Introduction

Lanthanide-doped materials show efficient anti-Stokes luminescence1,2,3, and have been playing important roles in many frontier fields such as super-resolution imaging4,5,6, upconversion laser7, optical tweezer8, nanothermometry9,10, 3D display11, information security12, and infrared photodetctor13. Owing to the unique 4 f configurations with abundant energy levels, lanthanide ions are able to produce upconversion emissions covering broad spectral ranges with highly photostable and color-tunable properties14,15. For the sensitizer-activator codoped materials, energy transfer plays a key role in enabling upconversion, such as energy transfer upconversion (ETU)16. A typical sensitizer is Yb3+ which can absorb the excitation energy of a commercial 980 nm diode laser and then activate the nearby emitters (e.g., Er3+) through an ETU process17,18,19. In contrast, recent work suggests that energy migration between sensitizers might occur in addition to the sensitizer-to-activator energy transfer (Fig. 1a), which might impose an impact on upconversion dynamics and, in particular on emission colors. Unlike energy transfer, energy migration is able to facilitate energy transport over a long distance (Fig. 1b)20. The manipulation of energy migration among Yb sublattice can produce color-switchable emissions20,21,22,23 and tunable lifetimes across a wide range24,25. It also helps realize the NIR-II responsive upconversion26 and photon avalanche upconversion6. However, energy migration and energy transfer usually occur simultaneously, making them extremely difficult to distinguish from each other for an in-depth investigation. Also, the details of energy migration, together with its impact on upconversion dynamics are still unclear for a sensitizer-activator system27,28,29.

Fig. 1: Proposed conceptual model for energy flux investigation.
figure 1

a Schematic of the competition between energy migration and energy transfer that occur simultaneously in a common sensitizer-activator coupled system. b Comparison of energy migration among sensitizers and energy transfer from sensitizer to activator that energy migration has a long transport distance. c Schematic of proposed NaYF4:Yb/Tm@NaYF4:Yb/Er@NaYF4:Nd core-shell-shell nanostructure for probing the energy migration (Yb3+→Yb3+) and energy transfer (Yb3+→Er3+) in the Yb3+/Er3+ codoped system. S, A, EM, ET, and IET represent sensitizer, activator, energy migration, energy transfer, and interfacial energy transfer, respectively.

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Recently, nanostructure engineering has shown to be a powerful platform to manipulate ionic interactions and upconversion performance2. We recently found that interfacial energy transfer (IET) in core-shell nanostructures is an alternative way to realize upconversion emissions from a set of lanthanide ions and tune emission colors26. Moreover, it can be used to examine the lanthanide ionic interactions on the nanoscale by separately incorporating lanthanides in properly designed regions in a core-shell-based nanostructure30. We reason that a proper design of IET in core-shell nanostructures would offer new chances for investigation of energy flux at sublattice in nanoparticles, and also contribute to versatile control of upconversion properties toward frontier applications30,31. On the other hand, theoretical modeling such as Monte Carlo simulation helps an in-depth understanding of energy migration27,32,33,34,35.

Here, we describe a mechanistic strategy to examine the competition between energy transfer and energy migration involving a sensitizer-activator upconversion system by constructing an IET-mediated core-shell-shell nanostructure (Fig. 1c). The Yb/Er couple in interlayer was selected because it is a typical sensitizer-activator scheme and has intense upconversion. The Nd3+ ions were introduced into the outermost shell to harvest the 808 nm excitation energy, and the NaYF4:Yb/Tm was designed as the core for detecting the energy migration. In this design, there would exist a competition between the energy transfer (Yb3+→Er3+) and the energy migration (Yb3+→Yb3+) which would activate the core with the observation of Tm3+ upconversion. Note that only Nd3+ ions are responsive to the 808 nm excitation laser in such a nanostructure, and the emission profiles of Er3+ and Tm3+ are easily separated in the emission spectra because of their different emission peaks (Supplementary Fig. 1). Therefore, the emission intensity change of Tm3+ in the core would reflect the energy migration over the NaYF4:Yb/Er interlayer together with its competition with the energy transfer from Yb3+ to Er3+. In addition, this model is also able to realize a color-switchable emission output by spatial and temporal manipulation of upconversion dynamics and promote its frontier applications.

