1. Introduction

Photon down-conversion is an effective method for generating the light of a new color, particularly when the fabrication of a high-efficiency light emitter for this color is difficult [1,2]. As an example, for yellow light generation, it is usually difficult to use either InGaN or AlGaInP material system for achieving a high emission efficiency [3,4]. Yellow light generation based on a color conversion process through colloidal quantum dots (QDs) can be a useful approach to achieve a higher emission efficiency. Color conversion is also useful for implementing the arrayed pixels of different emitting colors in display application [5,6]. Green- and red-emitting QDs can be placed in different pixels on a blue-emitting LED base to convert blue light into the designated colors. A color conversion process is realized through the acceptor absorption of the emitted photons from the donor and then the emission of the acceptor. However, the color conversion efficiency of such a far-field process is limited by the absorption cross section of the acceptor. If the distance between the donor and acceptor can be reduced to a scale of tens nm, the acceptor can absorb the energy of the strong near field produced by the donor, resulting in a higher absorption efficiency and hence a more effective color conversion process. With the development of the nano-process technology, such a near-field interaction, known as the Förster resonance energy transfer (FRET) [7–11], becomes feasible for color conversion application.

To implement an nm-scale distance between a donor and an acceptor, the insertion of the donor and/or acceptor into a nanoscale cavity is an attractive method. When a quantum well (QW) in an LED serves as the donor in an energy transfer process, surface nano-holes can be fabricated to penetrate through the QW structure for inserting color-converting QDs such that the distance between an inserted QD and the portion of the QW near the nano-hole sidewall is small for producing FRET and hence enhancing color conversion [12–17]. In such an implementation, the FRET effect has been claimed typically based on the observations of a higher color conversion efficiency and a shorter (longer) photoluminescence (PL) decay time of the donor (acceptor) emission, when compared with a reference sample of overlaying QDs onto a planar-surface LED. These observations are interpreted simply as the results of the short distance between the QDs in the nano-holes and the QW. However, such an interpretation oversimplifies the near-field interactions in such a nanoscale-cavity structure. Other important mechanisms exist in such a surface nano-hole with inserted QDs and nearby QWs for enhancing color conversion. The understanding of such mechanisms will help us in developing novel techniques for further improving the color conversion efficiency.

In this paper, we elucidate an important mechanism not mentioned before, i.e., the nanoscale-cavity effect, in such a surface nano-hole structure through the implementation of a surface nano-hole LED, the measurement of time-resolved PL (TRPL), and a numerical simulation study. This nanoscale-cavity effect shows a near field behavior and is different from that caused by the cavity resonance of a far field. More precisely, in an FRET process, the acceptor absorbs the near-field energy of the donor, whose distribution is affected by the nano-hole structure. Also, the emission behavior of the acceptor is influenced by the nano-hole structure. Therefore, the FRET efficiency can be enhanced through the nanoscale-cavity effect. In this paper, first, we fabricate a blue-emitting LED with a surface nano-hole array on its p-type mesa for inserting a photoresist solution, which contains red-emitting QDs, to show an enhanced color conversion efficiency and a higher modulation bandwidth, when compared to a reference LED sample of a planar p-type mesa overlaid with the photoresist solution. The cause for the enhanced color conversion efficiency is studied with the TRPL measurements of two nano-hole samples, including one with and another without the QW structure. The results indicate that by confining QDs inside the nano-holes in the sample without QW, the emission efficiency of the QDs can be enhanced. In other words, without FRET, QD emission can already be significantly enhanced through the nanoscale-cavity effect. Therefore, in a nano-hole sample with QWs, the observed FRET can be enhanced via this nanoscale-cavity effect. A numerical simulation study is undertaken to confirm the enhanced emission and FRET through the nanoscale-cavity effect. In particular, the FRET efficiency can be significantly enhanced when the donor dipole, which represents a QW oscillator, is oriented perpendicular to a nano-hole sidewall.

