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The modulation bandwidths of the light-emitting diodes (LEDs) of different mesa sizes with and without surface plasmon (SP) coupling effect are compared. Due to the significant increase of carrier decay rate, within the size range of LED square-mesa from 60 through 300 micron and the injected current-density range from 139 through 1667 A/cm2, the SP coupling can lead to the enhancement of modulation bandwidth by 44-48%, independent of the variations of LED mesa size or injected current level. The enhancement ratios of modulation bandwidth of the samples with SP coupling with respect to those of the samples without SP coupling are lower than the corresponding ratios of the square-root of photoluminescence decay rate due to the increases of their RC time constants (the product of device resistance and capacitance). The increases of the RC time constants in the samples with SP coupling are attributed to the increases of their device resistance levels when the Ag nanoparticles and GaZnO dielectric interlayer are added to the LED surface for effectively inducing SP coupling.
© 2015 Optical Society of America
1. Introduction
Besides the application to solid state lighting, InGaN/GaN quantum-well (QW) light-emitting diodes (LEDs) have been considered for the development of visible communications [1–5]. Combining with the function of general lighting, LEDs can be used for indoor short-range data transmission. In this regard, besides high emission efficiency, a large modulation bandwidth becomes an important target in the development of visible LED. For increasing the modulation bandwidth of an LED, usually the efforts focus on the design of LED structure to reduce the capacitance (C) such that the product of its resistance (R) and capacitance (RC time constant) can be decreased. Micro-LEDs of small mesas have been developed for reducing the RC time constants in such devices [6–16]. However, with a reduced mesa size, the LED output power is decreased. Although an array of micro-LED can provide us with high output power, the required denser circuit grid makes the fabrication cost higher. Also, the overall capacitance of such a micro-LED array can still be quite large. An alternative approach is needed for enhancing the modulation bandwidth of an LED without sacrificing its output power level or RC time constant. For this purpose, enhancing the radiative recombination rate of carriers in the QWs of an LED is a useful development direction since the modulation bandwidth of an LED is related to the carrier decay rate in its QWs besides the device RC time constant. Also, the enhancement of radiative recombination rate can increase LED output power that can compensate the output power reduction in decreasing the mesa size. Besides the factor of RC time constant, the modulation bandwidth of an LED is controlled by a decay time constant, τ, which is given by [17, 18]
This decay time (τ) is related to the carrier decay rate (B), injection current density (J), and active layer thickness (d). Here, q is the electron charge. The modulation bandwidth of an LED increases with the decrease of this decay time constant. Therefore, when the carrier decay rate is increased, the injection current density is increased, or the thickness of the active layer is decreased in an LED, its modulation bandwidth is enhanced. This decay time constant τ and the RC time constant are equally important in determining the modulation bandwidth of an LED although it is difficult to resolve the relation or interplay between these two factors.To increase the carrier decay rate in the QWs of an LED without sacrificing its output power, the technique of surface plasmon (SP) coupling in an LED is useful. It has been demonstrated that SP coupling in an LED can enhance the carrier decay rate through the increased overall emission rate of the SP-exciton coupling system [19–22]. In this coupling process, energy of carriers in a QW is effectively transferred into an SP mode for radiation such that the carrier density decays very fast. In other words, the effective radiative recombination rate is enhanced. It is noted that in such a coupling process, the internal quantum efficiency (IQE) of a QW and the light extraction efficiency of a device can be increased, leading to higher overall emission efficiency or a higher output power level [19–22]. Therefore, by using the SP-coupling technique, not only the modulation bandwidth of an LED can be enhanced, but also its output power level can be raised. However, as mentioned above, the RC time constant or the lateral dimension of an LED is still an important factor for enhancing its modulation bandwidth. Hence, a combination of the SP coupling technique with a reasonably small mesa size can optimize the LED performance of maximizing both modulation bandwidth and output power level.
In this paper, we demonstrate the enhancement effects of modulation bandwidth through SP coupling in InGaN/GaN QW LEDs of different mesa sizes. The SP coupling is implemented by depositing Ag nanoparticles (NPs) on the p-GaN layer with a dielectric interlayer (DI) in between. The use of the DI can blue shift the localized surface plasmon (LSP) resonance peak from the green into blue range for effectively coupling with the blue-emitting QWs of an LED [23]. To minimize the effect on device resistance of the LED, we use ZnO with highly-degenerate Ga doping (GaZnO) as the DI material. GaZnO is a good conductor under direct current drive, but is a dielectric material of ~1.8 in refractive index in the optical frequency range. The results show that both the SP-coupling effect and device mesa size play important roles in increasing the modulation bandwidth of an LED. The enhancement percentage of modulation bandwidth through SP coupling is not significantly changed in varying the LED mesa size. In section 2 of this paper, the sample structures and their fabrication procedures are described. The optical characterization results of the samples are given in section 3. Then, the basic measurement results of LED performances are presented in section 4. The modulation responses of those LED samples are reported in section 5. Discussions of the modulation responses are made in section 6. Finally, conclusions are drawn in section 7.
