Pathway Towards High-Efficiency Eu-doped GaN Light-Emitting Diodes

A physically intuitive current injection efficiency model for a GaN:Eu quantum well (QW) has been developed to clarify the necessary means to achieve device quantum efficiency higher than the state-of-the-art GaN:Eu system for red light emission. The identification and analysis of limiting factors for high internal quantum efficiencies (IQE) are accomplished through the current injection efficiency model. In addition, the issue of the significantly lower IQE in the electrically-driven GaN:Eu devices in comparison to the optically-pumped GaN:Eu devices is clarified in the framework of this injection efficiency model. The improved understanding of the quantum efficiency issue through current injection efficiency model provides a pathway to address the limiting factors in electrically-driven devices. Based on our developed injection efficiency model, several experimental approaches have been suggested to address the limitations in achieving high IQE GaN:Eu QW based devices in red spectral regime.

. Model of the trap assisted excitation of Eu +3 ion in GaN:Eu QW active region. (a) The confined electron-hole in the GaN:Eu QW are captured by the traps (purple arrows) which are close to the vicinity of Eu +3 ion and results in (b) complex formation. (c) After the complex formation the electron-hole pair can recombine at the trap level by releasing a non-radiative energy to the crystal lattice (brown arrow) or release a non-radiative energy used for the excitation of the nearby Eu +3 ion (energy transfer process-gold arrow) or it can dissociate by releasing the electron-hole back to the GaN:Eu QW. Similarly, the excited Eu +3 can recombine non-radiatively by releasing energy to the crystal lattice (brown arrow) or release non-radiative energy for complex formation (energy back-transfer process, dark blue arrow) or recombine radiatively with photon emission (red arrow).
SCiENtifiC RepoRts | 7: 14648 | DOI: 10.1038/s41598-017-15302-y Electrical model. In the electrically-driven GaN:Eu QW device, carriers are injected into the GaN:Eu QW active region from the barriers. Our analysis is similar to the current injection efficiency analysis in a typical QW without the presence of RE elements 54,55 . The presence of Eu +3 ions modifies these rate equations to account for coupling with Eu +3 ions and complexes.
Previous experimental work on QW devices have shown that the carriers injected into the QW can escape to the barrier due to the high thermionic emission energy 56 . The thermionic-related carrier escape process needs to be accounted in the determination of IQE of electrically-driven QW based devices. In addition, the non-radiative and spontaneous radiative recombination process of carriers in the GaN host and Al x Ga 1−x N barreirs are also taken into consideration in the electrically-driven GaN:Eu QW.
The carrier rate equations both in the barrier (N B ) and GaN:Eu QW active region (N QW ) are given by: where, the V B, V QW , V Eu are the volumes of the barrier, GaN:Eu QW and Eu-doped region of the GaN:Eu QW respectively. The I tot is the total injected current in the barriers which is assumed to be equal to the total injected current into the device, τ e is the carrier thermionic escape time form the GaN:Eu QW active region to the barriers, τ B is the carrier lifetime in the barrier described by the non-radiative and spontaneous radiative processes in the barrier, and τ bw is the barrier-well lifetime 54,57 . The radiative and non-radiative carrier processes in the GaN host are described by the τ sp and τ nr respectively. In general, the non-radiative and spontaneous radiative recombination rates in the GaN host and Al x Ga 1−x N barriers are functions of the carrier concentrations in the QW and barrier, the bimolecular recombination coefficient B, Shockley-Hall-Read (SHR) constant A, and Auger coefficient C. More details regarding the non-radiative and spontaneous radiative recombination processes of carriers in the GaN host and Al x Ga 1−x N barriers, as well as the thermionic escape from GaN:Eu QW active region to the Al x Ga 1−x N barriers can be found in refs 54,55,[57][58][59][60] . The rate equations of complexes (N c ) and excited Eu +3 ions (N Eu ) in the GaN:Eu QW active region are: where, the N and N traps are the concentrations of Eu +3 ions and traps in the GaN:Eu QW active region, respectively. The parameters C c_cap , C bt and C tr are defined as the capture, back-transfer and transfer coefficients in cm 3 /s respectively. For the rate equations (3) and (4), a general capture, back-transfer and transfer rate can be defined as: tr Eu tr0 Eu tr Equations (5)-(7) account for saturation in the excited Eu +3 concentration as well as in the concentration of formed complexes, when substituted in the rate equations (3) and (4). The subscript 0 denotes the relative capture, transfer and back-transfer rate and the term in the parenthesis denotes the degree of the respective excitation of Eu +3 ion and the complex concentration. Thus, the terms of 1/τ c_cap , 1/τ tr and 1/τ bt can be viewed respectively as the general capture transfer and back-transfer rates of the system.
