1 Thermal Conductivity of Silicon Nanowire Arrays with Controlled ...


1 Thermal Conductivity of Silicon Nanowire Arrays with Controlled ...

consideration of wave-like phonon transport, otherwise neglected in traditional particlerelaxation-time approaches.In the current paper, we use time domain thermoreflectance (TDTR) to experimentallystudy the thermal properties of arrays of vertically-aligned Si nanowire with controlledroughness. TDTR has several advantages over the conventional approach of measuring asingle nanowire using microfabricated test platforms: (1) Since the nanowires remainintegrated to the substrate, the potential for nanowire damage by the scraping process isminimized; (2) A large number of nanowires are sampled during each experiment, typically~10,000; (3) No microfabrication or micromanipulation is required, greatly expediting themeasurement process; (4) The formation of good thermal contacts is greatly simplified, andthe thermal interface conductance is easily measured.Fabrication of roughened Si nanowire array is accomplished by a recently developedtwo-step wet etch technique, which will be published in detail elsewhere, [20] but the mostimportant aspects are described here. The process begins with a lightly P-doped Si wafer(ρ~10 Ω-cm) with a layer of native oxide. A thin layer of Ag (~10 nm as measured by acalibrated quartz crystal monitor) is then deposited by e-beam evaporation and subsequentlyannealed at 350°C for 4 h under 3-8 x 10 -7 Torr pressure which thermally dewets the Ag,forming truncated spherical particles (contact angle >90°) on the surface. The size of theparticles and the inter-particle spacing depend on the thickness [21] of the Ag as well as theannealing temperature and time; the conditions described above generated particles withaverage diameter ~100-150 nm. The particles are used as a shadow mask to form a gold mesh(10 nm Au deposited by e-beam evaporation). The removal of Ag particles and lift-off ofexcess Au is achieved by sonicating the samples in a selective etchant(NH 4 OH(32%):H 2 O 2 (30%):methanol = 1:1:2; v:v:v). The remaining Au mesh is used ascatalyst for a highly anisotropic metal-assisted chemical etch [22-24] (MacEtch), composed ofHF(49%):H 2 O 2 (30%):ethanol = 13:2:19 (v:v:v). Nanowires arrays were etched to be between3

500 nm-1200 nm in length (~2 min. etch). Under these conditions, tapering, which dependson the HF:H 2 O 2 ratio and ethanol concentration, is minimized and typical rms variation of thenanowire length is only ~2-4% of the total length. The Au mesh was subsequently removedusing a 90 sec aqua regia etch.The as-synthesized vertical nanowire arrays were smooth with roughness between 0-1 nm rms, and the area fraction of all arrays was between 17%-29%. To independentlyintroduce roughness, a 6-8 nm layer of Au was deposited by sputtering using a rotating andtilting (0 - 30° with random movement) sample holder, to form nanoscale islands on thesidewalls of the nanowires. A dilute MacEtch solution composed ofHF(49%):H 2 O 2 (30%):H 2 O = 1:1:24 (v:v:v) was then used to controllably generate roughness,with the etch time determining the final degree of roughness (figure 1). The roughenedsamples (≈4 cm 2 each) were split in two, with one sample being used for HRTEM roughnesscharacterization and the other for TDTR measurements.To create a smooth surface suitable for TDTR measurements, a commerciallyavailable spin-on glass (SOG), (Filmtronics, Siloxane 500F) was spin coated into thenanowire arrays such that the SOG was slightly thicker than the nanowires. The SOG wasthen reactively ion etched in CHF 3 until the thickness of the SOG is within about ~20 nm ofthe nanowire as verified in side view SEM for each sample. Samples were then coated in~70 nm Al by magnetron sputtering (with precise thickness (+/-4 nm) determined bypicosecond acoustics for individual samples). The reflectivity of each sample was comparedto a reference sample of a smooth, oxidized Si wafer coated by Al, and all reported samplesdisplay specularity greater than 90%, but with most being indistinguishable from the smoothAl reference sample to within experimental uncertainty.Time domain thermoreflectance was used to characterize the thermal conductivity ofthe roughened Si nanowire arrays. Our measurement system and methods of data reduction[25, 26]have been described in detail previously. However,for nanowire arrays embedded in a4

