Surface plasmon coupling with radiating dipole for enhancing the emission efficiency of a light-emitting diode

Yang Kuo; Shao-Ying Ting; Che-Hao Liao; Jeng-Jie Huang; Chih-Yen Chen; Chieh Hsieh; Yen-Cheng Lu; Cheng-Yen Chen; Kun-Ching Shen; Chih-Feng Lu; Dong-Ming Yeh; Jyh-Yang Wang; Wen-Hung Chuang; Yean-Woei Kiang; C. C. Yang

doi:10.1364/OE.19.00A914

1. Introduction

InGaN-based light-emitting diode (LED) has become the key component for the applications of solid-state lighting, liquid-crystal-display backlighting, and color display. Although nowadays the industry can manufacture blue LEDs of high emission efficiencies, that of a longer-wavelength LED is still quite low due to the poor crystal quality of the grown InGaN/GaN quantum wells (QWs) [1]. For a specific high indium content to achieve long-wavelength emission, the growth temperature of QW needs to be reduced. In this situation, the defect density in the crystal is increased leading to low emission efficiency. The high emission efficiencies of InGaN-based blue LED and InGaAsP-based red LED plus the low emission efficiencies of InGaN- and InGaAsP-based green LEDs lead to the problem of “green gap” in LED development. To improve the crystal quality of a high-indium InGaN/GaN QW, various approaches have been demonstrated. It was proposed to deposit thin InN layers between an InGaN well layer and the surrounding GaN barrier layers for improving the QW crystal quality [2]. Also, a prestrained growth technique was illustrated for increasing indium incorporation in growing a high-indium InGaN/GaN QW [3]. With this technique, the QW growth temperature can be elevated to achieve higher crystal quality [4]. Meanwhile, the high p-GaN growth temperature (normally higher than 930 °C) was supposed to damage the high-indium InGaN/GaN QWs beneath. An effort of lowering the growth temperature of the p-GaN layer has been made [5]. Although those efforts have led to the improvements of the emission efficiency of a green LED, its efficiency level is still significantly lower than that of a blue LED. Any other approach, other than crystal quality improvement, is needed for further enhancing the efficiency of a long-wavelength InGaN-based LED.

Besides the “green gap” problem, the other crucial issue in LED development is the external quantum efficiency (EQE) droop effect at a high injection current level. It has been proposed that the EQE droop might be caused by the tunneling process due to the screening of the carrier localization potentials in an InGaN/GaN QW and the local heating during carrier transport along the dislocations [6]. It was also suggested that the droop might be produced by carrier overflow from localized states and hence recombination at nonradiative recombination centers [7]. Meanwhile, a few groups attributed this effect to the Auger recombination process [8–10]. Some other groups proposed the cause of carrier leakage due to the polarization fields [11–13]. The Auger process can be suppressed by using a design of a double heterostructure or wide-QW active region, leading to a reduction of carrier density [8,11]. On the other hand, the use of quaternary alloys for enabling an independent control over interface polarization charges and band gap to reduce electron leakage from the active region and hence to decrease EQE droop was demonstrated [12]. In addition, the AlGaN current blocking layer might not be efficient enough at high current injection due to the piezoelectric field at the GaN/AlGaN interface [13]. Although different mechanisms have been proposed for the causes of EQE droop, carrier overcrowding in the LED active region is the key reason for this effect. Any method, which can be used for decreasing the carrier density through an alternative emission channel, will be useful for reducing the EQE droop effect.

In this paper, we introduce an optical approach for enhancing the emission efficiency and reducing the EQE droop effect of an LED. In enhancing the emission efficiency, this approach is particularly effective for an LED of relative lower internal quantum efficiency (IQE), such as a green LED. This approach is based on surface plasmon (SP) coupling with the radiating dipoles (electron-hole pairs) in the QWs of an LED by inducing SP modes on the metal nanostructures at the LED top. In the first part of this paper (section 2), the basic concept of SP coupling with a dipole will first be introduced, followed by reviewing several experimental demonstrations of using such SP coupling mechanisms for increasing LED efficiency, reducing the EQE droop effect, and producing partially polarized LED output. Then, in the second part (section 3), we present the theoretical and numerical study results of SP coupling with a radiating dipole in a system including the dipole and a nearby metal nanoparticle (NP) to show the enhancements of dipole strength and total radiated power. Also, their dependencies on the dipole orientation and the separation between the dipole and the metal NP are reported. This part includes the subsections for describing the problem geometry, theoretical formulations, numerical results, and discussions. The conclusions of the whole paper are drawn in section 4.

