Thermally induced variations of strain condition and ... - OSA Publishing

Thermally induced variations of strain condition and emission behavior in flat and bendable lightemitting diodes on different substrates Chun-Han Lin, Chia-Ying Su, Erwin Zhu, Chieh Hsieh, Charng-Gan Tu, Yu-Feng Yao, Hao-Tsung Chen, Che-Hao Liao, Horng-Shyang Chen, Yean-Woei Kiang, and C. C. Yang* Institute of Photonics and Optoelectronics, and Department of Electrical Engineering, National Taiwan University, 1, Roosevelt Road, Section 4, Taipei, 10617 Taiwan *[email protected]

Abstract: The emission behaviors of four light-emitting diodes (LEDs) of different substrate structures, including a lateral LED grown on sapphire, a vertical LED wafer-bonded onto Si (111), a bendable LED Ag-epoxied onto a flat metal, and another bendable LED Ag-epoxied onto a metal of a curved surface, under different duty cycles of current injection are compared. Their different variation trends of emission behavior with injection duty cycle are attributed to the different thermally-induced strain conditions in the epitaxial layers, which are controlled by their substrate structures, in increasing injection duty cycle or current level. The results of Raman scattering measurements during LED operation show that a stronger tensile strain is generated under heating for reducing the quantum-confined Stark effect and hence increasing emission efficiency when the epitaxial layer is not tightly bonded onto a hard substrate. Such a behavior is particularly stronger when the epitaxial layer is bent. ©2015 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (250.5590) Quantum-well, -wire and -dot devices.

References and links 1.

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Received 24 Nov 2014; revised 1 May 2015; accepted 2 Jun 2015; published 4 Jun 2015 15 Jun 2015 | Vol. 23, No. 12 | DOI:10.1364/OE.23.015491 | OPTICS EXPRESS 15491

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1. Introduction Thermal effect is a crucial factor for determining the performance of a light-emitting diode (LED). Efforts have been made for minimizing heat generation and removing the generated heat to optimize LED performance. Generally speaking, LED heating can produce three important effects, including long-term crystal quality degradation for reducing operation lifetime, defect activation for reducing emission efficiency, and band gap shrinkage for redshifting emission wavelength. However, the heating of the epitaxial layer can also affect its strain distribution. Such strain redistribution is caused by the thermal expansion of the epitaxial layer and its counteraction with the thick substrate. Because the strain redistribution can affect the quantum-confined Stark effect (QCSE) in a quantum well (QW) structure [1–5], heating can influence emission efficiency through other mechanisms besides the generation of thermally-activated defects. To optimize the performance of an LED, various substrates have been used for supporting the epitaxial nitride layers. Because of its low cost and mature overgrowth techniques, sapphire is still the most commonly used substrate for growing nitride LED structures. Due to the smaller lattice size of sapphire, when compared with GaN, a compressive strain is generated in the overgrown nitride epitaxial layer. To solve the electrically and thermally insulating problems of sapphire substrate, substrate liftoff techniques have been developed for fabricating vertical LEDs [6–11]. In such a device, the nitride epitaxial layer is wafer-bonded onto a conductive substituting substrate, such as Si, via a wafer-bonding metal layer for improving the electrical and thermal behaviors of the LED. In this situation, the epitaxial layer is still under compressive strain. Recently, this research group has fabricated a bendable LED through the removal of the wafer-bonded Si substrate from a vertical LED structure [12]. The LED epitaxial layer together with the wafer-bonding metal layer becomes bendable and can be epoxied onto a metal surface of a large curvature. It was found that before it was overheated, the bendable LED had higher output intensity, when compared with a vertical LED of the same epitaxial structure, particularly when injection duty cycle was large. This

