Optical properties of plasmonic light-emitting diodes based on flip-chip III-nitride core-shell nanowires Mohsen Nami* and Daniel F. Feezell Center for High Technology Materials, Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87106, USA * [email protected]

Abstract: In this work, we utilize the finite difference time domain (FDTD) method to investigate the Purcell factor, light extraction efficiency (EXE), and cavity quality parameter (Q), and to predict the modulation response of Ag-clad flip-chip GaN/InGaN core-shell nanowire light-emitting diodes (LEDs) with the potential for electrical injection. We consider the need for a pn-junction, the effects of the substrate, and the limitations of nanoscale fabrication techniques in the evaluation. The investigated core-shell nanowire consists of an n-GaN core, surrounded by nonpolar m-plane quantum wells, p-GaN, and silver cladding layers. The core-shell nanowire geometry exhibits a Purcell factor of 57, resulting in a predicted limit of 30 GHz for the 3dB modulation bandwidth ©2014 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (250.5403) Plasmonics.

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#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29445

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#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29446

1. Introduction Metal-clad semiconductor nanocavities have attracted significant attention as a means to enable continued size scaling of photonic devices beyond the diffraction limit. The primary motivations for these devices are their potential for thresholdless lasing [1], high-speed modulation [2–4], low power consumption [5,6], and dense integration. These features may be attractive for optical communications, chemical and biological sensing, and fluorescence imaging. Among devices based on metal-clad nanocavities, plasmonic nanolasers (and spasers) have been heavily researched as the nanoscale counterparts to conventional dielectric diode lasers [7]. A key consideration in the operation of plasmonic nanolasers is overcoming the high optical losses associated with the metal cladding layers. Although optically pumped [8,9] and electrically injected [10–15] plasmonic nanolasers have been theoretically predicted and experimentally realized, the practicality of electrically injected devices with strong mode confinement in three dimensions remains an open question [16,17]. More specifically, the threshold current density of a plasmonic nanolaser with three-dimensional mode confinement (i.e., a spaser) was predicted to be ~1 MA/cm2 [18]. Thus, the requirement of low power consumption may be difficult to attain in room temperature electrically injected plasmonic nanolasers. Furthermore, concerns have been raised regarding the linewidth and speed of plasmonic nanolasers [18]. As an alternative, plasmonic nanoscale light-emitting diodes (PNLEDs), or surface plasmon emitting diodes (SPEDs), utilizing incoherent spontaneous emission may provide many of the attractive characteristics of plasmonic nanolasers without requiring large operating current densities [17–21]. PNLEDs have the potential for excellent high-speed performance [22] and can operate with lower power consumption since they are not required to reach threshold. The primary challenge associated with an efficient, highspeed PNLED is simultaneously achieving a high spontaneous emission rate (Purcell factor) and reasonable light extraction efficiency (EXE) from the cavity. Furthermore, any electrically injected nanophotonic device requires the difficult nanoscale integration of a pnjunction with a substrate, dielectric layers, and metal electrodes. 2. Background The modulation bandwidth of a conventional planar LED is limited by the natural rate of spontaneous emission in the bulk or quantum well material. Since the spontaneous emission lifetime is typically on the order of one to a few nanoseconds, the modulation bandwidth of a conventional LED is well below 1 GHz. However, the natural spontaneous emission rate can be enhanced by modifying the local density of optical states (LDOS) by placing the emitter within a wavelength-sized cavity [23]. In 1946, E. M. Purcell first showed that the rate of spontaneous emission in a cavity could be enhanced by F, where F is the Purcell factor and is given by [24]:

3  Q (1)   4 2  n  Veff where Veff is the effective mode volume, Q is the cavity quality factor, 𝜆 is the mode wavelength, and n is the effective refractive index. A large quality factor and/or a small mode volume are therefore required to achieve a large Purcell factor. However, a high-speed PNLED requires that the quality factor remains sufficiently small to prevent the photon lifetime from dominating the modulation bandwidth. Therefore, high-speed PNLEDs must rely on ultra-small mode volumes to achieve large Purcell factors and high modulation bandwidths. For example, recent work predicts that PNLEDs can achieve ultra-high modulation bandwidths (>100 GHz) if mode volumes on the order of ~ 0.01(𝜆/2n)3 can be achieved [22]. Plasmonic nanocavities based on metal-clad nanowires (NWs) are well suited to achieve the required mode volumes in PNLEDs. Although dramatic enhancements in the spontaneous 3

