Transcript Slide 1

Use of Coupled Rate Equations to Model NIR-to-Visible Upconversion Kinetics
3+
3+
in Er , Yb :NaYF4 Nanocrystals
Robert B. Anderson1, Ge Yao2, QuocAnh N. Luu2, Mary T. Berry2, P. Stanley May2, Steve Smith1
1Nanoscience
and Nanoengineering, South Dakota School of Mines and Technology,
Rapid City, South Dakota 57701 USA
2Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069 USA
Objective
Results
The upconversion group at USD can produce very high quality Er3+,
Yb3+:NaYF4 nanocrystals. The objective for this research is to posit a rateequation model for the Er3+, Yb3+:NaYF4 system and to obtain values for the
model parameters by fitting the resulting model curves to time-resolved
photoluminescence data obtained using pulsed NIR excitation. Our most recent
measurements were taken of an Er3+, Yb3+:NaYF4 dry-powder sample at USD
using a pulsed dye laser with an excitation wavelength of 950nm at differing
pulse energies.
Examples of green (540nm), red (660nm) and NIR (1500nm) emissions
following pulsed NIR (950nm) excitation, overlaid with our simulation results.
Both data sets have been normalized to their peak value.
Green Er3+: 4S3/2, 2H11/2 →4I15/2
E-level diagram
4
F7/2
2
H11/2
S3/2
20
n6
4
4
Energy (103 cm-1)
Upconversion (UC) phosphors are able convert incident light into light of a
shorter wavelength. The (erbium) Er3+, (ytterbium) Yb3+: NaYF4 system is the
most efficient upconversion phosphor known, and yet the quantitative aspects of
the mechanism responsible for upconversion, such as the values of key
microscopic rate constants, have not been determined. In this work, the
dynamics of the photo-physical processes leading to near-infrared (NIR) to
visible upconversion in Er3+, Yb3+: NaYF4 nanocrystals are investigated using a
nonlinear rate-equation model. Following selective 950nm (NIR) pulsed
excitation of Yb3+, the population density of the excited states of the Er3+ and
Yb3+ ions are followed as a function of time. The results of these time-resolved
luminescence measurements are compared with the simulated results of our rate
equation model. Based upon the quality of the resulting fits we conclude that the
model successfully describes the upconversion process within the nanocrystals.
Rate-equation model
The rate equations describe the time-dependent populations for both the Yb3+
(n’1, n’2) and Er3+ (n1, n2, n3, n5, n6) ionic levels. The state labels correspond to
those in the energy-level diagram.
'
'
'
'
'
'
n2'  Fn1'  kYb n2'  k ET 1n1n2'  k ET
n
n

