SUPPLEMENTAL MATERIAL
S1. Determination of the thermal conductivities and the heat transfer coefficient required
in the modeling for the optimal design of SThM probe
The thermal conductivities of the materials composing the SThM probe (metal films, SiO2,
SiNx), required to solve the governing equation and boundary conditions for Tj (eqs. (9) and (10)
in main text), are determined as follows.
In adopting the thermal conductivities of the gold and chromium films composing the
thermocouple junction at the end of the tip, we consider their thickness dependence. The
thickness of each metal film is less than 50 nm and on the order of the mean free path of the
electron, which is the dominant energy carrier in a metal. To take into account of the influence of
the boundary scattering in the regime where the film thickness is larger than the electron mean
free path, the thermal conductivity is obtained by:
for mfp  L  Lcrit ,
k '/ kbulk  1  2mfp /(3 L) ,
(S1)
where k', kbulk, mfp, L, and Lcrit are the thermal conductivity of the metal at the corresponding
thickness, the bulk thermal conductivity of the metal, the electron mean free path, the film
thickness, and the critical film thickness, respectively. 1 However, since there does not seem to
exist general guidelines for predicting values of the thermal conductivities for L < mfp, the
thermal conductivity in this regime is estimated using kinetic theory as: 1
for L  mfp ,
1
1
k  Ccmfp  CcL ,
3
3
(S2)
where C (≡Ce) is the electron specific heat per unit volume and ċ is the mean electron velocity 4.
According to eq. (S2), as the film thickness is reduced down to 10 nm, the thermal conductivity
of the gold film decreases to about 25% of its bulk value and that of the chromium film reduces
to about 60% of its bulk value.
1
For the SiO2 layer, we use a bulk thermal conductivity of 1.1 W/m K. The bulk value can
be used since the parts of the SThM probe composed of SiO2, where the thickness of the
cantilever and hollow tip are 1.5 μm and the width of the cantilever is 17 μm, are sufficiently
larger than the mean free path of phonons in bulk SiO2 (~0.6 nm). We ignore the contribution
from the SiNx layer in the modeling because the thermal conductance of SiNx layer (thermal
conductivity of 5.5 W/m K and thickness of 50 nm) is much smaller than those for the other
layers.2
The heat transfer coefficient through the air gap between the probe and the sample surface
in the governing equation and boundary conditions for Tj (eqs. (9) and (10) in main text) is
determined as follows. We assume that the heat transfer through the air gap occurs vertically
from the surface of the probe to the sample surface right below. Then, the length of the heat
transfer path between the probe and the sample can be denoted as H in Fig. S1. Based on this
assumption, the heat transfer coefficient, heff, is obtained as: 3
for H /   100 ,
heff  ka / H
for 1  H /   100 ,
heff 
( ka )
2(2  A)
; f 
(1  2 f  )
A(  1) Pr
(S4)
for H /   1 ,
heff 
CV
3(1  2 f )
(S5)
(S3)
where , ka, A,, Pr, C, and Vare the mean free path of air molecule, the thermal conductivity of
air, the thermal accommodation coefficient of air (~0.9), ratio of air heat capacity, Prandtl
number, heat capacity of air molecules, and velocity of air molecules, respectively.
2
FIG. S1. The schematic diagram of the structure and materials of the thermocouple SThM probe
fabricated in this study (not to scale). The tip-sample heat transfer at the thermal contact is
omitted4.
S2. Fabrication process for nano-thermocouple junction
In this study, in order to realize NP SThM with low noise, we design and fabricate the
thermocouple SThM probe through a rigorous theory of quantitative measurement. The structure
and the fabrication process of the thermocouple SThM probe developed in this study is
fundamentally similar to those of a previous work.4 However, in order to improve Sprobe and
minimize ΔTn, we develop a new fabrication process for nano-thermocouple junctions. We
minimize the thickness of the metal film on the probe tip, which turns out to be one of the
dominant deciding factors of Sprobe, and evaporate metal films on the cantilever with a thickness
3
large enough to minimize the electrical resistance, which is a major determining factor for ΔTn.
The details of the fabrication process for this design are as follows and shown in Fig. S2.
After the SiO2 hollow tip is fabricated using the same fabrication process explained in the
previous study,4 a thin metal film on the probe tip is first formed while keeping the metal film on
the cantilever thick. Using electron-beam evaporation we deposit a gold film that is the first
metal layer composing the nano-thermocouple junction. A uniform amount of metal is deposited
per unit normal area with electron beam evaporation. Since the surface area of the probe tip is
about three times larger than the cross-sectional area of the tip base, the metal film deposited on
the tip (10, 20, 30 nm) become about three times thinner than that on the cantilever (30, 60, 90
nm). Second, the insulation layer between the two metal films composing the nano-thermocouple
junction at the probe tip, SiNx, is deposited by a plasma-enhanced chemical vapor deposition
(PECVD) process and then selectively etched by reactive ion etching until the tip of the gold
layer emerges about 100 nm away from the tip end. Finally, the chromium layer (10, 20, 30 nm)
is deposited by sputtering and a 90 nm thick chromium film is additionally evaporated excluding
the region of the probe tip via a lift-off process. As a result, the metal films on the cantilever are
thickened (100, 110, 120 nm) enough to sufficiently decrease the electrical resistance of the
probe.
4
FIG. S2. The fabrication process for minimizing the thickness of only the metal films composing
the nano-thermocouple junction on the tip. (a) The formation of a thermally grown SiO2 tip. (b)
Deposition of a gold film using e-gun evaporation. (c) Deposition and partial etch of a PECVD
SiNx layer. (d) Sputtering the thin chromium film. (e) Evaporating the thick chromium film. (f)
Scanning electron micrographs of the thermocouple probe (chromium films with different
thickness are shown).
5
References
1
F. P. Incropera, D. P. Dewitt, T. L. Bergman, A. S. Lavine, Fundamentals of Heat and
Mass Transfer, 6th ed.; John Wiley & Sons, Inc.: Hoboken, NJ, 2007; pp 60-64.
2
L. Shi, O. Kwon, C. Miner, A. Majumdar, J. Microelectromech. Syst. 10, 370(2001).
3
W. M. Rohsenow, H. Y. Choi, Heat, Mass, and Momentum Transfer; Prentice-Hall:
Englewood Cliffs, NJ, 1961.
4
K. Kim, J. Chung, G. Hwang, O. Kwon, J. S. Lee, ACS nano 5, 8700(2011).
6