2. Review of surface plasmon coupled light-emitting diode

2.1 Introduction

SP represents collective oscillation of excited electrons at the interface between a metal and a dielectric or semiconductor. Such an energy entity includes the electromagnetic field distribution of skin depth inside the metal and the evanescent or near-field distribution inside the dielectric or semiconductor [14]. At an extended metal/dielectric interface, such an energy entity can propagate along the interface and is called a surface plasmon polariton (SPP) [15]. On the other hand, such an energy entity can exist as local electron oscillation around a metal NP or nanostructure and is called a localized surface plasmon (LSP) [16]. Either SPP or LSP, an SP can interact with nearby light emitter through its evanescent or near-field coverage for enhancing emission [17–22]. From a viewpoint analogous to amplified spontaneous emission, the interaction or coupling between an SP and a light emitter (radiating dipole) can be regarded as a process of amplifying the evanescent or near field of the SP by a gain medium, which includes the radiating dipole. In other words, the radiating dipole transfers energy into the SP for emission, similar to the mechanism of stimulated emission. An SPP can effectively radiate when the momenta of the SPP and photon are matched that can usually be implemented through a rough metal interface or a metal-grating structure. LSP can effectively radiate without any extra mechanism. Therefore, SP coupling with a light emitter can effectively create an alternative emission channel, i.e., SP radiation. This process becomes practically useful in a light-emitting device of relatively poorer crystal quality in its active region. Although metal dissipation can cause SP loss, as long as this energy loss is smaller than that due to the non-radiative recombination process in the active region, emission enhancement of the device can be expected. In other words, SP coupling is particularly useful for increasing emission efficiency of a light-emitting device of inherently low IQE. However, the upper limit of IQE for efficiency enhancement is an engineering issue. It is noted that SP can also produce the effect of light extraction enhancement besides the aforementioned effective IQE increase in a device.

2.2 Emission efficiency enhancement of surface plasmon coupled LED

The coupling of either SPP or LSP can be used for enhancing the emission efficiency of an LED. In a blue InGaN/GaN single-QW LED of ~440 nm in emission wavelength and ~40% in IQE, an Ag layer was coated on the top of the p-GaN layer to induce SPP. To avoid Ag diffusion into the p-GaN layer, a thin SiN layer (~10 nm in thickness) was deposited before Ag coating. To reduce the distance between the Ag layer and the InGaN/GaN QW for effective SP-QW coupling, the total thickness of the p-GaN layer and a p-AlGaN electron blocking layer was reduced to 80 nm. Output enhancements of 25-50% from this device were observed [23]. Here, the IQE is defined as the ratio of the integrated photoluminescence intensity at room temperature over that at a low temperature (<10 K). As mentioned earlier, the emission enhancement is more effective for an LED of lower IQE. It has been demonstrated that the emission intensity of a green single-QW LED at 535 nm of ~7% in IQE was enhanced by up to 120%, when compared to a control sample of the conventional configuration, through SP-QW coupling [24]. In this device, Ag nanoislands of ~100 nm in size were formed on the top of the p-GaN layer by thermal annealing a deposited thin Ag layer. The LSP resonance wavelength increased with Ag nanoisland size, which increased with the deposited thin film thickness. By depositing an Ag thin film of 12 nm and thermal annealing it at 200 °C for 40 min in ambient N₂, the LSP resonance peak was located around 535 nm, matching the LED QW emission wavelength. By comparing with a reference sample of 12-nm uniform Ag thin film on the top, which could result in SPP coupling, the emission efficiency of the LED sample of Ag nanoislands, which could produce LSP coupling, could be enhanced by >100%. Here, one can see that a well-designed metal nanostructure to generate strong SP resonance around the QW emission wavelength is a crucial issue for effectively enhancing LED emission efficiency.

2.3 Reduction of droop effect through surface plasmon coupling

As discussed earlier in section 1, the key cause for the EQE droop effect of an LED is the overcrowded carriers in its active region. If the energy of part of injected carriers can be transferred into another emission channel, the carrier density in the active region can be maintained at a low level of high EQE. By using the SP-QW coupling mechanism for fast (in tens fs) and effectively transferring carrier energy into SP, the high injection current is practically split into two emission channels of carrier radiative recombination and SP radiation. In other words, the carrier energy, which is expected to be lost in a conventional LED, is now at least partially directed into SP radiation. In this situation, the EQE droop effect can be reduced. Such a reduction behavior has been demonstrated in a green two-QW LED of ~515 nm in wavelength [25]. In this implementation, a grid current spreading structure was formed on the top of an LED, which included a 20-nm p-AlGaN layer and a 60-nm p-GaN layer. The current spreading regions consisted of a layer of Ni (5nm)/Au (5nm). The square regions between the current spreading grids were deposited with Ag of 10 nm in thickness when SP-QW coupling was to be generated. A control LED sample was prepared by covering the whole p-GaN mesa by the current spreading layer (no Ag deposition). Also, a reference sample was fabricated by using the aforementioned current spreading grid structure but without Ag deposition in the square regions. Compared with the control and reference samples, those LED samples of Ag depositions in different grid geometries provided us with significantly stronger outputs. Also, their injection current densities of individual maximum EQEs became larger and their EQE drooping slopes beyond the individual maximum EQEs became smaller. In other words, the EQE droop effects of those LED samples with SP-QW coupling were reduced (by a level >20%). To confirm that such an LED performance improvement was indeed caused by SP-QW coupling, another set of LED sample with a thicker p-GaN layer (120 nm in thickness) was fabricated. With the distance of >140 nm between the Ag/GaN interface and the first QW, the SP-QW coupling became negligibly weak. Indeed, in this set of sample, the aforementioned phenomena of emission enhancement and droop effect reduction were not observed. Because SP coupling is a near-field interaction process, the comparison between the samples of different distances between the metal bottom surface and the first QW is an effective approach for confirming the mechanism of SP-QW coupling. Normally, when this distance is larger than 100 nm, the coupling effect becomes negligibly weak. The relatively thinner p-GaN layer in an LED of effective SP-QW coupling may lead to poorer current spreading and increase the device resistance. Therefore, the current spreading layout in an SP coupled LED needs to be well designed. However, in a vertical LED, which is the major trend of high-power LED development, such a current spreading problem does not exist.

