Designing thermal diodes is attracting a considerable amount of interest recently due to the wide range of applications and potentially high impact in the transportation and energy industries. Advances in nanoscale synthesis and characterization are opening new avenues for design using atomic-level tools to take advantage of materials properties in confined volumes. In this paper, we demonstrate using advanced modeling and simulation the rectification properties of tapered-channel thermal diodes relying on asymmetric heat flow brought about by thermal conductivity differences between the liquid and solid phases of suitably selected phase-change materials (PCM). Our prototypical design considers Ga as PCM and anodized alumina as the structural material. First, we use a thresholding scheme to solve a Stefan problem in the device channel to study the interface shape and the hysteresis of the phase transformation when the temperature gradient is switched. We then carry out finite-element simulations to study the effect of several geometric parameters on diode efficiency, such as channel length as aspect ratio. Our analysis establishes physical limits on rectification efficiencies and point to design improvements using several materials to assess the potential of these devices as viable thermal diodes. Finally, we demonstrate the viability of proof-of-concept device fabrication by using a non-conformal atomic layer deposition process in anodic alumina membranes infiltrated with Ga metal.

1.
G.
Wehmeyer
,
T.
Yabuki
,
C.
Monachon
,
J.
Wu
, and
C.
Dames
, “
Thermal diodes, regulators, and switches: Physical mechanisms and potential applications
,”
Appl. Phys. Rev.
4
,
041304
(
2017
).
2.
B.
Li
,
L.
Wang
, and
G.
Casati
, “
Thermal diode: Rectification of heat flux
,”
Phys. Rev. Lett.
93
,
184301
(
2004
).
3.
P.
Ben-Abdallah
and
S.-A.
Biehs
, “
Phase-change radiative thermal diode
,”
Appl. Phys. Lett.
103
,
191907
(
2013
).
4.
E.
Pereira
and
R. R.
Ávila
, “
Increasing thermal rectification: Effects of long-range interactions
,”
Phys. Rev. E.
88
,
032139
(
2013
).
5.
T.
Hess
,
L.
Maier
,
P.
Corhan
,
O.
Schäfer-Welsen
,
J.
Wöllenstein
, and
K.
Bartholomé
, “
Modelling cascaded caloric refrigeration systems that are based on thermal diodes or switches
,”
Int. J. Refrig.
103
,
215
222
(
2019
).
6.
A. L.
Cottrill
and
M. S.
Strano
, “
Analysis of thermal diodes enabled by junctions of phase change materials
,”
Adv. Energy Mater.
5
,
1500921
(
2015
).
7.
C. B.
Sobhan
and
G. P.
Peterson
,
Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications
(
CRC Press
,
2008
).
8.
T.
Luo
and
G.
Chen
, “
Nanoscale heat transfer—from computation to experiment
,”
Phys. Chem. Chem. Phys.
15
,
3389
3412
(
2013
).
9.
L.
Caffarelli
and
L.
Evans
, “
Continuity of the temperature in the two-phase stefan problem
,”
Arch. Ration. Mech. Anal.
81
,
199
220
(
1983
).
10.
I. I.
Danilyuk
, “
On the stefan problem
,”
Russian Math. Surveys
40
,
157
(
1985
).
11.
A.
Visintin
, “Stefan problem with surface tension,” in Mathematical Models for Phase Change Problems (Springer, 1989), pp. 191–213.
12.
A. M.
Meirmanov
,
The Stefan Problem
(
Walter de Gruyter
,
2011
), Vol. 3.
13.
Z.
Liu
,
K.
Muldrew
,
R. G.
Wan
, and
J. A. W.
Elliott
, “
Measurement of freezing point depression of water in glass capillaries and the associated ice front shape
,”
Phys. Rev. E
67
,
061602
(
2003
).
14.
F.
Liu
,
L.
Zargarzadeh
,
H.-J.
Chung
, and
J. A.
Elliott
, “
Thermodynamic investigation of the effect of interface curvature on the solid–liquid equilibrium and eutectic point of binary mixtures
,”
J. Phys. Chem. B
121
,
9452
9462
(
2017
).
15.
B.
Widom
, “
Interfacial tensions of three fluid phases in equilibrium
,”
J. Chem. Phys.
62
,
1332
1336
(
1975
).
16.
C.
Herring
, “
Some theorems on the free energies of crystal surfaces
,”
Phys. Rev.
82
,
87
(
1951
).
17.