Results

As a proof of concept, the NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/0-2 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles were first synthesized through a chemical coprecipitation method (Fig. 2a and Supplementary Note 1), showing a monodisperse feature and hexagonal phase (Supplementary Figs. 2, 3a). The clear lattice fringes with a d-spacing of 0.51 nm together with the corresponding Fourier transform diffraction pattern (Supplementary Fig. 3b, c) obtained from high-resolution transmission electron microscopy (TEM) images indicate its single crystalline property. The core-shell-shell nanostructure was confirmed by the lanthanide distributions in the element mapping results (Supplementary Fig. 3d–i), and is also supported by the upconversion emission spectra (Supplementary Fig. 4). The synthesis of samples shows good reproducibility as evidenced by that from different batches under identical synthetic conditions (Supplementary Figs. 5, 6). Note that the ion intermixing at the core-shell interfacial region can be ignored in our samples (Supplementary Figs. 7, 8)36,37,38,39.

Fig. 2: Investigation of energy migration in a sensitizer-activator codoped system.
figure 2

a Schematic of the competition between energy migration and energy transfer in the NaYF4:Yb/Tm@NaYF4:Yb/Er@NaYF4:Nd core-shell-shell nanostructure under 808 nm excitation. The control sample structure without doping Er3+ in the interlayer is also presented. b Upconversion emission spectra of the NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/0,2 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles under 808 nm excitation. c Emission intensities of Tm3+ as a function of Er3+ concentration in the interlayer for (b) samples. d The characteristic ratio parameter (γEM) versus Er3+ concentration for (c) samples and the simulation result of a normalized number of excited Yb3+ (Nex) traveling into the core region under steady-state excitation with an energy transfer rate of 9500 s−1. The error bars are defined as the average of γEM for the 450, 475, and 695 nm emissions. e, f The measured and simulated time-dependent upconversion emission profiles of Tm3+ at 695 nm for (c) samples under pulsed 808 nm excitation. g CIE chromatic coordinates of the upconversion emissions from (c) samples. Insets show the emission photographs with Er3+ concentrations from 0 to 2 mol%. h Upconversion emission spectra of NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/0.1 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles by tuning pulse width of 808 nm laser with a frequency of 100 Hz. i Time-dependent upconversion emission profiles for (h) sample. j Schematic of a possible mechanism for the color-tunable upconversion under non-steady-state excitation. RET and NRET represent resonant and non-resonant energy transfer, respectively.

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To investigate the photophysical processes, we first carried out the steady-state upconversion research40. For the sample without doping Er3+ in the interlayer, i.e., NaYF4:Yb(20 mol%), typical upconverted emissions of Tm3+ at 450 nm (1D2 → 3F4 transition), 475 nm (1G4 → 3H6 transition) and 695 nm (3F2,3 → 3H6 transition) are clearly observed upon the 808 nm laser excitation. In contrast, for the NaYF4 interlayer without doping Yb3+, the 808 nm excitation cannot activate the Tm3+ in the core directly because of a long spatial separation between them (Supplementary Fig. 9). This confirms that there exists an efficient energy migration channel over the Yb sublattice in the interlayer that can bridge the energy transport from the outermost sensitization shell to the luminescent core. When Er3+ was codoped in the interlayer, its upconverted emissions were recorded (Fig. 2b), suggesting the occurrence of Yb3+ to Er3+ energy transfer. More importantly, with the increase of Er3+ concentration, the Tm3+ emissions show a rapid decline because partial excitation energy was blocked and transferred to Er3+ in the interlayer (Fig. 2c and Supplementary Figs. 10, 11). Note that the presence of Yb3+ in the core is used to enhance the upconversion of Tm3+ for easy detection (Supplementary Fig. 12)41,42. The energy transfer from Er3+ to Yb3+ (or Tm3+) can be ignored (Supplementary Fig. 13), and the presence of Er3+ in the interlayer has a negligible impact on Tm3+ emissions in core (Supplementary Fig. 14). As a control, the doping of only Er3+ in the interlayer (i.e., NaYF4:Er) cannot lead to the emission of Tm3+ in core (Supplementary Fig. 9). This further demonstrates the effectiveness of our design that the Tm3+ emissions are only activated via the Yb-mediated energy migration channel. These results suggest that there exists a fierce competition between energy transfer (Yb3+→Er3+) and energy migration (Yb3+→Yb3+) in the NaYF4:Yb/Er interlayer. The energy migration among sensitizers would reduce the upconversion intensity by consuming the excitation energy in a sensitizer-activator coupled system.