From the viewpoint of understanding the physical mechanism for the observed enhanced color conversion behavior in a surface nano-hole structure, in this paper we elucidate a key mechanism not been discovered before, i.e., the nanoscale-cavity effect. The discovery of this mechanism is important for further designing color conversion devices with nanoscale cavity structures. From the viewpoint of further improving an LED with surface nano-holes for color conversion application, in this paper we introduce the technique of immersing QDs in a photoresist for patterning the QD distribution on an LED. This technique can be used not only for controlling the lateral distribution of QD, but also for minimizing the environmental effect on a QD such that its non-radiated recombination caused by surface states does not increase when it is inserted into a nano-hole. In section 2 of this paper, the fabrication conditions and procedures of the LED samples are described. The LED performances, including the emission behaviors of the QWs and QDs, and the modulation bandwidths are reported in section 3. The TRPL study data are presented and discussed in section 4. The numerical study results are demonstrated and interpreted in section 5. Further discussions about the experimental data are given in section 6. Finally, conclusions are drawn in section 7.

2. LED device fabrication conditions and procedures

To understand the color-conversion performance of an LED with red-emitting QDs inserted into a nanoscale cavity, we prepare a blue-emitting LED sample with a nano-hole array on its p-type mesa surface. In this LED sample, a photoresist solution containing red-emitting colloidal QDs is inserted into the holes. For comparison, another LED sample without nano-hole is fabricated by overlaying the device with the photoresist solution. The technique of immersing QDs in the photoresist for applying to the samples, which was not used for a surface nano-hole LED before, has three advantages for our study. First, the environmental conditions of the QDs in different samples can be controlled to be the same such that the non-radiative recombination process of the QDs is fixed for us to compare the radiative recombination processes among different samples. Second, a photolithography technique can be used for patterning the spatial QD distribution on an LED sample. Third, the photoresist solution can fill up the surface nano-holes such that the QD distribution among different nano-holes is uniform. Figure 1(a1) schematically illustrates the LED structure before surface nano-hole fabrication or photoresist solution application. Such an as-grown LED structure for fabricating the LED sample without (with) a nano-hole array is designated as samples I (II). Figure 1(b1) schematically illustrates the LED structure after nano-hole fabrication based on sample II, which is designated as sample II-H. Here, the etching for forming those nano-holes penetrates through the whole blue-emitting QW structure (denoted by “QWs” in the figures). The used LED epitaxial structure was grown on patterned c-plane sapphire substrate and was provided by Epistar Optoelectronics Corporation, Hsinchu, Taiwan. Its emission peak wavelength is 448 nm. The internal quantum efficiency of the QWs is calibrated based on temperature-dependent PL measurement to give a number slightly higher than 80% [18]. The total thickness of the p-type layers is larger than 120 nm. The photoresist solution of QD is applied to LED samples I and II-H to give samples I-Q and II-H-Q, respectively, with their structures schematically illustrated in Figs. 1(a2) and 1(b2), respectively. Here, the red filled circles stand for red-emitting QDs embedded in the solidified photoresist. Before solidification, the photoresist solution can flow into the patterned nano-holes.

 

Fig. 1. (a1) Schematic illustration of the structure of LED samples I and II [(b1) sample II-H]. (a2) Schematic illustration of the structure of LED sample I-Q [(b2) II-H-Q] after the application of the photoresist solution of QD.

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The used CdZnSeS/ZnS QDs are purchased from Taiwan Nanocrystals Inc. Hsinchu, Taiwan. The QDs are capped with an amphiphilic polymer, i.e., poly(isobutylene-alt-maleic anhydride), and hence is negatively charged with zeta potentials at -25.6 mV [19]. Their emission peak wavelength is 625 nm. The amphiphilic polymer capped QD is a sphere-like particle of 8-10 nm in size. To immerse QDs in the photoresist, which is SU-8, the water solvent of QDs is replaced first by ethanol and then by propylene glycol methyl ether acetate (PGMEA) through centrifugations [20,21]. QDs can be uniformly dispersed in a PGMEA solution after sonication. For forming the photoresist solution with QDs, we mix 50-mL PGMEA solution of QDs with 380-mg photoresist of SU-8 and stir the mixer through sonication. The QD concentration in the photoresist solution is estimated to be 5 wt%. To deposit an SU-8 solution onto an LED sample in designated surface regions, a drop of the SU-8 solution of ∼30 µL in volume is applied to the LED sample of 1 cm x 1 cm in size, which contains 80 LED devices, followed by a spin process of 300 rpm for 30 sec. Then, the sample is baked first at 65 °C for 20 min and then at 95 °C for 40 min. Next, a mask aligner is used to expose the photoresist with 10 mW/cm² in UV intensity for 180 sec. After that, we bake the sample again first at 65 °C for 1 min and then at 95 °C for 4 min. Finally, the sample is immersed in the developer solution for 6 min to remove the unwanted portions of photoresist, including the immersed QDs.

