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Ultra-Low Thermal Conductivity in W/Al2O3 Nanolaminates

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Science  13 Feb 2004:
Vol. 303, Issue 5660, pp. 989-990
DOI: 10.1126/science.1093711

Abstract

Atomic layer deposition and magnetron sputter deposition were used to synthesize thin-film multilayers of W/Al2O3. With individual layers only a few nanometers thick, the high interface density produced a strong impediment to heat transfer, giving rise to a thermal conductivity of ∼0.6 watts per meter per kelvin. This result suggests that high densities of interfaces between dissimilar materials may provide a route for the production of thermal barriers with ultra-low thermal conductivity.

Materials with structure on nanometer-length scales are being studied for their promise of providing novel optical, electrical, magnetic, or mechanical properties. The thermal properties of nanostructured materials, however, have received much less attention (1). In general, internal interfaces impede the flow of heat: The interface disorder scatters phonons at grain boundaries or interfaces between similar materials, and the differences in elastic properties and densities of vibrational states inhibit the transfer of vibrational energy across interfaces between dissimilar materials. Thus, it may be expected that materials engineered with high interface densities should reduce the thermal conductivity and improve the performance of thermal barriers (2) and of materials used in thermoelectric energy conversion (3). Conversely, the thermal resistance of interfaces degrades the performance of materials intended for thermal management, such as polycrystalline diamond (4) and nanoscale composites (5).

The interface thermal conductance G is defined by = GΔT, where is the heat flux normal to the interface and ΔT is the temperature drop at the interface. If a nanolaminate made of alternating layers of two materials has an interface spacing δ and the series resistance of the interfaces dominates the thermal transport, then the thermal conductivity Λ of the nanolaminate is simply Λ = δG. Values of G for individual solid-solid interfaces have been measured (6) to be as small as G ≈ 50 MW m–2 K–1. If this small conductance could be maintained with δ= 2 nm, the resulting material would have an extremely low thermal conductivity of Λ = 0.1 W m–1 K–1. For comparison, the thermal conductivities of amorphous oxides (7) or strongly disordered crystalline oxides (8, 9) fall in the range 1.3 < Λ < 3.0Wm–1 K–1 at temperatures near 300 K. Although several examples of multilayers, superlattices, and nanocrystalline materials (10) have been studied (1), none show conductivities significantly below the values typical of disordered dielectrics.

We prepared three sets of nanolaminate samples: two sets were synthesized by atomic layer deposition (ALD) with substrate temperatures of 177°C and 300°C, and a third set was deposited by magnetron sputtering with substrates near room temperature (11). In ALD, a cycle of gas-phase reactants is used to deposit a fixed amount of material per cycle. In the steady state, alternating exposures to Al(CH3)3 and H2O deposit 0.11 nm of amorphous Al2O3 (12), and each alternating exposure to WF6 and Si2H6 deposits ∼0.5 nm of W (13). The nanolaminate samples are 40 to 70 nm in total thickness. The Si substrates are first coated by ∼2 nm of Al2O3; the top layer of each nanolaminate is Al2O3.

To measure the nanolaminate thermal conductivity, we applied time-domain thermoreflectance (14, 15), but modified the analysis to take advantage of the extra information in the out-of-phase signal of the lock-in amplifier (11, 16, 17). The thermal model (17) used to analyze the raw data has several parameters, but the only important unknowns are the thermal conductance of the Al/Al2O3 interface at the top of the nanolaminate and the property we seek, the thermal conductivity of the nanolaminate. For example, a 10% change in the assumed value of the heat capacity of the nanolaminate film changes the best-fit thermal conductivity by only 1%. Film thicknesses are measured by picosecond acoustics or x-ray reflectivity; heat capacities are taken from literature values; and the thermal properties of the Si substrate are relatively unimportant, because of the small thermal conductance of the nanolaminate films. We separately measured the thermal conductance of an Al/Al2O3/Si stack using a 2-nm alumina film, and we used this conductance in the model to account for the series thermal conductance of the Al/Al2O3 and Al2O3/Si interfaces. G was 80 MW m–2 K–1 at room temperature and decreased to 35 MW m–2 K–1 at 80 K. The heat flow was primarily one-dimensional, but our thermal model takes into account the full three-dimensional heat flow in cylindrical coordinates using the algorithm described by Feldman (18).

