Thermal transport properties of metallic nanowires are crucial to the near-junction heat dissipation of transistors. However, the understanding of the size-dependent thermal conductivity of these advanced interconnect metals is still limited. In this work, we select nine candidate metals and investigate the size effect on thermal transport properties by the mode-level first-principles method combining with the Boltzmann transport equation. Their thermal conductivity, the phonon contribution, and the Lorenz ratio in nanowires with characteristic size from 3 to 30 nm are analyzed. While all these metals have lower bulk thermal conductivity than Cu, we find some of these metals have larger thermal conductivity with characteristic size smaller than 10 nm. We identified that their smaller electron mean free path is the key factor. Moreover, the contribution of phonon thermal conductivity is smaller than 25% to total thermal conductivity. The Lorenz ratio is found to be slightly larger than the Sommerfeld value, mainly due to the phonon contribution. This work can provide important guidance for selecting advanced interconnects in the development of next-generation integrated circuits.
REFERENCES
1.
P.
Benkart
,
A.
Kaiser
,
A.
Munding
,
M.
Bschorr
,
H. J.
Pfleiderer
,
E.
Kohn
,
A.
Heittmann
,
H.
Huebner
, and
U.
Ramacher
, “
3D chip stack technology using through-chip interconnects
,” IEEE Des. Test Comput.
22
, 512
(2005
).2.
D.
Gall
,
J. J.
Cha
,
Z.
Chen
,
H.-J.
Han
,
C.
Hinkle
,
J. A.
Robinson
,
R.
Sundararaman
, and
R.
Torsi
, “
Materials for interconnects
,” MRS Bull.
46
, 959
(2021
).3.
I.
Jain
,
A.
Gupta
,
T. B.
Hook
, and
A.
Dixit
, “
Modeling of effective thermal resistance in sub-14-nm stacked nanowire and FinFETs
,” IEEE Trans. Electron Devices
65
, 4238
(2018
).4.
D.
Gall
, “
The search for the most conductive metal for narrow interconnect lines
,” J. Appl. Phys.
127
, 050901
(2020
).5.
S.
Kumar
,
C.
Multunas
,
B.
Defay
,
D.
Gall
, and
R.
Sundararaman
, “
Ultralow electron-surface scattering in nanoscale metals leveraging Fermi-surface anisotropy
,” Phys. Rev. Mater.
6
, 085002
(2022
).6.
J.
He
,
Y.
Ren
,
J.
Pan
,
J.
Liu
, and
M.
Chan
, “
A novel 3D integrated circuit technology based on stacked FinFET-CMOS structure
,” Sens. Transducers
235
, 15
(2019
).7.
T.
Li
,
J.
Hou
,
J.
Yan
,
R.
Liu
,
H.
Yang
, and
Z.
Sun
, “
Chiplet heterogeneous integration technology—Status and challenges
,” Electronics
9
, 670
(2020
).8.
E.
Pop
, “
Energy dissipation and transport in nanoscale devices
,” Nano Res.
3
, 147
(2010
).9.
Z.
Cheng
,
L.
Liu
,
S.
Xu
,
M.
Lu
, and
X.
Wang
, “
Temperature dependence of electrical and thermal conduction in single silver nanowire
,” Sci. Rep.
5
, 10718
(2015
).10.
F.
Völklein
,
H.
Reith
,
T. W.
Cornelius
,
M.
Rauber
, and
R.
Neumann
, “
The experimental investigation of thermal conductivity and the Wiedemann–Franz law for single metallic nanowires
,” Nanotechnology
20
, 325706
(2009
).11.
J.
Wang
,
H.
Yu
,
T.
Walbert
,
M.
Antoni
,
C.
Wang
,
W.
Xi
,
F.
Muench
,
J.
Yang
,
Y.
Chen
, and
W.
Ensinger
, “
Electrical and thermal conductivities of polycrystalline platinum nanowires
,” Nanotechnology
30
, 455706
(2019
).12.
S. D.
Sawtelle
and
M. A.
Reed
, “
Temperature-dependent thermal conductivity and suppressed Lorenz number in ultrathin gold nanowires
,” Phys. Rev. B
99
, 054304
(2019
).13.
J.
Wang
,
Z.
Wu
,
C.
Mao
,
Y.
Zhao
,
J.
Yang
, and
Y.
Chen
, “
Effect of electrical contact resistance on measurement of thermal conductivity and Wiedemann-Franz law for individual metallic nanowires
,” Sci. Rep.
8
, 4862
(2018
).14.
N.
Stojanovic
,
J. M.
Berg
,
D. H. S.
Maithripala
, and
M.
Holtz
, “
Direct measurement of thermal conductivity of aluminum nanowires
,” Appl. Phys. Lett.
95
, 091905
(2009
).15.
Q.-Y.
Li
,
K.
Takahashi
, and
X.
