CONCLUSION AND FUTURE WORK
This dissertation investigates the electrical and thermal transport in peri- odic holey silicon nanostructure. In 2-D periodic holey structure, we focus on a simultaneous measurement of all three material properties, which has rarely been realized previously for silicon nanostructure. Using a self-heating 3ω method, we are able to measure the thermal conductivity of 2-D holey silicon which only requires the sample portion to be suspended, eliminating complexity of previously reported micro-fabricated devices. We also imple- mented frequency domain Seebeck measurement on the same device. Our technique demonstrated a complete ZT measurement on silicon nanostruc- ture. In 3-D periodic structure, silicon inverse opals, phonon transport is largely affected by the removal of materials (high porosity) in continuum regime. After accounting for the porosity effect, we found the phonon mean free path is limited by grain boundaries. At low temperature, the unusual power dependence on temperature reveals possible coherent scattering by the intergrain region. In this chapter, we will summarize our findings and briefly discuss the future direction for silicon based thermoelectric application.
Electrical measurement on 2-D periodic holey silicon shows unaffected elec- trical conductivity for limiting dimension down to 120 nm. This is attributed to the smaller mean free path of electrons at room temperature. In addition, it is found the Seebeck coefficient becomes smaller than bulk silicon at sim- ilar doping concentration. While it is hard to argue the change in diffusion part, we hypothesize quenched phonon drag is the reason behind the reduc- tion in S. In silicon nanostructure, long wavelength phonons are randomized by boundary scattering before momentum transfer to electrons. This hy- pothesis is partially validated by the temperature trend in our Seebeck data, which clearly shows the dominance of diffusion contribution. We extracted the phonon drag component by comparing our measurement with reported
bulk S. The extracted Sph can be fitted by a solution to the BTE with cou-
pled electron and phonon transport. The excellent agreement in temperature trend also supports our hypothesis.
However, the quenched phonon drag has a negative implication toward thermoelectric application. At optimal doping concentration (∼ 4×1019
cm−3), phonon drag contributes ∼ 25% of total Seebeck coefficient. Ex- cluding phonon drag results a 40% reduction in power factor. Even if we assume the amorphous limit of the lattice thermal conductivity, ZT at 300 K is ∼ 0.47 at best.
As for thermal conductivity measurement, we demonstrated effective re- duction using periodic holey structure. We also found thermal conductivity is below the corresponding Casimir limit if the neck distance is taken as lim- iting dimension. The exact reason is unclear, however, similar phenomena have also been observed in other measurements [12,14]. Due to the constraint in fabrication, we were not able to achieve structures with limiting dimension less than 120 nm. The overall reduction in material thermal conductivity is about 10 times from bulk silicon.
Amongst all samples, the best thermoelectric figure of merit ZT for that sample is 0.036 at room temperature. While the reported highest ZT for silicon holey structure is 0.4, our sample represents a regime where electrical conductivity is preserved and thermal conductivity is only modestly reduced. Further reduction in thermal conductivity will likely result an inferior elec- trical conductivity [12].
Thermal conductivity measurements on silicon inverse opals show effec- tive thermal conductivities .1 W/mK and material thermal conductivities .10 W/mK at room temperature. The relatively low thermal conductivities are significant in photonic applications where even relatively small absorp- tion can cause significant temperature rise. In exploring phonon transport in these structures, we find that frequency-dependent, coherent phonon grain boundary scattering explains the data across the temperature range of the measurement down to 30 K. Compared to previous measurements, inverse opals provide access to more uniform grains across the entire sample since grain growth is restricted by the thickness of the silicon shell. On the ba- sis of the thermal conductivity analysis, we hypothesize that the intergrain
region is thinner and possesses lesser disorder than typical polysilicon films. This is likely the reason for the clear frequency dependence in our data at low temperatures that is not observed in previous measurements. Assuming that inverse opals can be heavily doped similar to bulk polysilicon, these materials become interesting for thermoelectric energy conversion at high temperatures. Theoretical calculations [31] show ZT ∼ 0.6 at 600 K, provid- ing impetus for future experiments. This work provides thermal conductivity data useful in technological applications of inverse opals and insight into the physics of phonon heat conduction in these structures.
Future work could focus on lowering the limiting dimension before electrical conductivity is affected. This objective requires careful structure engineering and device integration. The target dimension is 50 nm [80]. However, it is unlikely to achieve significant enhancement in ZT using silicon nanostruc- ture. Beyond thermoelectric applications, selectively launching phonons with specific frequency could potentially decouple energy transport and phonon- electron interaction. Measurement wise, it could lead to the restoration of phonon drag in silicon nanostructures.
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