The surface nano-hole array is fabricated after the process of an LED device is completed. To fabricate a surface nano-hole array on the LED mesa, a SiO₂ layer and a photoresist (mr-6000E) layer are first coated onto the sample surface. Then, a nano-imprint stamp is used to press the sample for forming a triangular nano-hole array on the mr-6000E photoresist layer of 180 nm in hole diameter and 380 nm in hole spacing (center-to-center). Next, reactive ion etching (RIE) processes with O₂ (for 5 min) and ChF₃ (for 3 min) plasma as etchants are applied to the layers of photoresist and SiO₂, respectively, for forming a hole array on these two layers. The mr-6000E photoresist is then removed with RIE again by using O₂ plasma as etchant for 20 min. The remaining SiO₂ pattern is used as the mask for etching the p-type layers, the QW structure, and part of the n-type layer in an LED sample with inductively coupled plasma RIE (ICP-RIE) and wet etching (with AZ400K). In the ICP-RIE process, Cl₂ and Ar plasma are used as etchants for 60 sec to fabricate nano-holes. Also, the AZ400K wet etching lasts for 7 min at the temperature of 80 °C to remove the damaged material on the nano-hole sidewall produced by ICP-RIE and make the sidewall smooth. Finally, the dipping of buffered oxide etchant for 1 min at room temperature is undertaken for removing the SiO₂ mask to give us an LED sample with a surface nano-hole array. Figure 2(a) shows the planar SEM image of an LED structure after a nano-hole array is fabricated on its p-type mesa surface (before photoresist solution application). Here, the dashed pink square marks the area of the p-type mesa of 300 µm in size. Also, the dashed green square indicates the outer-boundary of the lower n-type mesa for fabricating square-ring-shaped n-electrode. Meanwhile, the dashed yellow square shows the outer-boundary of the square-ring-shaped p-electrode for spreading injected current. The p-electrode also includes the central circular area and the connecting cross-shaped pattern. The nano-holes are fabricated in the four areas surrounded by the p-electrode circuit. The SEM image by magnifying the area circled by the red rectangle in Fig. 2(a) is shown in Fig. 2(b). Here, we can see that the planar dimension of a hexagonal-shaped hole is around 215 nm. Figure 2(c) demonstrates the cross-sectional SEM image of a nano-hole array to show that the depth of the nano-holes is around 340 nm. This depth is larger than the total thickness of the QW structure plus all the p-type layers in the used LED epitaxial sample. Figure 2(d) shows a cross-sectional SEM image of the nano-hole array after it is overlaid with the solidified photoresist solution of QD. Here, the blurred image of the nano-holes implies that the photoresist solution is indeed inserted into those holes. The inserted QDs are too small to be seen in such an SEM image.

 

Fig. 2. (a) Plane-view SEM image showing the planar layout of an LED structure with surface nano-holes on the p-type mesa. The yellow, pink, and green dashed squares indicate the outer boundaries of the p-electrode, p-type mesa, and n-type mesa, respectively. (b) Plane-view SEM image showing the nano-hole array within the area circled by the red rectangle in part (a). (c) Cross-sectional SEM image showing the nano-hole geometry. (d) Cross-sectional SEM image showing the structure after the photoresist solution is inserted into the nano-holes.

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3. LED characterization results

Figure 3(a1) shows the electroluminescence (EL) spectra of sample I with injected current increased from 1 through 100 mA. The spectral peak is slightly blue-shifted when injected current increases due to the carrier screening of the quantum-confined Stark effect. The insert of Fig. 3(a1) shows the photograph of lit LED sample I at 100 mA in injected current. Figure 3(a2) shows the EL spectra of sample I-Q at various injected current levels. With the applied QDs, the red component in an EL spectrum appears with its intensity significantly higher than the corresponding blue component. The insert of Fig. 3(a2) shows the photograph of lit LED sample I-Q at 100 mA in injected current. Figures 3(b1) and 3(b2) show the results of samples II and II-H-Q, respectively, similar to those of samples I and I-Q in Figs. 3(a1) and 3(a2), respectively. The relative intensities of the red and blue components in those two samples with QDs are quite different, as to be discussed later.