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result was attributed to the larger thermal expansion of the wafer-bonding metal layer for applying a strong tensile strain to the nitride epitaxial layer in the heating process of the bendable LED such that the QCSE in its QWs was reduced. Such a tensile strain was weaker in a vertical LED because of the moderation of the wafer-bonded Si substrate. Although the thermally induced output enhancement was demonstrated in a bendable LED and the attributed mechanism was proposed, the evidence for this attribution and the details of the proposed mechanism have not been demonstrated yet. In particular, the comparison of the heating effect between lateral, vertical, and bendable LEDs has not been made. Such a comparison can help us in further understanding the effect of LED heating and the advantage of a bendable LED. A bendable LED has potential application to flexible display and lighting [13–17]. In this paper, we compare the heating effects between four LED samples of different substrate structures, including a lateral LED grown on sapphire substrate, a vertical LED wafer-bonded onto a Si (111) substrate, a bendable LED Ag-epoxied onto a flat metal substrate, and another bendable LED Ag-epoxied onto a curved metal substrate. The different heating effects between those samples are attributed to the different strain distributions caused by the different counteracting results of thermal expansion between the epitaxial layer and the underlying layers (including the wafer-bonding metal and substrate). Raman shifts of the epitaxial layers under different heating conditions are measured for demonstrating the strain distributions. In section 2 of this paper, the sample structures and fabrication procedures of the four LED samples are presented. The characterization results of those LED samples under different conditions of injection duty cycle are reported in section 3. Then, the Raman scattering measurement results are discussed in section 4. Further discussions on the measurement results are made in section 5. Finally, the conclusions are drawn in section 6. 2. Sample structures and fabrication procedures The general descriptions of the four LED samples (samples A-D) are given in row 2 of Table 1. The device structures of samples A-D are schematically demonstrated in Figs. 1(a)-1(d), respectively. Sample A represents a standard lateral LED grown on c-plane sapphire substrate. In this sample, after the growths of a thin buffer layer [not shown in Fig. 1(a)] at a low temperature (grown at 530 °C) and a 1-μm un-doped GaN layer (grown at 1010 °C), an LED structure, including a 2-μm n-GaN layer (grown at 1010 °C), a five-period InGaN (3 nm, grown at 740 °C)/GaN (15 nm, grown at 860 °C) QW structure (emission wavelength at ~455 nm), a 20-nm p-AlGaN (grown at 960 °C), and a 120-nm p-GaN (grown at 960 °C), is deposited. For fabricating LED sample A, a mesa of 300 μm x 300 μm in dimension is defined through lithography and inductively coupled plasma reactive ion etching. Its p-type surface is covered by a Ni (5 nm)/Au (5 nm) layer over the whole mesa for current spreading and a Ni (20 nm)/Au (100 nm) layer in patterned regions for p-contact and surface current flow. Sample B [see Fig. 1(b) for the structure] is a vertical LED fabricated based on the epitaxial structure of sample A through the procedures of wafer-bonding onto an n-Si (111) substrate and laser liftoff of sapphire substrate. The metal layers for wafer bonding on the nitride epitaxial layer and Si substrate include Ni (5 nm)/Ag (150 nm)/Ti (50 nm)/Au (1 μm)/In (1 μm) and Ti (50 nm)/Au (1 μm)/In (1 μm), respectively. After laser liftoff of sapphire substrate, a polishing process is applied for removing the un-doped GaN layer to expose the N-face n-GaN layer. Then, an LED mesa of also 300 μm x 300 μm in dimension is defined. The process for the vertical LED is completed after the depositions of a Ti (5 nm)/Au (5 nm) layer over the whole mesa for current spreading and a Ti (20 nm)/Au (100 nm) layer in the same patterned regions for n-contact and surface current flow on the N-face n-GaN layer. The wafer-bonding metal is used as the p-contact of the device. The bendable LEDs of samples C and D are fabricated by wet-etching the Si substrate of a vertical LED of sample B with HF/HNO3 mixed solution. After the removal of the Si substrate, the LED structure of the nitride epitaxial layer together with the wafer-bonding metal layer becomes curved, as shown in the pictures of Figs. 2(a) and 2(b). In sample C, the LED structure is Ag-epoxied onto a flat iron plat of 20 mm x 20 mm x 1 mm in dimension, as schematically demonstrated in Fig. 1(c)

