NANO LETTERS
Thermal Conductance of InAs Nanowire Composites
2009 Vol. 9, No. 12 4484-4488
Ann I. Persson,†,‡ Yee Kan Koh,*,†,§ David G. Cahill,§ Lars Samuelson,| and Heiner Linke‡,| Physics Department and Materials Science Institute, UniVersity of Oregon, Eugene, Oregon 97403, Department of Material Science and Engineering, UniVersity of Illinois, Urbana, Illinois 61801, and Solid State Physics and The Nanometer Structure Consortium, Lund UniVersity, Box 118, 221 00 Lund, Sweden Received August 27, 2009
ABSTRACT The ability to measure and understand heat flow in nanowire composites is crucial for applications ranging from high-speed electronics to thermoelectrics. Here we demonstrate the measurement of the thermal conductance of nanowire composites consisting of regular arrays of InAs nanowires embedded in PMMA using time-domain thermoreflectance (TDTR). On the basis of a proposed model for heat flow in the composite, we can, as a consistency check, extract the thermal conductivity Λ of the InAs nanowires and find ΛNW ) 5.3 ( 1.5 W m-1 K-1, in good agreement with theory and previous measurements of individual nanowires.
Understanding and controlling heat flow in nanowires (NWs) are important for optimizing heat dissipation in electronic and optoelectronic devices, as well as for minimizing parasitic heat flow in NW-based thermoelectric devices.1 Scattering of phonons at the surfaces of the NW reduces the lattice thermal conductivity of the NW compared to its bulk counterpart.2,3 Most measurements of the thermal conductivity of NWs to date have been carried out on individual NWs, which is an advantage when studying how the thermal conductance is related to the crystal structure and its quality, surface roughness, and diameter of the individual NW.4-8 However, many future NW-based devices will be based on a large number of densely packed NWs, perhaps supported by a matrix material, and it may not be the properties of isolated NWs that control the final performance but rather a combination of the NWs and the matrix material. The resulting thermal conductivity of the NWs and the matrix, the socalled NW composite, depends on the NW diameter and array geometry9,10 but also on the character of the NW/matrix interface and the presence of additional components such as insulating shells and metal wrap-gates in structures for highspeed electronics.11-13 Here we demonstrate how to measure the thermal con* Corresponding author. Address: Frederick Seitz Materials Research Lab, 104 South Goodwin Ave, Urbana, IL 61801. Tel: +1 217 244 2207. Fax: +1 217 244 2946. E-mail:
[email protected]. † These authors contributed equally to the work. ‡ University of Oregon. § University of Illinois. | Lund University. 10.1021/nl902809j CCC: $40.75 Published on Web 10/01/2009
2009 American Chemical Society
ductance of NW composites using time-domain thermoreflectance (TDTR), a technique that has previously been established for characterization of the thermal transport properties of thin films and interfaces.14,15 Our measurements show that the thermal conductivity of the NW composite as measured by TDTR depends on the penetration depth of the thermal waves that are used in the experiment. We relate this behavior to the length scale for temperature equilibration between the NWs and the surrounding matrix material by carrying out finite element method (FEM) analysis of the heat flow through the NW composite. This procedure also allows us to determine the thermal conductivity of the NWs in the NW composite. For this first test of the use of TDTR for measurements of NW arrays, the following conditions are important for the NW samples. First, to ensure sufficient sensitivity to the properties of the NWs, the areal packing density should be high. Second, a thin Al film is required on top of the NWs to provide a surface with high thermoreflectance for TDTR measurements. Third, to facilitate data interpretation, the top ends of the NWs should be in contact with the thin Al film without roughening the surface of the Al too much and affecting the optical properties of the Al film. Therefore, NWs of uniform length are desired. The NWs were nucleated by Au seed particles deposited on an InAs (111)B substrate and grown using chemical beam epitaxy (CBE). For growth of NW arrays with high areal packing density in this growth system, where the NWs start competing for growth material if they are spaced less than ∼1 µm, the growth rate and final length depend on both the
Figure 1. (A) SEM image of the InAs NW array grown perpendicular on a (111)B InAs substrate. For imaging, the NWs were tilted 30°. The scale bar is 5 µm. (B) SEM image of the same array as in (A), but larger magnification. The scale bar is 500 nm. The NWs are 52 ( 4 nm in diameter and 430 ( 40 nm in length. The spacing between each NW in the array is 200 nm, and the areal packing density x ) 0.061 ( 0.009.
spacing and the diameter of the NWs.16,17 Therefore, to achieve a uniform length of the NWs it is necessary to ensure that the NWs are evenly spaced and have the same diameter. For seed particles, we used Au disks fabricated by electronbeam lithography, thermal evaporation, and lift-off.17 The Au disks were positioned in a hexagonal lattice, such that each disk in the 90 × 90 µm2 array was separated from its six nearest neighbors with a spacing of 200 nm. Trimethylindium and tert-butylarsine were used as group III and group V growth sources with source pressures 0.15 and 1.5 mbar, respectively, and the growth temperature was ≈430 °C. Figure 1 shows images taken with a scanning electron microscope (SEM) of the NW array after growth. The resulting NWs were 52 ( 4 nm in diameter, and had an areal packing density of x ) 0.061 ( 0.009. The lengths of the NWs were 430 ( 40 nm, which corresponds to a growth rate of 8.6 nm/min. This growth rate is in good agreement with previous results of growth of NWs of the same diameter and spacing.17 To deposit the Al layer needed for the TDTR technique, we used the following procedure. After growth, the NW array was completely embedded in ≈850 nm thick poly(methyl methacrylate) (PMMA). With an ozone plasma, the PMMA layer was then etched down until the tops of the NWs in the array were above the PMMA surface, enough to ensure contact with the Al film without creating excessive unevenness of the Al surface. Finally, a 90 nm thick Al film was deposited by thermal evaporation. Figure 2 shows a schematic of the cross section of the sample structure and a corresponding SEM image. The PMMA-embedded NW array will from now on be referred to as the NW composite. We occasionally observe voids in the NW composite in some of the SEM images; see Figure 2C. We estimate the volume percentage of the voids to be
