 100 card edge contacts, fifty to a side.

A Cromemco S-100 bus ZPU card, 1976.  This card used a Zilog Z-80 microprocessor.
A Cromemco S-100 bus ZPU card, 1976. This card used a Zilog Z-80 microprocessor operating at 4 MHz. (Via Wikimedia Commons.)

Those early days were also the days of impact printers. Eventually, I obtained a Diablo daisy wheel printer to print data files and drafts of scientific papers and reports. Although this printer would quickly print entire files at one time, it would also print a single character at a time in a tip-tap rhythm reminiscent of a typewriter. On one slow day, probably while waiting for some experiment to finish, I had the idea to use the computer to simulate a person's typing at a typewriter.

Having the computer send a stream of evenly-spaced characters at ten words per minute wouldn't be a good simulation. People do not type that regularly; instead, they type in fits, sometimes faster, sometimes slower. My computer simulated typing more convincingly through use of 1/F noise (one-over-F noise). 1/F noise, which is often called "pink noise," is one type of noise that electronic component designers have been fighting for decades.

The first discovered electronic noise was Johnson-Nyquist noise, found in experiments by John B. Johnson in 1926, and explained by his Bell Labs colleague, Harry Nyquist, in back-to-back papers in the Physical Review.[1-2] This voltage noise, present across any resistor at any temperature above absolute zero, is given as,

 Nyquist equation for thermal noise

where vn is the root-mean-square (rms) noise voltage, kB is the Boltzmann constant (1.3806 x 10−23 joule/kelvin), R is the resistance (ohms), T is the absolute temperature (kelvin), and Δf is the frequency interval over which the noise voltage is measured (hertz). This noise doesn't depend on where the frequency interval is taken, so it's frequency-independent noise, often called "white noise." It can be called 1/F0 noise, since taking frequency to the zero power yields one. Most radio frequency connections are made at fifty ohms; and, for that source impedance, there's a nanovolt of noise in every hertz bandwidth at room temperature.

One-over-F noise is different from white noise, since it increases at lower frequencies. If you look at a noise source on an oscilloscope, you'll see the overall "fuzz" caused by white noise, but this white noise will ride atop a wandering baseline of 1/F noise. This noise was first discovered in vacuum tubes, but it's found in all electronics, and even other physical systems. In semiconductor devices, it's generally caused by defects at material interfaces where electrons and holes are randomly captured and released. It's not important at higher frequencies, and there's a "corner frequency" defined as the point where the pink and white noise components are equal.

As the above thermal noise equation expresses, if you want lower noise, you need to go to lower temperature. That's why sensitive amplifiers for many experiments are cooled to cryogenic temperatures. Now, an international team of scientists from Chalmers University of Technology (Gothenburg, Sweden), the Universidad de Salamanca (Salamanca, Spain), the Low Noise Factory AB (Mölndal, Sweden), and the California Institute of Technology (Pasadena, California) has found that there's a thermal noise at low temperatures that can't be removed. That's a noise caused by self-heating at cryogenic temperatures.[3-5]

Microwave amplifiers operating at low temperature are important in radio astronomy, and they enabled observations of the cosmic microwave background radiation. The amplifiers are transistorized low-noise amplifiers, and scientists at Chalmers University of Technology and a Chalmers spin-off, the Low Noise Factory, are developing optimized indium phosphide transistors for low noise amplification. As Jan Grahn, a professor of microwave technology at Chalmers, says,
"Cooling the amplifier modules to -260 degrees Celsius enables them to operate with the highest signal-to-noise ratio possible today... These advanced cryogenic amplifiers are of tremendous significance for signal detection in many areas of science, ranging from quantum computers to radio astronomy.”[5]
When these amplifiers were cooled to just a tenth of a degree above absolute zero (-273° Celsius), it was expected that the only noise would be that associated with so-called "hot electrons." Instead, it was found that self-heating of the transistors was a problem, since the mechanism for heat transfer in solids, the phonons, are not that effective at such low temperatures.[3-5]

At about 20 kelvin, the high energy phonons that are most efficient at transporting heat are absent, so only low energy phonons are there to transfer heat. Says Austin Minnich , an assistant professor in Caltech's Division of Engineering and Applied Science and an author of the study, "As a result, the transistor heats up until the temperature has increased enough that high-energy phonons become available again."[4]

A scanning electron microscope image of an indium phosphide high electron mobility transistor
A scanning electron microscope image of an indium phosphide high electron mobility transistor, with an inset showing the region affected by self-heating. (Chalmers University of Technology image.)

Although this type of noise had been known for many years, its importance at very low temperatures wasn't realized. A chance meeting at Caltech between Joel Schleeh, first author of the study and a postdoc at Chalmers, and Minnich launched the research project. Schleeh was seeing more noise than he thought he should in such amplifiers, and conversation with Minnich connected this finding with phonons.[4]

One thing about noise, everyone wants to get rid of it, and this research has suggested some possibilities for doing this. The transistor design could be changed to allow phonons to operate in a larger volume. Says Minnisch, "If you can make the phonon generation more spread out, then in principle you could reduce the temperature rise that occurs."[4] The research was funded by the Swedish Governmental Agency for Innovation Systems (Vinnova), the National Science Foundation, and a Caltech start-up fund.[4-5]


  1. J. B. Johnson, "Thermal Agitation of Electricity in Conductors," Phys. Rev., vol. 32 (July 1, 1928), pp. 97ff..
  2. H. Nyquis, "Thermal Agitation of Electric Charge in Conductors," Phys. Rev., vol. 32 (July 1, 1928), pp. 110ff..
  3. J. Schleeh, J. Mateos, I. Íñiguez-de-la-Torre, N. Wadefalk, P. A. Nilsson, J. Grahn, and A. J. Minnich, "Phonon black-body radiation limit for heat dissipation in electronics," Nature Materials (advance online publication, November 10, 2014), doi:10.1038/nmat4126.
  4. Ker Than, "Heat Transfer Sets the Noise Floor for Ultrasensitive Electronics," California Institute of Technology Press Release, November 10, 2014.
  5. Noise in a microwave amplifier is limited by quantum particles of heat, Chalmers University of Technology Press Release, November 10, 2014.

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