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Abstract
The inner mechanisms accounting for the efficiency droop in III-Nitride based LEDs have been investigated extensively. Here we give a brief discussion of the possible mechanisms： defect &dislocations related SRH non-radiative recombination， reduced spontaneous emission， Auger non-radiative recombination， electron leakage， polarization field， current crowding effect. Dislocations do not strongly impact high-current performance； a reduced spontaneous emission reduces internal quantum efficiency （IQE）； Defect-assisted and polarization field induced Auger process， electron overflow will strongly influence the droop characteristics at elevated current injection. Current crowding should results to a lower IQE.
Introduction
Due to the rapid advance in epitaxial growth， chip design and fabrication technologies， great progress have been achieved in III-Nitrides based light emitting diodes （LEDs）. In order to ultimate substitute the conventional lighting sources， efficiency is still in needs to be further improved. “efficiency droop” describes a commonly known phenomenon that LEDs suffer from severe external quantum efficiency （EQE） loss at the high current injection condition1. The inner mechanisms accounting for the efficiency droop have been investigated and proposed by different groups， which includes the polarization mismatch and the drifting current in p-GaN layer1， the dislocations-related defects2， the poor hole injection3， the delocalization of carriers4， and Auger recombination5.However， due to different sample preparation methods and test conditions， it is still under debate and deserved further deep investigation. In this paper， we will examine the different responsible mechanisms and give a mini review on efficiency droop of III-Nitride based LEDs.
ABC Model
The total decay rate for the carriers in the quantum wells （QWs） can be written as in the following：
（1）
Where n represents the QW carrier density， A is the SRH parameter， and the corresponding An in the right part of equ.（1） represents the dislocation related SRH contribution； B is the radiative coefficient and C is the Auger coefficient， f（n） is used to represent the leakage current. So the radiative recombination efficiency can be written as：6
（2）
Droop mechanisms
Defect &Dislocations related mechanism
Typical nonradiative electron–hole recombination at crystal defects is described by the SRH model. S. F. Chichibu et al7 conclude that localizing valence states associated with atomic condensates of In–N preferentially capture holes， which have a positive charge similar to positrons. The holes form localized excitons to emit the light， some of the excitons recombine at non-radiative centres. Fig. 1 shows the calculated IQE droop curves with different A values. As we can see， with higher A values， i.e. dislocation & defect density， the IQEpeak decreased and the current corresponding to IQEpeak increased， IQE approaches closely at elevated current. The droop length thus surprisingly increased with a higher dislocation. Martin F. Schubert et al8 experimentally found that： dislocations do not strongly impact high-current performance； instead they contribute to increased nonradiative recombination at lower currents and a suppression of peak efficiency. The effect of dislocation &defect on IQE and IQE droop can be understand as this： at low current density， almost all the carriers were localized at a potential minima， and the IQE exhibited less dependence with TD density. However， at high carrier density， the localized carriers at potential minima will gradually release into conduction band due to band filling effect and easily move to the site around dislocations. The recombination mechanism could be both SRH and Auger， we will continue this discussion in Auger part. Spontaneous emission
Some researchers found the radiative recombination B varies with different carrier density. David9 employed the relationship and extracted the parametersB0=7×10-11cm3s-1and n0=5×1018cm-3. We also plot IQE curves with different B values in Fig. 2. Obviously， IQE increases and IQE droop was suppressed with a higher B value. The current corresponding to IQEpeak varies negligently for different B values.
Auger recombination
Auger recombination is a type of non-radiative recombination， describing a physical phenomenon in which excess electron energy was transferred to other electrons or holes. The probability of Auger process inversely related with energy band gap， so it is generally considered negligible in wide-gap materials. However， many researchers have extracted the C values， which are much higher than the theoretically predicted values. Through photoluminescence （PL） lifetime studies on quasi-bulk InGaN layers， Shen et al.10. extracted an Auger coefficient of C～2×10-30 cm6/s. As can be seen from Fig. 3， with C increased， IQE decreases greatly， especially at high injection current. Recalling from the defect related non-radiative part， we suggest a dislocation-assisted mechanism. Because if it is the SRH dominates， the nonradiative recombination-rate should be saturated at high current density. However， this is contradictory with our calculation and the experimental results.
