Supplemental Materials: Role of Direct Electron-Phonon Coupling across Metal-Semiconductor
Interfaces in Thermal Transport via Molecular Dynamics
Keng-Hua Lin and Alejandro Strachan
School of Materials Engineering and Birck Nanotechnology Center,
Purdue University, West Lafayette, Indiana 47907, USA
I.
Definition of Electron-phonon Coupling Factor
The electron-phonon coupling factor, G, is the energy exchange rate between all the electrons
and the phonons in the system and is defined as:
1
G
elec
atom
V  (Tave  Tave
)
2
 T jatom  T jelec 

Fi






w
*
(
r
)

   0  i
ij 
2
jmetal 
all mi   i 



(S1)
elec
atom
where V is the volume of the metal layer. Tave
and Tave
are the averaged electronic temperature
and the averaged atomic temperature of the metal layer at that timestep. For our system, G is 4.3
x 1016 W(m3∙K)-1 calculated from 0 – 0.3 ps during the equilibration process, where the electrons
and the phonons are far away from equilibrium, for the local coupling case.
II.
Energy Conservation
The temporal evolutions of the total energy and the energy of the atomic subsystem of the
metal-semiconductor system during the initial energy transfer stage (0 – 5 ps) are shown in Fig.
S1. The significant change of the energy of the atomic subsystem is caused by the equilibration
between the atomic and electronic subsystems during the energy transfer process. However, the
total energy of the whole system is still conserved for both the local and non-local coupling cases.
Fig. S1 Total energy and the energy of the atomic subsystem during the initial energy transfer
stage (0-5 ps) for the (a) local and (b) non-local coupling cases.
III.
Timescales for Electron-phonon Equilibration
The timescales of electron-phonon equilibration are not affected by the spatial extent of
electron-phonon coupling (local or non-local coupling) in pure metals. As shown in Fig. S2, the
initial electronic and atomic temperatures of Al are assigned to 600 K and 300 K, respectively.
These two subsystems are then equilibrated via local [Fig. S2(a)] and non-local [Fig. S2(b)]
couplings with electron-phonon coupling rates of 0.00017 ps-1 and 0.0017 ps-1. The spatial extent
of electron-phonon coupling has negligible effects on the timescales of electron-phonon
equilibration.
Fig. S2 (a) Equilibration between the electronic and atomic temperatures for the local coupling
case with electron-phonon coupling rates of 0.00017 ps-1 and 0.0017 ps-1. (b) Equilibration
between the electronic and atomic temperatures for the non-local coupling case with electronphonon coupling rates of 0.00017 ps-1 and 0.0017 ps-1.