The injection efficiency of GaN:Eu QW active region is the ratio of the current arising from the radiative and non-radiative de-excitation of Eu +3 ions to the total current injected into the GaN:Eu QW system I tot , and can be expressed as: where, the I Eu represents the total recombination current arising from the radiative and non-radiative de-excitation of the Eu +3 ion and is defined as: where, the q is the electron charge.
Solving the system of equations (1)-(4) under steady state condition the current injection efficiency of the electrical model is obtained: where, the 1/τ Eu and 1/τ comp are rates related to Eu +3 and complex: IQE electrical i nj electrical rad η =η ⋅η where, the η rad is the radiative efficiency of the Eu +3 ions defined as the ratio of radiative to both radiative and non-radiative de-excitation of Eu +3 ions:  [61][62][63][64] . For the same reason, the Al x Ga 1−x N barriers are not excited and hence the non-radiative and radiative process of carriers in the barriers can be neglected.
In the optically-pumped GaN:Eu QW, the assumption that the GaN:Eu QW active region is excited resonantly above the bandgap with a photon flux ϕ, results in a rate equation of carriers in the GaN:Eu QW active region (N QW ) of: where, the α is the absorption coefficient of GaN and the ϕ is the photon flux of the excitation. The first term of the right part of equation (16) can be viewed as the corresponding current I tot arising from the creation of carriers due to absorption of the incident photon flux and is equal to: The rate equations of complexes (N c ) and excited Eu +3 ions (N Eu ) in the GaN:Eu QW active region are same as in the case of electrically-driven GaN:Eu QW and are given from equations (3)-(4). The injection efficiency for the optical model is defined as:  The internal quantum efficiency for the optical model is given from equation (14) with the respective injection efficiency.
Comparison between optical and electrical model. The analysis of the current injection efficiency model indicates fundamental differences in the excitation path of Eu +3 ion in the GaN:Eu QW active region for the optically-pumped and electrically-driven GaN:Eu QW. In Fig. 2 a flow chart depicts the related mechanisms and phenomena along the excitation path of Eu +3 ion in the GaN:Eu QW for both models.
More specifically, the presence of the barrier level in the electrical model results in transport phenomena of the carriers. The effect of barrier-well lifetime which depends on the mobility of the carriers and the temperature T strongly influences the injection efficiency in the active region in a similar way as in the case of a QW without the presence of RE elements 55,60 . Additionally, recombination mechanisms (monomolecular, bimolecular and Auger recombination) also exist in the barrier. Further, the barrier opens an extra path for the carriers through the recycling mechanisms (red arrows in Fig. 2), increasing the probability of carrier deviation from the Eu +3 excitation path. The thermionic escape from QW to the barrier, which is proportional to the concentration of carriers (N QW ), becomes stronger with increasing the current density 54,58,59 . The transport phenomena and thermionic process limit the injection efficiency and internal quantum efficiency in the electrically-driven GaN:Eu QW device as opposed to optically-pumped GaN:Eu QW in which these phenomena do not exist.

Simulation Results
This section presents how the parameters such as SHR constant A, capture time τ cap0 , transfer time τ tr0 , back-transfer time τ bt0 , dissociation time τ diss , and Eu +3 radiative lifetime τ rad , affect the injection efficiency of electrically driven and optical-pumped Eu-doped GaN QW active region. The QW and barrier parameters used for the simulations, such as the values of effective masses and mobilities, can be found in reference 57 . The bimolecular recombination coefficient B and Auger coefficient C are fixed to 10 −11 cm 3 /s and 10 −32 cm 6 /s respectively 57 . Note that the A, B and C coefficients, which describe the radiative and non-radiative processes in the GaN host and Al x Ga 1−x N barriers, are assumed to be the same for the barriers and the well. The Al composition was set at x = 10% for the Al x Ga 1−x N barriers. Table 1 presents the parameters used in the numerical calculation of the injection efficiency for the GaN:Eu QW active region. References 65,66 were used as a starting point for the relative times between the GaN host, traps-complexes and Eu +3 ions.