 

Fig. 3. (a1) EL spectra of sample I at 1-100 mA in injected current. The insert shows the photograph of the lit LED of sample I at 100 mA in injected current. (b1), (a2), (b2) Results of samples II, I-Q, and II-H-Q, respectively, similar to those in part (a1) for sample I.

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Figure 4 shows the variations of the normalized EL intensity with injected current of samples I, I-Q, II, II-H, and II-H-Q. An EL intensity is obtained by integrating over the whole spectrum, including the red and blue components. Here, the curves for samples I and I-Q are normalized with respect to the EL intensity of sample I at the injected current of 100 mA. Similarly, the results for samples II, II-H, and II-H-Q are normalized with respect to the EL intensity of sample II at the injected current of 100 mA. Here, one can see that after the application of the photoresist solution of QD onto the top surface, the EL intensities are reduced. After photon down-conversion, the overall EL intensity is naturally decreased because of the photon energy loss in converting blue light into red. The EL intensity of sample II-H is higher than that of sample II due to the stronger light extraction caused by nano-hole scattering and other mechanisms to be discussed later, even though part of QW emission volume is etched. Figure 5 shows the variations of injected current with applied voltage (I-V curves) in samples II, II-H, and II-H-Q. Here, we can see that the turn-on voltage is essentially unchanged after the nano-holes are fabricated and then the photoresist solution of QD is applied to the LED device. However, the differential resistance is increased from 26 to 33.6 Ω after the nano-holes are fabricated, but then slightly reduced to 32.4 Ω after the photoresist solution of QD is applied. Such an increase of device resistance is mainly caused by the degradation of current spreading after the nano-holes are fabricated. The insert of Fig. 5 shows the I-V curves in the range of reverse applied voltage for the three samples. Here, we can see that after nano-hole fabrication and photoresist solution application, the produced current leakages are small, always at the level of 10⁻⁷ mA. Although the etching process for fabricating nano-holes can produce material damage on the sidewall, the small current leakage implies that the effect of the surface defects caused by the material damage is weak.

 

Fig. 4. Normalized EL intensities of the LED samples under study versus injected current. The results of samples I and I-Q (II, II-H, II-H-Q) are normalized with respect to the intensity of sample I (II) at 100 mA in injected current.

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Fig. 5. I-V curves of samples II, II-H, and II-H-Q. The insert shows the I-V curve portion in the range of reverse applied voltage for the three samples.

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With the left ordinate, Fig. 6 shows the ratios of the integrated intensity of the red component over that of the blue component (R/B ratio) in samples I-Q and II-H-Q. Here, in increasing injected current, either R/B ratio curve rises first to reach a maximum at 70 mA and then slightly descends. The R/B ratio of sample II-H-Q is significantly higher than that of sample I-Q implying that the color conversion is enhanced by inserting QDs into the nano-holes. Such a behavior has been attributed to the FRET from the QWs into QDs because those QDs inside a nano-hole become close to the QWs in an LED sample [12–17]. However, as to be explained below, another important mechanism exists to enhance color conversion. With the right ordinate, Fig. 6 also shows the enhancement factor of the R/B ratio of sample II-H-Q with respect to that of sample I-Q. In row 2 (3) of Table 1, we compare the normalized EL intensity (R/B intensity ratio) at 100 mA in injected current between samples I-Q and II-H-Q. One can see that for either parameter, that of sample II-H-Q is higher than that of sample I-Q. The numbers inside the parentheses in Table 1 show their increment percentages.

 

Fig. 6. Left ordinate: Ratios of the integrated red intensity over the integrated blue intensity (R/B ratios) of samples I-Q and II-H-Q as functions of injected current. Right ordinate: Enhancement factor of the R/B ratio of sample II-H-Q with respect to that of sample I-Q.

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Table 1. Key results of LED performances and TRPL measurements

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We also measure the modulation responses of the emitted blue and red lights of LED samples I-Q and II-H-Q. Figure 7 shows the modulated signal intensities as functions of modulation frequency of their emitted blue, red, and mixed lights. The modulation bandwidths, which are defined as the modulation frequencies leading to the signal intensity -3 dB below the low- frequency level, of those emitted color components are shown in row 4 of Table 1. Here, the three numbers between slashes correspond to the modulation bandwidths of blue, red, and mixed lights. One can see that the modulation bandwidth of either blue, red, or mixed light of sample II-H-Q is higher than the corresponding value of sample I-Q. The nanoscale-cavity effect can increase the LED modulation bandwidth.