2.4 Partially polarized output from surface plasmon coupled LED

Polarized LED is a desired device for the application of liquid-crystal-display backlighting. Various LED configurations have been designed for producing partially polarized LED outputs, including the use of non-polar or semi-polar crystal growth [26–28] and polarization-sensitive surface structures, such as photonic crystals [29,30]. Besides these configurations, SP coupling can also be used for producing partially polarized LED output. Because an SP represents a polarized electromagnetic energy distribution, its radiation must be polarized [31]. If we can design a metal structure for generating a dominating SP mode of preferred polarization, the SP-QW coupling will result in partially polarized LED output with the dominating polarization direction the same as that of the SP mode. The simplest metal structure for generating a dominating SP mode is a one-dimensional metal grating. By properly adjusting the period of a metal grating, an SPP of the same energy as that of QW emission can be momentum matched with photon for effective radiation. Also, by choosing appropriate grating groove parameters, an LSP of the same energy as that of QW emission can be generated for effective coupling with the QW. Either the SPP or LSP has the dominating electrical field in the direction perpendicular to the grating groove direction. Partially polarized outputs have been obtained from LEDs with one-dimensional Ag gratings on their tops [32,33]. In one of such implementations, periodical grooves of several hundreds nm in period, 15 nm in groove depth, and 50% in duty cycle were first formed on the 55-nm p-GaN layer of a 515-nm single-QW LED structure with the techniques of electron-beam lithography and dry etching [32]. Then, the grooves were covered by an Ag layer of 45 nm in thickness. Compared with a reference sample of Ag coverage of the similar thickness on the flat p-GaN layer, the emission efficiency of the metal-grating LED of 500 nm in grating period was enhanced by 87%. Also, its output was partially polarized with the polarization ratio (the intensity of the stronger polarization component over that of the weaker one) at ~1.7. By increasing the groove depth to 30 nm, the emission efficiency was enhanced by 200%. However, the polarization ratio was reduced to 1.51. By increasing the p-GaN layer thickness to 120 nm, a negligibly small polarization ratio was observed, indicating weak polarization-dependent diffraction in such a device. Also, the SP-QW coupling effect for producing the partially polarized output was confirmed. The optimized condition of 500 nm in grating period might correspond to effective coupling and radiation of an SPP or LSP mode. This issue deserves further investigation.

3. Theoretical study of surface plasmon coupling with radiating dipole

3.1 Introduction

Besides experimental implementations of SP coupled LED, theoretical and numerical studies have also been performed for understanding the physics behind the coupling mechanisms [19,20,22,34–39]. However, those theoretical and numerical studies in the past were based on an incomplete model, in which the SP mode was induced by a radiating dipole of a fixed strength. In other words, it was assumed that the radiating dipole condition was not affected by the surrounding field distribution built through the interaction between the induced SP mode and the dipole. Based on this model, the SP-dipole coupling strength may be underestimated. Although the past studies can also provide us with important information about SP coupling, a more accurate evaluation of SP-dipole coupling is useful for more precisely designing the device structure of an LED to optimize its performance. In this section, we describe the theoretical evaluation of the SP coupling with a radiating dipole based on a more complete model, in which the feedback effect of SP on the dipole behavior is included. To include this effect, the dipole is assumed to act as a two-level oscillation system. Although in an LED, an induced SP mode may couple with multiple radiating dipoles in a QW, to simplify the theoretical problem, we consider the coupling system of a single dipole. Also, although the used metal structure for generating SP can be quite complicated, in this basic demonstration, we consider a spherical Ag NP for producing LSP coupling. Meanwhile, usually in an LED, the metal structure is placed on the top of the p-GaN layer. However, in our evaluation, without loss of basic physics, we assume that both the dipole and metal NP are embedded in GaN. If the metal NP is placed on the surface of a GaN layer, the SP resonance wavelength will be blue shifted by several tens to ~100 nm [24].