host matrix material there are several unique aspects to the data acquisition and reduction.Koh et al. [27] have previously reported that thin film composites of vertically aligned InAsnanowire arrays with PMMA matrix filler display effective properties that depend on themodulation frequency, and an effective thermal interface conductance well-below any knownphysical interface. We observe this to be true for the current Si nanowire arrays as well(figure 2a). Low effective thermal interface conductance is due to the fact that most of theheat is channeled through the nanowire which, due to the low area fraction, amplifies itseffective interface resistance by an amount, ~1/x, where x is the area fraction of nanowires. Inthe current study, effective thermal interface conductances are observed to be between25-40 MW/m 2 -K, consistent with a 20-30% areal fraction of nanowires.The frequency-dependence of the composite thermal conductivity can be understoodby examining the origin of the out-of-phase signal in TDTR. The out-of-phase signal dependssensitively on the surface temperature response to a sinusoidal heat input at the modulationfrequency; [26] at high modulation frequency, the diffusion distance for heat in the matrixmaterial is much smaller than the distance between adjacent nanowires. Thus, temperature isnot uniform in the lateral direction except at the surface, where the array is connected by ahigh thermal conductivity metal. In this limit, the heat flux divides such that that the averageresponse at the surface is indistinguishable from an effective medium with effusivity,(κC) eff= x (κC) wire+ (1− x) (κC) SOG(1)However, at low frequency, heat fully penetrates the matrix material in the lateral direction, sothat the temperature is roughly isothermal in-plane. In this case, the surface temperatureresponse is indistinguishable from that of an effective medium withC eff= xC wire+ (1− x)C SOG(2)κ eff= xκ wire+ (1− x)κ SOG(3)5

In the intermediate frequency range, the behavior cannot be captured by a simple effectivemedium model. Transient finite element analysis is capable of modeling the intermediatecases; however, performing the simulation of TDTR data requires a summation over thefrequency response at thousands of frequencies for each time-delay curve, [26] which was notpractical. Rather, finite element calculations were used only to verify that the transition fromthe high to low frequency regime is controlled by the thermal diffusion distance in the spinon-glasscompared to the nanowire spacing, and that at the lowest experimental frequencies,the frequency response is well-represented by the effective medium theory in equations 2 & 3.The measurements at either modulation frequency limit can be used as a simple way todetermine the thermal conductivity of the nanowires,κ wire. In the current work, the lowfrequency limit is used since it is sensitive to the properties deeper within the nanowire arraysand is less sensitive to knowledge of the matrix properties. This requires that the properties ofthe filler SOG be known; the properties of a pure SOG film (220 nm) were measured at twomodulation frequencies (1.6 MHz and 9.8 MHz) to separately determine the thermalconductivity (0.36+/-0.3 W/m-K) and specific heat capacity (1.3+/- 0.1 MJ/m 3 -K); thethermal conductivity is close to previously measured spin-on-glass with similar composition(~0.38 W/m-K), [28, 29] and the specific heat capacity is near that of other siloxanes such asPDMS (1.3-1.5 MJ/m 3 -K). [30]From the low frequency limit of the composite thermal conductivity, the thermalconductivity of the nanowires is then extracted using equations 2 & 3. The extracted valuesare plotted in figure 2b. The error-bars for the measurement are larger than typical for TDTRmeasurements (~20% instead of ~10%) [31] for several reasons; in addition to the usual errorcontributions coming from uncertainty in the transducer thickness and heat capacity (~8%together) [31] , there is uncertainty in the nanowire length (~10%), the areal fraction ofnanowires (~10% uncertainty based on SEM images at various locations on the chips), and asignificant error in the phase of the reference channel due to the lower signal-to-noise ratio6

and smaller jump in the in-phase signal at zero time delay that occurs at low frequency [31] (upto 10% in some cases).After uncertainties are taken into account, nanowire arrays with low roughness havethe highest thermal conductivity, albeit slightly below what has been observed in the case of asimilarly-sized nanowire grown by a vapor-solid-liquid (VSL) process and reportedpreviously. [4]Previously measured VLS nanowires all have been [111] oriented, whereas inthe current study [100] oriented wire were produced, due to the orientation of the startingwafer. In the Casimir regime, the thermal conductivity of [111] oriented wires are expected tobe ~50% smaller than [100] wires, due to phonon focusing effects; [10] however, comparing thecurrent data to the single nanowire measurement of Li et al., [4] that behavior was not observed.In qualitative agreement Hochbaum et al., [14] several highly roughened nanowire arrays areobserved with thermal conductivity well below what is explainable from boundary scatteringfrom the nanowire sidewalls (figure 3), with our lowest measured values near 10 W/m-K.In figure 3b, we have adopted the model developed by Morelli [32] to predict theexpected thermal conductivity. The basic elements of the model are that: (1) it is a modifiedversion of the Callaway model; [33] (2) phonon dispersion is treated as isotropic and linear withan energy cutoff determined by the maximum energy of the acoustic branch rather than aDebye frequency; (3) three distinct polarizations are treated; (4) mode-dependent scatteringrates are calculated using Matthiessen’s rule, considering normal and umklapp phononphononprocesses, isotope scattering, and boundary scattering where the boundary scatteringlength is taken as the diameter of the nanowire in our case. The model implicitly neglectsanisotropic effects such as phonon focusing and conduction by optical phonons, but correctlypredicts the thermal conductivity of individual Si nanowires measured by Li et al.. [4]Comparing our experimental results to the predicted values for nanowires in this size range,the lowest thermal conductivities measured are about 4 times lower than would be expected.7