Zhang
, “
Frequency-domain Raman method to measure thermal diffusivity of one-dimensional microfibers and nanowires
,” Int. J. Heat Mass Transfer
134
, 539
(2019
).16.
Y.
Xiong
,
Y.
Zhao
,
Y.
Tao
,
F.
Yao
,
D.
Li
, and
D.
Xu
, “
Effective Lorenz number of the point contact between silver nanowires
,” Nano Lett.
20
, 8576
(2020
).17.
N.
Stojanovic
,
D. H. S.
Maithripala
,
J. M.
Berg
, and
M.
Holtz
, “
Thermal conductivity in metallic nanostructures at high temperature: Electrons, phonons, and the Wiedemann-Franz law
,” Phys. Rev. B
82
, 075418
(2010
).18.
Y.
Hu
,
S.
Li
, and
H.
Bao
, “
First-principles based analysis of thermal transport in metallic nanostructures: Size effect and Wiedemann-Franz law
,” Phys. Rev. B
103
, 104301
(2021
).19.
Y.
Zhao
,
M. L.
Fitzgerald
,
Y.
Tao
,
Z.
Pan
,
G.
Sauti
,
D.
Xu
,
Y.-Q.
Xu
, and
D.
Li
, “
Electrical and thermal transport through silver nanowires and their contacts: Effects of elastic stiffening
,” Nano Lett.
20
, 7389
(2020
).20.
W.-T.
Peng
,
F.-R.
Chen
, and
M.-C.
Lu
, “
Thermal conductivity and electrical resistivity of single copper nanowires
,” Phys. Chem. Chem. Phys.
23
, 20359
(2021
).21.
R.
Franz
and
G.
Wiedemann
, “
Ueber die wärme-leitungsfähigkeit der metalle
,” Ann. Phys.
165
, 497
(1853
).22.
A.
Sommerfeld
, “
Zur elektronentheorie der metalle auf grund der fermischen statistik
,” Z. Phys.
47
, 43
(1928
).23.
H.
Bao
,
J.
Chen
,
X.
Gu
, and
B.
Cao
, “
A review of simulation methods in micro/nanoscale heat conduction
,” ES Energy Environ.
1
, 16
(2018
).24.
Y.
Sheng
,
S.
Wang
,
Y.
Hu
,
J.
Xu
,
Z.
Ji
, and
H.
Bao
, “
Integrating First-principles-based non-Fourier thermal analysis into nanoscale device simulation
,” IEEE Trans. Electron Devices
71
, 1769
(2024
).25.
L.
Chen
,
D.
Ando
,
Y.
Sutou
,
D.
Gall
, and
J.
Koike
, “
NiAl as a potential material for liner- and barrier-free interconnect in ultrasmall technology node
,” Appl. Phys. Lett.
113
, 183503
(2018
).26.
L.
Chen
,
S.
Kumar
,
M.
Yahagi
,
D.
Ando
,
Y.
Sutou
,
D.
Gall
,
R.
Sundararaman
, and
J.
Koike
, “
Interdiffusion reliability and resistivity scaling of intermetallic compounds as advanced interconnect materials
,” J. Appl. Phys.
129
, 035301
(2021
).27.
A.
Jog
and
D.
Gall
, “
Resistivity size effect in epitaxial iridium layers
,” J. Appl. Phys.
130
, 115103
(2021
).28.
A.
Jog
,
T.
Zhou
, and
D.
Gall
, “
Resistivity size effect in epitaxial Rh(001) and Rh(111) layers
,” IEEE Trans. Electron Devices
68
, 257
(2021
).29.
A.
Jog
,
P.
Zheng
,
T.
Zhou
, and
D.
Gall
, “
Anisotropic Resistivity Size Effect in Epitaxial Mo(001) and Mo(011) Layers
,” Nanomaterials
13
, 957
(2023
).30.
G.
Chen
, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons
(
Oxford University Press
, 2005
).31.
S.
Li
,
Z.
Tong
,
X.
Zhang
, and
H.
Bao
, “
Thermal conductivity and Lorenz ratio of metals at intermediate temperatures with mode-level first-principles analysis
,” Phys. Rev. B
102
, 174306
(2020
).32.
A.
Jain
and
A. J. H.
McGaughey
, “
Thermal transport by phonons and electrons in aluminum, silver, and gold from first principles
,” Phys. Rev. B
93
, 081206
(2016
).33.
S.
Poncé
,
E. R.
Margine
,
C.
Verdi
, and
F.
Giustino
, “
EPW: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions
,” Comput. Phys. Commun.
209
, 116
(2016
).34.
B.
Liao
,
B.
Qiu
,
J.
Zhou
,
S.
Huberman
,
K.
Esfarjani
, and
G.
Chen
, “
Significant reduction of lattice thermal conductivity by the electron-phonon interaction in silicon with high carrier concentrations: A first-principles study
,” Phys. Rev. Lett.
