Effects of electron-boundary scattering on changes in thermoreflectance
in thin metal films undergoing intraband excitations
Patrick E. Hopkins
a͒
Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque,
New Mexico 87185-0346, USA
͑Received 16 December 2008; accepted 12 March 2009; published online 8 May 2009͒
As characteristic sizes and lengths scales continue to decrease in nanostructures, carrier scattering
processes at the geometric boundaries and interfaces in nanosystems become more prevalent. These
scattering events can lead to additional resistances. This paper investigates electron-boundary
scattering processes by examining changes in thermoreflectance signals in thin films after short
pulsed laser heating. To take electron-boundary scattering into account, an additional scattering term
is introduced into the Drude model for the complex dielectric function. Using an intraband
thickness-dependent reflectance model, transient thermoreflectance data of Au films subject to
intraband excitations are analyzed with the electron-boundary scattering Drude model introduced in
this work. The electron-boundary scattering rate is determined from Au thermoreflectance data,
showing that after short pulsed laser heating, electron-boundary scattering rates can be almost three
orders of magnitude greater than the electron-electron and electron-phonon scattering rates. The
scattering rates determined from the thermoreflectance data agree well with the theoretical
predictions for electron-boundary scattering calculated from an electron-boundary scattering model
for disordered conductors in the event of an electron-phonon nonequilibrium. © 2009 American
Institute of Physics. ͓DOI: 10.1063/1.3117486͔
I. INTRODUCTION
Heat transfer in nanostructures is drastically altered by
carrier scattering events.
1
As characteristic sizes and lengths
scales continue to decrease, the carrier scattering processes at
the geometric boundaries and interfaces in nanosystems be-
come more prevalent. These scattering events can lead to
additional resistances, leading to hot spots and device heat-
ing, and must be understood to effectively engineer nanoma-
terial systems.
In metal and doped semiconductor systems, thermal
transport and resistances are governed by electron scattering
events such as electron-electron and electron-phonon inter-
actions. These electronic processes can be observed via pho-
tonic excitations and reflectance monitoring. A common
technique to measure electron-electron and electron-phonon
interactions and thermalization times is the pump-probe tran-
sient thermoreflectance ͑TTR͒ technique.
2–10
In the TTR
technique, the change in reflectance of the surface of a metal
film, ⌬R, is measured after a short pulse heating event. This
change in reflectance is related to the various electron-
electron and electron-phonon scattering processes, and ⌬R
can be used to determine the rates of these scattering pro-
cesses. In films with thicknesses on the order of the electron
mean free path, electron-boundary scattering at the film/
substrate interface can affect ⌬R,
7
and in this case, ⌬R is
related to electron-boundary scattering rates.
In this work, ⌬R in metal films is studied after intraband
electron excitations. The reflectance models for ⌬R devel-
oped in this work use multiple reflection theory to account
for photon-substrate interactions and how this interaction af-
fects pulse energy absorption in the metal film. The depen-
dency of ⌬R on electron-electron, electron-phonon, and
electron-substrate scattering rates as a function of electron
temperature is studied by modifying the Drude model for the
intraband component of the dielectric function. The modified
Drude model is used to develop an intraband reflectance
model for ⌬R that accounts for electron-boundary scattering.
Electron-boundary scattering rates are deduced by compar-
ing the thermoreflectance model to TTR data on thin Au
films on Si and glass ͑SiO
2
͒ substrates. The electron-
boundary scattering rates determined from ⌬R are compared
to a model for electron-boundary scattering during an
electron-phonon nonequilibrium that is derived in this work.
II. ⌬R/ R AFTER INTRABAND EXCITATIONS IN THIN
FILMS
In thermoreflectance experiments, it is the change in re-
flectivity ⌬R resulting from a change in temperature in the
sample which is measured. The change in reflectance of a
metal can be related to the change in temperature through the
change in the complex dielectric function ⌬͑
,⌬T͒
=⌬
1
͑
,⌬T͒+i⌬
2
͑
,⌬T͒, where ⌬
1
͑
,⌬T͒ and
⌬
2
͑
,⌬T͒ are the changes in the real and imaginary parts
of the complex dielectric function, respectively.
11
For ul-
trashort laser pulses with pulse widths less than the electron-
phonon thermalization time ͑t
pulse
Ͻ
ep
͒, the resulting reflec-
tance, and thus the dielectric function, is a function of
both the change in electron and phonon temperatures
⌬T
e
and ⌬T
p
: ⌬͑
,⌬T
e
,⌬T
p
͒=⌬
1
͑
,⌬T
e
,⌬T
p
͒
+i⌬
2
͑
,⌬T
e
,⌬T
p
͒. For small changes in temperature,
͑⌬T
e
,⌬T
p
Ͻ150 K͒, ⌬ can be expressed as a linear change
in ⌬T
e
and ⌬T
p
,
3,12,13
a͒
Electronic mail: pehopki@sandia.gov.
JOURNAL OF APPLIED PHYSICS 105, 093517 ͑2009͒
0021-8979/2009/105͑9͒/093517/6/$25.00 © 2009 American Institute of Physics105, 093517-1