We discuss the influence of V-pits and their energy barrier, originating from its facets of () planes, on the luminescence efficiency of InGaN LEDs. Experimental analysis using cathodoluminescence (CL) exhibits that thin facets of V-pits of InGaN quantum wells (QWs) appear to be effective in improving the emission intensity, preventing the injected carriers from recombining non-radiatively with threading dislocations (TDs). Our theoretical calculation based on the self-consistent approach with adopting k⋅p method reveals that higher V-pit energy barrier heights in InGaN QWs more efficiently suppress the non-radiative recombination at TDs, thus enhancing the internal quantum efficiency (IQE).
© 2014 Optical Society of America
Despite continuous progress of InGaN-based blue light-emitting diodes (LEDs) for the display unit and the general illumination [1–3], understanding their emission efficiency still remains in doubt and thus requires further investigation. In particular, unexpectedly high emission efficiency of InGaN-based LEDs with high defect density, typically larger than 108 cm−2 in GaN hetero-epitaxy on foreign substrates, lies still under the debate within the research community. Plausible explanations, preventing the non-radiative recombination at the defects, such as exciton localization [4–6], thickness fluctuation , and V-pit formation [8, 9] are proposed. In addition, the emission efficiency of InGaN LEDs reaches their maximum at low current density (< 10 Acm−2) and then severely decreases as the injection current increases. This phenomenon is well-known as “efficiency droop”, which hinders achieving high-power and high-efficiency of InGaN LEDs. At present, there is a lack of consensus regarding the origin of this efficiency droop although various mechanisms such as carrier delocalization , Auger recombination [10, 11], insufficient hole injection [12, 13], carrier leakage [14, 15], and piezoelectric polarization effect  are proposed. Recently, Hangleiter et al and other research groups reported that thinner facets of V-pit side planes () in InGaN quantum wells (QWs) are found to emit the shorter wavelength, indicating the formation of higher energy barrier [8, 9, 17]. They also claimed that this V-pit barrier energy should be taken into account to describe the explanation for the emission efficiency of InGaN LEDs. Hader et al  and Wang et al  calculated the quantum efficiency in InGaN LEDs with taking into account the defect-related non-radiative recombination. However, the influence of this V-pit barrier height on the emission efficiency has been rarely investigated so far.
In this paper, it is found from cathodoluminescence (CL) analysis that the radiative recombination can benefit from the formation of V-pits around TDs on the InGaN light-emitting layers. We also investigate the influence of V-pit barrier height on the emission efficiency of InGaN LEDs. We claim that higher emission efficiencies of InGaN LEDs at high carrier injection or lower efficiency droop can be achieved via the morphological and compositional control of V-pits around TDs.
In order to investigate the optical properties of InGaN QWs, we have grown two different InGaN/GaN superlattices (SLs) with different In composition on n-GaN template. Twenty pairs of 2.1/2.4 nm InGaN/GaN SLs with low In (~4%) composition, called low In SLs, and five pairs of 3/5 nm InGaN/GaN MQWs with high In (~14%) composition, called high In SLs, are grown on 3 μm n-GaN template by metalorganic chemical vapor deposition (MOCVD). A 5 nm GaN capping layer is deposited to avoid any In desorption from high In composition layer. The CL measurement using 5 keV acceleration voltage is carried out under vacuum of 10−6 mbar and at room temperature to investigate the effect of the threading dislocations and V-pits on the emission properties of low and high In SLs.
3. Emission properties of InGaN/GaN superlattices
The optical characterization of InGaN/GaN SLs and QWs is proceeded to investigate the role of TDs and V-pits as shown in Fig. 1 (a)-(d).Figure 1 (a) exhibits the field-emission scanning electron microscope (FESEM) image of InGaN MQWs surface, featuring the randomly-distributed V-pits with a density of about 3 × 108 cm−2. Large (~175 nm) and small (~48 nm) lateral sizes of V-pits are observed from FESEM images, in which the TDs with different core energies [20, 21], lower for edge and higher for screw TDs, can lead to different sizes of V-pits while growing In-containing superlattices. In particular, the () facets of large V-pitsare clearly formed due to the reduced growth rate. The formation of V-pits within In-containing SLs could be resulted from the strain relaxation between InGaN and GaN. It is generally believed that large and small V-pits are responsible for the screw- and -edge component dislocations respectively.