114
, 115901
(2015
).35.
J. M.
Ziman
, Electrons and Phonons: The Theory of Transport Phenomena in Solids
(
Oxford University Press
,
Oxford
, 2001
), p. 285
.36.
A. F.
Mayadas
and
M.
Shatzkes
, “
Electrical-resistivity model for polycrystalline films: The case of arbitrary reflection at external surfaces
,” Phys. Rev. B
1
, 1382
(1970
).37.
L.
Dong
,
X.
Wu
,
Y.
Hu
,
X.
Xu
, and
H.
Bao
, “
Suppressed thermal conductivity in polycrystalline gold nanofilm: The effect of grain boundary substrate
,” Chin. Phys. Lett.
38
, 027202
(2021
).38.
C.
Durkan
and
M. E.
Welland
, “
Size effects in the electrical resistivity of polycrystalline nanowires
,” Phys. Rev. B
61
, 14215
(2000
).39.
J. S.
Chawla
,
F.
Gstrein
,
K. P.
O'Brien
,
J. S.
Clarke
, and
D.
Gall
, “
Electron scattering at surfaces and grain boundaries in Cu thin films and wires
,” Phys. Rev. B
84
, 235423
(2011
).40.
Q. G.
Zhang
,
B. Y.
Cao
,
X.
Zhang
,
M.
Fujii
, and
K.
Takahashi
, “
Influence of grain boundary scattering on the electrical and thermal conductivities of polycrystalline gold nanofilms
,” Phys. Rev. B
74
, 134109
(2006
).41.
M. A.
Schneider
,
M.
Wenderoth
,
A. J.
Heinrich
,
M. A.
Rosentreter
, and
R. G.
Ulbrich
, “
Current transport through single grain boundaries: A scanning tunneling potentiometry study
,” Appl. Phys. Lett.
69
, 1327
(1996
).42.
Y.
Tao
,
Y.
Zhao
,
M.
Akter
,
T. T.
Xu
,
Y.
Chen
, and
D.
Li
, “
Non-monotonic boundary resistivity for electron transport in metal nanowires
,” Appl. Phys. Lett.
118
, 153105
(2021
).43.
P.
Giannozzi
,
S.
Baroni
,
N.
Bonini
,
M.
Calandra
,
R.
Car
,
C.
Cavazzoni
,
D.
Ceresoli
,
G. L.
Chiarotti
,
M.
Cococcioni
,
I.
Dabo
,
A.
Dal Corso
,
S.
de Gironcoli
,
S.
Fabris
,
G.
Fratesi
,
R.
Gebauer
,
U.
Gerstmann
,
C.
Gougoussis
,
A.
Kokalj
,
M.
Lazzeri
,
L.
Martin-Samos
,
N.
Marzari
,
F.
Mauri
,
R.
Mazzarello
,
S.
Paolini
,
A.
Pasquarello
,
L.
Paulatto
,
C.
Sbraccia
,
S.
Scandolo
,
G.
Sclauzero
,
A. P.
Seitsonen
,
A.
Smogunov
,
P.
Umari
, and
R. M.
Wentzcovitch
, “
QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials
,” J. Phys.
21
, 395502
(2009
).44.
G.
Fugallo
,
M.
Lazzeri
,
L.
Paulatto
, and
F.
Mauri
, “
Ab initio variational approach for evaluating lattice thermal conductivity
,” Phys. Rev. B
88
, 045430
(2013
).45.
W. S.
Walston
and
R.
Darolia
, “
Effect of alloying on physical properties of NiAl
,” MRS Online Proc. Libr.
288
, 237
(1992
).46.
J.
Fan
and
G. S.
Collins
, “
Point defects in NiAl near the equiatomic composition
,” Hyperfine Interact.
60
, 655
(1990
).47.
A.
Wang
,
S.-H.
Li
, and
H.
Bao
, “
Thermal transport mechanism of electrons and phonons in pristine and defective HfB2
,” Rare Met.
42
, 3651
(2023
).48.
K.
Moors
,
B.
Sorée
,
Z.
Tőkei
, and
W.
Magnus
, “
Resistivity scaling and electron relaxation times in metallic nanowires
,” J. Appl. Phys.
116
, 063714
(2014
).49.
P.
Zheng
and
D.
Gall
, “
The anisotropic size effect of the electrical resistivity of metal thin films: Tungsten
,” J. Appl. Phys.
122
, 135301
(2017
).50.
Y. P.
Timalsina
,
X.
Shen
,
G.
Boruchowitz
,
Z.
Fu
,
G.
Qian
,
M.
Yamaguchi
,
G.-C.
Wang
,
K. M.
Lewis
, and
T.-M.
Lu
, “
Evidence of enhanced electron-phonon coupling in ultrathin epitaxial copper films
,” Appl. Phys. Lett.
103
, 191602
(2013
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