2. Sample structures and fabrication procedures
Two similar LED epitaxial structures are grown with metalorganic chemical vapor deposition on c-plane sapphire substrate. Either epitaxial structure successively consists of a 1-μm u-GaN layer, a 2-μm n-GaN layer, a five-period QW structure (including a ~3 nm InGaN well and ~10 nm u-GaN barriers on both sides in each period), a 20-nm p-AlGaN layer, and a p-GaN layer. The two LED epitaxial structures have different p-GaN thicknesses, one at 120 nm and the other at 50 nm. The QW emission wavelengths of both epitaxial structures are around 476 nm. Each LED epitaxial structure is used for fabricating five LED samples of different square-mesa sizes at 300, 240, 180, 120, and 60 μm. Those LED samples fabricated on the epitaxial structure of 120-nm (50-nm) p-GaN layer are successively designated as samples A-300 through A-60 (B-300 through B-60). The circular p-contact areas at the mesa centers have the diameters of 60, 48, 36, 24, and 12 μm for samples A-300 through A-60 or samples B-300 through B-60, respectively. By adding a GaZnO DI layer of 10 nm in thickness and then randomly distributed Ag NPs on samples B-300 through B-60, we obtain samples C-300 through C-60, respectively. The collective designation of sample A, B, or C is used to refer to the samples of different mesa sizes in the same group when their values of a specific parameter are essentially the same. Rows 1 and 2 of Table 1 show the designations of samples A-C and their structure features, respectively. The 10-nm GaZnO DI is deposited with molecular beam epitaxy at 250 °C in substrate temperature. Its resistivity, mobility, and electron concentration are 1.6 x 10−4 Ω-cm, 22 cm2/V-s, and 1.5x1021 cm−3, respectively [24]. Also, the transmission of a GaZnO layer of 250 nm in thickness is higher than 90% in the visible range. The Ag NPs are formed by depositing a thin Ag layer of ~2 nm in thickness (growth time of 200 sec with the average growth rate of 0.01 nm/sec in an electron-beam evaporator) on the GaZnO DI, followed by a thermal annealing process for 30 min at 300 °C with ambient nitrogen. The inset of Fig. 1 shows the tilted scanning electron microscopy (SEM) image of the Ag NPs on the GaZnO DI. The average planar diameter of the quasi-spherical Ag NPs is ~43 nm. After mesa definition and metal contact formation, a Ni (5 nm)/Au (5 nm) current spreading layer is added to the top surfaces of all the aforementioned samples.
Table 1. Assignments of samples and their optical characterization results
Fig. 1 Transmission spectra of samples C-300 through C-60. The vertical dashed line indicates the QW emission spectral peak at 476 nm. The inset shows the SEM image of the Ag NPs on the GaZnO DI.
3. Optical characterization results
In Fig. 1, we show the transmission spectra of samples C-300 through C-60. There are five curves in this figure although it is difficult to differentiate one from the other. The transmission spectrum of a sample similar to C-300 without Ag NPs is used as the baseline for obtaining the measurement results shown in Fig. 1. Here, the depressions correspond to the mixed effects of different LSP resonance modes of a single Ag NP and different LSP resonance peaks of individual Ag NPs of different sizes. The depression depths represent the collective LSP resonance strengths. The depression minimum of the transmission spectrum varies slightly from 477.8 through 481.6 nm, as shown in row 4 of Table 1. The minima of the broad depressions are close to the QW emission wavelengths around 476 nm, as marked by the vertical dashed line in Fig. 1 and shown in row 3 of Table 1, such that the LSP resonance strengths at the QW emission wavelengths of samples C-300 through C-60 are about the same.
