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Table of contents
Introduction
1 The Hot-Carrier Solar Cell
1.1 Third generation Photovoltaics: beyond the Shockley-Queisser limit
1.1.1 The last decade objective
1.1.2 « There’s plenty of room above »
1.1.3 Promising already existing technologies
1.2 Carrier cooling, the hot topic
1.2.1 Carrier-carrier scattering
1.2.2 Intravalley versus intervalley scattering
1.2.3 Auger scattering and carrier multiplication
1.2.4 The role of phonons in carrier cooling
1.3 Hot Carrier Solar Cell: the ultimate PV device
1.3.1 Principle and comparison with a single p-n junction solar cell
1.3.2 Maximum efficiencies expected
1.3.3 Recent experimental achievements on hot-carrier solar cell issues
1.4 Materials for hot-carrier solar cell absorber
1.4.1 Carrier cooling and atomic scale engineering
1.4.2 Formal requirements
1.4.3 Physical challenges for materials science
1.5 Open questions
2 Phonons: density of final states
2.1 The Physics of phonons
2.1.1 Interatomic force constants
2.1.2 Equation of motion, dynamical matrix and secular equation
2.1.3 Phonon dispersion and one-phonon density of states
2.2 Phonon decay
2.2.1 Conservation rules
2.2.2 Decay channels nomenclature
2.2.3 Engineering phonon band structure for hot-carrier solar cells
2.2.4 Need for a complete picture
2.3 Phonons within Density Functional Perturbation Theory
2.3.1 Principle and formalism
2.3.2 Successes and limitations
2.4 Two-phonon final states in bulk semiconductors
2.4.1 Practical implementation
2.4.2 Detailed two-phonon states analysis
2.4.3 Discussion
2.5 Gaps in the density of states of nanostructured materials
2.5.1 Practical implementation of PhDOS calculation on large systems
2.5.2 Application to superlattices
2.5.3 Application to quantum dots
2.6 Gaps in the density of states, a lost cause ?
2.6.1 Superlattice: how gaps are filled
2.6.2 Quantum dot: how gaps vanish because dots are not round
2.6.3 How it turns out that gaps are sufficient but not necessary
2.7 Conclusion on the two-phonon final states investigation
3 Phonons: decay rate
3.1 LO-phonon lifetime
3.1.1 Phonon decay from experiment
3.1.2 Lifetime in bulk materials
3.2 Formalism – Beyond the harmonic approximation
3.2.1 Derivation
3.2.2 State of the art of phonon lifetime calculation
3.2.3 Drawbacks of tantalizing approximations
3.2.4 Misleading success in fitting experimental data
3.3 Third order anharmonic tensor within DFPT
3.4 Practical implementation
3.4.1 Phonons eigenvectors and eigenfrequencies
3.4.2 q-space mesh and energy smearing
3.4.3 The two-phonon density of final states
3.4.4 Validation and commentary on DFPT for HCSC
3.5 Application to SiSn
3.5.1 Two-phonon density of states
3.5.2 Lifetime of the LO-phonon: beyond the zone centre approximation
3.5.3 Lifetime dependence on the LO-phonon reciprocal position
3.5.4 Eventual photovoltaic efficiency
3.6 Towards higher orders-phonon processes
3.6.1 Previous discussions on four-phonon processes
3.6.2 Estimation of the four-phonon processes contribution
3.6.3 Consecutive three-phonon processes
3.6.4 Crystal symmetry and higher-order anharmonic tensors
3.7 Conclusions on LO phonon lifetime calculations for HCSC
3.7.1 SiSn features as references
3.7.2 Limitations
3.7.3 Towards other ways to hinder carrier cooling
4 Electron-phonon interaction
4.1 Dimensionality issue
4.1.1 Electron cooling in superlattices
4.1.2 Self-induced electric field and intraband scattering
4.1.3 [InAs]n-[GaAs]n
4.2 Directionally dependent electron-phonon interaction model
4.2.1 Electron-phonon coupling strength
4.2.2 Electron wave function
4.2.3 Electron evolution equations
4.3 Full-band cascade: practical implementation
4.3.1 Electronic band
4.3.2 Phonon polar field
4.3.3 Electronic cascade
4.3.4 Validation: bulk case
4.4 Effects of the superlattice size
4.4.1 Effect on the electric field
4.4.2 Effect on the electron-phonon interaction dimensionality
4.5 Conclusions on the electron-phonon interaction in superlattices
4.5.1 Approach and results
4.5.2 Approximations and subsequent limitations
4.5.3 Perspective on the hot-carrier effect in superlattices
Conclusion