F

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29447

emission rate were recently predicted for a substrate-free Ag-clad GaN NW with an axial InGaN active layer [25], practical fabrication limits likely preclude that particular structure from being used as an electrically injected device. More recently, we examined the Purcell factors and EXEs for a variety of Ag-clad GaN/InGaN core-shell and axial PNLED structures incorporating substrates, pn-junctions, dielectric layers, and electrodes [26]. However, extraction of light from the previously investigated structures primarily occurred through a ~300 µm thick substrate, which severely reduced the light power density at the extraction surface, thus limiting the amount of useful light that could be coupled to a fiber or directed into free space. Considering these limitations, it is desirable to develop a flip-chip configuration in which the substrate has been removed and the light extraction surface is in close proximity (~100 nm) to the nanowire emitter. In this work, we present and investigate a top-emitting flip-chip PNLED with the substrate removed that includes the components required for electrical injection. The structure is based on a Ag-clad GaN/InGaN hexagonal core-shell nanowire with a tapered base. We propose a flip-chip fabrication process for this device and utilize the finite difference time domain (FDTD) method to investigate the Purcell factor, EXE, and the near-field intensity. We determine the spatial and wavelength dependence of the Purcell factor in the cavity and observe the classic trade-off between Purcell factor and EXE. We also investigate the dependence of EXE on the n-GaN thickness and present a structure with a buried dielectric layer to increase the EXE. Finally, we comment on the maximum carrier-lifetime-limited modulation bandwidth that is theoretically attainable from these structures. 3. Proposed device structure and fabrication steps Figure 1 shows a schematic of the proposed PNLED structure, which consists of a flip-chip Ag-clad GaN/InGaN core-shell nanowire. The n-GaN core is 50 nm tall and the diameter is 14 nm. The active region is circumscribed around the core and consists of a single 3-nm-thick nonpolar InGaN quantum well. The quantum well (QW) is surrounded by a 10-nm-thick pGaN layer and an optically thick (~300 nm) Ag cladding layer (T Ag). The thicknesses of the n-GaN (TGaN), SiNx, Au (TAu), and Al2O3 (sapphire) (Ts) submount are 100 nm, 25 nm, 1 µm and 300 µm, respectively. The width of the Ag cladding (L) and Al 2O3 submount (D) are 2 µm and 4 µm, respectively. At the bottom of the NW core, a tapered base is included to enable a higher and more uniform Purcell factor [26]. The tapered base has a height of 25 nm and a taper angle of 62°. The tapered NW structure can be experimentally realized under particular growth conditions in which the 10 11 semipolar family of planes is thermodynamically stable during only the initial stages of growth [27,28]. Figure 2 illustrates the fabrication steps that could potentially be used to produce an electrically injected flip-chip PNLED structure. The proposed process leverages band-gap selective photoelectrochemical (PEC) etching [29,30] of an InGaN sacrificial layer embedded beneath the NW to enable substrate removal. The first step in the fabrication process would utilize electron beam lithography and selective-area epitaxy [31,32] to pattern and grow the core-shell nanowire structure shown in Fig. 2(a). The NW would then be coated in thick Ag for the plasmonic effect and thick Au for subsequent flip-chip bonding (Fig. 2(b)). Wet and dry chemical etching would then be used to define a device mesa and expose the InGaN sacrificial etch layer (Fig. 2(c)). The structure would then be flip-chip bonded using Au-Au bonding techniques to an Al2O3 host submount coated in Au. Band-gap selective PEC etching would then be used to separate the device mesa from the substrate (Fig. 2(d-e)), effectively

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29448

Fig. 1. (a) Schematic of a core-shell nanowire structure with a hexagonal cross-section and a tapered base. The taper has a 40 nm width at the base and a 14 nm width at the top. (b) Crosssection of the core-shell nanowire structure as viewed from the top, showing the location of the n-GaN core, InGaN active region, p-GaN shell, and silver cladding.