k
n
n

k
n
n

k
n
n
1 3 1
ET 2 2 2
ET 2 5 1
ET 3 3 2
15
F9/2
n5
4
10
4
4
5
kET3
I9/2
I11/2
n3
I13/2
n2
0
4
nanocrystals in PMMA
excited by an (invisible) 950nm NIR laser.
Image taken at USD upconversion lab.
NIR frustrated total internal reflection
illumination of Er3+, Yb3+:NaYF4 nanocrystals
in PMMA, spin-coated on glass slides. Image
taken at SDSMT ultrafast spectroscopy lab.
Red Er3+: 4F9/2 → 4I15/2
E-level diagram
Mechanism of NIR-to-Visible Upconversion
Upconversion (UC) refers to nonlinear optical processes characterized by the
consecutive absorption of two or more pump photons via intermediate long-lived
energy states followed by emission at a wavelength shorter than the pump
wavelength.
Er3+,
Yb3+:
Referring to the diagram below, for the
NaYF4 upconversion
phosphor, NIR excitation light is absorbed by Yb3+ via the 2F7/2→2F5/2 transition.
Electronic excitation energy is then non-radiatively transferred from Yb3+ (2F5/2)
to Er3+ (4I15/2) (labeled below as kET1). A subsequent energy transfer from Yb3+(
2F
3+ (4I
3+ to the 4S , 2H
)
to
Er
)
ions
further
promotes
Er
5/2
11/2
3/2
11/2 excited-state
manifold, from which green UC emission (Er3+: 4S3/2, 2H11/2 →4I15/2) occurs
centered near 540 nm.
Red UC emission, corresponding to the Er3+: 4F9/2 → 4I15/2, centered near 660
nm, can occur either following Er3+: 4S3/2, 2H11/2 →4F9/2 relaxation or via a
separate feeding mechanism involving Er3+( 4I11/2) → Er3+ ( 4I13/2) relaxation
followed by Yb3+ (2F5/2), Er3+ (4I13/2) →Yb3+ (2F7/2), Er3+ (4F9/2) energy transfer.
Yb3+ and Er3+ energy level diagram
4
F7/2
2
H11/2
S3/2
20
n n  0.06k R1n6  0.05k R 2 n5  k R 3  k NR 2 n3  k
'
'
ET 1 3 1
nn k
'
ET 1 1 2
n5
4
n n  kCR n1n6
'
ET 3 3 2
4
'
'
n2  k NR 2 n3  0.28k R1n6  0.05k R 2 n5  0.19k R 3 n3  k n2 n2  k ET 2 n2 n2'  k ET
n
n
2 5 1  k CR n1n6
n1  0.66k R1n6  0.90k R 2 n5  0.81k R 3 n3  k n2 n2  k
n n  kCR n1n6
15
4
10
F9/2
n5
I9/2
4
n6
kNR1
kR2
I11/2
n3
2
n2 '
F5/2
kET2
'
'
ET 1 3 1
4
5
I13/2
n2
Simulation
kYb
To fit the model parameters to the experimental data we developed a custom
simulation. This simulation consists of two parts: a numerical integration to
generate a system time-evolution from the rate equation model, and a nonlinear
optimal fitting routine that adjusts our model parameters in search of the best fit
for the experimental data. Our method for the nonlinear fitting is known as the
“Nelder-Mead nonlinear simplex method”. This method was selected for its
simple implementation and its lack of a need for the calculation of gradients.
Nelder-Mead Nonlinear Simplex
Minimization
xL
The Nelder-Mead technique is a direct search
method of optimization based upon a simple
heuristic: within a collection of points move away
from the least optimal point. So, in our Ndimensional parameter space we form an N+1 x
H
point “simplex” (triangle), find the “cost” of each
point and proceed to move away from least optimal
point through the centroid of the remaining points.
We then proceed in evolving the simplex based
upon the comparison of our new point with our
remaining points and repeating.
0
4
Yb3+
1500nm (NIR) Er3+: 4F13/2 → 4I15/2
E-level diagram
4
F7/2
2
H11/2
S3/2
20
n2
4
4
15
n6
F9/2
n5
kR1
4
10
I9/2
4
I11/2
kR2
n3
kR3
0
I13/2
4
2
n2 '
F5/2
kET2
kNR2
n2
kn2
contracted
reflected
centroid
F7/2
'
'
n 5  k NR1 n6  k ET 2 n 2 n 2'  k ET
2 n5 n1  k R 2 n5
4
extended
2
n1'
n1
I15/2
Er3+
5
kYb
kCR
n1
I15/2
Er3+
2
n1 '
F7/2
Yb3+
'
'
n 2  k NR 2 n3  0.28k R1 n6  0.05k R 2 n5  0.19k R 3 n3  k n2 n2  k ET 2 n2 n2'  k ET
2 n5 n1  k CR n1 n6
Conclusion and Future
xNH
Comparison
The cost or figure of merit uses two types of data:
1) the peak-normalized photoluminescence decay curves collected from three observable Er3+
emissions (centered near 540nm, 660nm, and 1500nm) and one emission common to both
Er3+ and Yb3+ ( near 1000nm)
2) the ratios of the integrated intensities from each of the emission peaks.
 Average the sum of the squares of the pointby-point differences between the experimental
and simulated decay-curves. Do this for all
the experimental decay curves.
 Compute the “ratio of ratios” for each of the
integrated intensity ratios.
 Simply add all the individual costs together for
our final fitting cost.
F7/2
Yb3+
Er
Energy (103 cm-1)
Yb3+:NaYF4
2
n1 '
n1
I15/2
3+
Energy (103 cm-1)
Er3+,
F5/2
kYb
'
'
n5  k NR1n6  k ET 2 n2 n2'  k ET
n
n
2 5 1  k R 2 n5
n n k
2
n2 '
n 6  k ET 3 n3 n 2'  k NR1  k R1 n6  k CR n1 n6
n6  k ET 3 n3n2'  k NR1  k R1 n6  kCR n1n6
n3  k
kCR
kR1
n1'  n2'
'
ET 1 1 2
n6
kNR1
N


1
1
   2 yˆ j  y(t j ) 2
N j 1 
2
dc

sim
ndenom
2

 ii  1  n sim
numer

sim
ndenom

sim
nnumer




2
2
total
  dc2   ii2
 The rate-equation model successfully describes the UC process in Er3+, Yb3+:
NaYF4 nanocrystals. We are getting good qualitative agreement with our
experimental data and the resulting rate constants are consistent with the
literature.
 In the future, we wish to study enhanced upconversion on engineered metal
substrates. With the capability to do good model fits, we will better
understand which rates within the model are modified by the metal surface.
References
Cuikun Lin, Mary T. Berry, Robert Anderson, Steve Smith, and P. Stanley May, “Highly Luminescent NIR-to-Visible
Upconversion Thin Films and Monoliths Requiring No High-Temperature Treatment”. Chemistry of Materials 21, 3406
(2009).
John A. Nelder, R. Mead, “A simplex method for function minimization”. Computer Journal 7, 308-313 (1965).
J.F. Suyver, J. Grimm, M.K. van Veen, D. Biner, K.W. Kramer, H.U. Gudel, “Upconversion spectroscopy and properties of
NaYF4 doped with Er3+, Tm3+ and/or Yb3+”. Journal of Luminescence 117, 1-12 (2006).
J.N. Demas, “Excited State Lifetime Measurements”. Academic Press, Inc. (1983).