In order to give a quantitative description of the competition between energy migration and energy transfer, we defined a characteristic parameter γEM which is equal to the ratio of Px/P0, where Px and P0 stand for the excitation energy reaching the core from the sample doping x mol% Er3+ and the control sample without doping Er3+, respectively (Fig. 2a). Actually, typical emission bands of Tm3+ at 450, 475 and 695 nm show a monotonous decrease with increasing Er3+ concentrations in the interlayer. The decline tendency of each Tm3+ emission is different, and those from higher energy levels exhibit a more rapid quenching process (Fig. 2c and Supplementary Fig. 11)12,43,44. Here we employed the average to evaluate the energy migration ratio. As shown in Fig. 2d, the γEM value decreases from 1.0 to 0.50 with Er3+ concentration from 0 to 2.0 mol%. This is because Er3+ ions can block and absorb the energy from Yb3+ and reduce the energy migration between Yb3+ ions. The γEM value of 0.50 means that only a half of the energy can reach the core via energy migration and the other half was transferred to Er3+ during the energy transport in the NaYF4:Yb/Er(20/2 mol%) interlayer (Fig. 2d, Supplementary Fig. 15 and Supplementary Tab. 1). Note that the energy transport in NaYF4:Yb/Er(20/2 mol%) is insensitive to the excitation power, showing similar γEM values at different excitation powers (Supplementary Fig. 16 and Supplementary Tab. 1). Such IET-mediated model also works for the investigation of energy migration in Yb3+/Tm3+ coupled system by selecting suitable dopants (Supplementary Fig. 17). We further used the Monte Carlo modeling to simulate the excitation energy traveling into the core region under steady-state excitation (Supplementary Note 2, Supplementary Figs. 18–20 and Supplementary Table 2), and the results agree well with the experimental observation of γEM trends in Fig. 2d (Supplementary Fig. 21). It also predicts more rapid rise times of Tm3+ in the samples after doping Er3+ in the interlayer, which was confirmed by the time-dependent upconversion emission profiles (Fig. 2e) and time-resolved Monte Carlo simulation (Fig. 2f). This suggests that the energy transfer to activator can accelerate the energy migration among sensitizer sublattice by reducing energy hop steps, despite less energy reaching the core24,45.

As both energy migration and energy transfer are closely dependent on the concentration of Yb3+ in the interlayer, we next investigated the role of Yb3+ concentration on the competition by designing the NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20-80/2 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles. Surprisingly, the γEM value decreases from 0.50 to 0.18 with increasing the Yb3+ concentration from 20 to 80 mol%, suggesting that less energy reaches the core via the energy migration channel. This means that energy transfer occurs more easily than energy migration at higher Yb3+ concentrations (Supplementary Tab. 3 and Supplementary Fig. 22). It may be a result of the smaller Yb3+-Er3+ separation than that of Yb3+-Yb3+ at higher Yb3+ concentrations (Supplementary Tab. 4 and Supplementary Note 3). When Yb3+ concentration reaches 40 mol%, the sample shows optimal upconversion of Er3+ (Supplementary Fig. 23). Elevating Yb3+ concentrations in the interlayer can accelerate energy migration and result in a faster rise time (Supplementary Fig. 24). In this case the increase of energy migration rate is dominant in contrast to the energy migration steps in the interlayer with a fixed distance27. The influence of NaYF4:Yb/Er(20/2 mol%) interlayer thickness on the energy migration was also investigated. It is found that increasing interlayer thickness decreases the emission intensity of Tm3+ (Supplementary Figs. 25, 26) and γEM values (Supplementary Figs. 27, 28 and Supplementary Table 5), as a result of much longer energy migration pathways together with more excitation energy transferred to Er3+ in a thicker layer.

Another merit of the core-shell-shell design is the gradual color change from blue to green with increasing Er3+ concentration in the interlayer (Fig. 2g, Supplementary Table 6 and Supplementary Fig. 11). Interestingly, the Tm3+ emissions decrease gradually with reducing the pulse width of 808 nm excitation laser, showing an obvious color change from cyan to green (Fig. 2g, h; Supplementary Tab. 7). Considering the negative exponential dependence of energy transfer rate on energy mismatch, the non-resonant Yb3+ to Tm3+ energy transfer needs a longer time to populate activator than the resonant Yb3+ to Er3+ energy transfer as evidenced by the slower rise time in time-dependent upconversion emission profiles (Fig. 2i, Supplementary Fig. 29). Moreover, such color-switchable feature can also be kept by manipulating the excitation frequency because increasing frequency results in shortened excitation time interval and prolonged excitation duration (Supplementary Fig. 30)20. The possible non-steady-state upconversion mechanism is presented in Fig. 2j. These observations confirm that the energy transport channels can be precisely designed and guided in the core-shell-shell nanostructure, which is crucially important for the mechanistic understanding of upconversion dynamics.