Fig. 2. Concept of a flip-chip PNLED fabrication process using photoelectrochemical etching to remove the substrate and expose the backside of the NW emitter. Such a structure would allow for fiber coupling or more efficient light extraction into free space than a structure with the substrate still incorporated.

removing the substrate and leaving the device bonded to the host submount [33]. Finally, a ring n-contact would be applied to the backside using conventional photolithography (Fig. 2(f)). The proposed process describes a practical approach to achieve electrically injected flip-chip PNLEDs and could be transferred to other III-V materials. 4. Simulation method A commercial-grade simulator based on the finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions) was used to perform the calculations. The FDTD method is a fully vectorial approach that naturally gives both the time domain and frequency domain

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29449

information [34]. The n-GaN, p-GaN, and InGaN dispersion relations were determined from [35], while that for the silver cladding layer was determined from [36]. The proposed core-shell PNLED inherently includes a nonpolar (m-plane) active region on the sidewalls of the n-GaN core. Nonpolar quantum wells are free from the polarizationrelated electric fields that plague polar (c-plane) quantum wells [37], which increases the overlap of the electron and hole wave functions and results in a shorter natural spontaneous emission lifetime. Previously, low-temperature time-resolved photoluminescence (PL) measurements on m-plane quantum wells yielded a ~10x decrease in the natural spontaneous emission lifetime compared to c-plane quantum wells [38]. To represent the quantum well emission, we used the common approach of incorporating a radiating electric dipole source at the location of the active region [39]. The emission from nonpolar InGaN quantum wells is well modelled by a single dipole source directed along the a-direction of the wurtzite crystal (z-direction in Fig. 1(a)) [40,41]. In the weak coupling regime where the Q parameter is low (i.e., dipole approximation), the Purcell factor (F) is defined as the ratio of the classical radiation power of a dipole in a cavity to the classical radiation power of a dipole in a bulk dielectric material [42,43]

F

cavity  spbulk Pclassical  bulk  spcavity Pclassical

(2)

where  spbulk is the spontaneous emission lifetime in bulk material and  spcavity is the spontaneous emission lifetime in a cavity. The Purcell factor is directly related to the LDOS, which describes the electromagnetic environment and can be calculated from the imaginary part of the dyadic Green’s function in the direction of the dipole moment at the dipole position [42]. Thus, Purcell enhancement of the spontaneous emission is a local effect. To account for this, the location of the dipole emitter was swept along the vertical dimension (Y, height) of the active region from 5 to 45 nm (Fig. 1(a)) and the Purcell factor was determined at each point. In order to find the EXE, a monitor was placed above the n-GaN air interface near the topside of the flipped structure. The size of the monitor was selected to collect all the power exiting the structure and the EXE was defined as the power exiting the structure divided by total power generated by the dipole inside the cavity. 5. Simulation results 5.1 Purcell factor and EXE Figure 3(a) shows the Purcell factor vs. wavelength for a dipole placed at various vertical locations along the active region of the tapered nanowire structure shown in Fig. 1. As shown in Fig. 3(a), the Purcell factor vs. wavelength is relatively uniform as a function of vertical position within the cavity and the peak Purcell factor occurs at 445 nm. The average of the Purcell factor at 445 nm for all of the dipole positions is 57. Figure 3(b) shows the crosssectional near field intensity in the cavity normalized to bulk GaN for a dipole source placed at Y = 25 nm. As expected, the field intensity is also peaked near 445 nm, is relatively uniform in the vertical direction within the nanowire, and drops to nearly zero within the GaN taper. This shows that the field is well contained within the wire despite the wire being open and unconfined on the substrate side.

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29450

Fig. 3. (a) Calculated Purcell factor vs. wavelength for dipole emitters placed at various vertical locations along the active region. (b) Near-field intensity cross-section normalized to bulk GaN for a dipole placed at Y = 25 nm and a monitor placed at the center along the Y direction.

Fig. 4. Calculated Purcell factor and EXE into air at 445 nm for dipole emitters placed at various vertical locations along the active region from 5 nm to 45 nm.

The high average Purcell factor indicates that a significant portion of the energy in the mode resides within the metal cladding or near the semiconductor-metal interfaces. Consequently, absorption losses will be high and the EXE into air is expected to be very low. Figure 4 shows the Purcell factor and EXE into air at 445 nm for a dipole placed at various vertical locations along the active region. When the dipole is swept vertically from 5 to 45 nm, the Purcell factor is relatively constant, increasing from a minimum of 53 to a maximum of 60. Conversely, the EXE is strongly non-uniform along the vertical direction of the cavity, decreasing from 0.7% to 0.16% as the dipole moves away from the open side of the nanowire. The average EXE into air is 0.44%, which is nearly the same as the EXE for a dipole placed at the point Y = 25 nm.

