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

A. Pitanti

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

Trento, 05/12/2008University of Trento,

Department of PhysicsPhD Workshop

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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.



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Γ XZ

-4

-2

0

2

4

6

8

10

eV

Si - octahedral B.Z.

Γ Z

-4

-2

0

2

4

6

8

10

eV

Si - tetragonal B. Z.

Wang et al., J. Crystal Growth 294, 486 (2006)

Material

3 - 5 nm

The nanocrystalline Si has the same crystallographic structure of bulk Si (two compenetrating fcc cells), but the Bloch theorem is not valid anymore.

• 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 X-valley transitions become quasi-direct.

Wolkin et al., PRL 82, 1999 (1997) [for Porous Si]



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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).



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Embedding the Si-nc inside the microdisk it is very easy to "charge" the dielectric cavity, but we have to deal with absorption losses.

10 m1 m760 780 800 820 840

Wavelength (nm)700 750 800 850 900

Wavelength (nm)

0-TE2,28

0-TE2,27

0-TE1,32

0-TE1,31

0-TE1,30



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Si-nc as light emitters:Purcell effect

TUNING THE QUALITY FACTOR:

MICRO-KYLIX RESONATORS



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600 650 700 750 800 850 900

103

104

105

106

Wavelength [nm]

QmatQradtotal Q

Towards a flexible device:Quality factor tuning

600 650 700 750 800 850 900

104

105

106

Wavelength [nm]

QmatQradtotal Q

matot r tad

1

Q

1 +

1

Q =

Q

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 ?



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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).

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.

A B C2 layer 3 layer 2 layer



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0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

750 775 800 825 850 875 900

PL

inte

nsity

(a.

u.)

Wavelength (nm)

Flat disk

-Kylix

Quality factor

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 (FSR ~ 0.5nm).

750 775 800 825 850 875

10

11

12

13

14

15

FS

R (

nm

)

Wavelength (nm)

Kylix Flat



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0.70 0.75 0.80 0.85 0.90103

104

105

106

Flat QRAD

Flat QMAT

Kylix QRAD

Kylix QMAT

Rad

iativ

e an

d M

ater

ial Q

s

Wavelength (m)


0.70 0.75 0.80 0.85 0.90

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Qua

lity

Fac

tor

Wavelength (m)

Flat sim Kylix sim Flat exp Kylix expl

The main difference between the kylix and the flatdisk seems to regard how the light is confined inside the active material.

725 750 775 800 825 850 875

500

1000

1500

2000

2500

3000

3500 Kylix Flat down-Kylix 5um flat

Q fa

cto

r

Wavelength (nm)

By changing the radius of curvature it is possible to effectively change the top of the Q-bands.



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ENHANCING THE SPONTANEOUS EMISSION:

THE PURCELL EFFECT



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Purcell empirically discovered an enhancement in the atomic spontaneous emission at radiofrequency (1964) when placed in a resonant circuit.

3rad,peak

P 2rad

Γ 3 λ QF = =

Γ 4π n V

The same enhancement has been demonstrated for optical frequency placed in a dielectric microcavities.

2

intSE 02

2π(r) = f H (r) i ρ(ω )

weak coupling regime, two-level system

(0) – Photonic density of states

Ideal system:• Emitter linewidth << cavity linewidth• (confinement factor) ~ 1 (~ 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



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Si-nc as light emitters:Singlet and Triple states in Si-nc

1 10 100

0.01

0.1

1

10

PL

lifet

ime

(ms)

Temperature (K)

PL

Inte

nsity

(a.

u.)

Region I: non-radiative recombination dominates

nr rad

1τ =

Γ +Γrad

PLnr rad

ΓI

Γ +Γ

Region II: radiative recombination dominatesEnhanced exchange interaction for excitons confined causes a large splitting into triplet and singlet states.

III

ΔkT

ΔkT

--1 -1tri sing-1

-

(3τ +τ e )τ =

(3+e )

sing

tri

singlet

tripletThe singlet transition is dipole-allowed, while the triplet transition is dipole forbidden.

Bisi, Ossicini and Pavesi, Surf. Sci. Reports 38, 1 (2000)



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Si-nc as light emitters:Singlet and Triple states in Si-nc

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.