In our analysis, the injection efficiency (η inj_optical , η inj_electrical ) is plotted with the excited Eu +3 concentration (N Eu ) versus the photon flux (ϕ) -optical model -and input current density (J) -electrical model - (Figs 3-5). As shown in Figs 3-5, the injection efficiency of the Eu-doped GaN QW active region exhibits the droop characteristics. Since the excited Eu +3 concentration cannot exceed the maximum available Eu +3 concentration in the active region, the excited Eu +3 concentration increases with the photon flux and the current density. At a point where the excited Eu +3 concentration saturates due to the maximum available Eu +3 concentration in the active region, the subsequent increase of photon flux and current density leads to the droop in the injection

Study I: Effect of Shockley-Hall-Read constant.
The SHR constant A is related to the non-radiative process of monomolecular recombination which takes place through defects in the crystal lattice. SRH mechanism has been shown to be a critical process affecting the injection efficiency of light emitting diodes 57 . As shown in Fig. 3, at low photon fluxes and current densities, the injection efficiency is higher as the SRH constant is smaller. Such characteristic is expected, since lower values of SRH constant indicate lower non-radiative recombination rates of carriers in the active region and barrier. As a result, the injection efficiency in the GaN:Eu QW active region increases for optical and electrical model. Interestingly, it should be noted that the increase of the SHR constant A would lead to slower saturation of the excited Eu +3 concentration as the photon flux and current density is increasing. This indicates that additional carriers are required through optical excitation in the optically-pumped device or electrical injection in the electrically-driven device to replace the carriers lost in the monomolecular non-radiative recombination process. Thus, higher photon fluxes and current densities are required to result in same Eu +3 excitation as opposed to lower values of A.
Study II: Effect of capture time. The capture of carriers from traps with a rate 1/τ cap0 results in the creation of complexes. A general capture time τ c_cap is given from equation (5) which is a function of the formed complexes (N c ). Figure 4 shows the effect of capture time τ cap0 both for optical and electrical model. Following the previous analysis, as the capture time decreases, the carriers are captured more efficiently from traps increasing the formation rate of complexes and consequently the excited Eu +3 concentration. This efficient capture of carriers from traps increases the injection efficiency and decrease the required amount of photon fluxes and current densities. This is observed as a shift towards lower photon fluxes and current densities of the excited Eu +3 concentration and injection efficiency for both models. For the optical model, the higher injection efficiency occurs for the lower capture time of τ cap0 = 10 −7 s where the injection efficiency drops from η inj_optical = 21% to η inj_optical = 0.2%. In contrast, for the electrical model it drops from η inj_electrical = 9% to η inj_electrical = 0.01%.
Study III: Effect of transfer time. The transfer time defines the rate at which complexes de-excite by releasing energy to a nearby Eu +3 ion. As shown in Fig. 5, the injection efficiency increases as the transfer time τ tr0 decreases, which is a result of the faster de-excitation of the complexes. Equation (4) indicates that the de-excitation rate of complexes, 1/τ tr , is essentially the excitation rate of Eu +3 ions. As a result, the higher excitation rates of Eu +3 ions result in faster saturation of excited Eu +3 concentration under steady state conditions. This is observed as a shift toward lower photon fluxes (ϕ) and current densities (J) of the excited Eu +3 concentration.  As it is shown in Fig. 6, by increasing the dissociation rate, the injection efficiency and excited Eu +3 concnetration drop significantly. More specifically, for the electrical model injection efficiency drops from η inj_electrical = 0.18% to almost η inj_electrical = 0.001%, while for the optical model drops from η inj_optical = 0.9% to almost η inj_optical = 0.01%. The changes in excited Eu +3 concnetration are identical for the two models.
A droop in the injection efficiency and excited Eu +3 concentration with the back-transfer rate is also observed for both models. More specifically, the droop starts when the back-transfer rate of 1/τ bt0 = 5 × 10 4 s −1 becomes comparable with the transfer rate of complexes, 1/τ tr0 = 2.77 × 10 4 s −1 . For back-transfer rates lower than 1/ τ bt0 = 5 × 10 4 s −1 , the injection efficiency and excited Eu +3 concentration remain unaffected.
In addition, the changes in the injection efficiency and excited Eu +3 concnetration with the back-transfer rate, are smaller as compared to the changes with the complex dissociation rate. As it can be seen from Fig. 2, the level at which the dissociation process takes place is distant from the level of Eu +3 ion. Thus, the carriers resulted from the dissociation of complexes have higher probability to deviate from the Eu +3 excitation path reducing in that way the injection efficiency and the excited Eu +3 concentration in the GaN:Eu QW active region.