The thermal conductivity of nanolaminate films at room temperature as a function of the interface density 1/δ (Fig. 1) reveals that all three sets of samples exhibited similar behavior: The thermal conductivity decreased with increasing 1/δ, and the reduction in Λ began to saturate at 1/δ > 0.4 nm–1. Sputtered nanolaminates showed a slightly higher thermal conductivity than ALD samples. At the highest interface densities, the thermal conductivity was a factor of ∼4 smaller than the series average of the conductivities of the alumina and W layers.

Fig. 1.

Room temperature thermal conductivity of W/Al2O3 nanolaminates as a function of interface density 1/δ; δ is the distance between interfaces. Solid circles, ALD nanolaminates deposited at 300°C; open circles, 177°C ALD deposition; solid triangles, nanolaminates deposited by magnetron sputtering. The dashed line is a fit using a constant W/Al2O3 interface thermal conductance of G = 260 MW m–2 K–1; the measured thermal conductivity of the alumina layers, Λ = 1.65 W m–1 K–1; and the thermal conductivity of W layers calculated from the electrical resistance and the Wiedemann-Franz law, Λ = 6.1 W m–1 K–1. The error bars reflect the combined uncertainties in film thickness, heat capacities, and reproducibility of the interface conductance at the top and bottom of the nanolaminate film.

We analyzed these data to estimate the thermal conductance G of each individual W/Al2O3 interface. The dashed line in Fig. 1 shows the expected thermal conductivity, assuming a constant G = 260 MW m–2 K–1 and fixed values for the thermal conductivities of the individual alumina and W layers. For the ALD nanolaminate with 1/δ = 0.35 nm–1 and a deposition temperature of 177°C, the thermal conductivity was almost wholly dominated by this interface conductance, i.e., Λ ≈ δG.

This experimental value for G is close to the prediction of the diffuse mismatch model (DMM) (19). In this model of interface thermal transport, lattice vibrations are assumed to be scattered strongly at the interface and to have a transmission coefficient given by the ratio of the densities of vibrational states on either side of the interface. Using a Debye model for the densities of states, we calculated that GDMM = 320 MW m–2 K–1 for W/Al2O3. Typically, the DMM overestimates the conductance near room temperature, because this model, when based on a Debye density of states, does not take into account the dispersion of the vibrational modes.

We continued the comparison between our data and the GDMM by examining the temperature dependence of the thermal conductivity (Fig. 2). The solid line in Fig. 2 is Λ = δGDMM; that is, the solid line shows the thermal conductivity of a hypothetical nanolaminate in which δ is 2.9 nm and the thermal conductivity is dominated by the diffuse mismatch value of the thermal conductance of the W/Al2O3 interfaces. The temperature dependence of the data and GDMM are similar, giving further support to our assertion that thermal transport in the nanolaminates is mostly controlled by the conductance of the interfaces.

Fig. 2.

Temperature dependence of the thermal conductivity of the W/Al2O3 nanolaminate deposited at 177°C when δ = 2.9 nm (open circles). Data for a fully dense amorphous Al2O3 film prepared by ion-beam sputtering (solid triangles) (7) are included for comparison. The dashed line is the calculated minimum conductivity Λmin for alumina; the solid line is Λ = δGDMM, where δ = 2.9 nm and GDMM is the calculated conductance of W/Al2O3 interfaces under the diffuse mismatch model (19).

Interfaces between dissimilar materials such as W and Al2O3 are effective in reducing the thermal conductivity of nanostructured materials, but the relatively high interface energy will limit the stability of these materials at the high service temperatures typically required of thermal barrier coatings. Applications of nanolaminates as thermal barriers at temperatures higher than 1000°C would require the development of material interfaces that satisfy the conflicting demands of low thermal conductance and exceptional thermal stability.

Supporting Online Material

sciencemag.org/cgi/content/full/303/5660/989/DC1

Materials and Methods

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