Next, we attempted to realize the red-to-green color-switchable upconversion using this conceptual model. Here the NaYF4:Er/Tm(50/0.5 mol%) core was adopted to generate pure red emission color of Er3+ by the assistance of [4F7/2; 4I11/2] → [4F9/2; 4F9/2] cross relaxation46,47. As shown in Fig. 3a, the Er3+ in the core can be activated by the energy channels of energy migration-mediated excitation [channel I: Nd3+ → Yb3+ (in interlayer) → Er3+ (in core)] or the direct excitation via ground state absorption (4I9/2 ← 4I15/2) of Er3+ under 808 nm excitation (channel II). The doping of Nd3+ can greatly improve absorption at 808 nm and enhance upconversion intensity under 808 nm excitation (Fig. 3b, c and Supplementary Figs. 31, 32). This means that the energy channel I contributes predominately to the red emission. Note that a high concentration of Nd3+ (50 mol%) was adopted to balance the direct excitation upon the 808 nm laser22,48,49. Power-dependent upconversion of the sample indicates similar slope values for red and green emissions (Supplementary Fig. 33). This is because the light output from Er3+ ions in both core and interlayer are governed by a two-photon upconversion process under 808 nm excitation50,51. However, a tuning of Er3+ concentration in the interlayer only produced a stable red emission color (Supplementary Figs. 34, 35), which may be due to the efficient IET from Yb3+ to Er3+ at high concentrations26,52, leading to a stronger red emission from the NaYF4:Er/Tm(50/0.5 mol%) core than that of the green emission from the NaYF4:Yb/Er(20/2 mol%) interlayer (Supplementary Fig. 36). To increase the green emission intensity, a series of NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(50 mol%) core-shell-shell samples with variable interlayer thicknesses were prepared (Supplementary Fig. 37). The green emission intensity was indeed increased with lifting the interlayer thickness despite a decrease for the red emission intensity (Fig. 3d and Supplementary Fig. 38). A thicker NaYF4:Yb/Er interlayer helps block the energy reaching the core region more efficiently and generate stronger green emission light of itself. A similar color change was observed under 980 nm excitation. A thicker NaYF4:Yb/Er interlayer helps enhance green emission by increasing absorption of 980 nm laser, while a too-thick interlayer will reduce the irradiation energy reaching the core region, leading to an optimal red emission with the thickness of 7.6 nm (Supplementary Fig. 39). Therefore, the red-to-green color-switchable upconversion can be readily accessible by simply tuning the excitation wavelengths under steady-state excitation (Fig. 3e and Supplementary Fig. 40).

Fig. 3: Tuning emission colors through non-steady state excitation.
figure 3

a Schematic of two possible excitation channels (I and II) to activate Er3+ in core for the NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(50 mol%) core-shell-shell nanostructure under 808 nm excitation. EM and ET represent energy migration and energy transfer, respectively. b, c Absorption spectra of (a) sample and NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4 core-shell-shell nanoparticles and (c) their emission spectra under 808 nm excitation. d The green and red light intensity versus NaYF4:Yb/Er thicknesses for (a) samples under 808 nm excitation. e Upconversion emission spectra of (a) sample (NaYF4:Yb/Er thickness: 11.0 nm) under 1530 and 808 nm excitations, respectively. Insets show the corresponding emission photographs. f Upconversion emission spectra of (a) sample (NaYF4:Yb/Er thickness: 4.9 nm) under 808 nm pulse laser excitation (100 Hz). Insets show the corresponding emission photographs. g, h Time-dependent upconversion emission profiles of (g) Er3+ at 540 and 654 nm for (f) sample and (h) that of Er3+ at 540 nm from NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(50 mol%) core-shell nanoparticles and at 654 nm from NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb(20 mol%)@NaYF4:Nd(50 mol%) core-shell-shell nanoparticles. i Schematic of possible mechanism for the red to green color-tunable upconversion under non-steady-state excitation. CR and MPR represent cross relaxation and multi-phonon relaxation, respectively.