Study V: Effect of radiative lifetime of Eu +3 ion -Enhancement of radiative efficiency. The parameters presented in the previous sections affect the internal quantum efficiency of the system by altering only the injection efficiency in the active region. The internal quantum efficiency is calculated from equation (14) with a radiative efficiency fixed at η rad = ~72% and follows the same trend of the injection efficiency. The radiative lifetime (τ rad ) and the non-radiative time (τ Eu_heat ) of Eu +3 ion determine the radiative efficiency of the GaN:Eu QW system. Lower radiative lifetime results in higher radiative efficiencies, assuming that the non-radiative lifetime of Eu +3 ion remains unchanged.
By reducing the radiative lifetime, the injection efficiency and excited Eu +3 concentration are significantly altered. The lower radiative lifetime indicates faster radiative de-excitation rate of excited Eu +3 ions, therefore, Figure 6. Injection efficiency and excited Eu +3 ion concentration of GaN:Eu QW active region as a function of (a) back-transfer rate 1/τ bt0 and (b) dissociation rate 1/τ diss . The η IQE is defined as η IQE = η inj •η rad and follows the same trend as the η inj of the optical and electrical model. The two models are compared for the same values of Eu +3 excited ion concentration in the GaN:Eu QW active region. density for electrical model. The η IQE follows the same trend as the η inj for the optical and electrical model. The non-radiative lifetime of Eu +3 ion is set to τ Eu_heat = 1 ms. Different radiative lifetimes correspond to different radiative efficiencies. For τ rad = 400 μs the radiative efficiency is η rad = 71.43%. Similarly, for τ rad = 200 μs / η rad = 83.3%, for τ rad = 70 μs / η rad = 93.46%, and for τ rad = 30 μs / η rad = 97.09%.
SCiENtifiC RepoRts | 7: 14648 | DOI:10.1038/s41598-017-15302-y higher injection efficiency can be achieved at a given photon flux and current density. This is clearly illustrated in Fig. 7. In addition, the resulted lower saturation values of excited Eu +3 ions, make the injection efficiency to be strongly altered at higher photon fluxes and current densities.
Attributing to the differences in complex interplays among the fundamental processes in the current injection process, the optical model exhibits higher injection efficiency as compared to the electrical model for the same values of excited Eu +3 concentration. In particular, the reduction of radiative lifetime from τ rad = 400 μs to τ rad = 30 μs, changes the excited Eu +3 concentration from N Eu = 8.4 × 10 18 cm −3 to N Eu = 3.25 × 10 18 cm −3 at a given ϕ = 4.7 × 10 18 cm −3 . Meanwhile, injection efficiency increases from η inj_optical = 0.62% to η inj_optical = 2.4% which is 3.8 times higher. A similar change in the excited Eu +3 concentration occurs at J = 1 A/cm 2 for the electrical model while the injection efficiency increases from η inj_electrical = 0.12% to η inj_electrical = 0.46% which is almost 3.8 times higher, same change as in the optical model. The reduction of the radiative lifetime is essential for achieving higher injection efficiencies at higher photon fluxes and current densities, while at the same time the radiative efficiency of Eu +3 ions is enhanced.

Comparison with experimentally reported data
In order to compare our work with experimentally reported values of GaN:Eu devices, the external quantum efficiency (η EQE ) for a GaN:Eu QW LED with a square device area of 1000 × 1000 μm is calculated. The external quantum efficiency is the product of the extraction efficiency (η extr ) and the internal quantum efficiency of the device. An extraction efficiency of η extr = 44% was used for our calculations, which is a typical value for GaN:Eu based device 48 . The details of each simulation are given in Table 2a and b. The numerical calculations for the external quantum efficiency are divided into two groups: Group A represents those which resulted in η EQE > 1% and Group B represents those which resulted in η EQE < 1%. In addition, both experimental studies revealed that higher injected current into the GaN:Eu device led to saturation in the EL spectra, which was attributed to the saturation of the excited Eu +3 ions. Similar findings have also been reported elsewhere 45,47 . Our study is consistent with the experimental observations that increasing the injected current will eventually result in the saturation of the excited Eu +3 concentration with a subsequent decrease in the injection efficiency and internal quantum efficiency the GaN:Eu QW active region.

Engineering the IQE of electrically-driven GaN:Eu QW
The increase of the injection efficiency, as well as its shift at higher input current densities is the desirable goal for highly efficient electrically-driven GaN:Eu based red light emitters. The numerical calculations from the current injection efficiency model, showed the pathway for high efficiency in the GaN:Eu QW system. By physically engineering the factors in the GaN:Eu QW system that affect injection efficiency (η inj ) is thus critical for achieving high internal quantum efficiency (η IQE ) in electrically-driven GaN:Eu QW based devices.
