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Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S3 — May. 5, 2014
  • pp: A779–A789
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On the mechanisms of InGaN electron cooler in InGaN/GaN light-emitting diodes

Zi-Hui Zhang, Wei Liu, Swee Tiam Tan, Zhengang Ju, Yun Ji, Zabu Kyaw, Xueliang Zhang, Namig Hasanov, Binbin Zhu, Shunpeng Lu, Yiping Zhang, Xiao Wei Sun, and Hilmi Volkan Demir  »View Author Affiliations


Optics Express, Vol. 22, Issue S3, pp. A779-A789 (2014)
http://dx.doi.org/10.1364/OE.22.00A779


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Abstract

Electron overflow limits the quantum efficiency of InGaN/GaN light-emitting diodes. InGaN electron cooler (EC) can be inserted before growing InGaN/GaN multiple quantum wells (MQWs) to reduce electron overflow. However, detailed mechanisms of how the InGaN EC contributes to the efficiency improvement have remained unclear so far. In this work, we theoretically propose and experimentally demonstrate an electron mean-free-path model, which reveals the InGaN EC reduces the electron mean free path in MQWs, increases the electron capture rate and also reduces the valence band barrier heights of the MQWs, in turn promoting the hole transport into MQWs.

© 2014 Optical Society of America

1. Introduction

2. Experiments

Two InGaN/GaN LED wafers were grown by a metal-organic chemical vapor deposition (MOCVD) system. LED I is the reference sample while LED II is the sample with InGaN as the EC layer. The growth of the two samples was initiated on c-sapphire patterned substrates with periodic cone patterns (with a diameter of 2.4 µm, a height of 1.5 µm and a pitch of 3 µm). First, a 30 nm low-temperature GaN nucleation layer was grown. Then a 4 μm u-GaN layer was deposited as the template for the subsequent epitaxial growth. In LED I, a 2 µm n-GaN layer with a Si doping concentration of 5 × 1018 cm−3 was grown before the five-period In0.15Ga0.85N/GaN MQW region. The thicknesses of quantum wells and quantum barriers are 3 and 12 nm, respectively. For LED II, a 20 nm n-type In0.10Ga0.90N EC layer of 5 × 1018 cm−3 Si doping concentration was grown before growing InGaN/GaN MQWs, for which the growth temperature was 748 °C while the quantum well growth temperature was 742 °C in our MOCVD chamber. Both LEDs I and II have a 20 nm p-Al0.15Ga0.85N as the EBL layer. Finally, the LED samples were both covered with 0.2 µm p-GaN layer as the hole injector. The effective hole concentration in EBL and p-GaN layers for LEDs I and II are estimated to be 3 × 1017cm−3.

The electroluminescence (EL) spectra and the optical output power were measured for the two LED samples using the calibrated integrating sphere attached to an Ocean Optics spectrometer (QE65000). The metal contacts were made by indium balls on LED dies with a diameter of 2.0 mm.

3. Results and discussion

Fig. 1 EL spectra for (a) LED I and (b) LED II under various injection current levels of 10, 20, 30 and 40 A/cm2.
The measured EL spectra are shown in Figs. 1(a) and 1(b) for LEDs I and II, respectively. It can be seen that the EL intensity for LED II is stronger than that for LED I from lower injection current density of 10 A/cm2 to higher injection current density of 40 A/cm2. We also observed a red shift of the emission wavelengths as a function of the increased injection current for both LED samples, and we attributed the red shift of the emission wavelength to the increased junction temperature during testing [3

3. Z.-H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the effect of step-dDoped quantum barriers in InGaN/GaN light emitting diodes,” J. Disp. Technol. 9(4), 226–233 (2013). [CrossRef]

5

5. Z.-H. Zhang, S. T. Tan, Z. Kyaw, Y. Ji, W. Liu, Z. Ju, N. Hasanov, X. W. Sun, and H. V. Demir, “InGaN/GaN light-emitting diode with a polarization tunnel junction,” Appl. Phys. Lett. 102(19), 193508 (2013). [CrossRef]

].

