⇦Chinese Physics Letters, 2017, Vol. 34, No. 1, Article code 017301 A Method to Obtain Auger Recombination Coefficient in an InGaN-Based Blue Light-Emitting Diode * Lai Wang(汪莱)1**, Xiao Meng(孟骁)1, Jung-Hoon Song2, Tae-Soo Kim2, Seung-Young Lim2, Zhi-Biao Hao(郝智彪)1, Yi Luo(罗毅)1, Chang-Zheng Sun(孙长征)1, Yan-Jun Han(韩彦军)1, Bing Xiong(熊兵)1, Jian Wang(王健)1, Hong-Tao Li(李洪涛)1 Affiliations 1Tsinghua National Laboratory on Information Science and Technology, and Department of Electronic Engineering, Tsinghua University, Beijing 100084 2Department of Physics, Kongju National University, Kongju 314701, South Korea Received 8 October 2016 *Supported by the National Key Research and Development Program of China under Grant No 2016YFB0400102, the National Basic Research Program of China under Grant Nos 2012CB3155605, 2013CB632804, 2014CB340002 and 2015CB351900, the National Natural Science Foundation of China under Grant Nos 61574082, 61210014, 61321004, 61307024, and 51561165012, the High-Technology Research and Development Program of China under Grant No 2015AA017101, the Tsinghua University Initiative Scientific Research Program under Grant Nos 2013023Z09N and 2015THZ02-3, the Open Fund of the State Key Laboratory on Integrated Optoelectronics under Grant No IOSKL2015KF10, the CAEP Microsystem and THz Science and Technology Foundation under Grant No CAEPMT201505, the Science Challenge Project under Grant No JCKY2016212A503, and the Guangdong Province Science and Technology Program under Grant No 2014B010121004.
**Corresponding author. Email: wanglai@tsinghua.edu.cn Citation Text: Wang L, Meng X, Song J H, Kim T S and Lim S Y et al 2017 Chin. Phys. Lett. 34 017301 Abstract We propose and demonstrate to derive the Auger recombination coefficient by fitting efficiency–current and carrier lifetime–current curves simultaneously, which can minimize the uncertainty of fitting results. The obtained Auger recombination coefficient is $1.0\times10^{-31}$ cm$^{6}$s$^{-1}$ in the present sample, which contributes slightly to efficiency droop effect. DOI:10.1088/0256-307X/34/1/017301 PACS:73.21.Fg, 73.40.Kp, 78.60.Fi © 2017 Chinese Physics Society Article Text Auger recombination (AR) is an intrinsic carrier dynamics process in semiconductors.[1] It decays the carrier radiative recombination efficiency especially when the carrier concentration is high or the AR coefficient $C$ is large. Recently, it was found that AR is probably responsible for the efficiency droop effect in GaN-based light-emitting diodes (LEDs) under high injection.[2] However, according to common semiconductor physics, the AR coefficient in wide-gap semiconductors should be much smaller than that in conventional III–V semiconductors.[3] For example, Hader et al.[4] calculated $C$ in an InGaN/GaN quantum well (QW) based on the microscopic many-body model and found that it is only $3.5\times10^{-34}$ cm$^{6}$s$^{-1}$. Bertazzi et al.[5] attributed the direct AR in InGaN material mainly to hole-hole-electron (hhe) recombination and the computed $C$ is lower than 10$^{32}$ cm$^{6}$s$^{1}$ based on the lowest-order perturbation theory and Fermi's golden rule. However, Piprek[3] and Verzellesi et al.[6] indicated in their respective review works that the AR can result in efficiency droop only if $C$ is beyond 10$^{-31}$ cm$^{6}$s$^{-1}$. This abnormal phenomenon has attracted widespread research interests. Shen et al.[7] first measured the AR coefficient in InGaN/GaN multi-quantum-well (MQW) by analyzing the photoluminescence efficiency droop curves of samples with different indium compositions and dislocation densities, and found that $C$ is around $1.4\times10^{30}$–$2.0\times10^{30}$ cm$^{6}$s$^{1}$. Delaney et al.