To confirm the SP coupling effects in samples C-300 through C-60, temperature-dependent photoluminescence (PL) measurement is undertaken for evaluating the IQEs of samples A-C. Because the IQE of a sample is independent of its mesa size, only one IQE value is obtained for either sample A, B, or C, as shown in row 5 of Table 1. Here, one can see that the IQE of sample A (35.5%) is significantly higher than that of sample B (25.2%) even though they have about the same emission wavelength. The higher IQE of sample A, which has a thicker p-GaN layer, can be attributed to the longer thermal annealing time for the QWs during high-temperature p-GaN overgrowth [25]. With the Ag NPs and DI on sample C, the SP coupling effect leads to an enhanced IQE at 46.6%, which is increased by ~31 and ~85% when compared with samples A and B, respectively. Time-resolved PL (TRPL) measurement can also be used for confirming the SP coupling effect. In Fig. 2, we show the TRPL profiles of samples A-C at room temperature. Here, the quasi-linear semi-log curves before 3 ns indicate essentially exponential decays of PL intensity. The deviations from the quasi-linear plots in the range of >3 ns in Fig. 2 are caused by the multiple reflections of PL signal in the samples. Therefore, only the range between the peak and 3 ns is used for fitting the exponential decay time of each curve. In row 6 of Table 1, we show the PL decay times of samples A-C. Here, the shorter PL decay time of sample B, when compared with sample A, can be attributed to the stronger non-radiative recombination in this sample since it has a lower IQE. The SP coupling effect in sample C leads to a significantly shorter PL decay time, when compared with sample B. The comparisons of IQE and PL decay time between samples B and C confirm the SP coupling effect in sample C. The SP coupling effect can be further confirmed by comparing the results between two samples with Ag NPs but with different p-GaN-layer thicknesses. Such a comparison has been made in a previous publication and is not repeated here [23].
4. Measurement results of light-emitting diodes
In Figs. 3(a)-3(c), we show the relations between injected current and applied voltage (I-V curves) of samples A-300 through A-60, B-300 through B-60, and C-300 through C-60, respectively, which are measured with a semiconductor device analyzer (B1500A, Agilent Technologies). In all the three groups of sample, a smaller mesa size leads to a larger device resistance level. In rows 2-4 of Table 2, we show the device resistance values of samples A-300 through A-60, B-300 through B-60, and C-300 through C-60, respectively. Here, the slightly higher device resistance in sample series B of a thin p-GaN layer, when compared with sample series A of a thick p-GaN layer, is attributed to the poorer current spreading in the thin p-GaN layer. Although the GaZnO layer is conductive, because of the different work functions between GaZnO (~4.2 eV) [26] and p-GaN (~7.6 eV) [27], the resistance levels in sample series C become slightly higher, when compared with sample series B. It has been reported that an appropriate thermal annealing process can reduce the contact resistance between GaZnO and p-GaN [28]. In Figs. 4(a)-4(c), we show the relations between device capacitance and reverse-biased voltage (C-V curves) of samples A-300 through A-60, B-300 through B-60, and C-300 through C-60, respectively, which are obtained by using an HP 4280A capacitance meter at 1 MHz. In each sample, the capacitance increases with decreasing reverse-biased voltage. Also, the capacitance increases with mesa size. Meanwhile, a thinner p-GaN layer leads to smaller capacitance. From the comparison between Fig. 4(b) and 4(c), we can see that the additions of the GaZnO DI and Ag NPs do not significantly change the capacitance level. The capacitance values of all the samples at −5 V are listed in rows 5-7 of Table 2. Then, the RC time constants of all the samples are listed in rows 8-10 of Table 2. Here, the numbers before the slashes within the parentheses represent the ratios of RC time constant with respect to the values of the samples with 60 μm in mesa size in individual sample series. Also, the numbers after the slashes within the parentheses represent the ratios of RC time constant with respect to the values of sample series B in individual sample groups of the same mesa sizes. One can see that although the device resistance increases with decreasing mesa size, the RC time constant decreases with decreasing mesa size because the device capacitance decreases significantly with decreasing mesa size.
Fig. 3 (a)-(c): Relations between injected current and applied voltage (I-V curves) of samples A-300 through A-60, B-300 through B-60, and C-300 through C-60, respectively.
Table 2. Characterization results of the LED samples with various mesa sizes
Fig. 4 (a)-(c): Relations between device capacitance and reverse-biased voltage (C-V curves) of samples A-300 through A-60, B-300 through B-60, and C-300 through C-60, respectively.
