Phonon-assisted up-conversion photoluminescence of quantum dots

Phonon-assisted up-conversion photoluminescence can boost energy of an emission photon to be higher than that of the excitation photon by absorbing vibration energy (or phonons) of the emitter. Here, up-conversion photoluminescence power-conversion efficiency (power ratio between the emission and excitation photons) for CdSe/CdS core/shell quantum dots is observed to be beyond unity. Instead of commonly known defect-assisted up-conversion photoluminescence for colloidal quantum dots, temperature-dependent measurements and single-dot spectroscopy reveal the up-conversion photoluminescence and conventional down-conversion photoluminescence share the same electron-phonon coupled electronic states. Ultrafast spectroscopy results imply the thermalized excitons for up-conversion photoluminescence form within 200 fs, which is 100,000 times faster than the radiative recombination rate of the exciton. Results suggest that colloidal quantum dots can be exploited as efficient, stable, and cost-effective emitters for up-conversion photoluminescence in various applications.

2. To estimate emission QYs, the authors measure absorption via sampling of excitation laser powers before and after samples with a power meter. Emission, by contrast, is measured using an integrating sphere. Because absorption and emission experiments are different, there will be measurement errors when data are combined to report an emission QY. This is described below. a. In a standard QY measurement, involving an integrating sphere, excitation light is introduced into the sphere. This excitation light passes multiple times through the sample. Light is absorbed across these multiple passes. Emission then occurs and both residual excitation light and resulting emission light are measured on a spectrometer simultaneously through the sphere's output port. A differential spectrum that involves a solvent blank enables the ratio of integrated, emission-toexcitation areas to be linked to an absolute emission QY. In the author's approach, absorption is measured on a separate instrument and considers only light that passes once though the sample. When this data is used together with the integrating sphere emission data, there will be a QY overestimate. This is because the author's approach underestimates the amount of light absorbed by samples, given that only one excitation pass occurs through the sample. Mixing and matching absorption and emission experiments will therefore lead to errors. b. Continuing on this thought, there is an additional source of error in the absorption measurement that stems from emission emanating from samples. Namely, because the employed photodiode is not frequency selective, it will not distinguish emission from excitation signals. Consequently, apparent transmitted excitation powers will be larger than what is actually true given an additional emission contribution. This leads to a second underestimation of sample absorption. What likely results is a QY overestimate. c. The reviewer thus requests that the authors provide a systematic error analysis emerging from points a and b above and provide that to readers in the Supplementary Material. d. Then, to further validate the employed QY measurement approach, the authors should provide experimental data for organic dyes having known emission quantum yields. e. Finally, the authors should directly compare their emission quantum yields (obtained using the stated approach) to values obtained exclusively using an integrating sphere. Any discrepancies should be explained.
3. Next, one of the more intriguing results of the paper is evidence for a relative temperature decrease of a toluene solution of NCs via sample volumetric changes. Provided is highly processed data that the reviewer believes arises from a comparison of volumetric changes in the NC solution relative to that of a control toluene specimen. The authors suggest that because a volume difference exists between the two specimens under irradiation that relative cooling is achieved when NCs are present. The reviewer finds this result intriguing. The reviewer, however, requests that the authors provide the raw data for sample and control volumetric changes. Volume calibration data for the control specimen should also be provided. Details of how control specimen volumes were calibrated for temperature should be provided. For example, how were control specimens heated and cooled? Details of the calculations used to link spectroscopic changes to specimen emission energies (via Varshni) to overall sample volumetric changes to eventual cooling powers should likewise be provided. Details of the sample preparation should also be presented. For example, are the solvents degassed prior to insertion into capillary tubes? 4. Continuing on this thought, in Figure 4B, there is only one data point to suggest that cooling has been achieved. The reviewer requests more data be taken so that error bars can be placed on all points. The reviewer also suggests that power-and below gap wavelength-dependent measurements be done for all cooling points. 5. The reviewer requests that the authors also show data for cooling and heating timescales. In effect, show data for the kinetics of cooling. Then turn off the sub gap excitation laser and let the sample warm up. Measure the associated heating kinetics. Characteristic cooling and heating timescales should then be compared to estimated cooling/heating times, based on the system's heat capacity and heat transfer parameters. In effect, the cooling/heating timescales should make sense.
Other comments: 1. For Figure 1a, the authors should provide the high wavelength part of the spectrum to show that there are no defect-related (i.e. deep-trap like) emission contributions to the data. 2. Page 3, line 39: Reference 2 by Rumbles shows up-conversion in a dye solution. However, the reviewer is concerned that the citation is not discussed within the wider context of laser cooling. As such, the introduction is misleading. Reference 2's claim of laser cooling is now widely regarded as false because claims in this paper have not been reproduced by other groups, despite numerous attempts. The reviewer therefore suggests that the introduction to this manuscript provide readers a more nuanced view of the current state of condensed phase laser cooling. 3. Page 11, line 17: Likewise, Reference 17 by Xiong represents another controversial paper that contains concerning claims about time scales required for heat transfer at nanometer length scales. The reviewer points to a recent discussion in Nature that highlights concerns that exist over Xiong's claims. The reviewer thus again requests that the authors provide readers a more representative and nuanced view of the current state of condensed phase laser cooling. As written, the introduction is misleading and implies that laser cooling for semiconductors has been achieved when, in fact, this is still highly debated. 4. Page 9, line 168: The authors refer to References 3 and 4 for potential suggestions for how to achieve net cooling with NC samples. Suggested sample refinements include changing surface ligands and solvent. References 3 and 4 are rare earth doped glasses and crystals. There are no ligands and solvents involved. The reviewer therefore suggests that the authors modify their sentence.
Reviewer #2 (Remarks to the Author): In this work, Ye et al make core shell CdSe/ CdS QDs and compare the photoluminescence when excited at two different wavelengths, both at the single particle and ensemble level. In particular, excitation is at wavelengths above and below the absorption maxima of the nanoparticles. While excitation at energies above this maxima results in routine Stokes-shifted PL, excitation at energies below this maxima is what the authors call 'upconversion'. They argue that this upconversion PL is single phonon assisted with various temperature dependent measurements and power dependence. They also create a sophisticated QD thermometer and show a lot of data, including photon correlations of single QDs measured with CW excitation.