Electron overflow and hole insufficient injection
It is a common problem of the electrons overflow beyond the QWs due to band flattened at high injection condition and this is AlGaN electron blocking layer is adopted in III-nitride LEDs11.Hot electrons and the associated ballistic and quasiballistic transport across the active regions of InGaN LEDs have been incorporated into a first order simple model by X. Ni12et. al to explains the experimental observations of electron spillover and the efficiency degradation at high injection levels. On the other hand， due to inefficient p-type doping and the low hole mobility， the hole injection is insufficient. Various other approaches have been proposed to cool down or block the injected hot electrons to reduce IQE droop， among them are electron cooler， staircase electron injector， p- AlInGaN/AlGaN EBL Layer， p-InGaN/AlGaN.
Polarization field and IQE droop
As well known， InGaN/GaN LEDs grown along [0001] orientation possess very strong positive polarization charges， which lowers the effective conduction band barrier height for electrons， thus making the EBL relatively ineffective in confining the electrons. Also Roman Vaxenburg13 found the polarization field in QWs not only suppresses the radiative recombination but also strongly enhances the rate of Auger recombination. So it is important to structure design to minimize the effect of the polarization field in III-nitride LEDs. Roman Vaxenburg13used a gradual variation of the QW layer composition， which compensates the effect of the electric field acting on holes. Semipolar and nonpolar growths have already yielded devices with superior performance. Zi-Hui Zhang14 proposed polarization self-screening effect through growing a p-type EBL with AlN composition partially graded along the [0001] orientation， which induces the bulk polarization charges. These bulk polarization charges are utilized to effectively self-screen the positive polarization induced interface charges located at the interface between the EBL and the last quantum barrier when designed properly. Current crowding effect on IQE and EQE droop
Most of the previous researches are concentrated on the vertical distribution of carriers in the multiple quantum wells. However， the in-plane （lateral） distribution of carriers is also important and crucial due to the current crowding effect （CCE）. The lateral carrier distribution obviously relates to IQE. Furthermore， since the current tends to crowd under the metal electrode， whereas large percentage of the generated photons cannot be extracted due to the electrode absorption. This certainly has a negative effect on the light extraction efficiency （LEE）， which is lacked in the previous part of this paper. As we know， the EQE is the product of the IQE and the LEE， so the variation of current diffusion shall have a significant influence on the IQE， LEE and thus ultimately the EQE droop level. By incorporating transparent conductive layer15， current blocking layer16 can increase the current spreading length and thus improve the efficiency and suppress the efficiency droop.
Conclusion
The inner mechanisms accounting for the efficiency droop in III-Nitride based LEDs have been investigated extensively. Here we give a brief discussion of the possible mechanisms： defect &dislocations related SRH non-radiative recombination， reduced spontaneous emission， Auger non-radiative recombination， electron leakage， polarization field， current crowding effect. Dislocations do not strongly impact high-current performance， instead they contribute to increased nonradiativere combination at lower currents and a suppression of peak efficiency； a reduced spontaneous emission reduces internal quantum efficiency （IQE） and deteriorates IQE droop； Defect-assisted and polarization field induced Auger process， electron overflow will strongly influence the droop characteristics at elevated current injection. Current crowding should results to a lower IQE， light extraction efficiency （LEE） and the ultimate external quantum efficiency （EQE）.
References
1.J. Cho， E. F. Schubert， and J. K. Kim， Laser & Photonics Reviews 7 （3）， 408-421 （2013）.
2.G. Venturi， A. Castaldini， and C. Humphreys， Applied Physics Letters 104 （21）， - （2014）.
