Thermal Conductivity Measurement of Individual Bi2Se3 Nanoribbon by Self-heating Three- Method
Guodong Li, Dong Liang, Richard L. Qiu, Xuan P. A. Gao a)
Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, United States
a)
Author to whom correspondence should be addressed. Electronic mail: xuan.gao@case.edu
S1. Suspending nanoribbons with HF etching
Buffered hydrogen fluoric (HF) acid was used to etch away the SiO2 underneath Bi2Se3 nanoribbons (NR)
to suspend the NR from substrate. Due to that the metal contacts were deposited on the Si/SiO2 substrate
before the HF etching, we noticed that the HF also had etching effect on the metal covering NR as shown
in Fig.1a in the main manuscript. Sometimes the HF etching caused the metal layer covering NR to peel
off completely as shown in Fig. S1. Nevertheless, many devices could maintain good Ohmic contact after
the HF etching process.
FIG. S1. SEM image of a Bi2Se3 nanoribbon device after 1min HF etching with a magnified view of the
area enclosed in the dashed line shown as the bottom right inset. Scale bar is 1m.
S2. Heat loss due to radiation
We have ignored the thermal loss due to radial radiation of nanoribbon, and it may appear that
radiation loss could introduce significant error in our measurements on nanoribbons which have high
surface-to-volume ratio. The error induced by ignoring radiative thermal loss was discussed at length in
Ref. [1]. Here we will use rough estimates to show that the thermal loss through radiation at nanoribbon
surface is much smaller than the heat transported along the axial direction. The radiative heat loss Prad is
given by1 Prad = 2(w+t)Ls(T4-T04)  8(w+t)LsT03 T , with , L, w, t as the emissivity, length, width and
thickness of nanoribbon and T0 and T are the bath and nanoribbon temperatures and T=T-T0<<T0.
s=5.6710-8W/m2-K4 is the Stefan-Boltzmann constant.1 The axial heat current carried via thermal
conductance of nanoribbon is Paxial = wtT/L. For nanoribbons with thermal conductivity ~ 0.1-1 W/mK as in our case, we obtain an error due to ignoring Prad to be Prad/Paxial  8(w+t)L2s T03/(wt) ~5×10-6
<<1 at T0=300K, for typical w=500nm, t=100nm,
L=1m and a worst case scenario of =1 (i.e.
nanoribbon as a black-body). This error is negligible and becomes even smaller at lower T0.
S3. Control experiment on Ag NW
We have performed a control experiment on a silver nanowire to calibrate the self-heating 3omega technique. Commercial silver nanowires with 60nm diameter (Blue Nano Inc.) were first dispersed
in ethanol and then transferred onto silicon wafer with 600 nm SiO2 on the surface. Photolithography was
utilized to define a four probe pattern. Given the thermal conductivity of silver nanowire is much larger
than that of SiO2, no HF etching was done on the as-fabricated device to suspect Ag nanowire since the
heat leakage through SiO2 is small. Fig.S2 (a) shows the temperature dependence of resistance in
temperature range 80K to 300K, with a derivative dR/dT equal to 0.03Ohm/K. Fig. S2 (b) plots the third
harmonic voltage versus the cube of excitation current at 300K. By linearly fitting the V3 vs. I03 data,
thermal conductivity of 477 W/Km at 300K was extracted, being very close to the bulk value of 429
W/Km at 300K.
(a)
(b)
25
24
12
10
8
22
V (V)
Resistance (Ohm)
23
V signal
Linear Fitting
Temperature=300K
21
20
6
4
=477 W/Km
19
2
18
17
80
120
160
200
240
280
320
0
0.00
0.05
Temperature (K)
0.10
3
0.15
3
I0 (mA )
FIG. S2. (a) The temperature dependent resistance of a silver nanowire with 60nm diameter. (b) The 3
signal V3 of silver nanowire and the linear fitting curve of V3 on I03 from which a thermal conductivity
of 477W/Km is obtained for silver nanowire at 300K.
References
[1] L. Lu, W. Yi and D. L. Zhang, Rev. of Sci. Instr. 72 (7), 2996 (2001).