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More interestingly, the green emission intensity shows a relative increase as compared to that of the red one by reducing the pulse widths of the excitation laser or its frequency, showing a gradual emission color change from red to green (Fig. 3f, Supplementary Table 8 and Supplementary Fig. 41). A similar color change was observed under 980 nm pulse laser irradiation. However, the 1530 nm pulse laser only produced a stable red emission color which is only responsive to the NaYF4:Er/Tm(50/0.5 mol%) core (Supplementary Fig. 42). This temporal color change could be explained by the non-steady-state upconversion53. The additional [4F7/2; 4I11/2] → [4F9/2; 4F9/2] cross-relaxation of Er3+ ions and/or nonradiative multi-phonon relaxation (4I11/2-to-4I13/2) would cause a delay in the population of the red-emitting energy level as evidenced in the time-dependent emission profiles (Fig. 3g, h)20,42,48. Note that the control samples, without manipulating energy transport only exhibit a stable red or green emission color (Supplementary Fig. 43). A thicker NaYF4:Yb/Er(20/2 mol%) interlayer benefits the green color output under short pulse excitation (Supplementary Fig. 44). The possible non-steady-state upconversion mechanism is illustrated in Fig. 3i.

The molecular photonic logic gates present an approach to information processing based on molecules with logic operations characteristics54,55. Here, the excitation pulse and frequency-modulated upconversion luminescence help the development of logical operations56,57,58. In this design, the laser pulse width is considered as one input where 0.2 and 2.0 ms stand for logical “1” and “0”, respectively. The excitation frequency serves as another input where 100 and 2000 Hz stand for logical “1” and “0”, respectively. The combination of pulse width of excitation laser and its frequency can induce reversible spectral emissions with specific green-to-red or blue-to-green intensity ratio to produce programmable optical signals (Fig. 4a). For the NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(50 mol%) and NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/0.1 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles, the defined threshold of the spectral output is 0.6, above which represents “1” (Fig. 4b, c). This established principle can transmit letters using standard ASCII codes through Logic AND or Logic NAND operations (Fig. 4d). The binary encoding codes of “0” and “1” can be further expressed by the emission colors to deliver the information of “SCUT” and “UCNP” (Fig. 4e, f). The information cascade of the logic operations was also presented by combining AND and OR logic gates (Supplementary Fig. 45). This logic operation is easy to be visualized and more convenient to identify encrypted information than the DNA or quantum dots-based optical circuits59,60. Moreover, such multi-wavelength excitable nanomaterials can also be used in information security. As shown in Fig. 4g, the red-pattered lotus can be easily distinguished from the dazzle light by switching the excitation wavelength to 1530 nm (or 808 nm). The green leaf was further observed under 808 nm laser irradiation with reduced pulse widths.

Fig. 4: Frontier applications.
figure 4

a Schematic of programmable emission output by controlling excitation frequency and pulse width. b, c The calculated green-to-red emission intensity ratio (I540 nm / I654 nm) and blue-to-green emission intensity ratio (I475 nm / I540 nm) in NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(50 mol%) and NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/0.1 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles, respectively. d Information processing of excitation frequency inputs with the letter “S” into optical signals using Logic AND gating (left), and with the letter “U” into optical signals using Logic NAND gating (right). The measured emission intensity ratio of spectral output above 0.6 thresholds represents “1”. e, f Multiplexed data processing through inputs modulation. The strings of excitation frequency signal with the encrypted information of “SCUT” and “UCNP” are converted into visible patterns for signal output. g The pattern of the red lotus was distinguished from a dazzle light by the irradiation of 1530 and 808 nm laser. The decoded information can be further observed by tuning the excitation pulse width of the 808 nm laser. The pattern was prepared by the NaYF4:Er/Tm(50/0.5 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(50 mol%) sample and the control nanoparticles include NaYF4:Yb/Er(20/2 mol%)@NaYF4, NaYF4:Yb/Tm(30/0.5 mol%)@NaYF4, and NaYF4:Yb/Ho/Ce(20/2/10 mol%)@NaYF4.

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Discussion

In summary, we have demonstrated a conceptual model that is able to quantify the energy transfer and energy migration in nanoparticles. A fierce competition exists between energy migration among sensitizers and energy transfer from a sensitizer to an activator in the sensitizer-activator coupled upconversion system, which can be precisely manipulated by tuning the doping concentrations, interlayer thickness, and nanostructure design. The dynamic control of energy flux also provides a way to modulate emission colors, and in particular, the switchable colors from blue to green and red to green have been realized by spatial and temporal tuning of upconversion dynamics, respectively. We envision that these results help inspire new ideas for the investigation of upconversion photophysics especially at the nanoscale, and would also benefit the development of nonlinear photonic devices in data encryption and information security.