3.2 Problem geometry and theoretical formulations

Figure 1 shows the geometry of the SP-dipole coupling system. The center of a spherical Ag NP with radius R is located at the origin of the coordinate system. A time-harmonically radiating dipole, oscillating as $p_{0} e^{- i ω t}$ , of a given orientation, represented by an arrow in Fig. 1, is placed at the coordinate of (0, 0, a). Here, p ₀ is the original dipole strength and ω is the oscillation angular frequency. The NP radius is fixed at R = 10 nm and the distance between the NP center and dipole, a, will be varied from 40 through 120 nm to see the effects of different coupling strengths. Only two dipole orientations, including the x and z directions, are considered. The dielectric constant of the infinitely large surrounding medium, ε_b, is assumed to be 6.25, corresponding to that of GaN. For numerical computations, the dielectric constant, ε_m, of Ag based on experimental measurement is used [40]. Such a dipole-NP system has been widely studied theoretically and numerically for understanding the absorption properties when a plane wave is incident [41–43] and studying the lasing behaviors of a dipole nanolaser [44] and a spaser [45]. Also, the Rabi splitting phenomenon was experimentally observed from a system of SP coupling with an InAs quantum dot, which is similar to the dipole-NP system in this study [46].

Fig. 1 Geometry of the dipole-NP system, including a spherical Ag NP with radius R centered at the coordinate origin and a radiating dipole located at (0, 0, a), which is represented by an arrow.

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In the dipole-NP system shown in Fig. 1, the electric field of the radiating dipole induces LSP resonance on the metal NP, resulting in a strong local field distribution in its vicinity. Such a strong field distribution due to LSP resonance will in turn affect the dipole strength, which corresponds to the radiative recombination rate of carriers in the active region of an LED. In other words, the LSP resonance causes a feedback effect on the radiating dipole. In our study, the radiating dipole is regarded as a saturable two-level system. We use the semi-classical theory for solving the problem of electromagnetic field interaction with the two-level system. To rigorously calculate the scattered electromagnetic field from the metal NP, we analytically solve the Helmholtz equation in a spherical coordinate system, instead of using the quasi-static approximation, which leads to inaccurate results when either R or a is large. Our results are accurate for arbitrary values of R and a. After a lengthy derivation, the scattered electric field at (0, 0, a) can be analytically expressed as

{\vec{E}}_{}^{(s)} = \hat{z} {\bar{p}}_{z} E_{0} f_{z}

for a z-oriented dipole and

{\vec{E}}_{}^{(s)} = \hat{x} {\bar{p}}_{x} E_{0} f_{x}

for an x-oriented dipole, where

f_{z} = \sum_{n = 1}^{\infty} n (n + 1) a_{n} h_{n}^{(1)} (k_{b} a),

f_{x} = \sum_{n = 1}^{\infty} \frac{2 n + 1}{2} {α_{n} {(\frac{d r h_{n}^{(1)} (k_{b} r)}{d r})}_{r = a} + β_{n} h_{n}^{(1)} (k_{b} a)},

a_{n} = - i (2 n + 1) k_{b} a h_{n}^{(1)} (k_{b} a) \frac{({\bar{ε} j_{n} (k_{m} R) (\frac{d r j_{n} (k_{b} r)}{d r}) |}_{r = R} - j_{n} (k_{b} R) {(\frac{d r j_{n} (k_{m} r)}{d r}) |}_{r = R})}{({\bar{ε} j_{n} (k_{m} R) (\frac{d r h_{n}^{(1)} (k_{b} r)}{d r}) |}_{r = R} - h_{n}^{(1)} (k_{b} R) {(\frac{d r j_{n} (k_{m} r)}{d r}) |}_{r = R})},

α_{n} = - i k_{b} a {(\frac{d r h_{n}^{(1)} (k_{b} r)}{d r}) |}_{r = a} {\frac{\bar{ε} {(\frac{d r j_{n} (k_{b} r)}{d r}) |}_{r = R} j_{n} (k_{m} R) - j_{n} (k_{b} R) {(\frac{d r j_{n} (k_{m} r)}{d r}) |}_{r = R}}{\bar{ε} {(\frac{d r h_{n}^{(1)} (k_{b} r)}{d r}) |}_{r = R} j_{n} (k_{m} R) - h_{n}^{(1)} (k_{b} R) {(\frac{d r j_{n} (k_{m} r)}{d r}) |}_{r = R}}},

