Hexagonal boron nitride (h-BN) is an indirect bandgap semiconductor that exhibits phonon-assisted luminescence. Theoretical calculations reproduce the position and intensity of luminescence peaks in h-BN and show they result from indirect excitons being replicated by different phonon modes. While the theory captures single-phonon processes, it cannot fully reproduce overtones involving higher-order phonon sidebands. Recent work has extended the theory to include a finer sampling of exciton and phonon dispersions in order to model multi-phonon scattering processes in the luminescence of h-BN.

1. Phonon-Assisted Luminescencein
hexagonal Boron Nitride
ElenaCannuccia
PhysicsDepartment, University of Rome“Tor Vergata”
Aix-Marseille Université (France)

2. 2
Luminescence:
SpontaneousEmission of Light

3. 3
Opto-electronic devices
Fiber Optic
Telecommunications
Solid-State lighting
Photodiode
Solar Cell
Laser
Communication

4. 4
Blue LED

5. 5
Theother colorsand theUV

6. 6
Hexagonal Boron Nitride
h-BN isa layered
crystal iso-structural to graphite.
Asgraphite, h-BN can beeasily exfoliated, and for this
reason it findsapplicationsaslubricant.

7. 7
h-BN hasawideband gap
and it’stransparent
h-BN emitslight in
theultraviolet
Hexagonal Boron Nitride
Yoichi Kubota et al.
Science 317, 932 (2007);
W. Aggoune C.Cocchi et al. PHYSICAL
REVIEW B 97, 241114(R) (2018)

8. 8
Breaking news
on h-BN !!!
Direct­bandgap properties and
evidence for ultraviolet lasing of h­BN
single crystal
K. Watanabe et al. Nature Materials 3, 404 (2004)*
*) results from Luminescence
measurements
Energy: 5.765 eV

9. 9
Hexagonal boron nitride is an indirect band­gap
semiconductor
G. Cassabois et al., Nature Photonics, 10, 262 (2016)*
*) results from Luminescence measurements
Energy: 5.765 eV
luminescence lines: phonon­assisted transitions (phonon replicas) from
an indirect exciton (iX) .
Breaking newson h-BN !!!

10. 10
Direct vsindirect semiconductors :
Phonon assistance
Indirect band gap semiconductors are not efficient for
photonics/optoelectronics

11. 11
Internal quantum yield
50%
ZnO
Bright Luminescence from Indirect and Strongly Bound Excitons in h-BN.
L. Schue et al. Phys. Rev. Lett. 122, 067401 (2019)

12. 12
50%
0.1%
ZnO Diamond
Internal quantum yield
Bright Luminescence from Indirect and Strongly Bound Excitons in h-BN.
L. Schue et al. Phys. Rev. Lett. 122, 067401 (2019)

13. 13
45%
0.1%
ZnO DiamondhBN
50%
Internal quantum yield
Bright Luminescence from Indirect and Strongly Bound Excitons in h-BN.
L. Schue et al. Phys. Rev. Lett. 122, 067401 (2019)

14. 14
Direct or indirect
band gap ...?
… That isthequestion

15. 15
h-BN band structure and ARPES
Direct observation of the band structure in bulk hexagonal boron
nitride
H. Henck, et al. PRB 95, 085410(2017)

16. 16
Electron energy loss spectroscopy
on h-BN: probing its indirect nature

17. 17
Origin of the EELS peaks
Loss function Peaksof L(q, ω) can beput in relation to
inter-band excitations(∝ Im[ε(q, ω)])
and plasmon resonances(|ε| ≈ 0)
Direct Observation of the Lowest Indirect Exciton
State in the Bulk of Hexagonal Boron Nitride
R. Schuster C. Habenicht, M. Ahmad, M. Knupfer, B.
Büchner, PRB 97, 041201 (2018)

18. 18
hBN optical properties and excitons
IP
Electron­hole
interaction
W. Aggoune C.Cocchi et al. PHYSICAL
REVIEW B 97, 241114(R) (2018)

19. 19
What about luminescence?

20. 20
Luminescence Theory
Quasi­equilibrium Bethe­Salpeter equation
Emission
Bethe-Salpeter
Equation
Absorption
Theory of photoluminescence in
semiconductors
K. Hannewald, S. Glutsch, and F.
Bechstedt
PRB 62, 4519 (2000).
Unified theory of quantized electrons,
phonons, and photons out of
equilibrium: A simplified ab initio
approach based on the generalized
Baym­Kadanoff ansatz
P.Melo and A. Marini
PRB 93, 155102 (2016)
L. Schue, et al. Nanoscale 8, 6986 (2016).

21. 21
Second step: Time dependent
perturbation theory 1/2
Westart with theelectron-phonon Hamiltonian:
exciton wave-function,
Hamiltonian written in theexcitonic basisset:
Thenew excitonic wave-functions:
Emission
Absorption

22. 22
Second step: Time dependent
perturbation theory 2/3
Static approximation for dipoles but not for thetransitions
and phonon modes are mapped at Γ point in asupercell
Exciton-phonon dipolematrix elementscan bewritten in termsof derivatives
and calculated by finite differences

23. 23
Second step: Time dependent
perturbation theory 3/3
Electron–phonon coupling from finite differences
B. Monserrat
J. of Phys.: Cond. Matt. 30, 083001(2018)
finite difference method
T

24. 24
Luminescence in h-BN
Theory
Experiment
Hexagonal boron nitride is an
indirect band­gap
semiconductor
G. Cassabois et al., Nature
Photonics, 10, 262 (2016)
Theory of phonon­assisted
luminescence in solids: application
to hexagonal boron nitride
E Cannuccia,et al.
arXiv preprint arXiv:1807.
Phys. Rev. B 99, 081109(R) (2019)
iX excitons are replicated by the different phonon modes
and acquire a finite optical weight.
We reproduce the position and the intensity
of various peaks.
The doublets are generated by LO­TO, and
LA­TA splitting.

25. 25
Something is missing
Higher­order
phonon sidebands
Overtones of interlayer shear modes in the phonon-assisted
emission spectrum of hexagonal boron nitride.
T. Q. P. Vuong et al, PRB, 95(4), 045207 (2017)
TheEPscattering is
limited to onephonon
at atime.
Wecannot reproduce
theovertonesinvolving
interlayer shear modes
and theasymmetric tails
of theemission peaks.
afinesampling of theexciton
and phonon dispersions.

26. 26
Excitons and Luminescence
Since excitons and optical phonons
responsible for luminescence have
similar radius, their coupling is efficient

27. 27
Conclusions
Codes
● Exciton interference in hexagonal boron nitride
L. Sponza, H. Amara, C. Attaccalite, F. Ducastelle, A. Loiseau
Phys. Rev. B 97, 075121 (2017)
● Theory of phonon-assisted luminescence in solids: application to hexagonal boron nitride
E. Cannuccia, B. Monserrat and C. Attaccalite
arXiv preprint arXiv:1807.11797
https://journals.aps.org/prb/accepted/0f07dY44I2c17655543b6447ed3bcca77be0b885f
● Direct and indirect excitons in boron nitride polymorphs: a story of atomic configuration and
electronic correlation
L Sponza, H Amara, C Attaccalite, S Latil, T Galvani, F Paleari, L Wirtz, F. Ducastelle
arXiv preprint arXiv:1806.06201
● Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride
C. Attaccalite, M Grüning, H Amara, S Latil, F Ducastelle
arXiv preprint arXiv:1803.10959
●
We extended luminescence theory to include phonon scattering
and interpret the luminescence spectra of h-BN in terms of phonon replica
References