According to Figs. 3(a) and 3(b), the incoming electrons are scattered and fall into the quantum wells (i.e., process ①) with τcap being the electron capture time, and a value of 4 × 10−12 s is used for electrons in the following simulations [18

18. D. Saguatti, L. Bidinelli, G. Verzellesi, M. Meneghini, G. Meneghesso, E. Zanoni, R. Butendeich, and B. Hahn, “Investigation of efficiency-droop mechanisms in multi-quantum-well InGaN/GaN blue light-emitting diodes,” IEEE Trans. Electron. Dev. 59(5), 1402–1409 (2012). [CrossRef]

]. Those fallen electrons thereafter on one hand are trapped onto the quantum energy levels and become bound electrons. Then, the recombination with holes and also in crystal defects takes place and it is depicted by process ②. The radiative recombination rates within the quantum wells can be generally expressed by Rrad=(nn0)/τrad, where n is the electron concentration received by process ① while n0 is the thermal-equilibrium electron concentration and τrad is the radiative recombination lifetime. Therefore, an increased n favors the radiative recombination processes. However, there is also a thermionic electron re-escape from the quantum wells and electrons become free again as illustrated by process ③ in Figs. 3(a) and 3(b). The re-escape process is modeled by the electron escape time, i.e., τesc, and it can be expressed by τesc=etQWn/Je [19

19. H. Zhao, G. Liu, J. Zhang, R. A. Arif, and N. Tansu, “Analysis of internal quantum efficiency and current injection efficiency in III-nitride light-emitting diodes,” J. Disp. Technol. 9(4), 212–225 (2013). [CrossRef]

], where n presents the electron concentration received by process ① while Je is the electron current caused by thermionic emission in any heterojunction. Process ④ denotes those electrons of a longer mean free path traveling to a remote position without being captured by quantum wells, which has to be suppressed for an enhanced n.

Now we have to find an approach to increase the electron concentration in the quantum wells. We set the number of the electrons injected into the n-GaN region to N0 for both LED samples. We neglect the electron loss through Shockley-Read-Hall (SRH) recombination in the n-GaN and n-In0.10Ga0.90N EC layers to simplify our model since the crystal quality of the two samples is identical. Furthermore, the hole concentration in the n-In0.10Ga0.90N EC is much lower than the electron concentration, so the electron loss through radiative recombination with holes is also negligible. For LED II with n-In0.10Ga0.90N EC layer, we assumed electrons of N2 are captured by the n-In0.10Ga0.90N EC layer with LO phonon emission, while the remaining electrons of N1 directly fly over the EC layer without undergoing thermalization. The electrons of N2 are then injected into InGaN/GaN MQW region after undergoing thermalization. Here, we correlate the quantum well captured electrons [i.e., process ① in Figs. 3(a) and 3(b)] with the electron mean free path (MFP) by Eq. (1) and Eq. (2) for LEDs I and II, respectively [20

20. C. S. Xia, Z. Q. Li, S. Yang, L. W. Cheng, W. D. Hu, and W. Lu, “Simulation of InGaN/GaN light-emitting diodes with a non-local quantum well transport model,” 12th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), 21–22(2012). [CrossRef]

]. Note that the electron loss due to processes ③ and ④ contribute to the electron overflow from the MQW region.
Nt=N0×[1exp(tQW/lMFP)]=(N1+N2)×[1exp(tQW/lMFP)]
(1)
Mt=N1×[1exp(tQW/lMFP)]+N2×[1exp(tQW/lMFPcooler)]
(2)
where tQWis the thickness of the quantum well, lMFP is the mean free path of electrons within the InGaN/GaN MQWs without electron thermalization and lMFPcooleris the mean free path of electrons in the InGaN/GaN MQWs with electron thermalization in the n-In0.10Ga0.90N EC layer. Here, the relationship between N0 and N2 in Fig. 3(b) can be expressed in Eq. (3), in which we assume the mean free path of electrons in the n-GaN layer before entering the n-In0.10Ga0.90N EC layer is lMFP. It is shown that, in order to have more electrons thermalized, it is useful to properly increase the thickness of the n-In0.10Ga0.90N EC layer (tcooler).

