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

Caroline Gorham3 October 2013

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csgorham@virginia.educarolinesgorham.com

Work thus far,

- vibrational mode theory for dielectric materials

D(ω) : density of statesvp : phase velocityv : group velocity

l: mean free path, l=v*τ where τ is scattering timef(ω, T) : Bose-Einstein distribution

Thermal conductivity (k) in dielectric materials

Density of States considerations

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))

[28]

Findings in agreement with MD studies of thermal conductivity in periodic v. aperiodic/q-periodic dielectric material [38]

d: average length of medium range order (m.r.o)a: average nearest neighbor distanceξ(ω) : length of full-localizationd : fracton (fully-localized vibration) dimensionv(ω)/ω < ξ(ω) : fully-localized vibration

(eso)“Einstein

Uncoupled oscillator”

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 []

Vibrational velocities

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)

Vibrational mean free paths

Amorphous silicon (a-Si)

a-Si mode properties: Dispersion

a-Si mode properties: Density of states and diffusivity

a-Si thermal properties: Heat capacity and thermal conductivity

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

Work to go,

- electron-boson interactions in amorphous materials

- application of science to organic semiconducting material, i.e., fullerene and fullerene derivatives

Funding - Nasa Space Technology Research Fellow 2013-?

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]

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Abstract can be found here: http://www.nasa.gov/spacetech/strg/2013_nstrf_gorham.html#.Uh4SXGSutmk

[3] [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]

[21]

Recent increased efficiencies due to [21]:

1) Use of high dielectric constant materials2) 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

Material selection

Fullerenes and fullerene derivatives

[22]

[23]

[24]

Fullerenes

Fullerene

Derivatives

C120O [25]

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

Wiedemann-Franz Law [36]

k in electrically conducting amorphous materials (k = kV + ke)

kV [W/m/K]: vibrational thermal conductivityke [W/m/K]: : electrical thermal conductivityL [WΩ/K2]: Lorenz numberσ [S/m]: electrical conductivityT [K]: temperature

Thus, ultimately, I plan to:- Tune the spectrum of vibrational localization to 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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APPENDIX 1: Parameters