Figure 1 (b) shows a panchromatic emission intensity of MQW surface, acquired from the same area in Fig. 1 (a). It is quite observable from the comparison of Fig. 1 (a) and (b) that the dark spots or non-radiative recombination areas coincide with the locations of V-pits. In optical characterization using CL, the bright region represents the higher intensity of cathodoluminescence throughout the radiative recombination of electrons and holes excited by the accelerated electrons [22, 23]. Inset in Fig. 1(b) shows the emission spectrum from the measured area, indicating two distinct peaks of approximately 390 nm and 445 nm arising from low and high In-containing SLs, respectively. It is also worth noting that radii of dark regions by large and small V-pits appear approximately same with their physical sizes. This not only supports the role of V-pits as non-recombination centers, but also suggests the carrier screening by V-pits preventing the carriers from recombining with TDs. In other words, the excited carriers on in-plane QWs tend to diffuse laterally until they recombine radiatively or non-radiatively [24, 25]. It is likely that the carriers in the vicinity of TDs are destined to non-radiately recombine with TDs unless TD coexists with V-pit. Fuhrmann et al investigated the role of V-pit around TD of AlGaN/GaN quantum wells emitting ultraviolet light . They claimed that the significant increase of emission efficiency in quantum wells can be ascribed to the carrier screening by the formation of V-pits around TDs while carriers are more likely to recombine with TDs without V-pits. Thus, we can also agree that V-pits around TDs play an important role of suppressing the non-radiative recombination in InGaN MQWs.
In contrast to panchromatic CL, monochromatic CL exhibits the emission intensity at the fixed wavelength. Figure 1(c) and (d) show the emission intensity of both SLs at 445 nm and
390 nm, respectively. Since the emission intensity from high In SLs is measured to be almost one order of magnitude higher than that from underling low In SLs primarily due to the electron penetration depth. Figure 1(c) exhibits no significant difference in terms of the emission distribution. However, it is found that low In SLs possess noticeably different emission features at 390 nm between large and small V-pits as shown in Fig. 1(d). The lateral sizes of dark spots by small V-pits become much larger than their physical sizes, suggesting that the non-radiative recombination domains are extended even outside V-pits . This should be understood by the lateral diffusion of carriers and formation of TDs without the facets as below.
The excited carriers tend to diffuse laterally on InGaN/GaN in-plane QWs until they recombine [24, 25]. As clearly seen from the transmission electron microscope image in Fig. 1 (e), small V-pits are formed in the middle of low In SLs while large ones are formed almost at the beginning of low In SLs. In the perspective of strain-energy for the V-pit evolution, it is intuitively reasonable that SLs with low In composition possess lower strain energy compared to high In SLs [26, 27]. This can give rise to different beginning points of small V-pit vertices, due to the accumulation of strain energy. In contrast to large V-pits, therefore, each small V-pit appears to have a TD intersecting low In SLs, leading to partially flat SLs without facets. These flat SLs without V-pits at the lower portion of low In SLs can make significant negative impact on the light emission as shown in Fig. 1(d). Since the facets of V-pits are known to play a major role of the carrier screening, TDs intersecting flat SLs can behave as much larger non-radiative recombination center.
Schematics in Fig. 2 depict the carrier recombination in the vicinity of V-pits. Figure 2(a) and 2(c) (Fig. 2(b) and 2(d)) show the large (small) V-pit in the physical domain and its schematic energy diagram with carrier recombination process, respectively. Figure 2(c) shows that the presence of V-pits at the entire part of low In SLs effectively suppresses the lateral diffusion into TDs, minimizing the dark spot sizes . On the other hand, as shown in Fig. 2(d), it is very likely that the carriers can excite over small V-pit energy barrier, diffuse, and recombine non-radiatively with TDs. This can cause a relatively large dark spot, which is also quite consistent with the CL intensity distribution by large and small V-pits shown in Fig. 1(d). The lateral sizes of dark spots by small V-pits can be estimated to be as large as about 400 nm on average from Fig. 1(d), almost eight times larger than their physical sizes while dark spots by large V-pits quite coincide with their physical sizes. This suggests that smaller sizes of V-pits could be disadvantageous for the optical emission of injected carriers in InGaN LEDs. In other words, the emission intensity can be enhanced via enlargement of small V-pits, one possible method of which might be to insert SLs with high In composition or to optimize the growth conditions of underlying GaN layer for V-pit formation at the beginning of SLs. Bright dots at the center of small V-pits can be resulted from the local emission at the flat SLs underneath them.
Overall, phenomenon including the existence of V-pit at the TDs and lateral diffusion process propose a possibility to understand the efficiency droop of InGaN LEDs as well as the unexpectedly high emission despite the high defect density.
