Phonovoltaic. III. Electron-phonon coupling and figure of merit of graphene:BN
Abstract
The phonovoltaic cell harvests optical phonons like a photovoltaic harvests photons, that is, a nonequilibrium (hot) population of optical phonons (at temperature Tp ,O) more energetic than the band gap produces electron-hole pairs in a p -n junction, which separates these pairs to produce power. A phonovoltaic material requires an optical phonon mode more energetic than its band gap and much more energetic than the thermal energy (Ep ,O>Δ Ee ,g≫kBT ), which relaxes by generating electrons and power (at rate γ˙e -p) rather than acoustic phonons and heat (at rate γ˙p -p). Graphene (h-C) is the most promising material candidate: when its band gap is tuned to its optical phonon energy without greatly reducing the electron-phonon (e -p ) coupling, it reaches a substantial figure of merit [ZpV=Δ Ee ,gγ˙e -p/Ep ,O(γ˙e -p+γ˙p -p) ≈0.8 ] . A simple tight-binding (TB) model presented here predicts that lifting the sublattice symmetry of graphene in order to open a band gap proscribes the e -p interaction at the band edge, such that γ˙e -p→0 as Δ Ee ,g→Ep ,O . However, ab initio (DFT-LDA) simulations of layered h-C/BN and substitutional h-C:BN show that the e -p coupling remains substantial in these asymmetric crystals. Indeed, h-C:BN achieves a high figure of merit (ZpV≈0.6 ). At 300 K and for a Carnot limit of 0.5 (Tp ,O=600 K) , a h-C:BN phonovoltaic can reach an efficiency of ηpV≈0.2 , double the thermoelectric efficiency (Z T ≈1 ) under similar conditions.
- Publication:
-
Physical Review B
- Pub Date:
- December 2016
- DOI:
- 10.1103/PhysRevB.94.245412
- Bibcode:
- 2016PhRvB..94x5412M