Methods

Materials

The materials including yttrium (III) acetate hydrate (99.9%), ytterbium (III) acetate hydrate (99.99%), erbium (III) acetate hydrate (99.9%), thulium(III) acetate hydrate (99.9%), holmium(III) acetate hydrate (99.9%), neodymium(III) acetate hydrate (99.9%), Y2O3 (99.99%), Yb2O3 (99.99%), Er2O3 (99.99%), Tm2O3 (99.99%), Ho2O3 (99.99%), Nd2O3 (99.99%), trifluoroacetic acid (98%), CF3COONa (98%), oleylamine (90%), oleic acid (90%), 1-octadecene (90%), sodium hydroxide (NaOH; > 98%), and ammonium fluoride (NH4F; > 98%) were all purchased from Sigma-Aldrich, and used as received unless otherwise noted.

Synthesis of nanoparticles

The nanoparticles were prepared by a co-precipitation method with some modifications. The core-shell and core-shell-shell nanoparticles were synthesized by a two-step and three-step co-precipitation epitaxial growth procedure by using the pre-synthesized core (or core-shell) nanoparticles as seeds. For instance, in the synthesis of NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/2 mol%)@NaYF4:Nd(20 mol%) core-shell-shell nanoparticles, the NaYF4:Yb/Tm(30/1 mol%) core and the NaYF4:Yb/Tm(30/1 mol%)@NaYF4:Yb/Er(20/2 mol%) core-shell nanoparticles were prepared in advance, which were then used as seeds for the following shell growth. The synthetic procedure for other control nanoparticles was identical to the above methods except for the use of different core nanoparticles as seeds and corresponding lanthanide shell precursors. The experimental details are provided in the Supplementary Information.

Characterization

Powder X-ray diffraction (XRD) data were recorded on a Philips Model PW1830 X-ray powder diffractometer with Cu Kα radiation (λ = 1.5406 Å). The TEM measurement was carried out on a JEOL JEM-1400 plus transmission electron microscope with an acceleration voltage of 120 kV. The high-resolution TEM measurement was carried out on a JEOL JEM-2100F transmission electron microscope with an acceleration voltage of 200 kV. The upconversion emission spectra were recorded by a Zolix spectrofluorometer equipped with external power-controllable laser diodes of 980, 808, and 1530 nm. The decay curves were measured using the same spectrofluorometer through the use of the pulse laser as an excitation source. The upconverting emission photographs under the excitation of 808 nm laser diodes were taken by a digital camera with a suitable optical filter. All the measurements were conducted at room temperature.

Calculation of γEM

For the sample without doping Er3+ in the interlayer, the Tm3+ in the core can be activated by the energy migration over Yb3+ ions in the interlayer under 808 nm excitation. The excitation energy from the interlayer to the core can be considered as P0. After doping Er3+ ions in the interlayer, there would exist a competition between energy migration (EM; Yb3+→Yb3+) and energy transfer (ET; Yb3+→Er3+), and only partial of the excitation energy (Px) can reach the core. For a photon upconversion process, we have

$$I\propto {P}^{n}$$
(1)

thus,

$$\frac{{I}_{x}}{{I}_{0}}={\left(\frac{{P}_{x}}{{P}_{0}}\right)}^{n}={{{\upgamma }}}_{{{\rm{EM}}}}^{n},$$
(2)

and

$${{{\upgamma }}}_{{{\rm{EM}}}}=\root{n}\of {\frac{{I}_{x}}{{I}_{0}}},$$
(3)

where I is light intensity, P is excitation power, and n is the photon number involved in an upconversion emission.

Monte Carlo simulation

The Monte Carlo simulation was carried out by the following model that the excited states of sensitizers in the upconversion system experience a three-dimensional random walk, and results in upconverted emission by the “collision” of two or more excited states. The energy transfer pathways from sensitizer (Yb3+) to activator (Er3+) in the interlayer were added in the simulation, leading to high non-radiative and radiative recombination rates from Er3+ and a decline of upconverted emission from Tm3+ in the core region. The details are provided in the Supplementary Information.