 

Fig. 7. Modulation signal intensities of the blue, red, and mixed lights of samples I-Q and II-H-Q versus modulation frequency.

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4. Time-resolved photoluminescence studies

To demonstrate the nanoscale-cavity effect in sample II-H-Q, a TRPL study is undertaken. Because of the mesa fabrication and electrode coverage, it is difficult to obtain a strong enough TRPL signal from either sample I-Q or II-H-Q. For the TRPL measurement, without mesa fabrication or electrode deposition, samples “Q (LED)” and “H-Q (LED)” are prepared by overlaying the same LED epitaxial structure with the photoresist solution of QD on a planar top surface and a surface with a nano-hole array, respectively. Meanwhile, similar samples on un-doped GaN templates are fabricated to give samples “Q (GaN)” and “H-Q (GaN)”. In these two samples, no QW structure exists. To clearly identify the nanoscale-cavity effect on QD emission, we clean the photoresist solution on the top surfaces, i.e., the portion of the photoresist solution not inserted into the nano-holes, in samples H-Q (LED) and H-Q (GaN) by sweeping the surfaces with wet cotton swabs before photoresist solidification. The clean condition on a surface is examined with SEM observation. Therefore, in these two nano-hole samples, the observed TRPL behaviors completely originate from the QDs inside the nano-holes. The TRPL measurement is excited by the second-harmonic (390 nm in wavelength and 1.5 mW in average power) of a femtosecond Ti:sapphire laser of 76 MHz in pulse repetition frequency. The signal is monitored by a photon counter of 2.5 ps in temporal resolution. Figure 8 shows the PL decay profiles of the QW emissions of samples Q (LED) and H-Q (LED) and the QD emissions of all those four samples prepared for TRPL study. Here, we can see that the decay rate of the QW emission of sample H-Q (LED) is higher than that of sample Q (LED). However, the decay rate of the QD emission of sample H-Q (LED) is significantly lower than that of sample Q (LED). On the other hand, the QD PL decay rate of sample H-Q (GaN) is higher than that of sample Q (GaN). In rows 5-7 of Table 1, we show the PL decay times of the QW and QD emissions in those samples for TRPL study. Here, we can see that the variations of decay time are consistent with what mentioned above about PL decay rate. The different QD PL decay behaviors between the samples based on the LED epitaxial structure and GaN template are caused by the FRET process in the samples based on the LED epitaxial structure. No FRET can occur in the samples based on the GaN template. The significantly shorter QD PL decay time in sample H-Q (GaN), when compared with that in sample Q (GaN), confirms the nanoscale-cavity effect on the QD emission efficiency. Detailed discussions about this issue will be given in section 6. It is noted that the calibration for a PL decay time is based on the decay-profile fitting with an extended-exponential model [22]. Because of the low decay rates in those samples, at the end of a pulse repetition period (∼13.16 ns) of the excitation laser, the PL intensity is still quite strong. In other words, the PL intensity does not decay to a negligible level before the next excitation pulse arrives. To accurately calibrate the decay time, we superpose the delayed components of the real PL decay profile, which is to be calibrated, by different periods of 13.16 ns for fitting a measured PL decay profile.

 

Fig. 8. Time-resolved PL decay profiles of the QW and QD emissions in samples Q (LED) and H-Q (LED), and the QD emissions in samples Q (GaN) and H-Q (GaN).