In Figs. 5(a)-5(c), we show the LED output intensities per mesa area as functions of injected current density of sample series A-C, respectively, by normalizing the results with respect to that of sample B-300 at 333 A/cm2 in current density. The output intensity in each sample is obtained by summing those of top and bottom emissions. Here, one can see that in either sample series, a smaller mesa size results in higher output intensity per mesa area. This trend is attributed to the higher light extraction efficiency in a device of a smaller mesa size. Among the three sample series, the variation trend of output intensity follows that of their IQEs. In rows 11-13 of Table 2, we show the normalized output intensities per mesa area of all the samples when the injected current density is 333 A/cm2. In row 11 (13), the numbers in the parentheses show the normalized values with respect to the level of sample A-300 (C-300). In Figs. 6(a)-6(c), we show the relative efficiencies as functions of injected current density of sample series A-C, respectively. The relative efficiency is obtained through the division of normalized intensity shown in Figs. 5(a)-5(c) by the product of the corresponding injected current density and applied voltage and then the normalization with respect to the maximum level in the same sample series. Here, one can see that the effect of efficiency droop is stronger in an LED of a larger mesa size in either sample series A, B, or C. Also, the samples with a thinner p-GaN layer have stronger efficiency droop effects, when compared with those of a thicker p-GaN layer. However, with SP coupling, the efficiency droop effects in the samples of a thinner p-GaN layer are significantly reduced. In rows 14-16 of Table 2, we show the efficiency droop ranges of all the samples. The efficiency droop range in each curve is defined as the reduction percentage of relative efficiency at 333 A/cm2 in current density with respect to the maximum level of the same curve. Here, one can see that with SP coupling in sample series C, their efficiency droop ranges are significantly smaller than those of samples series B.
Fig. 5 (a)-(c): LED output intensities per mesa area as functions of injected current density of sample series A-C, respectively, by normalizing the results with respect to that of sample B-300 at 333 A/cm2 in current density.
Fig. 6 (a)-(c): Relative efficiencies as functions of injected current density of sample series A-C, respectively.
5. Modulation responses
Figure 7 shows the setup for measuring the modulation bandwidth of an LED. Here, a spectrum analyzer (GW Instek Spectrum Analyzer GSP930) is used for providing an alternating-current (AC) voltage signal of 100 mV in modulation depth to combine with a direct-current (DC) voltage signal from a power supply. The mixed voltage signal drives the LED to emit light, which is collected by a fiber and detected by a photoreceiver (Newport 1591FC-AC 3-GHz photoreceiver). Then, the modulation bandwidth is monitored by the spectrum analyzer. The modulated signal pattern is also monitored by an oscilloscope for making sure that it is not distorted. In Figs. 8(a)-8(c), we show the modulation responses of samples series A-C, respectively, when the injected current density is fixed at 139 A/cm2. In each sample series, a smaller mesa size leads to a larger modulation bandwidth. Here, the modulation frequency for the signal amplitude dropping to −3 dB of the direct-current level is defined as the modulation bandwidth. The modulation bandwidths of all the samples when injected current density is 139 A/cm2 are listed in the last three rows of Table 2. Here, the numbers before the slashes within the parentheses show the enhancement ratios of modulation bandwidths with respect to the values of the samples with the mesa size at 300 μm in individual sample series. Also, the numbers after the slashes within the parentheses represent the ratios of modulation bandwidth with respect to the values of sample series B in individual sample groups of the same mesa sizes. One can see that by reducing the mesa size from 300 to 60 μm, the modulation bandwidth is increased by 199, 194, and 190% in sample series A-C, respectively. Without SP coupling, the modulation bandwidths of the samples with a thinner p-GaN layer are slightly larger than those with a thicker p-GaN layer. In comparing sample series B and C, the modulation bandwidths can be enhanced by 45-48% through SP coupling.
Fig. 8 (a)-(c): Modulation responses of samples series A-C, respectively, when the injected current density is fixed at 139 A/cm2.
In Figs. 9(a)-9(c), we show the modulation responses of samples A-60, B-60 and C-60, respectively, when injected current increases from 10 through 60 mA. In either sample, the modulation bandwidth increases with injected current. Their modulation bandwidths are listed in Table 3. Here, the numbers before the slashes within the parentheses show the enhancement ratios of modulation bandwidth with respect to the values at the injected current of 10 mA in individual samples. Also, the numbers after the slashes within the parentheses represent the ratios of modulation bandwidth with respect to the values of sample B-60 at different injected current levels. We can see that by increasing injected current from 10 through 60 mA, the modulation bandwidths can be enhanced by 187, 185, and 186% in samples A-60, B-60, and C-60, respectively. Also, in comparing samples B-60 and C-60, the modulation bandwidths can be enhanced by 43-45% through SP coupling.
Fig. 9 (a)-(c): Modulation responses of samples A-60, B-60 and C-60, respectively, when injected current increases from 10 through 60 mA.