Material quality. The SHR constant A is related to defects present in the barrier and QW. Higher values of A reflect poor material quality which is detrimental for IQE of the device. The numerical calculation of IQE of the electrically-driven GaN:Eu QW device, showed an increase 62% in the IQE at 5 mA when the SHR constant A decreased by 98% ( Fig. 8(b), Simulation I and Simulation II). High quality Al x Ga 1−x N alloy material with low defect concentration can be fabricated with advanced growth techniques, such as MOCVD by carefully adjusting the growth parameters [67][68][69][70] . This low defect concentration suppresses the SHR mechanisms and is expected to increase the IQE of GaN:Eu QW based device.
Carrier capture process, back-transfer process and complex related processes. The capture time of carries form traps, the lifetime parameters related to complexes and the back-transfer process, depend on the nature of those elements as well as on the interaction between them and with the host. This work quantitatively verified that a significant enhancement of the IQE of the electrically-driven GaN:Eu QW device can be achieved by changing these lifetimes. A decrease of 90% both in capture time and transfer time resulted in an IQE increase of ~33% at 5 mA and ~24% at 20 mA ( Fig. 8(b), Simulation II and Simulation III). Recent studies have shown that through defect engineering such as co-doping with magnesium (Mg), and also through manipulation of growth conditions, can result in the enhancement of the IQE of GaN:Eu device 44,49,50,52,53,71 . Europium and trap concentration in the GaN host and thermionic emission process. Another parameter that can be engineered is the number of available traps (N traps ) and Eu +3 ion concentration (N). In this work, the effect of these two parameters is not presented. However, these values can be modified to increase the injection efficiency. More specifically, by increasing the amount of available traps (N traps ), the general capture rate according to equation(5) will be increased giving rise to the injection efficiency. Similarly, the simultaneous increase of Eu +3 ion concentration (N) will also increase the transfer rate according to equation (7). As a result, the injection efficiency will be increased at higher input current densities and photon fluxes.
SCiENtifiC RepoRts | 7: 14648 | DOI:10.1038/s41598-017-15302-y In our study the Al composition of the barrier was set to 10%. Higher Al composition will increase the conduction and valence band offsets and will suppress the carrier thermionic escape the barrier 57 . Thus, engineering the barrier height for carriers is crucial for higher injection efficiencies in the GaN:Eu QW active region.
Radiative lifetime of Eu +3 ion. The radiative efficiency of Eu +3 ion can also be modified through the engineering of radiative lifetime of Eu +3 ions. Our numerical calculations of IQE of the electrically-driven GaN:Eu QW device, showed that changing the radiative lifetime from τ rad = 200 μs to τ rad = 100 μs results in an increase   of ~144% of the IQE at 20 mA of the GaN:Eu QW device ( Fig. 8(b), Simulation III and Simulation IV). It has been experimentally demonstrated that by utilizing surface-plasmon (SP) in GaN-based QW can dramatically increase the radiative efficiency of the system [72][73][74][75] . The photon density states near the SP frequency (ϖ sp ) are increased from Purcell factor. For the case of GaN:Eu QW system, by carefully engineering the deposited materials used as SP, the SP frequency can be adjusted to coincides with the frequency of the emitted photons of Eu +3 ions. This approach will increase the radiative efficiency and consequently the internal quantum efficiency of the GaN:Eu based devices.

Summary
In summary, we developed a physically intuitive current injection efficiency model for optically-pumped and electrically-driven GaN:Eu QW and we demonstrated the pathway for enhancing the internal quantum efficiency (η IQE ) of a GaN:Eu QW system. It was shown that the saturation of excited Eu +3 concentration with the photon flux and input current density, is the main cause of the current injection efficiency droop in the GaN:Eu QW active region. Through the manipulation of the characteristic times along the excitation path of Eu +3 ion, the injection efficiency (η inj ) and internal quantum efficiency (η IQE ) of GaN:Eu QW system can be significantly enhanced. In addition, the discrepancy between the efficiencies of optically-pumped and electrically-driven GaN:Eu QW is explained in the framework of the current injection efficiency models. Our findings through the analysis within the current injection efficiency model also clarify the necessary means towards the practical realization of highly efficient red light GaN:Eu QW LED.