Reviewer #3 (Remarks to the Author):
This is a very interesting, important, and well-written manuscript which presents very welldesigned experiments and corresponding data to support its conclusions. It shows that CdSe/CdS core-shell QDs can exhibit very efficient up-conversion PL (UCPL) that does not involve photoexcitation of occupied defect states within the semiconductor "bandgap" followed by thermalactivation of the carrier-occupied defects to generate carriers at their parent band-edge, followed ultimately by radiative band-band recombination. Instead, the UCPL is shown to originate from a multi-phonon assisted absorption process across the band gap, followed by coherent carrierphonon coupling (viz. in the conduction band) to establish an energetic carrier-multiphonon distribution in the excited band (viz. conduction band), which then leads to a more energetic excited state band-band radiative transition, producing UCPL. In essence the Ground State (valence band) carrier-phonon coupled distribution is transferred by bandgap photons to the Excited State carrier-phonon distributions, and relaxation of the excited state produces upconverted photons emitted via PL. But I have two comments/questions the authors should consider in a minor revision: 1. CdSe is in its bulk a direct semiconductor requiring no phonon involvement, so why is the photoexcitation in CdSe QDs an indirect transition characterized by phonon assistance? THis should be explained. I suggest the authors look at the paper in J. Electronic Materials, 28, No5, 414-425 (1999) to find answers that may apply here. 2. The model for the UCPL described here is not clearly described in a clear diagram.  Our revision and responses: We thank the reviewer for his/her positive feedback on our work. Extensive revisions are made to address his/her concerns (see below).

Comment 1:
In the manuscript, the authors describe a three step model to explain the UCPL mechanism in CdSe/CdS NCs, in which electron-phonon coupled states assist subgap excitation (schematic diagram shown in Figure 4C These results should then be compared to obtained experimental results.

