Rui Li Journal Club, 02.04.08 Electrical Engineering Boston University
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Transcript of Rui Li Journal Club, 02.04.08 Electrical Engineering Boston University
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Generalized rate-equation analysis of excitation exchange between silicon nanoclusters and
erbium ions
Rui LiJournal Club, 02.04.08
Electrical Engineering
Boston University
A. J. Kenyon, M. Wojdak, and I. AhmadDepartment of Electronic and Electrical Engineering, University
College LondonW. H. Loh and C. J. Oton
Optoelectronics Research Centre, University of Southampton
Physics Review B 77, 035318 (2008)
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Outline
• General form of coupled rate equations: two-level system
• Effective excitation cross section• Stretched exponential rise/decay• Complicated rate equation model
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General form of coupled rate equations: two-level systems
Si-ncs Er
* *0A B B
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Effective excitationcross section
Pacifici’s PhD thesis
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Effective excitation cross section
eff
0
1A
effA
A
is misleading? γ is more robust
001
Aeff A
A
AA
(Weak pumping condition)
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Stretched exponential rise
: 0 ~ 1
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Stretched exponential decay
•Auger nonradiative recombination.•Variations of size, shape and environment of Si-ncs.•Energy transfer between ncs.•Different decay channels (radiative and nonradiative recombinations).•Intrinsic property of Si-ncs as indirect-gap semiconductor nanocrystals.
Delerue et al. Phys. Rev. B 73, 235318 (2006)
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Two energy transfer processes?
Fujii et al. J. Appl. Phys. 95 1 (2004)
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Si-ncs in SRN decay: three effective decay parameters needed to fit the data
0 10 20 30 401E-4
1E-3
0.01
0.1
1
Experimental data of SRN decay Multiexponential decay
Time (ns)
PL
Inte
nsity
(a
rb. u
nits
)
1 D1
2 D2
3 D3
0.03 4.57
0.23 1.04
0.74 0.27
ns
ns
ns
302010 )(3
)(2
)(10
DDD xxxxxx eeeyy
We need to develop a rate equation model that includes 3 exponentials
and coupling with Er ions
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1 2 3
1 2 3
1 11 0
1
2 22 0
2
3 33 0
3
1
b b b b
b bSi nc P b
D
b bSi nc P b
D
b bSi nc P b
D
n n n n
n nt n n
t
n nt n n
t
n nt n n
t
Si-ncs population is divided into three parts nb1, nb2 and nb3 with different decay times and weighted absorption cross sections.
A rate equation modelwith 3 exponentials is sufficiently accurate
Fitting parameters:
D3D2D1321
Weighting factors
Population constraint
Donor emission
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Origin of non-single exponential rise
Inhomogeneity may from
•Coupling coefficient γ
•Si-ncs decay time τA
•Si-ncs absorption cross section σ
•Excitation photon flux Φ
Gaussian Beam
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Coupling Coefficient g
16 2 18 -2 -1 -6A
17 -3B 0i
10 cm =5 10 cm s 2 10 s
~ 10ms A 10 cm
In order to have stretched or multiexponential behavior, we need to have, for at least one class i with gi
12 3 -1~ 10 cm si
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Saturation of rise rate
1. In homogeneity
2. Up-conversion
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Experiments: Si-ncs lifetime shortening
Donor lifetime shorteningUnderlying assumption: Er does not
introduce significant non-radiative contributions
0 10 20 30 401E-4
1E-3
0.01
0.1
1
Experimental data of SRN decay Experimental data of Er:SRN decay Multiexponential decay Multiexponential decay with 2
Time (ns)
PL
Inte
nsi
ty (
arb
. un
its)
31
30
3
32
1 18 /
1 20 /
0.7 4 12
0.3
/
1 15 /
T
a
b
E cm
n E cm
N E cm
s
E cm s
A Gaussian beam is considered
Si 49%
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Conclusion
• Coupled rate equation model
• Validity of effective excitation cross section
• Stretched (multiexponential) rise/decay (inhomogeneity τA γ σ? Φ?)
• Lifetime shortening
• How complicated a simple model should we have to fit the experimental data?
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1 11 0 1 1 1
1
2 21 0 2 2 1
1
3 32 0 1 3 1
2
4 42 0 2 4 1
2
5 53 0 1
3
b ba Si nc P b b
D
b bb Si nc P b b
D
b ba Si nc P b b
D
b bb Si nc P b b
D
b ba Si nc P b
D
n nt n n n N
t
n nt n n n N
t
n nt n n n N
t
n nt n n n N
t
n nt n n
t
5 1
6 63 0 2 6 1
3
22 22 1 1 2 1 2 22
b
b bb Si nc P b b
D
Er P T a b b b up ESA PA
n N
n nt n n n N
t
N Nt N N n N n N C N t N
t
Energy coupling model with 3 “effective” decays
Si-ncs
Er
1 2 3
1 2 3 4 5 6
1
1a b
b b b b b b bn n n n n n n
• 2 coupling parameters (fast, slow)• 3 decay amplitudes
Gaussian Beam
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Thank you !