Thermal Conductivity Measurement of Individual Bi2Se3 Nano-ribbon by Self-heating Three- Method

Guodong Li, Dong Liang, Richard L. Qiu,Xuan P. A. Gaoa)

Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, United States

a)Author to whom correspondence should be addressed. Electronic mail:

S1. Suspending nanoribbons with HF etching

Buffered hydrogen fluoric (HF) acidwas 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 offcompletely as shown in Fig. S1. Nevertheless, many devices could maintain good Ohmic contact after the HF etching process.

FIG.S1.SEM image of a Bi2Se3nanoribbon 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 by1Prad = 2(w+t)Ls(T4-T04) 8(w+t)LsT03 T , with, L, w, tas 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.1The axial heat current carried via thermal conductance of nanoribbon is Paxial = wtT/L. For nanoribbons with thermal conductivity~ 0.1-1 W/m-K 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 typicalw=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 3-omega 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 cubeof excitation current at 300K. By linearly fitting the V3vs. I03data, thermal conductivity of 477 W/Km at 300K was extracted, being very close to the bulk value of 429 W/Km at 300K.

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 I03from 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).