N2=N0×[1exp(tcooler/lMFP)]
(3)

The comparison between Eqs. (1) and (2) reveals that, to increase the number of the quantum well captured electrons, the electron mean free path within the InGaN/GaN MQW region must be reduced such that lMFPcooler<lMFP. Therefore, one has to understand the working mechanisms of the InGaN EC layer in reducing the electron mean free path. The electron mean free path is a function of the thermal velocity (i.e., vth- electron thermal velocity before undergoing thermalization and vthcooler- electron thermal velocity after undergoing thermalization) and the scattering time (τSC), which is set to 0.0091ps [11

11. X. Ni, X. Li, J. Lee, S. Liu, V. Avrutin, U. Ozgur, H. Morkoc, and A. Matulionis, “Hot electron effects on efficiency degradation in InGaN light emitting diodes and designs to mitigate them,” J. Appl. Phys. 108(3), 033112 (2010). [CrossRef]

,12

12. X. Ni, X. Li, J. Lee, S. Liu, V. Avrutin, U. Ozgur, H. Morkoc, A. Matulionis, T. Paskova, G. Mulholland, and K. R. Evans, “InGaN staircase electron injector for reduction of electron overflow in InGaN light emitting diodes,” Appl. Phys. Lett. 97(3), 031110 (2010). [CrossRef]

], as shown in Eqs. (4.1) and (4.2), respectively. Moreover, vth and vthcoolercan be expressed in Eqs. (5.1) and (5.2), respectively.
lMFP=vth×τSC
(4.1)
lMFPcooler=vthcooler×τSC
(4.2)
vth=2×[E+qV]/me
(5.1)
vthcooler=2×[E+ΔEcωLO+qVΔEc]/me=2×[E+qVωLO]/me
(5.2)
where E is the excess kinetic energy in the n-GaN layer referenced to the conduction band of the n-GaN layer, and me is the effective mass of electrons. The first ΔEcrepresents the kinetic energy received by the electrons when jumping over the conduction band offset between n-GaN and n-In0.10Ga0.90N EC layer. ωLOmeans the energy loss by phonon emission. qVis the work done to the electrons by the polarization induced electric field in the in-plane compressive n-In0.10Ga0.90N EC layer. The ΔEcin Eq. (5.2) depicts the energy loss for electrons when climbing over the conduction band offset between the n-In0.10Ga0.90N EC layer and the first quantum barrier. In our calculation, in order to consider the crystal relaxation by generating misfit dislocations, we only assumed 40% of the theoretical polarization induced charge density [21

21. V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III–V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002). [CrossRef]

]. Meanwhile, we assume the energy band offset ratio between InGaN and GaN to be 70:30 [22

22. J. Piprek, “Efficiency droop in nitride-based light-emitting diodes,” Phys. Status Solidi A 207(10), 2217–2225 (2010). [CrossRef]

], and thus ΔEcbetween n-GaN and n-In0.10Ga0.90N EC layer is 379.64 meV. Here we also assume the thermionic emission process dominates over the intra-band tunneling in the process of the electrons transport into the first quantum well. Thus ΔEccan be eliminated as shown in Eq. (5.2). The energy loss through LO phonon emission is 92 meV, i.e., ωLO = 92 meV [23

23. M. F. Schubert and E. F. Schubert, “Effect of heterointerface polarization charges and well width upon capture and dwell time for electrons and holes above GaInN/GaN quantum wells,” Appl. Phys. Lett. 96(13), 131102 (2010). [CrossRef]

]. Since the electric field within the EC layer is not linear and varies with position, we use APSYS simulator to calculate it [3

3. Z.-H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the effect of step-dDoped quantum barriers in InGaN/GaN light emitting diodes,” J. Disp. Technol. 9(4), 226–233 (2013). [CrossRef]