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5. Simulation results

To further understand the nanoscale-cavity effects on the QD emission behavior and the FRET process from a QW into a QD inside a nano-hole, a numerical simulation study on the structure schematically shown in Fig. 9(a) is undertaken. In this structure, a QD (represented by the red filled circle), which serves as the acceptor in the FRET process, is located inside a cylindrical nano-hole fabricated on a GaN QW template (refractive index n₂). The nano-hole is filled with the photoresist of n₁ in refractive index. The depth and cross-sectional diameter of the nano-hole are d and b, respectively. The depth of the QD position is a. Right to the nano-hole, a radiating dipole, which is denoted by an arrow, for representing a QW is located at the same depth as that of the QD inside the nano-hole. This radiating dipole serves as the donor in the FRET process. The distances from the nano-hole sidewall to the donor and acceptor are s and t, respectively. For comparison, the structure of a reference sample is schematically shown in Fig. 9(b), in which a GaN QW template is overlaid with a thick layer of photoresist. The position of the QD-acceptor is vertically aligned with that of the dipole-donor. The distances from the photoresist/GaN interface to the donor and acceptor are s and t, respectively. The method for numerical simulation has been introduced in our previous publications [23,24]. To evaluate the radiation behavior of a dipole, we first compute its radiated electromagnetic field when it is placed in a homogeneous spherical background space. Then, the total field is evaluated in the real structure for simulation based on the commercial software of COMSOL. By subtracting the radiated field of the dipole from the total field, we obtain the scattered field, which is used for evaluating the feedback effect on the dipole radiation behavior from the surrounding structure. With the available scattered field, the optical Bloch equations are solved to give the strength and orientation of the dipole modified by the feedback effect. From the modified dipole, the final electromagnetic field distribution and the total radiated power can be numerically computed. With the feedback process, the effect of the scattered field caused by the nanoscale cavity on the radiation behavior of the dipole is included. In other words, the Purcell effect is practically taken into account [25].

 

Fig. 9. (a) Schematic illustration for the simulation structure of a photoresist-filled surface nano-hole on a QW template with an inserted QD-acceptor and a dipole-donor representing a portion of a QW outside the nano-hole. (b) Schematic illustration for the simulation reference structure of a planar surface with the dipole-donor and QD-acceptor embedded in the layers of n₂ (GaN) and n₁ (photoresist) in refractive index.

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For numerical computations, the geometric parameters in Figs. 9(a) and 9(b) are set at d = 300 nm, b = 200 nm, a = 150 nm, and t = s = 30 nm. Also, n₁ and n₂ are assumed to be 1.577 and 2.399, respectively. In Fig. 10, we show the spectra of the normalized field intensity produced by the donor at the acceptor position and the normalized radiated power produced by the acceptor for the structure shown in Fig. 9(a). They are normalized with respect to their counterparts in the reference structure shown in Fig. 9(b). In other words, the results of the field intensity and radiated power shown in Fig. 10 represent their enhancement ratios in comparing the nano-hole structure in Fig. 9(a) with the planar structure in Fig. 9(b). In Fig. 10, two planar polarization conditions for the QW donor are considered. Actually, the results of the x- and y-dipole in the reference structure shown in Fig. 9(b) are the same. It is noted that the orientation of the x-dipole in the structure of Fig. 9(a) is perpendicular to the photoresist/GaN interface and hence its emission behavior is similar to that of the z-dipole in the structure of Fig. 9(b). However, since z-dipole does not exist in an InGaN/GaN QW, the comparison between the case of x-dipole in the nano-hole structure and the z-dipole case in the planar structure does not have any physical meaning in practice. Therefore, we use the results of x-dipole in the planar structure for normalizing those of x-dipole in the nano-hole structure. In Fig. 10, one can see that the field intensity at the acceptor position produced by the x-dipole donor is generally stronger than that produced by the y-dipole donor. In particular, their difference on the long-wavelength side is quite large. Above 385 nm, the normalized field intensity in either polarization is larger than unity, indicating the relatively stronger near field distribution inside the nano-hole produced by a nearby QW portion. The normalized radiated power of the acceptor inside the nano-hole is also enhanced in either polarization. This result is consistent with the variation of QD decay time shown in the bottom row of Table 1. The emission of a QD inside a nano-hole is enhanced through the nanoscale-cavity effect. The FRET efficiency relies on (1) the acceptor absorption of the near field energy produced by the donor and (2) the acceptor emission efficiency. The former is proportional to the near field intensity at the acceptor position if the absorption cross section of the acceptor is not influenced by its surrounding structure. Therefore, the enhancement factor of FRET efficiency can be evaluated by multiplying the aforementioned normalized intensity at the donor emission wavelength (450 nm) by the normalized radiated power at the acceptor emission wavelength (625 nm). The results are summarized in Table 2. Here, in the case of x-dipole (y-dipole), the absorption and emission of the acceptor in the nano-hole structure are enhanced by the factors of 1.46 (1.21) and 1.68 (1.64), respectively, leading to an FRET enhancement factor of 2.45 (1.98). The nanoscale-cavity effect can enhance not only the emission of a QD inside a nano-hole, but also the efficiency of the FRET from a QW into a QD in a nano-hole. Since the distances between the donor and acceptor in the structures of Figs. 9(a) and 9(b) are the same and their interface geometries are similar, the experimentally observed FRET behavior through the insertion of QDs into a nano-hole is caused not only by the short distance between the QW and QD, but also by the nanoscale-cavity effect of the nano-hole. Although we use only one set of geometric parameters for numerically demonstrating the enhancement behaviors in this paper, we actually obtain the similar numerical results in varying the geometric parameters.

