A four-probe thermal transport measurement method for nanostructures

Abstract

Several experimental techniques reported in recent years have enabled the measurement of thermal transport properties of nanostructures. However, eliminating the contact thermal resistance error from the measurement results has remained a critical challenge. Here, we report a different four-probe measurement method that can separately obtain both the intrinsic thermal conductance and the contact thermal resistance of individual nanostructures. The measurement device consists of four microfabricated, suspended metal lines that act as resistive heaters and thermometers, across which the nanostructure sample is assembled. The method takes advantage of the variation in the heat flow along the suspended nanostructure and across its contacts to the four suspended heater and thermometer lines, and uses sixteen sets of temperature and heat flow measurements to obtain nine of the thermal resistances in the measurement device and the nanostructure sample, including the intrinsic thermal resistance and the two contact thermal resistances to the middle suspended segment of the nanostructure. Two single crystalline Si nanowires with different cross sections are measured in this work to demonstrate the effectiveness of the method. This four-probe thermal transport measurement method can lead to future discoveries of unique size-dependent thermal transport phenomena in nanostructures and low-dimensional materials, in addition to providing reliable experimental data for calibrating theoretical models.

Temperature and Thickness Dependences of the Anisotropic In‐Plane Thermal Conductivity of Black Phosphorus

“…Representative thermal resistance measurement results are shown in Figure S2 of the Supporting Information. Compared to previous reports of four‐probe thermal transport measurements of nanowire and microwire samples, a modified analytical solution has been derived in this work to account for the finite contact width of the 2D sample in the data analysis, as explained in the Supporting Information, where Figure S3 (Supporting Information) also shows the use of angle‐resolved polarized Raman spectra to determine sample crystallographic orientation.…”

“…Four‐Probe Thermal Measurement : The thermal transport measurements were performed with the sample located in a high‐vacuum variable‐temperature cryostat at temperatures less than or equal to 350 K to avoid sample degradation at higher temperatures . A detailed description of the measurement technique and uncertainty analysis is described in a previous publication . An improved analytical solution of four‐probe thermal measurements of 2D samples is described in the Supporting Information.…”

In-plane Thermal Conductivity Measurement with Nanosecond Grating Imaging Technique

“…Vigorous efforts have been made to measure the thermal conductivity in micro-/nanoscale electronic materials, such as thin films [1][2][3], nanowires [4,5], superlattices (SLs) [6][7][8], and 2D semiconductors [9,10]. Among the many approaches developed in recent decades for thermal conductivity measurement in micro-/nanostructures, the most commonly used include the 3ω method [1,2], time-domain thermoreflectance (TDTR) [3,11,12], Transient Thermal Gratings (TTG) [13], Raman spectroscopy [14][15][16], and the four-probe thermal measurement method [17]. The 3ω method provides accurate measurement of cross-plane thermal conductivity, especially in bulk materials and low-κ dielectric films.…”

“…However, accurate calibration of Raman peak shift over a wide range of temperatures is necessary to achieve a satisfactory uncertainty of the measured thermal conductivity, and the materials to be measured must be Raman active and sensitive enough. The four-probe thermal measurement method can measure intrinsic thermal conductance and thermal contact resistance in individual nanostructures [4,17,30]. This method consists of four suspended metal lines that function as both resistive heaters and thermometers, with the sample bridging across the four micro-fabricated metal lines [17].…”

“…The four-probe thermal measurement method can measure intrinsic thermal conductance and thermal contact resistance in individual nanostructures [4,17,30]. This method consists of four suspended metal lines that function as both resistive heaters and thermometers, with the sample bridging across the four micro-fabricated metal lines [17]. Intrinsic thermal properties can be measured very accurately with the four-probe method, but a new device needs to be fabricated for each sample, which could be very challenging.…”