Manipulating heat fluxes at the nanoscale has become increasingly important in modern microelectronics. However, many methods of heat manipulations rely on complex nanofabrication. Here, we propose simple designs for collimation and focusing of thermal phonons based on parabolic mirrors that require no nanofabrication. We perform Monte Carlo simulations of a ballistic phonon transport in silicon membranes with parabolic boundaries. Our simulations demonstrate that parabolic surfaces can act as parabolic mirrors for phonons, thus collimating or focusing phonon fluxes in semiconductors. Such parabolic mirrors can create a directional flux of thermal phonons emitted from a nanoscale hot spot or focus a collimated phonon flux into a hot spot. These devices open new possibilities in the thermal management of low-temperature systems, such as quantum circuits or cryogenic particle detectors.
References
1.
E.
Pop
, “Energy dissipation and transport in nanoscale devices
,” Nano Res.
3
, 147
–169
(2010
).2.
M.
Maldovan
, “Phonon wave interference and thermal bandgap materials
,” Nat. Mater.
14
, 667
–674
(2015
).3.
M.
Maldovan
, “Sound and heat revolutions in phononics
,” Nature
503
, 209
–217
(2013
).4.
M.
Nomura
, J.
Shiomi
, T.
Shiga
, and R.
Anufriev
, “Thermal phonon engineering by tailored nanostructures
,” Jpn. J. Appl. Phys.
57
, 080101
(2018
).5.
T.
Vasileiadis
, J.
Varghese
, V.
Babacic
, J.
Gomis-Bresco
, D.
Navarro Urrios
, and B.
Graczykowski
, “Progress and perspectives on phononic crystals
,” J. Appl. Phys.
129
, 160901
(2021
).6.
M.
Nomura
, R.
Anufriev
, Z.
Zhang
, J.
Maire
, Y.
Guo
, R.
Yanagisawa
, and S.
Volz
, “Review of thermal transport in phononic crystals
,” Mater. Today Phys.
22
, 100613
(2022
).7.
M.
Sledzinska
, B.
Graczykowski
, J.
Maire
, E.
Chavez-Angel
, C. M.
Sotomayor-Torres
, and F.
Alzina
, “2D phononic crystals: Progress and prospects in hypersound and thermal transport engineering
,” Adv. Funct. Mater.
30
, 1904434
(2020
).8.
Y.
Tian
, T. A.
Puurtinen
, Z.
Geng
, and I. J.
Maasilta
, “Minimizing coherent thermal conductance by controlling the periodicity of two-dimensional phononic crystals
,” Phys. Rev. Appl.
12
, 014008
(2019
).9.
N.
Zen
, T. A.
Puurtinen
, T. J.
Isotalo
, S.
Chaudhuri
, and I. J.
Maasilta
, “Engineering thermal conductance using a two-dimensional phononic crystal
,” Nat. Commun.
5
, 3435
(2014
).10.
J.
Maire
, R.
Anufriev
, R.
Yanagisawa
, A.
Ramiere
, S.
Volz
, and M.
Nomura
, “Heat conduction tuning using the wave nature of phonons
,” Sci. Adv.
3
, e1700027
(2017
).11.
R.
Anufriev
, J.
Maire
, and M.
Nomura
, “Review of coherent phonon and heat transport control in one-dimensional phononic crystals at nanoscale
,” APL Mater.
9
, 070701
(2021
).12.
J.
Ravichandran
, A. K.
Yadav
, R.
Cheaito
, P. B.
Rossen
, A.
Soukiassian
, S. J.
Suresha
, J. C.
Duda
, B. M.
Foley
, C.-H.
Lee
, Y.
Zhu
, A. W.
Lichtenberger
, J. E.
Moore
, D. A.
Muller
, D. G.
Schlom
, P. E.
Hopkins
, A.
Majumdar
, R.
Ramesh
, and M. A.
Zurbuchen
, “Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices
,” Nat. Mater.
13
, 168
–172
(2014
).13.
B.
Saha
, Y. R.
Koh
, J. P.
Feser
, S.
Sadasivam
, T. S.
Fisher
, A.
Shakouri
, and T. D.
Sands
, “Phonon wave effects in the thermal transport of epitaxial TiN/(Al,Sc)N metal/semiconductor superlattices
,” J. Appl. Phys.
121
, 015109
(2017
).14.
R.
Anufriev
and M.
Nomura
, “Ray phononics: Thermal guides, emitters, filters, and shields powered by ballistic phonon transport
,” Mater. Today Phys.
15
, 100272
(2020
).15.
R.
Anufriev
, A.
Ramiere
, J.
Maire
, and M.
Nomura
, “Heat guiding and focusing using ballistic phonon transport in phononic nanostructures
,” Nat. Commun.
8
, 15505
(2017
).16.
Y.
Xiao
, Q.
Chen
, and Q.
Hao
, “Inverse thermal design of nanoporous thin films for thermal cloaking
,” Mater. Today Phys.
21
, 100477
(2021
).17.
J.
Li
, L.
Weng
, and A.
Ramiere
, “Design of thermal lens phononic nanostructure to generate tunable hotspots using quasi-ballistic phonon transport
,” J. Appl. Phys.
131
, 195102
(2022
).18.
S.
Wang
, Y.
Xiao
, Q.
Chen
, and Q.
Hao
, “Engineering thermal transport within Si thin films: The impact of nanoslot alignment and ion implantation
,” iScience
25
, 105386
(2022
).19.
M.
Verdier
, R.
Anufriev
, A.
Ramiere
, K.
Termentzidis
, and D.
Lacroix
, “Thermal conductivity of phononic membranes with aligned and staggered lattices of holes at room and low temperatures
,” Phys. Rev. B
95
, 205438
(2017
).20.
R.
Anufriev
, S.
Gluchko
, S.
Volz
, and M.
Nomura
, “Probing ballistic thermal conduction in segmented silicon nanowires
,” Nanoscale
11
, 13407
–13414
(2019
).21.
A.
George
, R.
Yanagisawa
, R.
Anufriev
, J.
He
, N.
Yoshie
, S.
Volz
, and M.
Nomura
, “Thermoelectric enhancement of silicon membranes by ultrathin amorphous films
,” ACS Appl. Mater. Interfaces
11
, 12027
–12031
(2019
).22.
N. K.
Ravichandran
, H.
Zhang
, and A. J.
Minnich
, “Spectrally resolved specular reflections of thermal phonons from atomically rough surfaces
,” Phys. Rev. X
8
, 041004
(2018
).23.
S. B.
Soffer
, “Statistical model for the size effect in electrical conduction
,” J. Appl. Phys.
38
, 1710
(1967
).24.
A. A.
Maznev
, “Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit
,” Phys. Rev. B
91
, 134306
(2015
).25.
C.
Shao
, Q.
Rong
, M.
Hu
, and H.
Bao
, “Probing phonon-surface interaction by wave-packet simulation: Effect of roughness and morphology
,” J. Appl. Phys.
122
, 155104
(2017
).26.
J. P.
Freedman
, J. H.
Leach
, E. A.
Preble
, Z.
Sitar
, R. F.
Davis
, and J. A.
Malen
, “Universal phonon mean free path spectra in crystalline semiconductors at high temperature
,” Sci. Rep.
3
, 2963
(2013
).27.
J. S.
Kang
, M.
Li
, H.
Wu
, H.
Nguyen
, and Y.
Hu
, “Experimental observation of high thermal conductivity in boron arsenide
,” Science
361
, 575
–578
(2018
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