4. Simulation for the effect of V-pit barrier on the efficiency of InGaN LEDs
Figure 3 illustrates the schematics of in-plane quantum well with the presence of V-pits and TDs and our approximated (one-dimensional) modeling approach for it. The upper part of Fig. 3(a) shows the physical structure of V-pits on in-plane QWs, in which V-pits are originated from TDs. Based on the structural and optical characterization from Fig. 2, the energy landscape can be approximately described as shown in the lower part of Fig. 3(a), similar to Fig. 4 in . This energy topography represents higher local energy barriers from the facets of V-pits and relatively flat energy plane for V-pit-free area in InGaN/GaN MQWs. For simple one-dimensional modeling, randomly positioned V-pits with various energy barrier heights as depicted in Fig. 3(a) are approximated by a constant V-pit barrier height over the in-plane quantum well. The top of V-pit energy barrier is measured from the bottom of ground conduction subband, and the constant barrier height is defined by the energy difference between the two. This schematic figure also indicates that the carriers should be excited above V-pit energy barrier to recombine in TDs. Figure 3(b) shows the density of states, the Fermi-Dirac distribution function, and carrier density distribution. In far right part of Fig. 3(b), the orange color region represents the carrier loss by the non-radiative recombination with TDs while the green one for radiative recombination. As more carriers are injected into InGaN QW, Fermi level, labeled EF in Fig. 3(b), will move upward, indicating that carriers with a higher energy will increase. This will eventually increase the probability of non-radiative recombination to TDs over V-bit barrier. It is necessary to calculate each energy levels such as the conduction band (E1), Fermi level (EF), and V-pit barrier height as a function of injected carrier density to estimate how much the carriers becomes excited over V-pit barrier height. Therefore, this calculation will enable us to exhibit the effect of constant V-pit barrier height on the concentration of carriers recombined to TDs at high carrier density.
We considered 3 nm In0.14GaN quantum well layer sandwiched by 4 nm GaN layer for one-dimensional simulation, in which a self-consistent approach of a bipolarly-coupled 4 × 4 k⋅p band model and the Hartree-type Poisson equation is employed with taking into account the polarization field and injected carrier density. The simulation parameters such as band-to-band interaction and strain parameters are adopted from the literature . Figure 4 (a) showsthe calculated energy band diagrams including the conduction and valence ground subband states, quasi-Fermi levels in InGaN/GaN single quantum well (SQW) structure along the polar c-axis at different sheet carrier densities. Here the spatially-separated wavefunctions, black solid lines in Fig. 3(a) and (b), are due to the intrinsic and strain-induced polarizations in the wurtzite nitride semiconductor. Adding more carriers alleviates the polarization field inside InGaN layer due to the band bending as shown in Fig. 4(b), explaining the reduced quantum confinement Stark effect (QCSE) [29, 30]. Figure 4(c) shows that the quasi-Fermi level is raised across the ground conduction subband and then the top of V-defect potential barriers as the sheet carrier density is increased. It indicates that the carriers become more energetic with increasing the probability of non-radiative recombination to TDs as the injection carrier density increases. Therefore, it is likely that the ratio of non-radiative carriers at TDs over V-pit barrier height to radiative carriers increases as more carriers are injected. One can imagine that this might be associated with the efficiency droop of InGaN LEDs at high injection currents.
Figure 5(a) shows the calculated radiative recombination rate (Wrad) with varied V-pit energy barrier height from 20 meV to 180 meV by 40 meV increment . It indicates that as the V-pit energy barrier becomes higher, radiative carriers can gradually obtain a larger value of in-plane wavevector corresponding to the V-pit barrier energy. Accordingly, Wrad is increased for higher V-pit energy barrier heights over a wide range of sheet carrier densities. At the same time, this leads to increased portion of radiative carrier density relative to the non-radiative carrier density to TD () for total injected carrier density (ninj) as shown in Fig. 5(b) with reducing the chances of carrier capture to TD. The calculated Wrad is within the range of reported values, implying the validity of our calculation [18, 32–34]. Without considering the effect of TDs and V-pits, which corresponds to the case of a very large V-pit barrier height, the behavior of Wrad approximately follows the quadratic dependence of sheet carrier densities.
In turn, it can be understood by the fact that the injected carriers located in the vicinity of V-pits tend to recombine radiatively due to the raised local V-pit potential barrier. In the experiment, it can be identified that this tendency can minimize the relatively dark area around V-pits, leading to the improved emission intensity of InGaN LEDs [22, 23]. The non-radiative carriers are nearly screened out if the V pit potential barrier approaches to 200 meV. Due to the limitation of one-dimensional simulation and other possible simplification, only qualitative discussions appear to be valid in this study. In other words, we claim that the improved emission intensity from InGaN/GaN SQW can be achieved by higher V-pit potential energy barrier height around TDs. Possible parameters affecting V-pit barrier heights are known to be the thickness of QWs in the facets and the In clustering around V-pits [9, 35, 36]. Indeed, some literature reported the improved light output of InGaN LEDs by increasing V-pit size of InGaN QW on purpose [37–39].