[8] considered that $C$ in an InGaN bulk layer can be up to $2\times10^{-30}$ cm$^{6}$s$^{-1}$ when the difference between the first and the second conduction bands is comparable with the bandgap, based on the first-principles calculation. Then, Kioupakis et al.[9] from the same group calculated phonon-assisted and alloy scattering-assisted AR coefficients and indicated that $C$ can reach about $3\times10^{-31}$ cm$^{6}$s$^{-1}$ in these indirect processes. Liu et al.[10] grew identical LED structures on sapphire and GaN substrates, and obtained $C$ of $5.69\times10^{-29}$ cm$^{6}$s$^{-1}$ and $2.96\times10^{-30}$ cm$^{6}$s$^{-1}$ by fitting the external quantum efficiency (EQE) versus injection current curves, respectively. David et al.[11] calculated the accurate carrier concentration in the active region based on carrier lifetime and derived $C=10^{-29}$ cm$^{6}$s$^{-1}$ by fitting internal quantum efficiency (IQE) versus carrier concentration curve taking phase-space filling into account. Zhang et al.[12] utilized the modulation delay time of a 410-nm LED to achieve $C=1.5\times10^{-30}$ cm$^{6}$s$^{-1}$ at room temperature. Laubsch et al.[13] measured the electroluminescence (EL) and photoluminescence (PL) of a 532-nm single-quantum-well (SQW) LED at 4 and 300 K, and obtained $C$ of $3.5\times10^{-31}$ cm$^{6}$s$^{-1}$ insensitive to temperature. In the investigations mentioned above, measuring $C$ experimentally is mainly through fitting the efficiency-current curves based on the $ABC$ model. To simplify the model, the current injection efficiency (CIE) is usually assumed to be 1. In this case, the efficiency droop is fully induced by AR. However, many investigations show that carrier leakage is also responsible for efficiency droop.[14,15] Thus keeping CIE=1 under high injection current seems slightly hasty and the derived $C$ should be larger than its actual value. Taking CIE into account in the $ABC$ model is more reasonable, while it is extremely difficult to describe it analytically. Thus it is often expressed as $f(n)$ in the model.[15] This method brings in more unknowns, which leads to the uncertainty of fitting results. On the other hand, the CIE and the carrier recombination coefficients not only determine the efficiency, but also influence the carrier lifetime. Therefore, fitting the efficiency–current and carrier lifetime–current curves simultaneously will be beneficial to improve the reliability of results.[16] In the present study, we carry out the above idea based on differential carrier lifetime measurement under different injection currents. Moreover, to improve the reliability of fitting results further, the CIE depending on the injection current is also experimentally measured by using the method described in Ref. [17]. Finally, an AR coefficient $C$ of $1.0\times10^{-31}$ cm$^{6}$s$^{-1}$ is obtained in our LED sample.
cpl-34-1-017301-fig1.png
Fig. 1. Experimental (a) IQE, CIE, and (b) carrier lifetimes of LED under different injection currents. IQE is calculated from EQE based on the light extraction efficiency of 80% assumption.
The LED sample studied here was grown on a patterned sapphire substrate by metal organic vapor phase epitaxy (MOVPE). The epitaxial structure includes a 4-μm n-GaN bulk layer, 20 pairs of In$_{0.04}$Ga$_{0.96}$N(2 nm)/GaN(2 nm), 6 pairs of blue In$_{0.15}$Ga$_{0.85}$N(3 nm)/GaN(10 nm) MQWs, a 30-nm p-Al$_{0.08}$Ga$_{0.92}$N electron-blocking layer (EBL) and a 150-nm p-GaN contact layer. The wafer was fabricated to $10\times23$ mil$^{2}$ face-up chips. The ITO film was deposited as p-type transparent electrodes by electron-beam evaporating. The bare chip was used to measure the CIE first, utilizing the method described elsewhere.