 

Fig. 10. Simulated spectra of the normalized field intensity produced by the donor at the acceptor position and the normalized radiated power produced by the acceptor for the structure shown in Fig. 9(a). The results are normalized with respect to their counterparts in the reference structure shown in Fig. 9(b). The two vertical dashed lines indicate the assumed donor and acceptor emission wavelengths at 450 and 625 nm, respectively.

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Table 2. Simulation results of the ratios of the donor-produced intensity at the acceptor position (at 450 nm in wavelength) and the acceptor-produced radiated power (at 625 nm in wavelength), and the FRET enhancement factors for the two dipole orientations

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6. Discussions

In both samples Q (GaN) and H-Q (GaN), the QDs are immersed in the SU-8 photoresist such that the non-radiative recombination rates of the QDs in the two samples are expected to be the same. Therefore, the higher PL decay rate of sample H-Q (GaN) shown in Fig. 8 or the shorter PL decay time shown in the bottom row of Table 1, when compared with that of sample Q (GaN), implies that the radiative recombination rate of a QD inside a nano-hole is higher. The results in those samples of no QW or FRET support the inference that the nanoscale-cavity effect can enhance the emission efficiency of a QD in a nano-hole. The numerical simulation results also confirm this inference. In samples Q (LED) and H-Q (LED), the FRET from the QWs into the QDs can occur. However, because the distance between the QWs and QDs are large (>120 nm) in sample Q (LED), the FRET in this sample must be weak that is supported by the comparable QD PL decay times between samples Q (GaN) and Q (LED) (12.42 ns versus 11.21 ns). In sample H-Q (LED), the short distance between the QDs and QWs guarantees a stronger FRET process, which is supported by the observations of increased QD PL decay time and decreased QW PL decay time, as shown in rows 5 and 6 of Table 1. Because of the energy transfer from the QWs into QDs, the QD (QW) PL decay time is elongated (shortened). The significant changes of QW and QD PL decay times imply that the FRET process can be further enhanced through the nanoscale-cavity effect. This speculation is confirmed by the simulation results discussed in section 5.

In row 3 of Table 1, we can see the increased R/B ratio in sample II-H-Q. This color conversion enhancement is partly caused by FRET (or nanoscale-cavity enhanced FRET) and partly caused directly by the nanoscale-cavity effect. It is noted that the diameter of the nano-holes is ∼215 nm, which is significantly larger than the effective range of FRET (at most several tens nm). Suppose that the QDs immersed in the photoresist is uniformly distributed in a nano-hole, plenty of inserted QDs are actually far away from the nano-hole sidewall or the QWs such that their FRET effects are weak. However, the nanoscale-cavity effect can still enhance the emission efficiencies of those QDs even though they are excited by the far-field blue light from the QWs. This effect can increase the red intensity and hence the R/B ratio. Actually, the blue light intensity inside a nano-hole can also be enhanced for increasing the power absorbed by the inserted QDs. The stronger blue intensity, including the far- and near-field components, inside a nano-hole can increase the radiated power of the QWs that can help in explaining the enhanced EL intensity in sample II-H, when compared with sample II (see Fig. 4). Therefore, the nanoscale-cavity effect is an important mechanism for increasing the R/B ratio in sample II-H-Q. The nano-hole structure in sample II-H-Q can enhance the radiated powers of both blue and red lights leading to the increased overall normalized intensity, as shown in Fig. 4 and row 2 of Table 1, when compared to sample I-Q. Also, the nano-hole structure leads to the enhanced light extraction, nanoscale-cavity effect, and FRET process, resulting in a higher blue PL decay rate and hence a larger blue modulation bandwidth. Although the FRET process leads to a lower red PL decay rate, driven by the enhanced modulation response of the QW emission, the modulation bandwidth of red light is also increased in sample II-H-Q. However, the increment is smaller, when compared with that of blue light.