M. R.
Landry
, “
Thermoporometry by differential scanning calorimetry: Experimental considerations and applications
,”
Thermochim. Acta
433
,
27
50
(
2005
).
18.
M.
Duggin
, “
The thermal conductivity of liquid gallium
,”
Phys. Lett. A
29
,
470
471
(
1969
).
19.
R.
Powell
,
M. J.
Woodman
, and
R.
Tye
, “
Further measurements relating to the anisotropic thermal conductivity of gallium
,”
Br. J. Appl. Phys.
14
,
432
(
1963
).
20.
D.
Turnbull
, “
Formation of crystal nuclei in liquid metals
,”
J. Appl. Phys.
21
,
1022
1028
(
1950
).
21.
D. P.
Woodruff
and
D. P.
Woodruff
,
The Solid-Liquid Interface
(
CUP Archive
,
1973
).
22.
M.
Losurdo
,
A.
Suvorova
,
S.
Rubanov
,
K.
Hingerl
, and
A. S.
Brown
, “
Thermally stable coexistence of liquid and solid phases in gallium nanoparticles
,”
Nat. Mater.
15
,
995
(
2016
).
23.
Typically, a Gaussian of the form: Hε=(ε)2exp(π|x|2/ε2).
24.
S.
Esedoazlu
and
F.
Otto
, “
Threshold dynamics for networks with arbitrary surface tensions
,”
Communicat. Pure Appl. Math.
68
,
808
864
(
2015
).
25.
G.
Thomas
,
L.
Maxime
, and
M.
Léonard
, “
An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems
,”
ESAIM: COCV
25
,
8
(
2019
).
26.
M.
Jacobs
and
F.
Léger
, “A fast approach to optimal transport: The back-and-forth method,” arXiv:1905.12154 (2019).
27.
J.
Lee
,
Y.
Kim
,
U.
Jung
, and
W.-S.
Chung
, “
Thermal conductivity of anodized aluminum oxide layer: The effect of electrolyte and temperature
,”
Mater. Chem. Phys.
141
,
380
(
2014
).
28.
A.
Ghanekar
,
J.
Ji
, and
Y.
Zheng
, “
High-rectification near-field thermal diode using phase change periodic nanostructure
,”
Appl. Phys. Lett.
109
,
123106
(
2016
).
29.
B.
Li
,
L.
Wang
, and
G.
Casati
, “
Thermal diode: Rectification of heat flux
,”
Phys. Rev. Lett.
93
,
184301
(
2004
).
30.
See http://www.inredox.com for more information about InRedox Inc.
31.
S. M.
George
, “
Atomic layer deposition: An overview
,”
Chem. Rev.
110
,
111
131
(
2010
).
32.
J.
Elam
,
D.
Routkevitch
,
P.
Mardilovich
, and
S.
George
, “
Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition
,”
Chem. Mater.
15
,
3507
3517
(
2003
).
33.
V.
Cremers
,
R. L.
Puurunen
, and
J.
Dendooven
, “
Conformality in atomic layer deposition: Current status overview of analysis and modelling
,”
Appl. Phys. Rev.
6
,
021302
(
2019
).
34.
J.
Chung
,
K.
Kim
,
G.
Hwang
,
O.
Kwon
,
S.
Jung
,
J.
Lee
,
J. W.
Lee
, and
G. T.
Kim
, “
Quantitative temperature measurement of an electrically heated carbon nanotube using the null-point method
,”
Rev. Sci. Instrum.
81
,
114901
(
2010
).
35.
F.
Menges
,
P.
Mensch
,
H.
Schmid
,
H.
Riel
,
A.
Stemmer
, and
B.
Gotsmann
, “
Temperature mapping of operating nanoscale devices by scanning probe thermometry
,”
Nat. Commun.
7
,
1
6
(
2016
).
36.
J. S.
Lundh
,
T.
Zhang
,
Y.
Zhang
,
Z.
Xia
,
M.
Wetherington
,
Y.
Lei
,
E.
Kahn
,
S.
Rajan
,
M.
Terrones
, and
S.
Choi
, “
2d materials for universal thermal imaging of micro-and nanodevices: An application to gallium oxide electronics
,”
ACS Appl. Electron. Mater.
2
,
2945
2953
(
2020
).
37.
G. M.
Carlomagno
and
G.
Cardone
, “
Infrared thermography for convective heat transfer measurements
,”
Exp. Fluids.
49
,
1187
1218
(
2010
).
You do not currently have access to this content.