researchers for the first time have applied a modern theory of heat transport in experiments with semiconductors used in computers and lasers, with implications for the design of devices that convert waste heat into electricity and the control of overheating in miniaturized and high–speed electronic components.

for more than a century heat transport in solids has been described in terms of the random chaotic motion of "energy carriers" similar to a milk drop dispersing in coffee and gradually transferring heat from hotter to colder regions. however, over the tiny distances of a few nanometers the motion of thermal energy behaves differently and resembles the structure of fractals, which are made up of patterns that repeat themselves at smaller scales infinitely.

"when we look at the problem of heat transport what is surprising is that the theory we use dates back to fourier, which was 200 years ago, and he developed it to explain how the temperature of the earth changes," said ali shakouri, purdue university's mary jo and robert l. kirk director of the birck nanotechnology center and a professor of electrical and computer engineering.  "however, we still use the same theory at the smallest size scale, say tens of nanometers, and the fastest time scale of hundreds of picoseconds."

a team from purdue and the university of california, santa barbara, has applied a theory based on the work of mathematician paul lévy in the 1930s, in experiments with the semiconductor indium gallium aluminum arsenide, which is used in high-speed transistors and lasers.

read more about this development at purdue university here

here is the abstract of the original study and link to the study itself

fractal le?vy heat transport in nanoparticle embedded semiconductor alloys    

amr m. s. mohammed,† yee rui koh,† bjorn vermeersch,† hong lu,† peter g. burke,† arthur c. gossard,† and ali shakouri*,†

†birck nanotechnology center, purdue university, west lafayette, indiana 47907, united states †materials department, university of california, santa barbara

corresponding author: ali shakouri, [email protected] 

materials with embedded nanoparticles are of considerable interest for thermoelectric applications. here, we experimentally characterize the effect of nanoparticles on the recently discovered lev?y phonon transport in semiconductor alloys. the fractal space dimension α ≈ 1.55 of quasiballistic (superdiffusive) heat conduction in (eras) x:ingaalas is virtually independent of the er content 0.001 < x < 0.1 but instead controlled by alloy scattering of the host matrix. the increased nanoparticle concentration does reduce the diffusive recovery length by an order of magnitude. the bulk conductivity drops by 3-fold, in close agreement with a callaway model. our results may provide helpful hints toward engineering superdiffusive heat transport similar to what has been achieved with light in lev?y glasses.