3.Y. Ji， Z.-H. Zhang， and H. V. Demir， Opt. Lett. 38 （2）， 202-204 （2013）.
4.A. Kim， W. G?tz， and R. Kern， physica status solidi（a） 188 （1）， 15-21 （2001）.
5.F. R?mer and B. Witzigmann， Opt. Express 22 （S6）， A1440-A1452 （2014）.
6.H.-Y. Ryu， H.-S.Kim， and J.-I. Shim， Applied Physics Letters 95 （8）， 081114 （2009）. 7.S. F. Chichibu， A. Uedono， and T. Sota， Nature materials 5 （10）， 810-816 （2006）.
8.M. F. Schubert， S. Chhajed， and M. A. Banas， Applied Physics Letters 91 （23）， 231114 （2007）.
9.A. David， and M. J. Grundmann， Appl. Phys. Lett.96， 103504（2010）.
10.Y. C. Shen， G. O. Mueller， and M. R. Krames， Appl. Phys. Lett.91（14），141101 （2007）.
11.J. Piprek and S. Nakamura， IEE Proc. Optoelectron.149， 145（2002）.
12.X. Ni， X. Li， and A. Matulionis， Journal of Applied Physics 108 （3）， - （2010）.
13.R. Vaxenburg， A. Rodina， and A. L. Efros， Applied Physics Letters 103 （22）， - （2013）.
14Z.-H. Zhang， W. Liu， and H. Volkan Demir， Applied Physics Letters 104 （24）， - （2014）.
15.L. Wang， Y. Zhang， and G. Wang， Applied Physics Letters 101 （6）， 061102 （2012）.
16.T.-M. Chen， K. Uang， and H. Kuan， Photonics Technology Letters， IEEE 20 （9）， 703-705 （2008）.
Fig. 1 IQE droop curves with different A values
Fig. 2 IQE curves with different B values
Fig. 3 IQE curves with different C values
The inner mechanisms accounting for the efficiency droop in III-Nitride based LEDs have been investigated extensively. Here we give a brief discussion of the possible mechanisms： defect &dislocations related SRH non-radiative recombination， reduced spontaneous emission， Auger non-radiative recombination， electron leakage， polarization field， current crowding effect. Dislocations do not strongly impact high-current performance； a reduced spontaneous emission reduces internal quantum efficiency （IQE）； Defect-assisted and polarization field induced Auger process， electron overflow will strongly influence the droop characteristics at elevated current injection. Current crowding should results to a lower IQE.
Introduction
Due to the rapid advance in epitaxial growth， chip design and fabrication technologies， great progress have been achieved in III-Nitrides based light emitting diodes （LEDs）. In order to ultimate substitute the conventional lighting sources， efficiency is still in needs to be further improved. “efficiency droop” describes a commonly known phenomenon that LEDs suffer from severe external quantum efficiency （EQE） loss at the high current injection condition1. The inner mechanisms accounting for the efficiency droop have been investigated and proposed by different groups， which includes the polarization mismatch and the drifting current in p-GaN layer1， the dislocations-related defects2， the poor hole injection3， the delocalization of carriers4， and Auger recombination5.However， due to different sample preparation methods and test conditions， it is still under debate and deserved further deep investigation. In this paper， we will examine the different responsible mechanisms and give a mini review on efficiency droop of III-Nitride based LEDs.