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and shown in the picture of Fig. 2(c). In sample D, the LED structure is Ag-epoxied onto the curved surface of a soldering iron rod of 2 mm in cross-sectional diameter and 52 mm in length with a cone-shaped end of 13 mm in length, as schematically demonstrated in Fig. 1(d) and shown in the picture of Fig. 2(e). Figures 2(d) and 2(f) show the pictures of lit LEDs of samples C and D, respectively. Table 1. Structures and characterization results, including emission wavelengths, normalized output intensities under various injection conditions, and device resistance levels, of the four samples. Sample

A

B

C

D

Structure

lateral LED grown on sapphire substrate

vertical LED wafer-bonded onto Si substrate

bendable LED Ag-epoxied onto flat metal substrate

bendable LED Ag-epoxied onto curved metal substrate

Spectral peak at 5 mA with 100% in duty cycle (nm)

455.1

455.2

455.0

455.1

Output intensity at 100 mA with 1% in duty cycle

1.21

1.02

1.12

1.21


1.16

1.09

1.28

1.46


1.11

1.18

1.57

1.85


1.05

1.26

2.15

2.66


1

1.32

2.45

2.26

IQE (%)

38.2

42.9

49.1

63.1

Device resistance (Ω)

22.2

18.2

19.6

20.2

Fig. 1. (a)-(d): Schematic demonstrations of the device structures of samples A-D, respectively.

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Fig. 2. (a) and (b): Pictures of the bendable epitaxial layer together with the wafer-bonding metal layer. (c): Picture of sample C on a flat iron plate. (d) Picture of sample C with a lit LED device. (e): Picture of sample D on an iron rod. (f) Picture of sample D with a lit LED device.

3. Characterization results of light-emitting diodes The LED output spectral peaks of the four samples when injection current of 5 mA with 100% duty cycle is applied are listed in row 3 of Table 1. All of them are close to 455 nm, indicating the wafer uniformity in epitaxial growth. Figures 3-6 show the variations of normalized LED output intensity (with the right ordinate) and relative emission efficiency (with the left ordinate) with injection current of samples A-D, respectively, for five duty cycles of current injection at 1, 25, 50, 75, and 100%. The modulation frequency for different duty cycles is 1 kHz. In all those figures, the output intensities are normalized with respect to the level of 100% in duty cycle at 100 mA in injection current of sample A. The normalized output intensities are presented by multiplying the measured data by a factor of 100 divided by the duty cycle (in percentage). The relative emission efficiency is obtained by dividing the output intensity by the product of the corresponding applied voltage and injected current and then normalizing with respect to the maximum level among the results under various current injection conditions. The output intensity of sample A is obtained by taking the summation of the collected powers from the p-GaN and sapphire sides of the device. The output intensities of samples B-D are obtained from the output power collected only from the n-GaN side because the p-GaN side is covered by the wafer-bonding metal layer. To collect the emitted power from an LED sample on either p-GaN or substrate side, we use a large focusing lens of 2 cm in diameter for focusing the output power into a fiber bundle. Because the emitted power from the LED edge is small, the measured output intensity includes almost all the emitted power from an LED for reasonable comparison between different samples. The normalized output intensities at 100 mA in injection current of all the four samples under five conditions of injection duty cycles at 1, 25, 50, 75, and 100% are listed in rows 4-8, respectively, of Table 1. In Fig. 3 for sample A, one can see that either output intensity or emission efficiency increases with decreasing injection duty cycle. The efficiency droop effect is weak when duty cycle is lower than 75%. It becomes stronger as duty cycle increases. The variation trends of output intensity and relative efficiency with duty cycle of sample B are reversed from those of sample A, as shown in Fig. 4. Here, one can see that either output intensity or emission efficiency increases with increasing duty cycle of current injection. The efficiency droop effect is weak except when duty cycle is smaller than 25%. In Table 1, one can see that the output intensity of sample B with 100% duty cycle is higher than that of sample A with 1% duty cycle. The differences between Figs. 3 and 4 indicate the different heating effects between the lateral and vertical LEDs. In sample B, because of the good heat conduction in the wafer-bonding metal layer and Si substrate, its heating effect is weaker and hence the temperature in its active region is lower, when compared with sample A, under the same current injection condition such that the device performance does not degrade with injection duty cycle. In other words, the output intensity and emission efficiency can increase with injection duty cycle.