From rows 2 and 3 of Table 1, we can see that the increments of the normalized intensity and R/B ratio are not large (5 and 10%, respectively) in sample II-H-Q. Such increments are significantly smaller than the variation ranges of PL decay time. These differences are attributed to the different surface conditions between samples II-H-Q and H-Q (LED). In sample H-Q (LED) for TRPL study, the surface photoresist and immersed QDs are removed such that the measured TRPL behaviors are completely caused by the QDs inserted into the nano-holes. On the contrary, in sample II-H-Q for LED characterization, the surface photoresist and QDs remain because the p-electrode metal of >120 nm in height hinders the sweeps of the surface photoresist and QDs and hence it is difficult to remove them from the mesa surface. In this situation, the emission behaviors of those QDs in the thick layer of solidified photoresist solution on the sample surface may dominate the observed results. In other words, only a small portion of QDs in sample II-H-Q is involved in the FRET and nanoscale-cavity effects. However, we can still conclude the observation of the color conversion enhancement in sample II-H-Q. To increase the contribution to the color conversion result from the QDs inserted into the nano-holes, we can increase the QD concentration in the photoresist solution and reduce the capping photoresist thickness.

In each curve of Fig. 10, below 550 nm in wavelength, we can see a weak oscillation behavior, which is caused by a certain cavity resonance effect of the emitted far field. For a radiating dipole in a given cavity structure, a far-field cavity resonance behavior can be observed at the short-wavelength limit, leading to the spectral oscillation of radiated power. This far-field behavior diminishes as wavelength becomes longer and the radiation behavior enters the near-field domain. In the nano-hole structures with the given geometric parameters for our experimental and simulation studies, the near-field behaviors dominate the radiations of the donor and acceptor in the visible and near-infrared ranges. The nanoscale-cavity effect here is caused by the near-field version of the Purcell effect. Although either the measured QD emission intensity in experiment or the calculated radiated power in simulation shows the far-field behavior of a QD or radiating dipole inside a nano-hole, its radiation behavior has been modified through the near-field version of the Purcell effect. In other words, the enhanced near field distribution inside the nano-hole excited by the original light emitter modifies its own radiation behavior through the Purcell effect (the feedback effect in simulation) such that its far field emission becomes stronger. This is one of the key issues of the nanoscale-cavity effect.

The nanoscale-cavity effect is controlled by the geometry of the nano-hole. It is speculated that the nanoscale-cavity effect becomes stronger when the dimension of the nano-hole is reduced under the condition that the viscous QD-immersed photoresist can be inserted into the nano-hole. However, the dependence of the nanoscale-cavity effect on the nano-hole geometry does not necessarily follow a simple rule. The study of this dependence is important for maximizing the nanoscale-cavity effect. Nevertheless, based on the nano-imprint lithography technique, it is expensive to change the diameter and period of the nano-hole array in experiment. A numerical study for first optimizing the parameters of the nano-hole array is a more reasonable approach to advance this research subject.

7. Conclusions

In summary, we have proposed the mechanism of the nanoscale-cavity effect and demonstrated its important role in enhancing the QD emission and the FRET from the QW into QD when red-emitting QDs are inserted into the deep surface nano-holes on a blue-emitting QW LED for increasing the color conversion efficiency. We first compared the color conversion behaviors between a blue-emitting QW LED sample with a surface nano-hole array filled by a photoresist solution of red-emitting QD on its p-type mesa and a reference LED sample of no nano-hole overlaid with the photoresist solution. The nano-holes penetrated through the whole QW structure such that the inserted QDs became close to the QWs. The nano-hole LED sample showed a higher color conversion efficiency and a higher modulation bandwidth, when compared with the reference sample. The TRPL studies based on the samples with and without the QW structure indicated that the nano-hole structure could produce a nanoscale-cavity effect to enhance the emission efficiency of the QDs inserted into the nano-holes and increase the efficiency of the FRET from the QWs into QDs. The nanoscale-cavity effects for enhancing QD emission and FRET were confirmed with the numerical simulation study. The nanoscale-cavity effect plays a crucially important role in enhancing the color conversion efficiency of an LED with a surface nano-hole array for embedding color-converting QDs. Although we have demonstrated the nanoscale-cavity effects on the emission and FRET behaviors in this paper, the detailed mechanisms of such an effect deserve further investigation.