Vibrational mode theory for dielectric materials & electron-boson interactions in amorphous m aterials

1. Vibrational mode theory for dielectric materials & electron-boson interactions in amorphous materials Caroline Gorham 3 October 2013 ___________________________________________ csgorham@virginia.edu carolinesgorham.com

2. Work thus far, - vibrational mode theory for dielectric materials

3. Thermal conductivity (k) in dielectric materials D(ω) : density of states vp : phase velocity v : group velocity l: mean free path, l=v*τwhere τ is scattering time f(ω, T) : Bose-Einstein distribution

4. (eso) “Einstein Uncoupled oscillator” d: average length of medium range order (m.r.o) a: average nearest neighbor distance ξ(ω) : length of full-localization d : fracton (fully-localized vibration) dimension v(ω)/ω < ξ(ω) : fully-localized vibration Density of States considerations [28] Non- localized (v = vp) (sl) Softly- localized (v < vp, λ>d ) (ql) Quasi- localized (v << vp, λ<d ) (fl) Fully- localized (inter-a, v(ω)/ω< ξ(ω)) Findings in agreement with MD studies of thermal conductivity in periodic v. aperiodic/ q-periodic dielectric material [38]

5. Vibrational velocities Propagating vibrations :: v=vp as generalization from Debye-Holloway model Soft and quasi-localized vibrations :: sine-type Born von Karman dispersion relationship fully-localized vibrations:: derived from the relationship between diffusivity [] and relaxation times []

6. Vibrational mean free paths softly-localized vibrations :: relaxation is described by the Soft-Potential model [31,32] quasi-localized vibrations :: relax predominately by a frequency-dependent boundary scattering mechanism [33] fully-localized vibrations:: normal mode decomposition relaxation times by Larkin et al. [x], along with diffusivity data, allows one to determine that the fully-local vibration will transition to other modes anharmonically, at ξ(ω)

8. Amorphous silicon (a-Si)

9. a-Si mode properties: Dispersion

10. a-Si mode properties: Density of states and diffusivity

11. a-Si thermal properties: Heat capacity and thermal conductivity

12. a-Si thermal properties: thermal conductivity accumulation and MFP v. wavenumber

13. Work to go, • electron-boson interactions in amorphous materials - application of science to organic semiconducting material, i.e., fullerene and fullerene derivatives

14. Funding - Nasa Space Technology Research Fellow 2013-? [3] [21] Optimizing materials for energy harvesting on interplanetary return missions Theorized thermo-photovoltaic (TPV) maximal efficiency of 85% [1, 2] - Parameters affecting power conversion efficiencies: photon absorption [4,5], e- excitation [6,7], diffusion of electron-hole pairs to their electrodes [7,8], waste heat removal [9], thermal emission spectra of the emitter [10,11] and black-body absorption in receiver Current inefficiency due to: 1) incurred resistances due to improperly spaced electron energy levels for charge generation and 2) e- transportation to and 3) collection at electrodes caused by poor spatial geometries [12,13] ___________________________________________ Abstract can be found here: http://www.nasa.gov/spacetech/strg/2013_nstrf_gorham.html#.Uh4SXGSutmk

15. Material selection [21] Organic semiconducting polymer: small-band gap [14], low thermal conductivity [15], controllable fractal-dendtritic growth [16,17,18], thin-film morphology [19], cost-effective [20], current organic-photovoltaic efficiency ~10-15% [21] Recent increased efficiencies due to [21]: 1) Use of high dielectric constant materials 2) materials with more ordered nano-morphologies 3) better charge transport properties and less electronic traps 4) 3rd generation concepts: hot carrier cell, multi e—hole pairs per photon, impurity photovoltaic and multiband cells

16. [22] Fullerenes Fullerenes and fullerene derivatives Fullerene [24] Derivatives [23] Active layer materials for polymer-based organic solar cells. PQT-12 and P3HT are donors while PCBM are acceptors [23]– thus blends will be used C120O [25]

17. k in electrically conducting amorphous materials (k = kV + ke) Wiedemann-Franz Law [36] kV [W/m/K]: vibrational thermal conductivity ke[W/m/K]: : electrical thermal conductivity L [WΩ/K2]: Lorenz number σ [S/m]: electrical conductivity T [K]: temperature • Thus, ultimately, I plan to: • Tune the spectrum of vibrational localizationto control the vibrational band-gaps [37], thereby: minimizing vibrational thermal conduction and electron-boson coupling • Tune the spectrum of e- localization to control the electronic energy-levels and band-gaps, thereby: optimizing photon absorption of the wavelengths abundant on the Martian surface and in Outer Space and subsequent charge generation • Understand the conduction electron-boson coupling factor for each vibrational regime:

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21. APPENDIX 1: Parameters