β_{n} = - i k_{b}^{3} a^{3} h_{n}^{(1)} (k_{b} a) {\frac{{(\frac{d r j_{n} (k_{b} r)}{d r}) |}_{r = R} j_{n} (k_{m} R) - j_{n} (k_{b} R) {(\frac{d r j_{n} (k_{m} r)}{d r}) |}_{r = R}}{{(\frac{d r h_{n}^{(1)} (k_{b} r)}{d r}) |}_{r = R} j_{n} (k_{m} R) - h_{n}^{(1)} (k_{b} R) {(\frac{d r j_{n} (k_{m} r)}{d r}) |}_{r = R}}},

\bar{ε} = \frac{ε_{m}}{ε_{b}},

k_{b} = \frac{ω \sqrt{ε_{b}}}{c}, k_{m} = \frac{ω \sqrt{ε_{m}}}{c},

E_{0} = \frac{p_{0}}{4 ε_{b} π a^{3}},

{\bar{p}}_{x} = \frac{p_{x}}{p_{0}},

and

{\bar{p}}_{z} = \frac{p_{z}}{p_{0}} .

Also,

h_{n}^{(1)} (z)

is the spherical Hankel function of the first kind of order n,

j_{n}^{} (z)

is the spherical Bessel function of the first kind of order n, c is the light speed in vacuum, and r is the radial coordinate of the spherical coordinate system.

To investigate the feedback effect of the LSP resonance on the two-level system, we solve the optical Bloch equations by using the aforementioned scattered field with the rotating-wave approximation and the dipole approximation [47]. For mathematical simplicity, we define the notation $ζ = | {\bar{p}}_{i} f_{i} |$ . Then, we can derive the governing equations from the steady state solutions of the optical Bloch equations to give

ζ = \frac{| f_{i} |}{| 1 + \frac{A f_{i}}{1 + B ζ^{2}} |} .

Here, i represents x or z. Also,

A = (i T_{2}) \frac{μ^{2}}{ℏ} \frac{E_{0}}{p_{0}} D^{(0)}, B = μ^{2} E_{0}^{2} \frac{T_{1} T_{2}}{ℏ^{2}},

T_{1}

is the spontaneous decay time,

T_{2}

is the dephasing time, μ is the dipole matrix element, and

D^{(0)} = ρ_{11}^{(0)} - ρ_{00}^{(0)}

is the population difference between the two energy levels in the absence of the metal NP. Once Eq. (8) is solved for ζ, we can find the dipole strength,

p_{i}

, from the following equation:

p_{i} = \frac{p_{0}}{1 + \frac{A f_{i}}{1 + B ζ^{2}}} .

The parameters used for numerical evaluations include T₁ = 10⁻⁹ s, T₂ = 2T₁, μ = 5 × 10⁻²⁹ C⋅m, and p ₀ = 2μ [48].

3.3 Numerical results

Figure 2 shows the dipole strength enhancement ratios, $| p | / p_{0}$ , of the x-oriented dipole as functions of wavelength when the distance between the dipole and the Ag NP center, a, varies from 40 through 120 nm. Recall that the NP radius is fixed at R = 10 nm. The ratio $| p | / p_{0}$ represents the dipole strength enhancement due to the feedback effect of the induced LSP. In Fig. 2, one can see that around 580 nm in wavelength, there is a Fano-like oscillation for each a value. In this figure, a dotted horizontal line is plotted to indicate the level of unity. The Fano-like oscillation magnitude becomes larger as the dipole-NP distance decreases. Also, its oscillation phase is reversed when a is increased from 80 to 100 nm. The observed Fano-like oscillation is due to the coupling of the radiating dipole with the LSP dipole resonance mode around 574.7 nm. The oscillation is caused by the phase retardation of the mirror dipole induced in the Ag NP. The interference between the original dipole oscillation and the feedback effect from the induced LSP results in the Fano-like shape. The dipole strength enhancement or reduction level increases with decreasing dipole-NP distance. When the distance is smaller than 80 nm, the coupling feature of another LSP resonance mode, i.e., the LSP quadrupole resonance mode, appears at the wavelength around 522.1 nm. The spectral location of the Fano-like oscillation shifts with a, leading to the general blue shift trend of the maximum dipole strength enhancement point as a is decreased. When a = 40 nm, the LSP-coupling induced dipole strength enhancement and reduction percentages can reach 20.7 and 9.3% at 574.7 and 618 nm, respectively. Figure 3 shows the dependencies of the maximum $| p | / p_{0}$ (the left ordinate) and the corresponding wavelength (the right ordinate) on the dipole-NP distance of the x-oriented dipole. Here, one can see that the maximum $| p | / p_{0}$ increases monotonically with decreasing a. The corresponding wavelength for maximum $| p | / p_{0}$ decreases with decreasing a until a becomes smaller than 55 nm.