Our revision and responses:
We thank the reviewer for raising this critical issue. We shall manifest below that such large up-conversion gain can be explained by the phonon-assisted 6, 8920 (2015)), the average up-convention energy gain (∆ avg ) is the energy difference between the average PL (the PL peak for QDs) and the excitation photon ( PL peak − ex ).
While the maximum up-conversion energy gain (∆ max ) is defined as the energy difference between the highest detectable photoluminescence photon and the excitation photon ( PL max − ex ). Experimentally, we determine PL max as the photon energy where the photoluminescence intensity is 3 times the standard deviation (std DEV) of the background noise above the average background signals at the high energy side of the PL spectrum.
Apparently, ∆ max is related to the sensitivity of the detector. The above parameters and their relationship are illustrated in Fig. R1 as well as Fig. 5a in the revised main text. Specifically, in the first step (phonon-assisted absorption), a sub-bandgap photon excites a QD from electronic ground-state to the electronic excited-state with energy compensated by phonons (Fig. R1, red arrow). As the reviewer pointed out, the transition probability decreases as the number of phonons involved increases. The phonon population ( p ) of a specific mode obeys Bose-Einstein statistics, as  (2017)).
We estimate the absorption probability in Fig. R2, which qualitatively matches the lowenergy tail of the absorption spectrum. In Fig. 1a in the main text, we used a 660 nm laser to excite QDs with their 1 st exciton absorption peak at 620 nm. Therefore, phonon-assisted absorption account for the energy gain of ~120 meV contributed by ~5 LO phonons. Based on Eq. R2, the excitation transition probability at 660 nm is 6.8% of that at 620 nm. The Next, the carriers form a quasi-equilibrium distribution on the electron-phonon coupled states by interacting with phonons with relatively low energies, such as acoustic phonons.
The phonon-assisted process occurs much faster than the exciton radiative decay.
Consequently, energy of the emitted photons shall follow equilibrium distribution, some of which can be much larger than that of the bandgap by absorbing LO phonons (Fig. R1, green and blue arrows). This process accounts for the up-conversion energy gain of It is worth noting that the energy gain in phonon-assisted emission occurs in both downconversion and up-conversion photoluminescence with identical value. According to measurements here, time constants of the thermo-equilibrium processes of the excitons R6 formed by either type of excitation are sub-picoseconds (Fig. 1c). The radiative decay (lifetime in tens of nanoseconds, Supplementary Fig. 10) for either type of excitations occurs from the same thermo-equilibrium distribution of excitons. In this sense, the energy gain of phonon-assisted emission contributed to the maximum energy gain (∆ max ) is not really an "up-conversion". Conversely, the energy gain in the phonon-assisted absorption exclusively occurs in up-conversion photoluminescence. Our revision and responses: We apologize for the confusion. Actually, we applied two independent QY measurements, and we did not use a power meter for absorption and an integrating sphere for emission in one quantum yield measurement.
The absolute quantum yield of the quantum dots excited at 450 nm was determined using an integral sphere system (Fig. R3a). Both the absorption and emission were determined according to the irradiance of the light exiting from the integrating sphere. The system was calibrated with a standard light source. The accuracy and reproducibility of the system has been confirmed by measuring the quantum yields of standard dyes, e.g.

R7
The UCPL quantum yield of the quantum dots excited at 638 nm was determined using a relative method, in which absorbance was measured by a power meter and photoluminescence was measured by a spectrometer. The quantum yield of the QDs excited at 638 nm was determined by taking the quantum yield of the same sample excited at 450 nm as reference. The accuracy of this method was confirmed by measuring both the absolute and relative quantum yields ( We use a relative method to determine the UCPL quantum yield, instead of using an integrating sphere system for absolute measurements. The absorbance of the sample excited at sub-bandgap wavelength is so low that the residual excitation light is much stronger than the photoluminescence. Furthermore, in terms of spectrum recording, subbandgap excitation and emission overlap with each other heavily. These facts make it difficult to accurately determine the absolute UCPL quantum yield of the sample using an integrating sphere system. In the relative method, collecting emission signal perpendicular to the excitation light minimizes the interference of the residual excitation light. The detailed description of the measurements is stated in the revised version of Supplementary Method 2.   While for the UCPL quantum yield measurements, a relative method is used where both the excitation light at 450 and 638 nm pass the sample only once (Fig. R3b). And the detected photoluminescence only produced when the excitation light passed the sample.

R10
Therefore, there should not be an overestimation of quantum yield in our approach. Our revision and responses: As mentioned above, no power meter was involved for the absolute QY measurements. During the relative QY measurements, the power meter was placed at the path of laser and ~0.2 m away from the cuvette when measuring the laser power propagating through the sample (Fig. R3b). The active detector area has a diameter of 9.7 mm which covers a solid angle of 1.85 msr from the exciting spot. The QD solution under test has an isotropic emission, and there will be less than 0.015% of the emitted light reaching the active area of the power meter. Therefore, the underestimation of sample absorption due to contribution from sample photoluminescence is as low as 0.015% for the relative QY measurements, which can be ignored. Our revision and responses: Yes, we did so periodically to check our systems. We sphere. Any discrepancies should be explained.