[17] Then, the same chip was packaged to evaluate its light power and peak wavelength using a calibrated integral sphere. Consequently, the EQE of LED depending on the injection current can be calculated. The differential carrier lifetimes under different injection currents is measured using the method the same as Ref. [16]. The IQE of LED can be calculated from EQE when the light extraction efficiency is assumed to be a typical value of 80%. The IQE, CIE and carrier lifetime $\tau$ depending on injection current $I$ are shown in Fig. 1. Although the IQE of the sample seems lower than the state-of-the-art one, it does not matter to validate the feasibility of the method. Based on the $ABC$ model taking carrier delocalization effect into account,[16,18] the relationships among IQE, CIE, carrier concentration in active region ($n$) and carrier lifetime ($\tau$) can be expressed as follows: $$\begin{align} {\rm IQE}=\,&{\rm CIE}\frac{Bn^2}{An+Bn^2+Cn^3},~~ \tag {1} \end{align} $$ $$\begin{align} \frac{1}{\tau }=\,&A+2Bn+3Cn^2,~~ \tag {2} \end{align} $$ $$\begin{align} n=\,&{\rm CIE}\frac{J\tau }{qd},~~ \tag {3} \end{align} $$ $$\begin{align} A=\,&r_{\rm L} \cdot A_{\rm L} +(1-r_{\rm L} )A_{\rm NL},~~ \tag {4} \end{align} $$ $$\begin{align} B=\,&r_{\rm L} \cdot B_{\rm L} +(1-r_{\rm L} )B_{\rm NL},~~ \tag {5} \end{align} $$ $$\begin{align} r_{\rm L}=\,&\frac{1+\exp (-\frac{1}{k})}{1+\exp (\frac{n-n_{\rm C} }{k\cdot n_{\rm C} })},~~ \tag {6} \end{align} $$ where $A$, $B$, and $C$ represent the Schockley–Read–Hall (SRH) recombination, radiative recombination, and AR coefficients, respectively, $q$ is the unit charge, $J$ is the current density, and $d$ is the active region thickness. Equations (4)-(6) reflect the carrier delocalization process as the carrier concentration increases, which has been proven very important especially when the current density is small. Here $A_{\rm L}$, $B_{\rm L}$ and $A_{\rm NL}$, $B_{\rm NL}$ represent the SRH and radiative recombination coefficients in localized centers and non-localized centers, respectively, $n_{\rm C}$ is the density of localized centers, and $k$ reflects the state density in these localized centers (a larger $k$ means a larger size and/or a deeper energy of localized center). Equations (1)-(3) establish the constraints among IQE, CIE, $\tau$, $n$, and $J$. Based on the experimental data, the unknowns can be derived by fitting IQE–$I$ and $\tau$–$I$ curves simultaneously. The fitting parameters are listed in Table 1 and the fitting curves are shown in Fig. 2. The AR coefficient $C$ is $1.00\times10^{-31}$ cm$^{6}$s$^{-1}$. According to Refs. [3,6], this value contributes only slightly to efficiency droop.
Table 1. Fitting parameters in Fig. 2.
$n_{\rm C}$ (cm$^{-3}$) $k$ $A_{\rm L}$ (s$^{-1}$) $A_{\rm NL}$ (s$^{-1}$) $B_{\rm L}$ (cm$^{3}$s$^{-1}$) $B_{\rm NL}$ (cm$^{3}$s$^{-1}$) $C$ (cm$^{6}$s$^{-1}$)
6$\times$10$^{17}$ 4 1.05$\times$10$^{6}$ 5.9$\times$10$^{6}$ 3.25$\times$10$^{-12}$ 1.85$\times$10$^{-12}$ 1.00$\times$10$^{-31}$
The debate on the origin of efficiency droop is not over. Researchers prefer more and more to believe that multi-origins are likely to exist in a practical LED, while their contributions to efficiency droop may be different. The dominant origin probably varies with the injection current density, which will be determined by the related parameters in LED. Thus the method exhibited here to obtain the AR coefficient is important for us to understand the efficiency droop and to optimize the material growth better.
cpl-34-1-017301-fig2.png
Fig. 2. Carrier lifetimes and IQE depending on the injection current. Dots: experimental data, and dashed line: fitting curves.