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Fig. 3. Variations of normalized LED output intensity (with the right ordinate) and relative efficiency (with the left ordinate) with injection current of sample A for five duty cycles of current injection at 1, 25, 50, 75, and 100%.

Fig. 4. Variations of normalized LED output intensity (with the right ordinate) and relative efficiency (with the left ordinate) with injection current of sample B for five duty cycles of current injection at 1, 25, 50, 75, and 100%.

The LED output behaviors of the bendable LEDs (samples C and D) are similar to that of the vertical LED (sample B); however, their variation ranges are significantly larger. In Fig. 5 for sample C, the output intensity increases with injection duty cycle significantly although it saturates when injection current is larger than 80 mA at 100% duty cycle. In Fig. 6 for sample D, the output intensity saturation becomes stronger when injection current is larger than 60 mA at 100% duty cycle, indicating the effect of overheating in this sample. In samples C and D, the efficiency droop effects are weak unless the device is overheated at 100% in duty cycle. In Table 1, one can see that the output intensities of samples C and D are generally significantly stronger than those of samples A and B. In particular, at 100 mA in injection current and 100% in duty cycle, the output intensity of sample C is 145 (113) % higher than the corresponding level of sample A (B). Also, at 100 mA in injection current and 75% in duty cycle, the output intensity of sample D is 161 (140) % higher than the corresponding level of sample A (B). It is noted that the only difference in structure between samples C and D is the radius of curvature of the metal substrate. The significantly smaller radius of curvature in sample D (1 mm), when compared with sample C (infinity), leads to a looser attachment through Ag epoxy between its wafer-bonding metal and the curved substrate surface such that the heat conduction becomes poorer. In this situation, under the same current injection condition, the temperature in the active region of sample D is expected to be higher than that in sample C such that the overheating behavior can be observed earlier in sample D in increasing either injected current or duty cycle. In row 9 of Table 1, we show the internal quantum efficiencies (IQEs) of the four samples. The IQE of a sample is obtained from the ratio of the integrated photoluminescence (PL) intensity at 300 K over that at 10 K. Here, one can see that a sample with a larger IQE has a higher output intensity and a higher overall

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efficiency. Based on the same epitaxial structure, the IQE is increased from 38.2% in a lateral LED structure (sample A) to 63.1% in a bendable LED on a curved substrate surface of 1 mm in radius of curvature (sample D).

Fig. 5. Variations of normalized LED output intensity (with the right ordinate) and relative efficiency (with the left ordinate) with injection current of sample C for five duty cycles of current injection at 1, 25, 50, 75, and 100%.

Fig. 6. Variations of normalized LED output intensity (with the right ordinate) and relative efficiency (with the left ordinate) with injection current of sample D for five duty cycles of current injection at 1, 25, 50, 75, and 100%.