Fig. 2 Spectral dependencies of $| p | / p_{0}$ on wavelength in the case of x-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 3 Dipole-NP distance dependencies of the maximum $| p | / p_{0}$ and the corresponding wavelength in the case of x-oriented dipole.

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Figure 4 shows the data similar to those in Fig. 2 for the z-oriented dipole. Similar Fano-like oscillations due to the coupling of the LSP dipole resonance and the phase reversal behaviors at different dipole-NP distances can be observed. The coupling feature of the LSP quadrupole resonance becomes observable around 520.7 nm when a is smaller than 80 nm. The Fano-like oscillation magnitude increases rapidly with decreasing a value until it reaches a certain value between 60 and 40 nm, at which the maximum $| p | / p_{0}$ level starts to drop. In the curve of a = 40 nm, one can see the broadened hump around 626.2 nm. The dropping and broadening trends at smaller dipole-NP distances are attributed to the saturation effect of the two-level system. When a = 60 nm, the LSP-coupling induced dipole strength enhancement and reduction percentages of the z-oriented dipole can reach 25.6 and 11.1% at 612 and 567.8 nm, respectively. Such levels are significantly larger than their counterparts of the x-oriented dipole, which are only 7.8 and 5.9%, respectively. Figure 5 shows the dependencies of the maximum $| p | / p_{0}$ (the left ordinate) and the corresponding wavelength (the right ordinate) on the dipole-NP distance of the z-oriented dipole. In this figure, the curve for the wavelength of maximum $| p | / p_{0}$ is truncated in the range of a > 105 nm because it becomes difficult to identify the maximum $| p | / p_{0}$ point in spectrum when the $| p | / p_{0}$ value is so close to unity in this range of a value. The variation trends in Fig. 5 are similar to those in Fig. 3. However, the maximum $| p | / p_{0}$ starts to decrease with decreasing a at a = ~52 nm due to the saturation effect of the two-level system. The blue-shifting trend of the wavelength of maximum $| p | / p_{0}$ with decreasing a is turned around at a = ~60 nm. The blue or red shift trend originates from the varying phase retardation of the LSP feedback effect.

Fig. 4 Spectral dependencies of $| p | / p_{0}$ on wavelength in the case of z-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 5 Dipole-NP distance dependencies of the maximum $| p | / p_{0}$ and the corresponding wavelength in the case of z-oriented dipole.

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Figure 6 shows the total radiated power enhancement ratios as functions of wavelength at several a values for the x-oriented dipole. The total radiated power is obtained by integrating the out-going power over the entire spherical surface at a far distance. The power ratio is defined as the total radiated power of the dipole-NP system over that in the case without the Ag NP. The radiated power has two contributions including the modified dipole and the induced LSP. Its level is controlled by the strengths of the modified dipole and the LSP resonance, and the relative phase retardation between the dipole and LSP radiation components. Here, although the oscillation magnitude becomes larger, the pattern of each curve in Fig. 6 is quite similar to its counterpart in Fig. 2. In the case of a = 40 nm, the maximum power enhancement ratio can reach 1.59 at 571.2 nm. Figure 7 shows the dependencies of the maximum power enhancement ratio and the corresponding wavelength on the dipole-NP distance for the x-oriented dipole. For comparison, in this figure, we plot the curves for both cases with (wF) and without (w/oF) the SP feedback effect. With the feedback effect, the two curves are similar to their counterparts in Fig. 3. The variation trends of the two curves in the case without the feedback effect are also quite similar except that the power enhancement ratio is significantly smaller, indicating the importance of the feedback effect.

Fig. 6 Spectral dependencies of total radiated power enhancement ratio on wavelength in the case of x-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 7 Dipole-NP distance dependencies of the maximum total radiated power enhancement ratio and the corresponding wavelength in the case of x-oriented dipole. Both the results under the conditions with the feedback effect (wF) and without this effect (w/oF) are plotted.

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Figure 8 shows the total radiated power enhancement ratios as functions of wavelength at several a values for the z-oriented dipole. It is interesting to note that the curve patterns in Fig. 8 are quite different from their counterparts in Fig. 4. In certain wavelength ranges, the radiated power is enhanced even though the dipole strength is suppressed. In other wavelength ranges, the radiated power is suppressed even though the dipole strength is enhanced. The most prominent difference can be seen in the curve of a = 40 nm. The broad hump of $| p | / p_{0}$ peaked around 626.2 nm in Fig. 4 results in a sharp peak around 587.2 nm and a dip around 634.7 nm of total radiated power in Fig. 8. The different curve patterns in Fig. 8 indicate that in the case of z-oriented dipole, the factor of relative phase retardation is quite important besides the strengths of the modified dipole and the LSP resonance in determining the total radiated power. Figure 9 shows the data similar to Fig. 7 for the z-oriented dipole. In this figure, the curve for the wavelength of maximum power enhancement ratio in the case with the feedback effect is truncated in the range of a > 95 nm because it becomes difficult to identify the maximum power enhancement point in spectrum when the enhancement becomes negligibly small in this range of a value. It is noted that the maximum power enhancement ratio in the case with the feedback effect becomes smaller than that in the case without the feedback effect when a is larger than 70 nm even though the maximum $| p | / p_{0}$ is still larger than unity (see Fig. 5). This result confirms the importance of the factor of relative phase retardation in determining the total radiated power.