In summary, a method to obtain the AR coefficient in an InGaN-based LED has been demonstrated. By fitting the efficiency–current and carrier lifetime–current curves simultaneously, the uncertainty of fitting parameters can be reduced in the $ABC$ model to an extreme. The AR coefficient $C$ derived in the tested sample is only $1.0\times10^{-31}$ cm$^{6}$s$^{-1}$, which contributes slightly to efficiency droop. References Direct Measurement of Auger Electrons Emitted from a Semiconductor Light-Emitting Diode under Electrical Injection: Identification of the Dominant Mechanism for Efficiency DroopEfficiency droop in nitride-based light-emitting diodesOn the importance of radiative and Auger losses in GaN-based quantum wellsA numerical study of Auger recombination in bulk InGaNEfficiency droop in InGaN/GaN blue light-emitting diodes: Physical mechanisms and remediesAuger recombination in InGaN measured by photoluminescenceAuger recombination rates in nitrides from first principlesIndirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodesEfficiency droop in InGaN/GaN multiple-quantum-well blue light-emitting diodes grown on free-standing GaN substrateDroop in InGaN light-emitting diodes: A differential carrier lifetime analysisDirect measurement of auger recombination in In[sub 0.1]Ga[sub 0.9]N/GaN quantum wells and its impact on the efficiency of In[sub 0.1]Ga[sub 0.9]N/GaN multiple quantum well light emitting diodesHigh-Power and High-Efficiency InGaN-Based Light EmittersOrigin of efficiency droop in GaN-based light-emitting diodesCarrier recombination mechanisms and efficiency droop in GaInN/GaN light-emitting diodesStudy on efficiency droop in InGaN/GaN light-emitting diodes based on differential carrier lifetime analysisEffect of p-AlGaN electron blocking layers on the injection and radiative efficiencies in InGaN/GaN light emitting diodesAn improved carrier rate model to evaluate internal quantum efficiency and analyze efficiency droop origin of InGaN based light-emitting diodes
[1]Schubert E F 2003 Light-Emitting Diodes (New York: Cambridge University Press) p 39
[2] Iveland J, Martinelli L, Peretti J, Speck J S and Weisbuch C 2013 Phys. Rev. Lett. 110 177406
[3] Piprek J 2010 Phys. Status Solidi A 207 2217
[4] Hader J, Moloney J V, Pasenow B, Koch S W, Sabathil M, Linder N and Lutgen S 2008 Appl. Phys. Lett. 92 261103
[5] Bertazzi F, Goano M and Bellotti E 2010 Appl. Phys. Lett. 97 231118
[6] Verzellesi G, Saguatti D, Meneghini M, Bertazzi F, Goano M, Meneghesso G and Zanoni E 2013 J. Appl. Phys. 114 071101
[7] Shen Y C, Mueller G O, Watanabe S, Gardner N F, Munkholm A and Krames M R 2007 Appl. Phys. Lett. 91 141101
[8] Delaney K T, Rinke P and van de Walle C G 2009 Appl. Phys. Lett. 94 191109
[9] Kioupakis E, Rinke P, Delaney K T and van de Walle C G 2011 Appl. Phys. Lett. 98 161107
[10] Liu Z, Wei T, Guo E, Yi X, Wang L, Wang J, Wang G, Shi Y, Ferguson I and Li J 2011 Appl. Phys. Lett. 99 091104
[11] David A and Grundmann M J 2010 Appl. Phys. Lett. 96 103504
[12] Zhang M, Bhattacharya P, Singh J and Hinckley J 2009 Appl. Phys. Lett. 95 201108
[13] Laubsch A, Sabathil M, Baur J, Peter M and Hahn B 2010 IEEE Trans. Electron Devices 57 79
[14] Kim M H, Schubert M F, Dai Q, Kim J K, Schubert E F, Piprek J and Park Y 2007 Appl. Phys. Lett. 91 183507
[15] Dai Q Shan Q Wang J Chhajed S Cho J Schubert E F, Crawford M H, Koleske D D, Kim M H and Park Y 2010 Appl. Phys. Lett. 97 133507
[16] Meng X, Wang L, Hao Z, Sun C, Han Y, Xiong B, Wang J and Li H 2016 Appl. Phys. Lett. 108 013501
[17] Oh N C, Lee J G, Dong Y, Kim T S, Yu H J and Song J H 2015 Curr. Appl. Phys. 15 S7
[18] Wang J, Wang L, Wang L, Hao Z, Luo Y, Dempewolf A, Müller M, Bertram F and Christen J 2012 J. Appl. Phys. 112 023107