Nanotubes and Nanowires

Figure 1: Click to enlarge

Nanowires and carbon nanotubes (CNTs) are the focus of intense research. Their unique electrical, thermal and mechanical properties hold great promise for next-generation microelectronics, energy conversion and materials. For many of these applications, it is essential to understand and control their thermal properties. We are working to measure the thermal conductivity of single nanowires and nanotubes. We are also developing theoretical models for nanowire phono thermal conductivity.

Thermal Measurements of Single Nanowires and Nanotubes

Figure 2: Click to enlarge

Figure 3: Click to enlarge

We are currently pursuing two different methods for measuring the thermal properties of single nanowires or nanotubes. The first method uses electron-beam lithography to pattern test metal structures that interface with a nanowire. A sample measurement setup is shown in Figure 2.

For the second method we are developing an integrated probe to simultaneously measure electrical conductivity, thermal conductivity, and Seebeck coefficient of individual nanowires and nanotubes inside a high-resolution TEM. This is shown in Figure 3. If successful, this will provide detailed information about the relationship between structure and thermal properties.

1ω, 2ω, and 3ω Methods for Thermal Measurements

To facilitate the measurement of nanowire properties, we have improved upon the 3ω method, which is commonly used to measure the thermal conductivity of a substrate adjacent to a strip heater, or the thermal conductivity and specific heat of a suspended wire. We have generalized the traditional analysis to now use thermal and electrical transfer functions which can be readily adapted to other experimental configurations. Voltage signals at 2ω and 1ω were identified that contain the same information about the thermal properties as the 3ω signal. The 2ω voltage requires a DC offset at the current source. The 1ω voltage requires a very stable current source, but eliminates the need for higher-harmonic detection. The 1ω method is also advantageous for studying the dynamics of systems with very fast thermal response times, such as nanowire.

Figure 4: Click to enlarge

As shown in Figure 4, the 1ω, 2ω, and 3ω methods compare favorably with experiments using a suspended platinum wire, and a line heater on a Pyrex substrate. With a modern lock-in amplifier, no common-mode voltage subtraction is necessary, which simplifies the experiment compared to the common practice of balancing a bridge or using a multiplying digital-to-analog converter. We also showed that the widespread practice of using a voltage source to approximate a current source is only valid when the sample resistance is small compared to the total electrical resistance of the circuit, and derived and experimentally verified a correction factor to be used otherwise.

Phonon Thermal Conductivity of Superlattice Nanowires

We have developed a model for the phonon thermal conductivity in superlattice (composite) nanowires. The model is fundamentally classical and three-dimensional. This apparently severe assumption is in fact well-justified by comparing the characteristic thermal phonon wavelength, lT, to the diameter of nanowires of interest. The phonon analogy to Wiens (photon) displacement law yields the helpful guideline that three-dimensional behavior can be justified whenever the temperature-diameter product, T*D, exceeds ~100 nm*K (for Si). Furthermore, by considering Ziman's [Electrons and Phonons] specularity parameter, diffuse rather than specular scattering is expected because the typical nanowire roughness is comparable to or even larger than lT.

Figure 5: Click to enlarge

The model divides a superlattice nanowire into a series of thermal resistances, capturing the three mechanisms of phonon scattering: volumetric scattering within the bulk, surface scattering at the wire side walls, and interface scattering between segments (Figure 5). With a small additional approximation, this can be presented in terms of Matthiessens rule and effective mean free paths. Roughly speaking, the analysis shows that the diameter effect becomes important when D is smaller than the bulk mean free path, and the superlattice effect becomes important when L is smaller than the bulk mean free path multiplied by (1-t)/t, where t is the energy transmissivity (Figure 5).

Figure 6: Click to enlarge

The model is in reasonable agreement with available experimental data [Li et al, Appl. Phys. Lett. 83, 2934 (2003), and 3186 (2003)] down to ~40 nm diameter, for both nanowires and superlattice nanowires, with minimal adjustable parameters. This is significant because it confirms our expectation that coherence and quantum confinement effects are negligible for this range of diameters and temperatures. However, the only experimental measurements of Si nanowires of D=22 nm at room temperature seem to contradict this interpretation, and it is still an open question as of March 2004. This motivates our current effort to measure the specific heat of nanowires, in order to better understand the nature of the transition from 3D to 1D phonon behavior.

References

  1. C. Dames and G. Chen, 1, 2, and 3&omega Methods for Measurement of Thermal Properties, Rev. Sci. Instrum. 76, 124902 (2005).
  2. Chris Dames and Gang Chen, Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires, J. Appl. Phys. 95, 682 (2004).
  3. C. Dames, M. S. Dresselhaus, and G. Chen, Phonon Thermal Conductivity of Superlattice Nanowires for Thermoelectric Applications, in Thermoelectric Materials 2003, Research and Applications, vol 793, eds. G. S. Nolas and J. Yang and T. P. Hogan and D. C. Johnson. From the Materials Research Society Fall 2003 Meeting, Symposium S, Paper S1.2.