
Mechanism for Efficiency Droop” [Phys. Rev. Lett. 
110, 177406 (2013)]. 
Cabalu, J.S., Thomidis, C., Moustakas, T.D., Riyopoulos, 
S., Zhou, L., Smith, D.J., 2006. Enhanced internal 
quantum efficiency and light extraction efficiency 
from textured GaN⁄AlGaN quantum wells grown by 
molecular beam epitaxy. J. Appl. Phys. 99, 064904. 
doi:10.1063/1.2179120. 
Cao, X.A., Arthur, S.D., 2004. High-power and reliable 
operation of vertical light-emitting diodes on bulk 
GaN. Appl. Phys. Lett. 85, 3971. 
doi:10.1063/1.1810631. 
David, A., Grundmann, M.J., Kaeding, J.F., Gardner, N.F., 
Mihopoulos, T.G., Krames, M.R., 2008. Carrier 
distribution in (0001)InGaN⁄GaN multiple quantum 
well light-emitting diodes. Appl. Phys. Lett. 92, 
053502. doi:10.1063/1.2839305. 
Delaney, K.T., Rinke, P., Van de Walle, C.G., 2009. 
Auger recombination rates in nitrides from first 
principles. Appl. Phys. Lett. 94, 191109. 
doi:10.1063/1.3133359. 
Della Sala, F., Di Carlo, A., Lugli, P., Bernardini, F., 
Fiorentini, V., Scholz, R., Jancu, J.-M., 1999. Free-
carrier screening of polarization fields in wurtzite 
GaN/InGaN laser structures. Appl. Phys. Lett. 74, 
2002. doi:10.1063/1.123727. 
Galler, B., Drechsel, P., Monnard, R., Rode, P., Stauss, P., 
Froehlich, S., Bergbauer, W., Binder, M., Sabathil, M., 
Hahn, B., Wagner, J., 2012. Influence of indium 
content and temperature on Auger-like recombination 
in InGaN quantum wells grown on (111) silicon 
substrates. Appl. Phys. Lett. 101, 131111. 
doi:10.1063/1.4754688. 
Hader, J., Moloney, J.V., Pasenow, B., Koch, S.W., 
Sabathil, M., Linder, N., Lutgen, S., 2008. On the 
importance of radiative and Auger losses in GaN-
based quantum wells. Appl. Phys. Lett. 92, 261103. 
doi:10.1063/1.2953543. 
Hangleiter, A., Hitzel, F., Netzel, C., Fuhrmann, D., 
Rossow, U., Ade, G., Hinze, P., 2005. Suppression of 
Nonradiative Recombination by V-Shaped Pits in 
GaInN/GaN Quantum Wells Produces a Large 
Increase in the Light Emission Efficiency. Phys. Rev. 
Lett. 95. doi:10.1103/PhysRevLett.95.127402. 
Huang, S., Fan, B., Chen, Z., Zheng, Z., Luo, H., Wu, Z., 
Wang, G., Jiang, H., 2013. Lateral Current Spreading 
Effect on the Efficiency Droop in GaN Based Light-
Emitting Diodes. J. Disp. Technol. 9, 266–271. 
doi:10.1109/JDT.2012.2225092. 
Iveland, J., Martinelli, L., Peretti, J., Speck, J.S., 
Weisbuch, C., 2013. Direct Measurement of Auger 
Electrons Emitted from a Semiconductor Light-
Emitting Diode under Electrical Injection: 
Identification of the Dominant Mechanism for 
Efficiency Droop. Phys. Rev. Lett. 110. 
doi:10.1103/PhysRevLett.110.177406. 
Kim, H., Cho, J., Lee, J.W., Yoon, S., Kim, H., Sone, C., 
Park, Y., Seong, T.-Y., 2007. Measurements of current 
spreading length and design of GaN-based light 
emitting diodes. Appl. Phys. Lett. 90, 063510. 
doi:10.1063/1.2450670. 
Kim, M.-H., Schubert, M.F., Dai, Q., Kim, J.K., Schubert, 
E.F., Piprek, J., Park, Y., 2007. Origin of efficiency 
droop in GaN-based light-emitting diodes. Appl. Phys. 
