1. Purcell effect and Quality factor tuning in Si-nc based microdisk resonators.
Alessandro Pitanti
Tutor: prof. Lorenzo Pavesi
Main co-workers: Mher Ghulinyan (FBK), Min Xie
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

2. Outline Si-nc as a light emitting material:
Introduction to the Whispering Gallery Mode system.
Theory and Simulations.
Cavity Quantum ElectroDynamic (CQED): The Purcell effect.
Quality factor tuning in exotic geometries (kylix microresonators).
Future perspectives and conclusions.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

3. Material
The nanocrystalline Si has the same crystallographic structure of bulk Si (two compenetrating fcc cells), but the Bloch theorem is not valid anymore.
Wang et al., J. Crystal Growth 294, 486 (2006)
3 - 5 nm
When the nc radius become comparable with the exciton radius we assist to quantum confinement effects (blue shift of the band gap).
Due to band folding the G-X-valley transitions become quasi-direct.
Wolkin et al., PRL 82, 1999 (1997) [for Porous Si]
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 3

4. Si-nc as light emitters: Whispering gallery mode resonator
The physical phenomenon was well known. Lord Rayleigh in 1914 was the first to described it mathematically for acoustic wave in St. Paul's cathedral dome (London).
The light propagates inside a dielectric with azimuthal simmetry by internal reflection interfering with itself after a round trip.
The optical mode is a quasi-guided mode: a percent of the mode (inversely proportional to the ray of curvature of the dielectric) is lost as radiation (leaky mode).
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

5. Si-nc as light emitters: Whispering gallery mode resonator
Embedding the Si-nc inside the microdisk it is very easy to "charge" the dielectric cavity, but we have to deal with absorption losses.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

6. TUNING THE QUALITY FACTOR: MICRO-KYLIX RESONATORS
Si-nc as light emitters: Purcell effect
TUNING THE QUALITY FACTOR:
MICRO-KYLIX RESONATORS
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 6

7. Towards a flexible device:
Quality factor tuning
Combining the radiative and material quality factors, the total Q appears like a band. In the real disk, the Q-band is convoluted with the Si-nc emission band.
With standard flat disk shifting the top of the band equals to change the disk size. Even if decreasing the size increases the FSR (+) at the same time it decrease the total Quality Factor (-).
Can we "tune" the band without changing the FSR and the Quality Factors of the resonator ?
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

8. Towards a flexible device:
Micro-kylix resonators
Using a hybrid (SRO-Si3N4 deposition) it is possible to create a new class of resonator: micro-kylix (micro-chalice).
2 layer
3 layer
Since SRO and Si3N4 have different geometric dilatation constants, when cooled down after deposition the residual stress raise (micro-kylix) or lower (micro-umbrella) the disk edge.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

9. Towards a flexible device:
Quality factor tuning
We obtain a blue-shift of the top of the band of about 60nm from flat to kylix microresonator.
Both the maximum quality factor value (~ 2500) and the Free Spectral Range are almost unchanged (DFSR ~ 0.5nm).
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

10. Towards a flexible device:
Quality factor tuning
The main difference between the kylix and the flat
disk seems to regard how the light is confined inside the active material.
By changing the radius of curvature it is possible to effectively change the top of the Q-bands.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

11. ENHANCING THE SPONTANEOUS EMISSION: THE PURCELL EFFECT
Si-nc as light emitters: Purcell effect
ENHANCING THE SPONTANEOUS EMISSION:
THE PURCELL EFFECT
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 11

12. Si-nc as light emitters: Purcell effect
Purcell empirically discovered an enhancement in the atomic spontaneous emission at radiofrequency (1964) when placed in a resonant circuit.
The same enhancement has been demonstrated for optical frequency placed in a dielectric microcavities.
r(w0) – Photonic density of states
weak coupling regime, two-level system
Ideal system:
Emitter linewidth << cavity linewidth
G (confinement factor) ~ 1 (e ~ constant where the optical mode propagates)
Emitter spatially located in a field antinode with the dipole parallel to the field component
negligible non-radiative recombination rate
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