Our revision and responses:
The photoluminescence quantum yield of quantum dots excited at 450 nm was obtained exclusively using an integrating sphere with uncertainty of ~0.01. The photoluminescence quantum yield of quantum dots excited at 532 nm obtained with the stated relative method is 0.98 (Supplementary Fig. 8), which is close to the value obtained exclusively using an integrating sphere (0.97, Fig. R5).  Our revision and responses: Thanks for the suggestions. We modified the main text and the Supplemental Information according to the reviewer's requests. Specifically, the raw data for sample and control volumetric changes have been added in Figure R6 (the revised Supplementary Fig. 22). Volume calibration data for the control specimen have been added in Figure R7 & R8 (the revised Supplementary Fig. 19 & 20). Details of how control specimen volumes were calibrated for temperature have been added in the revised Supplementary Method 3. More details of the sample preparation have been given in the revised Method section in the main text.
In the original manuscript, we used PL peak position of QDs to link temperature and volumetric change of the QD sample. The control specimen was not directly calibrated for temperature. However, we used the same quartz tube for both control and sample measurements and the thermal expansion properties of the control and the sample should R15 be almost identical. Hence, it is reasonable to assume the temperature-volume relationship is the same for the control and the sample.
In order to establish the temperature-volume relationship directly and more strictly in the revised manuscript, we used a temperature-controlled water-bath (Fig. R7) to calibrate the temperature-volume relation for the control specimen and QD sample, respectively. We attached a marker with sharp edges on the quartz tube to indicate the position change of the liquid level. We put control specimen or QD sample (in a capillary tube) into a water bath with designated temperatures. The temperature of water bath was monitored using a calibrated thermometer and the volume change was acquired by taking pictures using a digital camera. To minimize errors, we used the same capillary tube for both control and sample measurements. The temperature-volume calibrations for control specimen and QD sample were carried out independently. The calibration curves of control specimen and QD sample were nearly identical ( Figure R8), which is consistent with our original assumption. The calibration method using water bath gives the similar calibration result with the calibration method using PL peak position ( Figure R9). The relationship between temperature change and PL peak position (obeying Varshni's equation) is shown in Supplementary Fig. 9.
In the revised manuscript, the sections correlating the PL peak position changes with the volume changes (original Supplementary Method 3 and original Supplementary Fig. 16) are deleted. Sections on calibrating the temperature-volume relationship using the waterbath method have been added as the revised Supplementary Method 3 and the revised Supplementary Fig. 19 & 20. The sample photo was re-taken as Supplementary Fig. 18a.
The main text has also been modified accordingly (Page 9, Line 166-168).  Comment 4: Continuing on this thought, in Figure 4B, there is only one data point to suggest that cooling has been achieved. The reviewer requests more data be taken so that error bars can be placed on all points. The reviewer also suggests that power-and below gap wavelength-dependent measurements be done for all cooling points.

Our revision and responses:
We thank the reviewer for his/her critical suggestions. We     In effect, the cooling/heating timescales should make sense.

Our revision and responses:
We thank the reviewer for suggesting an insightful analysis to further strengthen scientific quality of the work. The temporal evolution of temperature during the laser was turned on/off is provided in Fig. R11(the revised Fig. 4c) and  We should emphasize that laser cooling is not the main concern of our work. We are aiming at applying up-conversion photoluminescence (as well as up-conversion electroluminescence presented in the Reviewer Only Material) in photoelectric devices, such as lighting, display, and solar cells to improve their power conversion efficiencies.
The revised figure 6 show an example of up-conversion photoluminescence applied in R26 lighting. Electronic Materials, 28, No5, 414-425 (1999) to find answers that may apply here. is forbidden due to energy conservation restriction, which helps to uncover the relatively R29 weak indirect process.

Our revision and responses
Furthermore, for quantum dots, absorption and emission of photons are mediated by excitons rather than free carriers. The momentum of excitons is not necessarily to be zero, so that one or more phonons can be needed for the conservation of momentum. Moreover, even if the momentum of excitons in quantum dots is equal to zero, excitons can still interact with phonons with zero momentum (phonons at the center of the Brillouin zone).