ABC Model
The total decay rate for the carriers in the quantum wells （QWs） can be written as in the following：
（1）
Where n represents the QW carrier density， A is the SRH parameter， and the corresponding An in the right part of equ.（1） represents the dislocation related SRH contribution； B is the radiative coefficient and C is the Auger coefficient， f（n） is used to represent the leakage current. So the radiative recombination efficiency can be written as：6
（2）
Droop mechanisms
Defect &Dislocations related mechanism
Typical nonradiative electron–hole recombination at crystal defects is described by the SRH model. S. F. Chichibu et al7 conclude that localizing valence states associated with atomic condensates of In–N preferentially capture holes， which have a positive charge similar to positrons. The holes form localized excitons to emit the light， some of the excitons recombine at non-radiative centres. Fig. 1 shows the calculated IQE droop curves with different A values. As we can see， with higher A values， i.e. dislocation & defect density， the IQEpeak decreased and the current corresponding to IQEpeak increased， IQE approaches closely at elevated current. The droop length thus surprisingly increased with a higher dislocation. Martin F. Schubert et al8 experimentally found that： dislocations do not strongly impact high-current performance； instead they contribute to increased nonradiative recombination at lower currents and a suppression of peak efficiency. The effect of dislocation &defect on IQE and IQE droop can be understand as this： at low current density， almost all the carriers were localized at a potential minima， and the IQE exhibited less dependence with TD density. However， at high carrier density， the localized carriers at potential minima will gradually release into conduction band due to band filling effect and easily move to the site around dislocations. The recombination mechanism could be both SRH and Auger， we will continue this discussion in Auger part. Spontaneous emission
Some researchers found the radiative recombination B varies with different carrier density. David9 employed the relationship and extracted the parametersB0=7×10-11cm3s-1and n0=5×1018cm-3. We also plot IQE curves with different B values in Fig. 2. Obviously， IQE increases and IQE droop was suppressed with a higher B value. The current corresponding to IQEpeak varies negligently for different B values.
Auger recombination
Auger recombination is a type of non-radiative recombination， describing a physical phenomenon in which excess electron energy was transferred to other electrons or holes. The probability of Auger process inversely related with energy band gap， so it is generally considered negligible in wide-gap materials. However， many researchers have extracted the C values， which are much higher than the theoretically predicted values. Through photoluminescence （PL） lifetime studies on quasi-bulk InGaN layers， Shen et al.10. extracted an Auger coefficient of C～2×10-30 cm6/s. As can be seen from Fig. 3， with C increased， IQE decreases greatly， especially at high injection current. Recalling from the defect related non-radiative part， we suggest a dislocation-assisted mechanism. Because if it is the SRH dominates， the nonradiative recombination-rate should be saturated at high current density. However， this is contradictory with our calculation and the experimental results.
Electron overflow and hole insufficient injection
It is a common problem of the electrons overflow beyond the QWs due to band flattened at high injection condition and this is AlGaN electron blocking layer is adopted in III-nitride LEDs11.Hot electrons and the associated ballistic and quasiballistic transport across the active regions of InGaN LEDs have been incorporated into a first order simple model by X. Ni12et. al to explains the experimental observations of electron spillover and the efficiency degradation at high injection levels. On the other hand， due to inefficient p-type doping and the low hole mobility， the hole injection is insufficient. Various other approaches have been proposed to cool down or block the injected hot electrons to reduce IQE droop， among them are electron cooler， staircase electron injector， p- AlInGaN/AlGaN EBL Layer， p-InGaN/AlGaN.