13. Si-nc as light emitters: Singlet and Triple states in Si-nc
Bisi, Ossicini and Pavesi,
Surf. Sci. Reports 38, 1 (2000)
Region I: non-radiative recombination dominates
Region II: radiative recombination dominates
Enhanced exchange interaction for excitons confined causes a large splitting into triplet and singlet states. II I D
tsing
ttri
singlet
triplet
The singlet transition is dipole-allowed, while the triplet transition is dipole forbidden.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 13

14. Si-nc as light emitters: Singlet and Triple states in Si-nc
Godefroo et al., Nature Nanotech. 3, 174 (2008)
The singlet state is associated to quantum confined states (excitons spatially delocalized).
The triplet state is associated to surface states (excitons spatially localized).
The Hydrogen Passivation (sintering) quenches the recombination at defect sites leading to a PL mainly generated from quantum confined excitons.
It is possible, evaluating Purcell enhancement, to estimate radiative lifetime of singlet related transition.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 14

15. Si-nc as light emitters: Purcell effect
Lifetime enhancement (LE):
Stretched exp.:
t = 14.42
b = 0.59
tPL = 22.2 ms
The trend of lifetimes measured in the dips is in agreement with quantum confined PL.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 15

16. Si-nc as light emitters: Purcell effect
The linear dependence of the dips lifetime with the wavelength confirm the hypothesis of PL due to Quantum Confinement.
The PL lifetime in the peaks grows slower with respect to the dip one.
The enhancement grows with the wavelength reaching a maximum of 17 % (LE = 1.17)
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 16

17. Si-nc as light emitters: Purcell effect
From the theoretical Purcell factor it is possible to estimate the radiative lifetime:
Lacking a clear estimation of the Purcell factor for our system, it is only possible to obtain an overestimation of radiative lifetime.
A radiative lifetime around 1 ms is compatible with the quantum confinement hypothesis.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 17

18. Conclusions and future perspectives.
We have demonstrated that Si-nc are good candidates as emitter in optical microcavities.
Purcell enhancement has been measured at room temperature, providing estimation of QD fundamental optical properties, radiative lifetime.
We have shown of is it possible to get an effective "Quality Factor" tuning employing stress-induced exotic resonator geometries.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

19. THANK YOU FOR YOUR ATTENTION.
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 19

20. Si-nc as light emitters: Whispering gallery mode resonator
a0 (microdisk)
~ 30cm-1
a0 (ellipsometer)
= 32cm-1
aabs = a0 + a(F)
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

21. Si-nc as light emitters: Whispering gallery mode resonator
Master equation for the electric field in cylindrical coordinates
WGM "quantum numbers": N-TEp,m
TE (TM) – quasi TE (TM) polarization
N – mode order of "slab-Z" equation
p – number of antinodes of Bessel function solution of r equation
m – number of nodes of Q equation solution 1.
Standard “slab waveguide equation” 2.
Azimuthal simmetry. m is the azimuthal mode number
3. Radial disk equation:
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

22. Towards a flexible device:
Quality factor tuning
The total thickness
The 3-layer (flat disk) and 2-layer (kylix)
slab waveguides show almost the same effective index (TM-polarization) but, more important, identical Confinement Factors.
The "average" group velocity in the real resonators are almost coincident:
Flat disk 800nm): vg = c
ng = 2.02
Kylix 800nm): vg = c
ng = 2.12
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008

23. Si-nc as light emitters: Purcell effect
Some corrections for non-ideal systems have been calculated in literature:
InAs quantum boxes
constant e
measured T = 100 K
Gerard and Gayral, J. Lightw. Tech. 17, 2089 (1999)
The main differences in our Si-nc based system:
l = 852nm
the dielectric constant can not be assumed independent from the position.
at room temperature, not negligible non-radiative recombination rate.
opportune corrections for a huge number of emitters spreaded both spatially and spectrally around the cavity resonances.
0-TE1,33
University of Trento,
Department of Physics
PhD Workshop
Trento, 05/12/2008 23