Figures 7(a)-7(d) show the pictures of lit LEDs of samples A-D, respectively, when injection current is 50 mA and duty cycle is 100%. Here, one can see that sample D is the brightest, followed by samples C, B, and then A, showing the same variation trend as that in Table 1. Figure 8 shows the relations between injection current and applied voltage (I-V curves) of the four samples. Here, no current leakage can be observed up to −5 V under reverse bias in all the four samples. The inset of Fig. 8 shows the magnified I-V curves in the voltage range of 5.24-5.96 V for differentiating the four curves from each other. The device resistance levels of the four samples are shown in the bottom row of Table 1. Here, one can see that the resistance levels in the devices of vertical current flow (samples B-D) are lower than that of lateral current flow (sample A). Those of the bendable LEDs (samples C and D) are slightly larger, when compared with the vertical LED (sample B), particularly when the LED epitaxial layer is bended in sample D. Figures 9(a)-9(d) show the variations of output spectral peaks with injection current at various duty cycles for samples A-D, respectively. In each sample, when duty cycle is 1%, the spectral peak shows a blue-shift trend with increasing injection current or carrier density in the QWs due to the screening of QCSE [18]. As duty cycle increases, the blue-shift trend becomes weaker and a red-shift trend can be observed in samples A, C, and D. The red-shift trend is mainly caused by device heating, which leads to band gap shrinkage of GaN. As shown in Fig. 9(a) for sample A, at a high duty cycle, the spectral peak blue-shifts first at low injection current and then red-shifts at high injection current. The red-shift trend in sample B #228414 - $15.00 USD (C) 2015 OSA


is weaker. The red-shift trends in samples C and D are stronger, when compared with sample A, indicating the strong heating effects in the bendable LEDs. The heating-induced spectral red-shift is particularly stronger when LED is bended in sample D. By comparing the relative efficiency at 10 mA in injected current between the group of samples A and B (see Figs. 3 and 4) and the group of samples C and D (see Figs. 5 and 6), we can see that at this low injected current level, the relative efficiency varies little in samples A and B, but increases significantly in samples C and D when injection duty cycle increases from 1 through 100%. This observation indicates that the heating effects in samples C and D are actually quite strong even when the injected current level is as low as 10 mA. Such heating effects can also be seen in Figs. 9(c) and 9(d), in which the blue-shift trend of spectral peak turns into the red-shift trend at 10 mA when duty cycle increases from1 through 100%.

Fig. 7. (a)-(d): Pictures of lit LEDs of samples A-D, respectively, when injection current is 50 mA and duty cycle is 100%.

Fig. 8. Relations between injection current and applied voltage (I-V curves) of the four samples. The inset shows the magnified I-V curves in the voltage range of 5.24-5.96 V for differentiating the four curves from each other.

4. Strain condition measurements The generally higher output intensities in the bendable LEDs (samples C and D), when compared with the lateral and vertical LEDs (samples A and B), are attributed to the differences of QCSE in their QWs. With a stronger QCSE, the potential of a QW is more tilted, leading to a larger separation between electrons and holes and hence a smaller radiative recombination rate [1–5, 18]. To understand the differences of intrinsic QCSE (without current injection) between the four samples, we measure the PL spectral peak variations in changing the reverse-biased voltage of the four samples. The results are shown in Fig. 10. Here, one can see that in each sample, the PL spectral peak blue-shifts with increasing reverse-biased voltage. Under reverse bias, the applied voltage tends to flatten the tilted potential in a QW, resulting in a larger effective band gap and hence a shorter emission wavelength [4, 5]. Hence, in increasing the reverse-biased voltage, the blue-shift range of PL spectral peak is roughly proportional to the potential tilt slope or the strength of QCSE. The blue-shift ranges of the four samples are listed in row 2 of Table 2. Here, one can see that sample D has the smallest blue-shift range, followed by samples C, B, and then A, indicating the weaker QCSEs in the vertical and bendable LEDs. In particular, the bendable LED with a curved substrate has the weakest QCSE. #228414 - $15.00 USD (C) 2015 OSA


Fig. 9. (a)-(d): Variations of output spectral peak with injection current at various duty cycles for samples A-D, respectively.