Table 3. Modulation bandwidths of samples A-60, B-60, and C-60 at various injected current levels
6. Discussions
Besides the factor of RC time constant, the modulation bandwidth of an LED is inversely proportional to the decay time given in Eq. (1) and hence increases with the square-roots of injected current density and carrier decay rate. In Fig. 10, we show the modulation bandwidths as functions of the square-root of injected current density (J) for samples A-60, B-60, and C-60, which have about the same RC time constant (see Table 2). Here, we can see that except the saturation trend at high current density, the three curves are quite linear, indicating that when the RC time constant is fixed, the variation of modulation bandwidth essentially follows Eq. (1). Regarding the factor of carrier decay rate (B), which is roughly equal to the inverse of PL decay time in TRPL measurement, from the bottom row of Table 1, one can see that the ratios of the square-root of inverse PL decay time in sample series A and C with respect to that in sample series B are 0.93 and 1.61, respectively. This ratio of sample A (C) is smaller (larger) than the corresponding value of modulation bandwidth shown in the last three rows of Table 2 (the numbers after the slashes within the parentheses), which is 0.97-0.99 (1.45-1.48) in sample A (C). In other words, although the increasing trend of modulation bandwidth is consistent with the increasing trend of the square-root of inverse PL decay time, the proportionality does not follow Eq. (1). More specifically, according to Eq. (1), the modulation bandwidth of an individual sample in series C of a particular mesa size is expected to be 61% larger than that of the corresponding sample in series B. However, the measured modulation bandwidths of sample series C are higher than those of sample series B by only 45-48%. The smaller enhancement ratio of modulation bandwidth of sample C with respect to that of sample B, when compared with the corresponding ratio of the square-root of inverse PL decay time, can be attributed to the relatively larger RC time constants in sample series C (see Table 2). However, the slightly larger RC time constant of sample A, when compared with sample B, cannot be used for explaining its larger ratio of modulation bandwidth, when compared with the ratio of the square-root of inverse PL decay time, even though all those ratios are quite close to unity. Some uncertain factors may exist to generate such a small discrepancy. Both factors of RC time constant and the decay time shown in Eq. (1) are important in determining the modulation bandwidth of an LED. However, their relative importance and possible interplay are still unclear. In a high-speed photodetector or electro-absorption modulator, the device response speed is also controlled by the two factors of carrier decay time and RC time constant. In a GaAs-based high-speed photodetector, normally the absorbing GaAs layer is grown at a low temperature to increase the defect density and hence shorten the carrier decay time [29, 30]. Also, the device geometry needs to be well designed for reducing the RC time constant [30]. To achieve the high-speed response in an electro-absorption modulator, its waveguide geometry needs to be optimized for minimizing the RC time constant [31]. Both factors of carrier decay time and RC time constant are important for an optoelectronics device of a high modulation bandwidth or high response speed.
Fig. 10 Modulation bandwidths as functions of the square-root of injected current density (J) for samples A-60, B-60 and C-60.
The major function of SP coupling for the significant enhancement of modulation bandwidth is the reduction of carrier decay time. As shown in the last two rows of Table 2 and the last two rows of Table 3, the ratios of modulation bandwidth of sample series C with respect to those of sample series B are almost independent of the variation of mesa size or injected current level. The ratios are maintained within the range of 1.44-1.48. This is so because SP coupling only affects the PL decay time or radiative recombination rate among those factors controlling the modulation bandwidth of an LED. The PL decay time does not significantly change with mesa size unless current spreading is poor. The PL decay time may vary with excited carrier density or equivalently, the carrier decay rate may change with injected current density. However, this effect is mixed with the factor of the J-1/2 dependence shown in Eq. (1). With the effective enhancement of modulation bandwidth through SP coupling, a relatively larger RC time constant or LED mesa size can be used for simultaneously achieving a given LED modulation bandwidth and a given output power level.
7. Conclusions
In summary, we have compared the modulation bandwidths between the LEDs of different mesa sizes with and without SP coupling effects. Due to the significant increase of carrier decay rate, within the size range of LED square-mesa from 60 through 300 micron and the injected current-density range from 139 through 1667 A/cm2, the SP coupling could lead to the enhancement of modulation bandwidth by 44-48%, independent of the variations of mesa size or injected current level. The enhancement ratios of modulation bandwidth of the samples with SP coupling with respect to those of the samples without SP coupling were smaller than the corresponding ratios of the square-root of PL decay rate due to the increases of their RC time constants. The increases of the RC time constants in the samples with SP coupling were attributed to the increases of their device resistance levels when the Ag NPs and GaZnO DI were added to the LED surface for effectively inducing SP coupling.
Acknowledgments
This research was supported by Ministry of Science and Technology, Taiwan, under the grants of NSC 102-2221-E-002-204-MY3, MOST 103-2120-M-002-002, and MOST 103-2221-E-002-139, and by the Excellent Research Projects of National Taiwan University (103R890951 and 103R890952). Also, this research is sponsored by US Air Force Scientific Research Office under the contract of AOARD-14-4105.
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