In summary, a technique for fabricating vertically aligned Si nanowires withcontrolled roughness based on a two-step wet etch process has been presented and used tostudy the thermal transport properties of rough Si nanowires with similar diameter and surfacecorrelation length using time-domain thermoreflectance. The measured thermal conductivityof highly roughened nanowires are found to be significantly below the boundary scatteringlimit predicted based on a modified Callaway model and below that previously measured forsmooth single nanowires of similar diameter. The lowest thermal conductivities are similarto that previously reported on individual roughened nanowire. However, in all nanowirearrays with low thermal conductivity, we observe significantly broadened Raman linewidths.The origin of the broadening is not well-understood, but could indicate microstructuralchanges that affect acoustic phonons.ExperimentalRoughness characterization: Roughness of the nanowires was determined by high-resolutiontransmission electron microscopy (HRTEM). A double-tilt holder was used to tilt thenanowire to [110] zone-axis enabling high resolution imaging of the Si/native-oxide boundary(

Area fraction characterization: The areal fraction and size distribution of each nanowirearray was measured by analysis of top view SEM using the software package ImageJ. Toprepare images for analysis, the images were thresholded and nanowires that were visiblyclumped were separately manually with a 1 pixel line, so that the size distribution statisticswere more representative. The area fraction observed from SEM over-predicts the nanowiresize when the nanowires are rough, therefore once the roughness is measured, the SEM areafraction is reduced by a factor (D − δ D) 2 / D 2 , where the diameter reduction is given byδ D = 2 2δ rms. For the roughest nanowires reported, this correction reduces the area fractionby ~15%.Time-Domain Thermoreflectance (TDTR): The time evolution of surface temperature ismeasured through temperature-dependent changes in the reflectivity, i.e., thethermoreflectance. We analyze the ratio of in-phase, V in(t) and out-of-phase V out(t) ,variations in the intensity of the reflected probe beam at the modulation frequency, f , of thepump beam as a function of delay time, t , between pump and probe [26] . The wavelength ofthe mode-locked Ti:sapphire laser is λ = 785 nm and the 1/ e 2 radius of both focused beamsis 14 µm. Pump and probe laser power were set to 20 mW and 14 mW respectively, which iscalculated to produce

using an Acton InSight spectrometer with 2.0 cm -1 /pixel bandwidth. We estimate that thelaser power of 2 mW produces less than a 10 K steady state temperature rise in the lowestthermal conductivity samples; we verified that the Raman peakwidths and peak positions donot depend on laser intensity. The measured peakwidth of bulk Si in our system is 4.24 cm -1 ;treating the measured intensity as a Lorentzian convolved with Gaussian function thatdescribes the instrumental broadening; [34] using the bulk Si peakwidth of 2.6 cm -1 , [34] theFWHM of the instrumental broadening is ~2.6 cm -1 .AcknowledgementsThis work was supported by the Advanced Research Projects Agency – Energy (ARPA-E)under contract DOE-DE-AR-0000041PF-ARRA. This work was carried out in part in theFrederick Seitz Materials Research Laboratory Central Facilities and the Micro and NanoLaboratory at the University of Illinois.12

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(A)(B)Figure 1. (A) Bright field transmission electron micrographs of nanowires obtained by postrougheningprocess (etch times increasing from left to right: 2, 10, 16 seconds respectively);the scale bar in the upper left corner of the left panel is 10 nm). Nanowires are aligned alongthe [110] zone axis. (B) rms roughness of Si nanowires after the post-roughening process, asdetermined from HRTEM images. Each point represents the average rms roughness for 3wires from the same nanowire array.15

(A)(B)Figure 2. (A) Effective thermal conductivity of several nanowire composite layers (opencircles) measured as a function of the modulation frequency. The spin-on-glass (solid circles)displays no significant frequency dependence. The low frequency limit of the measurementsis used in conjunction with equations 2 & 3 to determine the thermal conductivity of thenanowires. (B) Silicon nanowire thermal conductivity for arrays of varied rms roughness:rms < 1nm (open squares), 1nm < rms < 2nm (open triangles), 2nm < rms

(A) (B) (C)√2σξ c /4Figure 3. (A) Height difference distribution functions measured for three representativenanowire arrays. (B) Thermal conductivity versus correlation length, ξ c; solid and opencircles are for nanowire profiles taken as the Si-SiO 2 interface and Air-SiO2 interfacerespectivitely. (C) Thermal conductivity versus rms roughness, σ .17

(A)(B)(C)(D)Figure 4. (A) . Raman scattering intensity for a 3.5 nm rms roughness nanowire array (solidcircles), a 1.0 nm rms roughness nanowire array (solid square), and bulk silicon (opencircles); Solid lines are best fit curves to the model, and the adjacent numbers are theassociated FWHM. The open squares and it’s fit are scaled by 0.25 to avoid visual overlapwith the solid circles. (B) Raman FWHM plotted against the etching time of the rougheningprocess. (C) the position of the Raman peak plotted against the Raman FWHM. (D) Thethermal conductivity of each nanowire array plotted against the corresponding Raman FWHM.18

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