Polarization field and IQE droop
As well known， InGaN/GaN LEDs grown along [0001] orientation possess very strong positive polarization charges， which lowers the effective conduction band barrier height for electrons， thus making the EBL relatively ineffective in confining the electrons. Also Roman Vaxenburg13 found the polarization field in QWs not only suppresses the radiative recombination but also strongly enhances the rate of Auger recombination. So it is important to structure design to minimize the effect of the polarization field in III-nitride LEDs. Roman Vaxenburg13used a gradual variation of the QW layer composition， which compensates the effect of the electric field acting on holes. Semipolar and nonpolar growths have already yielded devices with superior performance. Zi-Hui Zhang14 proposed polarization self-screening effect through growing a p-type EBL with AlN composition partially graded along the [0001] orientation， which induces the bulk polarization charges. These bulk polarization charges are utilized to effectively self-screen the positive polarization induced interface charges located at the interface between the EBL and the last quantum barrier when designed properly. Current crowding effect on IQE and EQE droop
Most of the previous researches are concentrated on the vertical distribution of carriers in the multiple quantum wells. However， the in-plane （lateral） distribution of carriers is also important and crucial due to the current crowding effect （CCE）. The lateral carrier distribution obviously relates to IQE. Furthermore， since the current tends to crowd under the metal electrode， whereas large percentage of the generated photons cannot be extracted due to the electrode absorption. This certainly has a negative effect on the light extraction efficiency （LEE）， which is lacked in the previous part of this paper. As we know， the EQE is the product of the IQE and the LEE， so the variation of current diffusion shall have a significant influence on the IQE， LEE and thus ultimately the EQE droop level. By incorporating transparent conductive layer15， current blocking layer16 can increase the current spreading length and thus improve the efficiency and suppress the efficiency droop.
Conclusion
The inner mechanisms accounting for the efficiency droop in III-Nitride based LEDs have been investigated extensively. Here we give a brief discussion of the possible mechanisms： defect &dislocations related SRH non-radiative recombination， reduced spontaneous emission， Auger non-radiative recombination， electron leakage， polarization field， current crowding effect. Dislocations do not strongly impact high-current performance， instead they contribute to increased nonradiativere combination at lower currents and a suppression of peak efficiency； a reduced spontaneous emission reduces internal quantum efficiency （IQE） and deteriorates IQE droop； Defect-assisted and polarization field induced Auger process， electron overflow will strongly influence the droop characteristics at elevated current injection. Current crowding should results to a lower IQE， light extraction efficiency （LEE） and the ultimate external quantum efficiency （EQE）.
References
1.J. Cho， E. F. Schubert， and J. K. Kim， Laser & Photonics Reviews 7 （3）， 408-421 （2013）.
2.G. Venturi， A. Castaldini， and C. Humphreys， Applied Physics Letters 104 （21）， - （2014）.
3.Y. Ji， Z.-H. Zhang， and H. V. Demir， Opt. Lett. 38 （2）， 202-204 （2013）.
4.A. Kim， W. G?tz， and R. Kern， physica status solidi（a） 188 （1）， 15-21 （2001）.
5.F. R?mer and B. Witzigmann， Opt. Express 22 （S6）， A1440-A1452 （2014）.
6.H.-Y. Ryu， H.-S.Kim， and J.-I. Shim， Applied Physics Letters 95 （8）， 081114 （2009）. 7.S. F. Chichibu， A. Uedono， and T. Sota， Nature materials 5 （10）， 810-816 （2006）.
8.M. F. Schubert， S. Chhajed， and M. A. Banas， Applied Physics Letters 91 （23）， 231114 （2007）.
9.A. David， and M. J. Grundmann， Appl. Phys. Lett.96， 103504（2010）.
10.Y. C. Shen， G. O. Mueller， and M. R. Krames， Appl. Phys. Lett.91（14），141101 （2007）.
11.J. Piprek and S. Nakamura， IEE Proc. Optoelectron.149， 145（2002）.
12.X. Ni， X. Li， and A. Matulionis， Journal of Applied Physics 108 （3）， - （2010）.
13.R. Vaxenburg， A. Rodina， and A. L. Efros， Applied Physics Letters 103 （22）， - （2013）.
14Z.-H. Zhang， W. Liu， and H. Volkan Demir， Applied Physics Letters 104 （24）， - （2014）.
15.L. Wang， Y. Zhang， and G. Wang， Applied Physics Letters 101 （6）， 061102 （2012）.
16.T.-M. Chen， K. Uang， and H. Kuan， Photonics Technology Letters， IEEE 20 （9）， 703-705 （2008）.
Fig. 1 IQE droop curves with different A values
Fig. 2 IQE curves with different B values
Fig. 3 IQE curves with different C values