Experimental demonstration of plasmon enhanced energy transfer rate in NaYF4:Yb3+,Er3+ upconversion nanoparticles

Energy transfer upconversion (ETU) is known to be the most efficient frequency upconversion mechanism. Surface plasmon can further enhance the upconversion process, opening doors to many applications. However, ETU is a complex process involving competing transitions between multiple energy levels and it has been difficult to precisely determine the enhancement mechanisms. In this paper, we report a systematic study on the dynamics of the ETU process in NaYF4:Yb3+,Er3+ nanoparticles deposited on plasmonic nanograting structure. From the transient near-infrared photoluminescence under various excitation power densities, we observed faster energy transfer rates under stronger excitation conditions until it reached saturation where the highest internal upconversion efficiency was achieved. The experimental data were analyzed using the complete set of rate equations. The internal upconversion efficiency was found to be 56% and 36%, respectively, with and without the plasmonic nanograting. We also analyzed the transient green emission and found that it is determined by the infrared transition rate. To our knowledge, this is the first report of experimentally measured internal upconversion efficiency in plasmon enhanced upconversion material. Our work decouples the internal upconversion efficiency from the overall upconverted luminescence efficiency, allowing more targeted engineering for efficiency improvement.


Rate equation analysis of the NIR PL decay.
The NIR PL decay follows the same equation as the rise except the pumping term: During the decay process, the population of N A2 and N A1 can be approximated by single For t  min 1 W A2 ,1 W A1 { }, the normalized population of N D1 can be approximated by The total decay rate W D1,decay of NIR PL is then given as, This is exactly the same as the rise rate expressed in equation (11) in the manuscript, except for the excitation term.

Discussion on the exponential fit of the transient NIR PL
Both the NIR decay and rise are essentially non-exponential but can be approximated by single exponential functions at the very beginning. Furthermore, the NIR decay deviates from single exponential function quicker than the NIR rise does as we mentioned in the manuscript. Here, we provide a more in-depth discussion on the single exponential approximation used to fit the initial part of the transient PL in this paper.
The normalized NIR rise curve can be expressed as I rise t ( ) = 1− e −W rise t where the rise rate W rise is given by equation (10) in the manuscript (denoted as W D1 ). We reproduce it here for readability: On the other hand, the normalized NIR PL decay has the expression given in equation (2) above. The overall decay rate may be written as,  Figure S1 for the nanograting sample with an excitation power of 52 kW/cm 2 . Both the rise and decay stay close to single exponential up to a few tens of microseconds. For t > 50 µs, the decay continues to deviate from single exponential while the rise remains reasonably close to single exponential. This explains the faster deviation from single exponential we observed in NIR decay PL, and also provides the justification for our choice of rise curves to conduct the detailed analysis.

Analysis of green PL decay
The decay curves of green emission under 980 nm laser excitation are shown in Figure   S2 for the nanograting and reference samples. Again, we observe slow decay at the beginning as a result of competition between upconversion and decay. Later, all decay curves follow the intrinsic decay as shown in green line in Figure S2. The equation (13) in manuscript applies for green emission decay process as well.
We re-write it here: The description and the values of the coefficients can be found in manuscript. In the decay process, the intermediate energy level population, N D1 and N A2 , can be approximated by single exponential decay: where N D1 0 and N A2 0 are the steady state population of D1 and A2 levels at t = 0, and W D1 and W A2 are the decay rate of N D1 and N A2 respectively. The ETU term can then be written as, Substituting this expression for c d 4 N D1 N A2 into equation (7), and solving for the normalized decay expression of green emission yields, where W total is the sum of decay rates W D1 and W A2 .
The experimentally measured green decay was fitted by equation (9)

UCNP synthesis and surface modification
UCNPs were synthesized using a modified co-precipitation method 1  As shown in the transmission electron micrographs (TEM) in Fig. S3, the nanoparticles were regular hexagonal platelets, indicating the formation of β-phase NaYF 4 nanocrystals. The mean lateral size was 32 nm. The Yb 3+ and Er 3+ doping densities were 18% and 2%, respectively. We also show the high-resolution transmission electron microscopy (HRTEM) image (Hitachi HF2000, Japan) and XRD pattern of the as-synthesized β-NaYF 4 in Fig. S4 from previous report 2 .The UCNPs were of good optical quality and exhibited strong upconverted luminescence under the excitation at 980 nm. The as-synthesized UCNPs are covered with oleic acid and thus not water-soluble.
To make them water-soluble and also to make the nanoparticle surface negatively  The scale bar applies to both TEM images. Figure  S4. High-resolution TEM and x-ray diffraction of β-NaYF 4 . 2

Layer-by-Layer Deposition of UCNPs
The layer-by-layer (LBL) deposition process driven by the electrostatic interaction was carried out by using polyelectrolytes as intermediaries. We conducted a series of atomic force microscopy scans to determine the thickness of one, three and five monolayers of UCNP samples. As shown in Fig. S5, the thickness increased linearly with the number of layers. The three-layer sample, which was used in this paper, had a thickness of 90 ± 2 nm.   Figure  S7. Experimental reflectance spectra of as-fabricated nanograting (gray) and nanograting-Si 3 N 4 -UCNP structure (blue). The simulated reflectance spectra for the two structures are also plotted with red and green lines.

Temperature of UCNPs
As described in the manuscript, the UCNP temperature can be extracted from the ratio of   Figure  S10. Energy transfer rate enhancement factor calculated for a donor-acceptor pair with a pair separation of 3.4 nm placed at various distances, z, from the silver surface. ω sp and λ sp represent the surface plasmon frequency and wavelength, respectively 6 . For the present case, λ sp = 340 nm.