The internal quantum efficiency (IQE) is defined by a product of the injection efficiency and radiation efficiency as shown below 40].
More specifically, Eq. (2) includes the carrier reduction by the non-radiative recombination by TDs, thereby accounting for the effect of V-pit barrier height in IQE calculation. It should be noted that non-radiative carriers via TD in the QW are distinguished from carriers which contribute to SRH and radiative recombinations in IQE calculation. In other words, non-radiative recombination due to TDs and the other defects such as point defects are included in R and An, respectively, while neglecting their mutual interaction or coupling. It was hypothesized earlier that this non-radiative recombination to the TDs can occur for injected carriers with energies lower than V-pit energy barrier height. In order to clearly distinguish the effect of V-pit at high injection current level associated with the efficiency droop of InGaN LEDs, we only consider the two terms in the denominator affecting IQE. One can include the higher order contributions to IQE such as the Auger recombination and the carrier leakage over the electron blocking layer for more complete approaches . In this study, we intend to limit our discussion to the influence of V-pit barrier energy on the efficiency droop of InGaN SQW. Further study will take into account other possible mechanisms for IQE calculation.
Figure 6 exhibits IQE curves with varying V-pit potential barrier heights as a function of injection current density. It is shown that the onset of IQE droop less than 10 A/cm2 becomes noticeable with smaller V-pit barrier height (< 100 meV). For V-pit energy barrier height approximately larger than 140 meV, IQE curve becomes nearly flat over current densities after reaching a peak in the low current density and gradually approaches to unity. As indicated by serial IQE curves, increase of V-pit barrier height improves IQE from the entire current injection regime. It also helps to reduce IQE droop and eventually make it nearly disappeared. This trend indicates that increase of V-pit barrier height lowers the probability of non-radiative recombination as an origin of IQE droop at the high injection regime. Thus, we observe that the alleviation of IQE droop can be achieved by the increase of V-pit potential barrier height in InGaN/GaN SQW.
Our proposed model considering the carrier reduction by V-pit can also explain IQE droop without introducing Auger recombination. Theoretical calculation reveals that IQE droop can become only observable with non-radiative Auger recombination or carrier leakage . It remains still arguable in LED community whether or not Auger recombination contribution is high enough to cause IQE droop in nitride semiconductors. In our approach, non-radiative recombination of injected carriers to TDs can be regarded the carrier leakage in IQE curves. The carrier leakage has also been a possible suspect for IQE droop. If Auger recombination is included in IQE expression, the carrier leakage could increase and then it will exacerbate IQE droop due to the transfer of energy to the carriers non-radiatively. In a real system, it might be almost impossible for IQE to approach to the unity in the operating injection current range even with ~200 meV V-pit barrier height due to other possible carrier loss mechanisms such as carrier overflow over the electron blocking layer, which can be described by the charge carrier transport. In addition, our simplified model could overestimate IQE curves due to possibly limited consideration of Non-radiative factors. However, it should be noted that V-pit barrier height should be considered as one of the important parameters affecting the IQE droop.
In addition to the improved optical efficiency by enlarged V-pit size, literatures have also dealt with the effect of V-pit sizes on the electrical characteristics of InGaN LEDs [38, 39, 41]. LEDs with lower leakage current, resulting from the tunneling between deep centers along TDs, as well as high optical output are of great significance in the LED industry. Larger V-pit sizes often suppress the reverse leakage current of LEDs . However, the excessive increase of V-pit size on QW planes could possibly lead to the smaller area of emissive region, consequently resulting in poor optical output of LEDs . Therefore, the QW structure with enlarged V-pits in InGaN LEDs need to be carefully designed in a way that V-pit barrier height remains as high as possible for the improvement of optical and electrical properties.
We investigate the influence of V-pits around TDs on the optical emission of InGaN LEDs. It was observed that the presence of V-pit around TDs suppresses the lateral diffusion of excited carriers into TDs, consequently preventing non-radiative recombination on MQW planes. We also carried out the simulation based on a 4 × 4 k⋅p method to understand the effect of V-pit barrier height on the efficiency droop in GaN based blue LEDs. Simulation results reveal that higher V-pit potential barriers alleviate the efficiency droop.
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