]. The calculated electric field is shown in Fig. 4.
Fig. 4 Calculated electric filed as a function of position within the EC layer at 20 A/cm2. The positive direction of the electric field is along the growth orientation, i.e., C + .
SinceqV=0tcoolerq×E(y)dy, qV equals to 27.82 meV in our case. When the carrier temperature is 500 K, lMFP is 14.47 nm while lMFPcooler is 1.32 nm. Obviously the In0.10Ga0.90N EC layer has a significant effect in reducing the electron mean free path in InGaN/GaN MQWs, and therefore increasing the quantum well capture efficiency of electrons, i.e., Mt>Nt. Here we only consider the constant mean free path in InGaN/GaN MQWs and did not consider its position dependence since doing so will not change the conclusion but only add more complexity to the calculation. Note, the electrons follow Fermi-Dirac distribution, and therefore Eq. (5.2) is valid when E+qVωLO>0 for those hot electrons with a high carrier temperature, while for those with E+qVωLO<0 (i.e., E+ΔEcωLO+qV<ΔEc) will be blocked by the conduction band offset between the EC layer and the first quantum barrier. However, the electrons will be accumulated in the EC layer until a high electron density is obtained, thus according to Je=4πe(kBT)2h3me*exp[ΔEc/kBT+ln(n/Nc)] [24

24. S. M. Sze, Physics of Semiconductor Physics, 2nd ed. (John Wiley & Sons, Hoboken,1981).

], where ΔEcis the conduction band offset between GaN and the EC layer, andNcis the effective density of state for electrons, while kBis Boltzmann constant, me*is the electron effective mass, h is the Planck constant and n is the electron density, the electrons still can transport into the active region.

With the above calculated values of the electron mean free path, we performed numerical simulations on the energy band diagrams, electron and hole distributions, electron currents and the radiative recombination rates for the two samples to confirm that the reduction of the electron mean free path by the In0.10Ga0.90N EC layer can enhance the optical output power performance of LEDs. In our simulation, APSYS simulator is used, which can well model the carrier transport processes [i.e., processes ①, ②, ③, and ④ in Figs. 3(a) and 3(b)] within the InGaN/GaN MQW region. The model of electron tunneling through the GaN layer between the n-InGaN EC and the first quantum well has not been used purposely to study the thermionic process for electron transport within that region. Besides the previously mentioned band offset ratio and polarization charge level, we also assumed 1 × 10−30 cm6/s as the Auger recombination coefficient [25

25. M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009). [CrossRef]

]. The SRH recombination lifetime in the InGaN/GaN MQW region is set to be 43 ns [25

25. M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009). [CrossRef]

]. Other parameters for nitrogen-containing compounds used in the simulation can be found somewhere else [26

26. I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003). [CrossRef]

].

The simulated energy band diagrams at 20 A/cm2 for LEDs I and II are shown in Figs. 5(a) and 5(b), respectively. We defined the effective valance band barrier height (ΔΦi) for different quantum barriers (QB1, QB2, QB3 and QB4). The value of ΔΦiare extracted and demonstrated in Table 1, from which we can see the effective valence band barrier heights of the quantum barriers for LED II is smaller than those for LED I. It has been reported that the effective valance band barrier height for the p-EBL can be reduced by employing GaN/InGaN as the last quantum barrier, hence promoting the hole injection into InGaN/GaN MQWs [27

27. Y.-K. Kuo, Y.-H. Shih, M.-C. Tsai, and J.-Y. Chang, “Improvement in electron overflow of near-ultraviolet InGaN LEDs by specific design on last barrier,” IEEE Photon. Technol. Lett. 23(21), 1630–1632 (2011). [CrossRef]

, 28

28. T. Lu, S. Li, C. Liu, Y. Zhang, Y. Xu, J. Tong, L. Wu, H. Wang, X. Yang, Y. Yin, G. Xiao, and Y. Zhou, “Advantages of GaN based light-emitting diodes with a p-InGaN hole reservoir layer,” Appl. Phys. Lett. 100(14), 141106 (2012). [CrossRef]

]. However, as found in this work, the same physical principle can be applied to the case when the n-type In0.10Ga0.90N layer is inserted between n-GaN layer and InGaN/GaN MQW region. As the polarization induced electric field within the n-type In0.10Ga0.90N layer opposes the built-in electric field of the diode, and thus the n-type In0.10Ga0.90N layer “pulls up” the valance band of the MQWs for a better hole transport across the active region.
Fig. 5 Energy band diagrams for (a) LED I and (b) LED II.