Fig. 10. PL spectral peak variations with reverse-biased voltage of the four samples. Table 2. Measured strain-related results, including PL spectral blue-shift ranges under reverse bias and Raman shifts under various measurement conditions, of the four samples. Sample

A

B

C

D

2.91

1.96

1.26

0.85

Peak position of Raman shift spectrum (cm )

571.4

569.6

566.9

566.3

Variation range of Raman shift at 20 mA in injection current by changing duty cycle (cm−1)

0.15

0.1

0.51

0.71

Variation range of Raman shift at 50 mA in injection current by changing duty cycle (cm−1)

0.35

0.21

2.03

2.53

Variation range of Raman shift at 25% in duty cycle by changing injection current (cm−1)

0.18

0.11

1.02

1.27

Variation range of Raman shift at 100% in duty cycle by changing injection current (cm−1)

0.36

0.22

2.06

2.56

PL spectral blue-shift range under reverse bias (nm) −1

The differences in QCSE among the four samples are related to the strain conditions of their epitaxial layers. Figure 11 shows the spectra of Raman scattering measurement of the four samples. Here, the peak in each curve corresponds to the E2 phonon feature of GaN. The vertical dashed line indicates the strain-free E2 phonon feature of GaN at 567.6 cm−1 [19]. The #228414 - $15.00 USD (C) 2015 OSA


dashed curves in Fig. 11 show the Gaussian fitting results to the solid curves of measured data for reading the peak positions. The peak positions of Raman shift spectra of the four samples are shown in row 3 of Table 2. We can see that in samples A and B, with the epitaxial layer grown on sapphire substrate and wafer-bonded onto Si substrate, the E2 phonon features are located at 571.4 and 569.6 cm−1, respectively, indicating that the nitride epitaxial layers are compressively strained. In the bendable LEDs, with the radii of curvature at infinity and 1 mm in samples C and D, the E2 phonon features are located at 566.9 and 566.3 cm−1, respectively, indicating that the nitride epitaxial layers have tensile strains now. A smaller radius of curvature leads to a stronger tensile strain. From the results in Figs. 10 and 11, one can see that the tensile strains in samples C and D result in weaker QCSEs, leading to stronger output intensities, when compared with samples A and B.

Fig. 11. Raman scattering spectra of the four samples showing the E2 phonon features of GaN. The vertical dashed line indicates the strain-free E2 phonon feature of GaN at 567.6 cm−1. The dashed curves show the Gaussian fitting results to the solid curves of measured data for reading the peak positions.

To further understand how the heating process changes the strain condition of the epitaxial layer and hence the QCSE strength in increasing injection current and duty cycle, Raman scattering measurements are undertaken under the conditions of fixing duty cycle (injection current) while varying injection current (duty cycle). Figures 12(a)-12(d) show the Raman scattering spectra of samples A-D, respectively, with five injection duty cycles at 1, 25, 50, 75, and 100% when injection current is fixed at 50 mA. In each part of the figure, again, the vertical dashed line indicates the strain-free E2 phonon feature of GaN at 567.6 cm−1. Also, the dashed curves show the Gaussian fitting results to the solid curves of measured data. Here, in each sample, the epitaxial layer becomes more weakly compressive-strained or more strongly tensile-strained when injection duty cycle increases. Similar variation trends are observed when the fixed injection current is reduced to 20 mA. Figures 13(a)-13(d) show the Raman scattering spectra of samples A-D, respectively, with six injection current levels at 0, 10, 20, 30, 40, and 50 mA when injection duty cycle is fixed at 100%. Here, in each sample, the epitaxial layer becomes more weakly compressive-strained or more strongly tensilestrained when injection current increases. Similar variation trends are observed when the fixed duty cycle is reduced to 25% and injection current varies from 0 through 100 mA. The variations of Raman shift in the four samples under the four measurement conditions are summarized in Figs. 14(a)-14(d). In Fig. 14(a) [14(b)], duty cycle is varied while injection current is fixed at 20 (50) mA. In Fig. 14(c) [14(d)], injection current is varied while duty cycle is fixed at 25 (100) %. In the measurement of fixing duty cycle at 100%, injection current is limited to 50 mA, beyond which the LED output noise becomes stronger than the Raman scattering signal such that the reading of Raman scattering data becomes difficult. The variation ranges of Raman shift under the four measurement conditions in Figs. 14(a)-14(d) (the difference between the data points at the left and right ends) are listed in rows 4-7 of Table 2. Here, one can see that under all the measurement conditions, sample B always has the smallest variation ranges of Raman shift among the four samples. The variation ranges of samples C and D are significantly larger than those of samples A and B. Sample D always has

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the largest variation range of Raman shift among the four samples. The results in Figs. 14(a)14(d) and Table 2 show that the strain variations in the epitaxial layers and hence the changes of QCSE in those samples are indeed caused by the heating effects, produced by current injection.