Godefroo et al., Nature Nanotech. 3, 174 (2008)



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PL,dip PL,peak non-rad P rad

PL,peak PL,dip non-rad rad

τ Γ Γ +F ΓLE= = =

τ Γ Γ +Γ

Lifetime enhancement (LE):

radP

PL

τF = (LE-1)+1

τ

0 100 200 300 400 500

0.1

1

Nor

mal

ized

inte

nsity

time (microseconds)

Stretched exp.:t = 14.42 = 0.59

PL = 22.2 s

The trend of lifetimes measured in the dips is in agreement with quantum confined PL. 760 770 780 790 800 810 820

10121416182022242628303234

lifet

ime

(mic

rose

cond

s)

Wavelength (nm)



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750 760 770 780 790 800 810

18

20

22

24

26

28

30

32

34

Peaks Dips

Life

time

(s)

Wavelength (nm)

• 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.

750 760 770 780 790 800 810

0

4

8

12

16

20

Life

time

En

ha

nce

me

nt (

%)

Wavelength (nm)

The enhancement grows with the wavelength reaching a maximum of 17 % (LE = 1.17)

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From the theoretical Purcell factor it is possible to estimate the radiative lifetime:

Prad PL

F -1τ = τ

LE-1

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.



765 770 775 780 785 790 795 800 8050

10

20

30

40

200

400

600

800

1000

tauPL

(mic

rose

cond

s)

Wavelength (nm)

Radiative lifetime

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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.



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THANK YOU FOR YOUR ATTENTION.



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(microdisk) ~ 30cm-1

0 (ellipsometer)= 32cm-1

abs = 0 +

0 25 50 75 100

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Inve

rse

Q

Pump power, mW

Experiment (= 754 nm)X10 -3

760 780 800 820 840 8600.0

2.0x103

4.0x103

Qexp

(nm)

Qtot

= 1/(Q-1

abs+Q-1

rad)

0.0

4.0x103

8.0x103

1.2x104

Qrad

760 780 800 820 840 860

4.0x103

8.0x103

Qabs


1 10 1000

500

1000

1500

2000

2500

3000

Q-f

act

or

Pump power, mW

849 nm 768 nm 754 nm

rad abs surf.scatt. surf.abs.

1 1 1 1 1= + + + +...

Q Q Q Q Qsurf.scatt. surad ab bs rf.a s.

1 1 1= +

Q Q Q

1 1+ + +...

Q Q



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2 2 2 202

1E(r)+ E(r) n (ρ,z) +k n (ρ,z)E(r)=0

n (ρ,z)

Master equation for the electric field in cylindrical coordinates

22 2 20 eff2

d Z+k (n (z)-n )Z=0

dz1.

Standard “slab waveguide equation”

22Θ

+m Θ=0

Θ( ) exp(im ) 2.

Azimuthal simmetry. m is the azimuthal mode number

2 2 22 20 2

1( ) 0eff

mk n

3. Radial disk equation:

WGM "quantum numbers": N-TEp,m

TE (TM) – quasi TE (TM) polarizationN – mode order of "slab-Z" equationp – number of antinodes of Bessel function solution of equationm – number of nodes of equation solution



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The total thickness

0.60 0.65 0.70 0.75 0.80 0.85 0.901.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

0.0

0.2

0.4

0.6

0.8

1.0

Sla

b w

g ef

fect

ive

inde

x

Wavelength (m) C

onfin

emen

t Fac

tor

() 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.

g

< >v =

<u>u��

The "average" group velocity in the real resonators are almost coincident:

• Flat disk (@ 800nm): vg = 0.4944 cng = 2.02

• Kylix (@ 800nm): vg = 0.4698 cng = 2.12



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Some corrections for non-ideal systems have been calculated in literature:

0-TE1,33

= 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.

2

2e 2c

P P 22 2c c max

E(r )ΔωF =F η

4(ω-ω ) +Δω E

��

Gerard and Gayral, J. Lightw. Tech. 17, 2089 (1999)

InAs quantum boxesconstant measured T = 100 K

The main differences in our Si-nc based system:

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