Table 1. Effective Valence Band Barrier Heights of InGaN/GaN MQWs for LEDs I and II

table-icon
View This Table

Fig. 6 Simulated (a) electron concentration along with the inset depicting the electron leakage out of the active region, (b) normalized electron current, (c) hole concentration, and (d) radiative recombination rates at 20 A/cm2 across the InGaN/GaN MQW region for LEDs I and II, respectively.
The simulated electron profiles for LEDs I and II are shown in Fig. 6(a). We can see that the electron overflow is reduced in LED II with the n-type In0.10Ga0.90N EC layer, compared to that in LED I. Meanwhile, the electron current distribution is also depicted in Fig. 6(b). Being consistent with Fig. 6(a), the electron leakage current into the p-type region is reduced from 26.56% to 18.86% at 20 A/cm2, if we compare LED II to LED I. It should be noteworthy that the thermionic emission for process ③ in Figs. 3(a) and 3(b) can also be expressed byJe=4πe(kBT)2h3me*exp[ΔEc_wb/kBT+ln(n/Nc)] [24

24. S. M. Sze, Physics of Semiconductor Physics, 2nd ed. (John Wiley & Sons, Hoboken,1981).

], where ΔEc_wbis the conduction band offset for InGaN/GaN MQWs, andNcis the effective density of state for electrons, while kBis Boltzmann constant, me*is the electron effective mass and h is the Planck constant. We can conclude that an increased electron concentration (i.e., n) within the InGaN/GaN MQWs enhances the electron re-escape process in Figs. 3(a) and 3(b) [29

29. B. Romero, J. Arias, I. Esquivias, and M. Cada, “Simple model for calculating the ratio of the carrier capture and escape times in quantum-well lasers,” Appl. Phys. Lett. 76(12), 1504–1506 (2000). [CrossRef]

]. However, we know that Mt>Nt, and thus LED II has a more severe electron re-escape process than LED I in Figs. 3(a) and 3(b). As a result, the reduced electron leakage in LED II is well attributed to the reduced electron mean free path by the n-type In0.10Ga0.90N EC layer that suppresses those electrons directly flying over the quantum wells. In addition, we also showed the hole profiles for LEDs I and II in Fig. 6(c), respectively. According to Fig. 6(c), we can see that LED II exhibits a more homogenous hole distribution across the InGaN/GaN MQWs than LED I, which is due to the reduced valence band barrier heights of InGaN/GaN MQWs by the InGaN EC layer as shown in Fig. 5. The radiative recombination rates for LEDs I and II are shown in Fig. 6(d). The increased electron capture efficiency and the improved hole transport in the InGaN/GaN MQWs due to the InGaN EC layer account for the enhanced radiative recombination rate for LED II, as indicated in Fig. 6(d).

4. Conclusions

In conclusion, the InGaN/GaN LED with an n-type In0.10Ga0.90N electron cooler layer has been demonstrated and investigated. The enhanced electron capture efficiency by the multiple quantum wells is attributed to a reduced mean free path after electrons undergo thermalization by phonon emission in the electron cooler layer. Moreover, we found the n-type In0.10Ga0.90N electron cooler layer also promotes the hole transport by “pulling up” the valence band of the quantum barriers. Thus, the increased electron capture efficiency and the improved hole transport across the multiple quantum wells lead to the improvement of the radiative recombination rate, and thus the enhanced optical output power and the reduced efficiency droop. Therefore, the InGaN electron cooler holds great promise for achieving better-performance InGaN/GaN LEDs and can be optimized using the electron mean-free-path model.

Acknowledgments

This work is supported by the National Research Foundation of Singapore under Grant No. NRF-CRP-6-2010-2 and NRF-RF-2009-09 and the Singapore Agency for Science, Technology and Research (A*STAR) SERC under Grant No. 112 120 2009.