Fig. 8 Spectral dependencies of total radiated power enhancement ratio on wavelength in the case of z-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 9 Dipole-NP distance dependencies of the maximum total radiated power enhancement ratio and the corresponding wavelength in the case of z-oriented dipole. Both the results under the conditions with the feedback effect (wF) and without this effect (w/oF) are plotted.

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3.4 Discussions

As demonstrated in Figs. 2, 4, 6, and 8, although the x-oriented dipole shows the similar spectral dependencies of the total radiated power and $| p | / p_{0}$ , those for the z-oriented dipole are quite different, particularly when a is small. The different behaviors between the x- and z-oriented dipoles can be understood by expressing the total radiated power enhancement ratio as α = g(λ)( $| p | / p_{0}$ )². Here, λ is the wavelength. Also, the expression g(λ) contains the factors of the spectral dependence of LSP radiation and the relative phase retardation between the radiation contributions of the dipole and induced LSP. In Fig. 10 , we plot g(λ) for the x- and z-oriented dipoles at a = 40 nm. Here, for the x-oriented dipole, g(λ) is relatively weakly dependent on wavelength, particularly on the short-wavelength side, when compared with a curve obtained by squaring the corresponding values in Fig. 2. However, g(λ) shows a sharp peak around the wavelength of LSP resonance for the z-oriented dipole. This peak is significantly sharper when comparing with a curve obtained by squaring the corresponding values in Fig. 4. Also, the Fano-like oscillation of g(λ) for the z-oriented dipole in Fig. 10 is phase reversed from that of $| p | / p_{0}$ in Fig. 4. The g(λ) behaviors in Fig. 10 explain that the spectral dependence of the total radiated power of the dipole-NP system in the case of x-oriented dipole is dominated by that of $| p | / p_{0}$ . On the other hand, in the case of z-oriented dipole, the spectral dependence of the total radiated power is dominated by g(λ), i.e., the factors of LSP resonance feature and the relative phase retardation between two emission sources.

Fig. 10 Spectral dependencies of g(λ) for the cases of x- and z-oriented dipoles at a = 40 nm.

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The issue of relative phase retardation can be more clearly realized from the radiation patterns of the dipole-NP system. Figures 11(a) –11(f) show the radiation patterns of the dipole-NP system in the case of x-oriented dipole at the wavelengths of 520.7 ((a) and (b)), 571.2 ((c) and (d)), and 610 nm ((e) and (f)) when a is equal to 40 nm. These wavelengths correspond to the two major maxima and the minimum in the curve of a = 40 nm in Fig. 6. In each figure, the numbers along the semicircle indicate the polar angle with zero for the z-axis. Figs. 11(a), 11(c), and 11(e) (Figs. 11(b), 11(d), and 11(f)) demonstrate the patterns when the azimuth angle is 0 (π/2). Three radiation patterns are plotted in each figure, including the case of the dipole-NP system with the feedback effect (black solid curve), the case of the dipole-NP system without the feedback effect (blue dashed curve), and the case of the dipole alone (red dash-dotted curve). Meanwhile, the two arrows of opposite orientations in each figure represent the radiating dipole and the dominating mirror dipole of LSP resonance in the Ag NP. With x orientation of the radiating dipole, the mirror dipole is roughly out of phase by π from the source dipole, particularly when the phase retardation or the dipole-NP distance is small, leading to a roughly destructive interference result. Such a destructively interfered result leads to a generally smaller total radiated power and weaker fluctuations around unity in g(λ), when compared with the case of z-oriented dipole. It is noted that all the patterns of the dipole-NP system in Figs. 11(a)–11(f) show asymmetric radiations tilted toward the z axis. The x-z-plane radiation patterns of the dipole-NP system in the case of z-oriented dipole at 450, 523.6, 587.2, and 634.7 nm are shown in Figs. 12(a) –12(d), respectively, when a = 40 nm. In this situation, the radiating dipole and the mirror dipole in the Ag NP are roughly in phase (when excluding the factor of phase retardation), leading to the roughly constructive interference results in the x-y plane, particularly when a is small. Therefore, the total radiated power becomes strongly dependent on the LSP resonance strength and the relative phase retardation of the two emission sources (dipole and LSP). Under such conditions, g(λ) is more sensitive to wavelength variation, when compared with the case of x-oriented dipole, as demonstrated in Fig. 10. In Figs. 12(c) and 12(d), one can again clearly see the asymmetric radiation patterns, tilted toward the z axis.