Fig. 12. (a)-(d): Raman scattering spectra of samples A-D, respectively, with five injection duty cycles at 1, 25, 50, 75, and 100% when injection current is fixed at 50 mA. The vertical dashed lines indicate the strain-free E2 phonon feature of GaN at 567.6 cm−1. The dashed curves show the Gaussian fitting results to the solid curves of measured data.

Fig. 13. (a)-(d): Raman scattering spectra of samples A-D, respectively, with six injection current levels at 0, 10, 20, 30, 40, and 50 mA when injection duty cycle is fixed at 100%. The vertical dashed lines indicate the strain-free E2 phonon feature of GaN at 567.6 cm−1. The dashed curves show the Gaussian fitting results to the solid curves of measured data.

5. Discussions The decreasing output intensity with increasing injection duty cycle in sample A is due to the heating process of current injection. In such a lateral LED grown on sapphire substrate, the thermal expansion of the epitaxial layer is counteracted by the tightly-bonded sapphire substrate, leading to a slight reduction of the strong compressive strain in the epitaxial layer (see Fig. 11 and row 3 of Table 2). Such a slight variation does not significantly reduce the strong QCSE in its QWs (see Fig. 10 and row 2 of Table 2). Therefore, in this sample, the

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thermally activated defects play the major role for reducing output intensity in increasing injection duty cycle. In this situation, a lower injection duty cycle leads to a weaker heating effect, and hence higher output intensity and weaker thermally-induced efficiency droop effect (see Fig. 3 and column 2 of Table 1). In sample B, with the epitaxial layer bonded to the wafer-bonding metal layer (including mainly Au, In, and Ag), the heated metals of larger thermal expansion coefficients (heat transferred from the epitaxial layer), when compared with that of GaN (see Table 3), can apply a tensile stress onto the epitaxial layer. Although the thermal expansion of the metal layer is counteracted by the Si substrate, which has a smaller thermal expansion coefficient (see Table 3), it can still produce a reduction of the intrinsic compressive strain in the epitaxial layer for weakening the QCSE in the QWs. In this situation, a higher injection duty cycle leads to a stronger heating effect and hence higher output intensity (see Fig. 4 and column 3 of Table 1). Also, the weaker QCSE or less tilted potential in the QWs can help in carrier capture of the QWs for reducing the efficiency droop effect (see Fig. 4) [20–22].

Fig. 14. Variations of Raman shift of the four samples under the following four measurement conditions. (a): Injection duty cycle is varied while injection current is fixed at 20 mA. (b): Injection duty cycle is varied while injection current is fixed at 50 mA. (c): Injection current is varied (up to 100 mA) while injection duty cycle is fixed at 25%. (d): Injection current is varied (up to 50 mA) while injection duty cycle is fixed at 100%. Table 3. Thermal expansion coefficients of several related materials in this study. Thermal expansion coefficient (x 10−6 K−1)

Au 14.2

Ag 18.9

In 32.1

Fe 11.8

GaN 5.6

Si (111) 2.6

In either sample C or D, when the Si substrate is removed, the compressive stress from the substrate is released such that the epitaxial layer (including mainly GaN) becomes tensilestrained (see Fig. 11 and row 3 of Table 2). With a tensile strain in the epitaxial layer, the compressive strain in an InGaN QW layer, which is produced by the surrounding GaN layers, can be reduced for weakening QCSE (see Fig. 10 and row 2 of Table 2). In particular, when the epitaxial layer is bended in sample D, the tensile strain becomes even stronger such that its QCSE is even weaker. In this situation, the output intensity can be higher even before a significant heating effect is produced (see column 5 of Table 1). When electric current is injected into either sample C or D for producing the heating effect, similar to sample B, the larger thermal expansion of the heated wafer-bonding metal layer can apply a tensile stress onto the epitaxial layer. However, samples C and D are different from sample B in substrate structure. In either sample C or D, the epitaxial layer together with the wafer-bonding metal layer is Ag-epoxied onto an iron substrate, which also has a large thermal expansion