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X. Ni, X. Li, J. Lee, S. Liu, V. Avrutin, U. Ozgur, H. Morkoc, A. Matulionis, T. Paskova, G. Mulholland, and K. R. Evans, “InGaN staircase electron injector for reduction of electron overflow in InGaN light emitting diodes,” Appl. Phys. Lett. 97(3), 031110 (2010). [CrossRef]

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D. Saguatti, L. Bidinelli, G. Verzellesi, M. Meneghini, G. Meneghesso, E. Zanoni, R. Butendeich, and B. Hahn, “Investigation of efficiency-droop mechanisms in multi-quantum-well InGaN/GaN blue light-emitting diodes,” IEEE Trans. Electron. Dev. 59(5), 1402–1409 (2012). [CrossRef]

19.

H. Zhao, G. Liu, J. Zhang, R. A. Arif, and N. Tansu, “Analysis of internal quantum efficiency and current injection efficiency in III-nitride light-emitting diodes,” J. Disp. Technol. 9(4), 212–225 (2013). [CrossRef]

20.

C. S. Xia, Z. Q. Li, S. Yang, L. W. Cheng, W. D. Hu, and W. Lu, “Simulation of InGaN/GaN light-emitting diodes with a non-local quantum well transport model,” 12th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), 21–22(2012). [CrossRef]

21.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III–V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002). [CrossRef]

22.

J. Piprek, “Efficiency droop in nitride-based light-emitting diodes,” Phys. Status Solidi A 207(10), 2217–2225 (2010). [CrossRef]

23.

M. F. Schubert and E. F. Schubert, “Effect of heterointerface polarization charges and well width upon capture and dwell time for electrons and holes above GaInN/GaN quantum wells,” Appl. Phys. Lett. 96(13), 131102 (2010). [CrossRef]

24.

S. M. Sze, Physics of Semiconductor Physics, 2nd ed. (John Wiley & Sons, Hoboken,1981).

25.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009). [CrossRef]

26.

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003). [CrossRef]

27.

Y.-K. Kuo, Y.-H. Shih, M.-C. Tsai, and J.-Y. Chang, “Improvement in electron overflow of near-ultraviolet InGaN LEDs by specific design on last barrier,” IEEE Photon. Technol. Lett. 23(21), 1630–1632 (2011). [CrossRef]

28.

T. Lu, S. Li, C. Liu, Y. Zhang, Y. Xu, J. Tong, L. Wu, H. Wang, X. Yang, Y. Yin, G. Xiao, and Y. Zhou, “Advantages of GaN based light-emitting diodes with a p-InGaN hole reservoir layer,” Appl. Phys. Lett. 100(14), 141106 (2012). [CrossRef]

29.

B. Romero, J. Arias, I. Esquivias, and M. Cada, “Simple model for calculating the ratio of the carrier capture and escape times in quantum-well lasers,” Appl. Phys. Lett. 76(12), 1504–1506 (2000). [CrossRef]

OCIS Codes
(160.6000) Materials : Semiconductor materials
(230.3670) Optical devices : Light-emitting diodes
(230.5590) Optical devices : Quantum-well, -wire and -dot devices

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: November 21, 2013
Revised Manuscript: March 19, 2014
Manuscript Accepted: March 25, 2014
Published: April 2, 2014

Citation
Zi-Hui Zhang, Wei Liu, Swee Tiam Tan, Zhengang Ju, Yun Ji, Zabu Kyaw, Xueliang Zhang, Namig Hasanov, Binbin Zhu, Shunpeng Lu, Yiping Zhang, Xiao Wei Sun, and Hilmi Volkan Demir, "On the mechanisms of InGaN electron cooler in InGaN/GaN light-emitting diodes," Opt. Express 22, A779-A789 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S3-A779


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References

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  28. T. Lu, S. Li, C. Liu, Y. Zhang, Y. Xu, J. Tong, L. Wu, H. Wang, X. Yang, Y. Yin, G. Xiao, and Y. Zhou, “Advantages of GaN based light-emitting diodes with a p-InGaN hole reservoir layer,” Appl. Phys. Lett.100(14), 141106 (2012). [CrossRef]
  29. B. Romero, J. Arias, I. Esquivias, and M. Cada, “Simple model for calculating the ratio of the carrier capture and escape times in quantum-well lasers,” Appl. Phys. Lett.76(12), 1504–1506 (2000). [CrossRef]

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