Fig. 11 Radiation patterns of the dipole-NP system in the case of x-oriented dipole at the wavelengths of 520.7 ((a) and (b)), 571.2 ((c) and (d)), and 610 nm ((e) and (f)) when a is equal to 40 nm. Parts (a), (c), and (e) ((b), (d), and (f)) demonstrate the patterns when the azimuth angle is 0 (π/2). Three radiation patterns are plotted in each part, including the cases with the feedback effect (black solid curve) and without the feedback effect (blue dashed curve), and the case of the dipole alone (red dash-dotted curve). The two arrows of opposite orientations in each part represent the radiating dipole and the dominating mirror dipole of LSP resonance in the Ag NP.

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Fig. 12 Radiation patterns of the dipole-NP system in the case of z-oriented dipole at 450 (a), 523.6 (b), 587.2 (c), and 634.7 nm (d) when a = 40 nm. In this situation, the two effective dipoles are roughly in the same orientation.

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In the experimental results of SP coupling reviewed in section 2, the distance between the metal/semiconductor interface and the first QW in an LED is in the range of 70-85 nm. With such LED structures, we could observe emission enhancements of more than several tens percent. However, from Figs. 6 and 8 of numerical calculations based on the coupling of a single radiating dipole and LSP modes on a single Ag NP, such a large enhancement in total radiated power can be obtained only when the dipole is located at a distance within ~50 nm from the metal surface. It is noted that the enhanced dipole strength in classical physics corresponds to the increased radiative recombination rate of carriers in a QW of an LED. The overall emission efficiency of an SP-coupled LED depends on at least three factors, including 1) the relative level of the modified radiative recombination rate and non-radiative recombination rate, 2) the induced SP strength and its radiation efficiency, and 3) the relative phase retardation of the dipole and SP radiations. The large emission enhancements in the experimental implementations can be attributed to several factors, which are not included in our simple model of the dipole-NP system. First, in an experimental implementation, an SP mode may couple with more than one dipole. It is expected that the coupling process will lock the phases and lead to coherent emissions of those coupled dipoles. An LED with partially coherent emissions of carriers will have stronger output intensity, when compared with that of purely incoherent emissions. The coupling of an SP mode with more than one radiating dipole deserves further investigation. The other important issue of SP coupling, which may be related to the effective emission enhancement of an LED, is the difference between LSP and SPP coupling. This issue can be theoretically studied by replacing the metal nanosphere in Fig. 1 by a metal block of flat surface. Other effects of using metal nanostructures on an LED for enhancing emission may include light extraction through metal scattering.

4. Conclusions

In summary, we have first reviewed the experimental demonstrations of LED fabrication with SP coupling with the radiating dipoles in its QWs. The SP coupling with a radiating dipole could create an alternative emission channel through SP radiation for enhancing the effective IQE when the intrinsic non-radiative recombination rate was high, reducing the EQE droop effect at high current injection levels, and producing partially polarized LED output by inducing polarization-sensitive SP for coupling. Then, we reported the theoretical and numerical study results of SP-dipole coupling based on a simple coupling model between a radiating dipole and the LSP induced on a nearby Ag NP. To include the dipole strength variation effect caused by the field distribution built in the coupling system, the radiating dipole was represented by a saturable two-level system. The spectral and dipole-NP distance dependencies of dipole strength enhancement and total radiated power increase of the coupling system were demonstrated and interpreted. The results showed that the dipole-SP coupling could indeed enhance the total radiated power. The enhancement was particularly effective when the feedback effect was included and hence the dipole strength was increased. Further theoretical and numerical investigations are needed for more closely simulating the real implementation of an LED with SP coupling.

Acknowledgments

This research was supported by National Science Council, The Republic of China, under the grants of NSC 99-2622-E-002-022-CC2, NSC 99-2221-E-002-123-MY3, NSC 99-2221-E-002-113, by Epistar Corporation (99H31022), by the Excellent Research Projects of National Taiwan University (99R80203 and 99R80306), and by U.S. Air Force Scientific Research Office under the contract of AOARD-10-4049.

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Surface plasmon coupling with radiating dipole for enhancing the emission efficiency of a light-emitting diode

Abstract

1. Introduction

2. Review of surface plasmon coupled light-emitting diode

2.1 Introduction

2.2 Emission efficiency enhancement of surface plasmon coupled LED

2.3 Reduction of droop effect through surface plasmon coupling

2.4 Partially polarized output from surface plasmon coupled LED

3. Theoretical study of surface plasmon coupling with radiating dipole

3.1 Introduction

3.2 Problem geometry and theoretical formulations

3.3 Numerical results

3.4 Discussions

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (12)

Equations (9)

Optics Express