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coefficient (see Table 3). Although the effectiveness of stress transfer through Ag epoxy is unclear, without being counteracted by a substrate, the heating effect of the wafer-bonding metal layer can apply a strong tensile stress onto the epitaxial layer such that its tensile strain increases and QCSE weakens significantly with increasing injection current or duty cycle (see Fig. 14 and columns 4 and 5 of Table 2). In this situation, the output intensities of samples C and D increase with increasing duty cycle. As discussed above, heating can lead to the reduction of QCSE and hence the enhancement of emission efficiency. However, heating can also degrade the performance of an LED. These two factors compete with each other. Before the over-heating condition is reached at high injected current or high duty cycle, the factor of QCSE reduction dominates in the bendable LEDs for increasing emission efficiency. Under the over-heating condition, the LED performance of sample D starts to degrade as shown in Fig. 6 when injected current is larger than 80 mA with 100% duty cycle. In Figs. 9(a) and 9(b) for the variations of the output spectral peak of samples A and B, respectively, one can see the stronger red-shift trend in sample A. This is so because the generated heat in sample B can be spread into the Si substrate for reducing the temperature in the epitaxial layer such that its thermally-induced band gap shrinkage is weaker, when compared with sample A. The stronger local heating effect in the epitaxial layer of sample A results in a stronger red-shift trend. On the other hand, the significantly stronger red-shift trends in samples C and D are related to their tensile-strained epitaxial layers. Under the tensile-strain condition, heating can lead to a larger lattice expansion and hence a stronger band gap shrinkage in the QWs, when compared with those under compressive strain in sample A or B. A stronger tensile strain in sample D can lead to even stronger band gap shrinkage such that its red-shift trend is even stronger, as shown in Fig. 9(d). The other factor for effectively stronger red-shift trends in samples C and D is their weaker QCSEs, with which the blue-shift trend due to the screening of QCSE in increasing injection current becomes weaker. It is noted that heat transfer from the wafer-bonding metal layer into the metal substrate through Ag epoxy in either sample C or D is not as effective as that in sample B. In sample B, the tight bonding between the metal layer and the Si substrate can lead to more effective heat transfer between them. In this situation, the heating effects in samples C and D are stronger than that in sample B for producing more effective spectral red-shift. These stronger heating effects also result in the slightly larger device resistance levels of samples C and D, when compared with sample B (see the bottom row of Table 1). 6. Conclusions In summary, we have compared the emission behaviors of four LEDs of different substrate structures, including a lateral LED grown on sapphire substrate, a vertical LED wafer-bonded onto Si (111) substrate, a bendable LED Ag-epoxied onto a flat iron plate, and another bendable LED Ag-epoxied onto a soldering iron rod, under different duty cycles of current injection. Their different variation trends of emission behaviors with injection duty cycle were attributed to the different strain conditions in the epitaxial layers, which were controlled by their substrate structures, under heating in increasing injection duty cycle or current. The results of Raman scattering measurements during LED operation showed that a stronger tensile strain is generated under heating for reducing the quantum-confined Stark effect and hence increasing emission efficiency when the epitaxial layer was not tightly bonded onto a hard substrate. Such a behavior was particularly stronger when the epitaxial layer was bent. Acknowledgments This research was supported by National Science Council, Taiwan, The Republic of China, under the grants of NSC 102-2221-E-002-204-MY3, MOST 103-2120-M-002-002, and MOST 103-2221-E-002-139, by the Excellent Research Projects (103R890951 and 103R890952) of National Taiwan University, and by US Air Force Scientific Research Office under the contract of AOARD-14-4105.

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