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29451

5.2 Effect of n-GaN thickness and core width In addition to the geometry and dimensions of the nanowire itself, the thickness of the n-GaN layer (TGaN) has an important effect on the EXE into air. Figure 5 shows the EXE into air at 445 nm vs. n-GaN thickness for a dipole placed at Y = 25 nm. As shown in Fig. 5, the EXE into air vs. n-GaN thickness has a sinusoidal behavior, showing a transmittance dependence similar to that of a Fabry-Pérot etalon. This behavior is due to the interference effect between forward and backward travelling photons. Similar Fabry-Pérot effects on EXE have been reported in GaN-based LEDs for solid-state lighting [44]. For a substrate thickness of 100 nm, the maximum EXE into air is obtained. Figure 5 illustrates the importance of accurately

Fig. 5. EXE into air at 445 nm for various thicknesses of n-GaN.

controlling the n-GaN thickness to achieve the highest possible EXE. The proposed flip-chip device affords this control, as it utilizes a highly selective PEC etching process. We have also investigated the dependence of the Purcell factor and EXE on the core-width. By increasing the core diameter from 14 nm to 60 nm, the Purcell factor at 445 nm decreases from 58 to 40 and the EXE into air increases from 0.44% to 0.51%. 5.3 Embedded dielectric structure The relatively high Purcell factor obtained in the structure shown in Fig. 1 also results in low EXE. It is desirable to explore additional configuration that might result in higher EXE. To achieve a high Purcell factor, a very thick Ag layer is unnecessary and a thinner layer on the order of 20-30 nm can be used. This enables an additional device geometry that utilizes an embedded dielectric layer to significantly increase the EXE without strongly decreasing the Purcell factor. The structure is shown in Fig. 6 and is the same as that shown in Fig. 1 except a SiNx layer is embedded within the silver cladding. The thickness of this layer (S) was swept from 0 to 40 nm for two different thicknesses of the first silver layer (T Ag1 = 20 nm and TAg1 =

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29452

Fig. 6. (a) Schematic of a core-shell nanowire structure with a hexagonal cross-section and a tapered base. A dielectric layer was added in order to increase the EXE. (b) Cross-section of the core-shell nanowire structure as viewed from the top, showing the location of the n-GaN core, InGaN active region, p-GaN shell, SiNx layer, and silver layer.

Fig. 7. Calculated Purcell factor and EXE into air at 445 nm for a dipole emitter placed at Y = 25 nm. The thickness of the SiNx layer (s) was swept from 0 to 40 nm and TAg1 is (a) 30 nm and (b) 20 nm.

30 nm). The Purcell factor and EXE into air are shown in Fig. 7. Figure 7 illustrates the clear trade-off between EXE and Purcell factor, whereby increasing the thickness of the SiN x layer the EXE increases and the Purcell factor decreases. Figure 7(a) shows the case for TAg1 = 30 nm, where increasing the thickness of the SiNx layer from 0 to 40 nm results in the EXE increasing from 0.43% to 0.86% and the Purcell factor decreasing from 59 to 51. Although the Purcell factor is reduced by 13%, the EXE increases by a factor of two. Figure 7(b) shows the case for TAg1 = 20 nm, where increasing the thickness of the SiNx layer from 0 to 40 nm results in the EXE increasing from 0.43% to 1.29% and the Purcell factor decreasing from 59 to 38. Although the EXE increases by a factor of three in this case, the Purcell factor is also significantly lowered. Schemes such as embedded dielectric layers could potentially be used to increase EXE without significantly lowering the Purcell factor.

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29453

5.4 Near-field intensity To understand the distribution of energy within the cavity and the metal cladding, we investigated the near-field intensity of the structure in Fig. 1 over the three possible cross sections of the nanowire. Figure 8(a) shows the top-view cross-section of the core-shell nanowire structure, the coordinate system, and the locations of the cross-sectional planes that were examined. Figure 8(b) shows the cross-sectional near-field intensity viewed from the top of the nanowire within the XZ plane at Y = 42 nm, revealing that the electric field is strongly confined near the interface between the p-GaN and the silver cladding. Figure 8(c) shows the cross-sectional near-field intensity for the XY plane at a position illustrated in Fig. 8(a), revealing that the electric field within the XY plane is also primary confined near the interface between the p-GaN and the silver cladding and that the field intensity is several times higher than that of the XZ cross-section. Figure 8(d) shows the cross-sectional nearfield intensity for the YZ plane at a position illustrated in Fig. 8(a). For the YZ cross-section, the peak of the electric field resides within the core of the semiconductor structure. However, the peak field intensity is lower for this cross section than for the XZ or XY cross-sections. The near-field intensity results are consistent with the high Purcell factor predicted for this structure in Section 5-1.

