Purcell effect and Quality factor tuning in Si-nc based microdisk resonators.

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 Wang et al., J. Crystal Growth 294, 486 (2006) The nanocrystalline Si has the same crystallographic structure of bulk Si (two compenetrating fcc cells), but the Bloch theorem is not valid anymore. 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

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. 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

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 3 layer 2 layer 2 layer Using a hybrid (SRO-Si3N4 deposition) it is possible to create a new class of resonator: micro-kylix (micro-chalice). 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. 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

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 singlet D triplet ttri tsing Bisi, Ossicini and Pavesi, Surf. Sci. Reports38, 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. I II 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

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

15. Si-nc as light emitters:Purcell effect Stretched exp.: t = 14.42 b = 0.59 tPL = 22.2 ms Lifetime enhancement (LE): 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

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

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

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

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 = 0.4944 c • ng = 2.02 • Kylix (@ 800nm): vg = 0.4698 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: • 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. l = 852nm 0-TE1,33 University of Trento, Department of Physics PhD Workshop Trento, 05/12/2008