Lett. 91, 183507. doi:10.1063/1.2800290. 
Kioupakis, E., Rinke, P., Delaney, K.T., Van de Walle, 
C.G., 2011. Indirect Auger recombination as a cause 
of efficiency droop in nitride light-emitting diodes. 
Appl. Phys. Lett. 98, 161107. doi:10.1063/1.3570656. 
Krames, M.R., Christenson, G., Collins, D., Cook, L.W., 
Craford, M.G., Edwards, A., Fletcher, R.M., Gardner, 
N.F., Goetz, W.K., Imler, W.R., Johnson, E., Kern, 
R.S., Khare, R., Kish, F.A., Lowery, C., Ludowise, 
M.J., Mann, R., Maranowski, M., Maranowski, S.A., 
Martin, P.S., O’Shea, J., Rudaz, S.L., Steigerwald, 
D.A., Thompson, J., Wierer, J.J., Yu, J., Basile, D., 
Chang, Y.-L., Hasnain, G., Heuschen, M., Killeen, 
K.P., Kocot, C.P., Lester, S., Miller, J.N., Mueller, 
G.O., Mueller-Mach, R., Rosner, S.J., Schneider, J., 
Richard P., Takeuchi, T., Tan, T.S., 2000. High-
brightness AlGaInN light-emitting diodes. pp. 2–12. 
doi:10.1117/12.382822. 
Krames, M.R., Shchekin, O.B., Mueller-Mach, R., 
Mueller, G.O., Zhou, L., Harbers, G., Craford, M.G., 
2007. Status and Future of High-Power Light-Emitting 
Diodes for Solid-State Lighting. J. Disp. Technol. 3, 
160–175. doi:10.1109/JDT.2007.895339. 
Li, C.-K., Wu, Y.-R., 2012. Study on the Current 
Spreading Effect and Light Extraction Enhancement of 
Vertical GaN/InGaN LEDs. IEEE Trans. Electron 
Devices 59, 400–407. 
doi:10.1109/TED.2011.2176132. 
Morkoç, H., 2008. Handbook of nitride semiconductors 
and devices. Wiley-VCH ; John Wiley, distributor], 
Weinheim : [Chichester. 
Mukai, T., Yamada, M., Nakamura, S., 1999. 
Characteristics of InGaN-Based 
UV/Blue/Green/Amber/Red Light-Emitting Diodes. 
Jpn. J. Appl. Phys. 38, 3976–3981. 
doi:10.1143/JJAP.38.3976. 
Ni, X., Fan, Q., Shimada, R., Özgür, U., Morkoç, H., 
2008. Reduction of efficiency droop in InGaN light 
emitting diodes by coupled quantum wells. Appl. 
Phys. Lett. 93, 171113. doi:10.1063/1.3012388. 
Piprek, J., Farrell, R., DenBaars, S., Nakamura, S., 2006. 
Effects of built-in polarization on InGaN-GaN 
vertical-cavity surface-emitting lasers. IEEE Photonics 
Technol. Lett. 18, 7–9. doi:10.1109/LPT.2005.860045. 
Romanowski, Z., Kempisty, P., Sakowski, K., Stra̧ k, P., 
Krukowski, S., 2010. Density Functional Theory 
(DFT) Simulations and Polarization Analysis of the 
Electric Field in InN/GaN Multiple Quantum Wells 
(MQWs). J. Phys. Chem. C 114, 14410–14416. 
doi:10.1021/jp104438y. 
Rozhansky, I.V., Zakheim, D.A., 2007. Analysis of 
processes limiting quantum efficiency of AlGaInN 
LEDs at high pumping. Phys. Status Solidi A 204, 
227–230. doi:10.1002/pssa.200673567. 
Schubert, M.F., Chhajed, S., Kim, J.K., Schubert, E.F., 
DecorrelationoftheLight-emitting-DiodeInternal-quantum-EfficiencyComponents-StudiesoftheElectron-hole
Concentration-ratioattheActive-regionEdge
45