Fig. 8. (a) Top-view cross-section of the core-shell nanowire structure shown in Fig. 1, the associated coordinate system, and the locations of cross-sectional planes. (b) Cross-sectional near-field intensity within the XZ plane (c) Cross-sectional near-field intensity within the XY plane. (d) Cross-sectional near-field intensity within the YZ plane.

6. Predicted maximum modulation speed A primary motivation for research on PNLEDs is their potential for high-speed modulation. High speeds are enabled when a large Purcell factor results in a significant reduction of the natural spontaneous emission lifetime. In this section, we predict the maximum carrierlifetime-limited modulation bandwidth for the Ag-clad flip-chip core-shell PNLEDs examined in this work. We first consider the natural spontaneous emission lifetimes for GaN/InGaN quantum wells. For polar c-plane InGaN quantum wells at a current density of 100 A/cm2, we assume a radiative lifetime (τr) of 3 ns and a non-radiative lifetime (τnr) of 5 ns, as reported by David and Grundmann [45]. For nonpolar m-plane InGaN quantum wells (core-shell structures), the lifetimes have been shown to be approximately 10X lower than those on c-plane [38], so for the nonpolar InGaN quantum wells of our core-shell nanowires

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29454

we assume the natural lifetimes without cavity effects are τr 0.3 ns and τnr 0.5 ns. The effective carrier lifetime (τeff) with cavity effects (i.e, Purcell enhancement) is given by:

1

 eff



F

r



1

(3)

 nr

where F is the Purcell factor and τeff is the Purcell reduced spontaneous emission lifetime. The 3dB bandwidth (f3dB) is given by [22]:

f3dB 

1 1 2  p2   eff2

(4)

where τp is the photon lifetime. For cavities with quality factors below several hundred, τp is a small portion of the overall lifetime in Eq. (4) and f3dB depends primarily on τeff. The 3dB bandwidth in this case is approximated by:

f3dB 

1 1 2  eff

(5)

Table 1 shows the wavelength at the peak of the Purcell factor, the average Purcell factor (F), the radiative lifetime (τr), the non-radiative lifetime (τnr), the cavity quality factor (Q), and the predicted maximum 3dB bandwidth for the core-shell structure shown in Fig. 1. With a Purcell factor of 57 and nonpolar InGaN quantum wells, a maximum modulation bandwidth of around 30 GHz is achievable. We note that this analysis considers only the carrier-lifetimelimited bandwidth and does not consider potential bandwidth limitations associated with parasitic resistance and capacitance. Table 1. Parameters used to predict the maximum carrier-lifetime-limited 3dB modulation bandwidth for the structure shown in Fig. 1. Structure

𝜆 (nm)

F

Figure 1

445

57

τr (ns) 0.3

τnr (ns) 0.5

τeff (ps) 5.2

Q 14

f3dB (GHz) 30.2

7. Conclusion We have investigated the Purcell factor, light extraction efficiency, and maximum carrierlifetime-limited modulation bandwidth of Ag-clad flip-chip GaN/InGaN core-shell nanowire light-emitting diodes. A flip-chip structure with the potential for electrical injection and an associated fabrication process were proposed. Examination of several metal-coated flip-chip PNLED structures revealed maximum Purcell factors of ~60 and maximum light extraction efficiencies of ~1% at 445 nm. We also examined the dependence of EXE on n-GaN thickness and determined the near-field intensity profiles within the cavity and metal cladding layers. Finally, using the reported values of natural spontaneous emission lifetime and the calculated Purcell factors, the maximum carrier-lifetime-limited 3dB modulation bandwidth was predicted to be ~30 GHz for these PNLEDs. Acknowledgment The authors would like to acknowledge useful discussions with Dr. Jeremy Wright and Dr. Ben Bryant. We also thank the University of New Mexico Center for Advanced Research Computing, funded in part by the National Science Foundation, for providing the highperformance computing resources used in this work. This work was supported by Defense Advanced Research Projects Agency (DARPA) under award number D13AP00055.

#222797 - $15.00 USD Received 15 Sep 2014; revised 7 Nov 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029445 | OPTICS EXPRESS 29455

Optical properties of plasmonic light-emitting diodes based on flip-chip III-nitride core-shell nanowires.

In this work, we utilize the finite difference time domain (FDTD) method to investigate the Purcell factor, light extraction efficiency (EXE), and cav...
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