Investigating defects in InGaN based optoelectronics: from material and device perspective

III-nitride optoelectronics have revolutionized solid-state lighting technology. However, non-radiative defects play a major bottleneck in determining the performance of InGaN-based optoelectronics devices. It becomes especially challenging when high indium is required to be incorporated to obtain emission at higher wavelength (>500 nm). In this research article, we are going to discuss our investigation on the origin of defects in InGaN-based optoelectronics devices from the material and device perspective and characterize them through various techniques. This article broadly consists of two parts. In the first part, we investigate defects in InGaN based optoelectronics from a material point of view. Here, we discuss the challenges in the growth of InGaN planar (2-dimensional) and nanowires (1-dimensional) with high indium (≥20%) incorporation using the plasma-assisted molecular beam epitaxy (PA-MBE) technique. Photoluminescence spectroscopy (PL) has been performed to characterize these grown samples to assess their optical quality. Atomic force microscopy (AFM) has been employed to characterize the surface morphology of grown InGaN layers. High-resolution transmission electron microscopy (HRTEM) and scanning electron microcopy (SEM) are also used to characterize InGaN planar and nanowire samples grown under various process conditions. In the second part, we investigate the role of defects on InGaN optoelectronics from a device point of view. Here, we discuss the fabrication of InGaN multi-quantum well-based light emitting diodes (LEDs). Temperature-dependent current versus voltage measurements are carried out to investigate the role of defects on carrier dynamics under forward and reverse bias conditions. Frequency-dependent capacitance versus voltage (CV) and conductance versus voltage (GV) techniques are employed extensively to characterize defects in fabricated InGaN LEDs.

grown single crystal layer faces several challenges mainly due to the lattice mismatch with underlying substrate. Another major challenge stems from the difference in thermal expansion coefficients, which results in stress and bowing in the grown layer mainly during post-growth cooling process. With the increasing thickness of the growing III-N layer, extrinsic stress can result in bigger cracks and even wafer breakage.
Defects can rightfully be called as the archenemies of optoelectronic devices. Carriers recombine nonradiatively through defects, producing no light in the process. Higher defect density reduces emission efficiency by opening an additional recombination path for injected carriers in the active region. Non-radiative defects in semiconductor crystal structures are commonly categorized into two types: threading dislocations (or line defects) and point defects. Threading dislocations arise during hetero-epitaxy planar growth owing to lattice mismatch between grown layer and the underlying substrate [12,13]. Initially, the grown layer starts to follow in-plane lattice parameter of the substrate, known as Pseudomorphic growth, resulting in elongation of out-ofplane lattice parameter of the grown film in the process [14]. However, tensile/compressive strain builds up in the layer if the in-plane lattice parameter of the grown layer is smaller/larger than that of the substrate. Once thin film grows beyond the critical thickness, the lattice strain relaxes by forming misfit dislocation at the interface. Single or multiple lines of atoms are found to be absent in the layer in the process, termed as threading dislocations that propagate along the crystal growth direction. These missing atoms create sub-bandgap energy states in the structure, resulting in non-radiative recombination [15]. Figure 2 depicts schematic representation of formation of threading dislocations during growth. For the growth of InGaN/GaN heterostructure, lattice mismatch increases with increasing indium incorporation, leading to a high density of threading dislocation, which acts as the centers of non-radiative recombination. As discussed before, threading dislocations can effectively be reduced in nanowire. Another growth parameter, playing trade-off between indium incorporation and crystal quality of InGaN is growth temperature. It is also observed that relatively lower growth temperatures must be used to negate the effect of indium desorption during growth. It is also observed that defect formation may occur due to high indium incorporation or low growth temperatures [16]. Low temperatures do not facilitate adatom diffusion during growth. This results in forming a polycrystalline structure with several grain boundaries, leading to poor structural and optical properties. As discussed, nanowire growth requires high temperatures for sidewall diffusion of adatoms. Low growth temperatures lead to inadequate sidewall diffusion and poor crystal quality of InGaN nanowires with high indium incorporation. Studies have shown that point defects surge significantly with high indium composition [17,18]. Nitrogen vacancies have the lowest formation energy in InN or InGaN with high indium composition [19,20]. Such point defects act as non-radiative recombination centers. Surface-to-volume ratio is another determining parameter for semiconductor optical devices as their surfaces house a significant number of dangling bonds, that act as active centers for SRH recombination. Although nanowires possess high crystal quality, it is of critical concern when very thin nanowires are grown. Researchers have been exploring various passivation techniques to neutralize the surface states of the nanowires in order to enhance optical emission.

Defects in bulk InGaN layers
Section 2 ascribes defects in InGaN with high indium composition to lattice mismatch and low temperature growth. This section discusses experimental evidence of defects due to varying indium composition of bulk InGaN planar structures by structural and optical characterizations.

Experimental
MOCVD-grown GaN layer on sapphire, also termed as GaN templates, are utilized as substrates for InGaN growth. Prior to planar InGaN growth, GaN buffer layers of thickness ∼600 nm is grown under the intermediate metal-rich condition to obtain a smooth surface at high substrate temperatures. Following GaN growth, ∼210 nm thick InGaN layers are grown in all the samples without pausing the growth to minimize thermal degradation of the layer. Details of the samples are given in table 1. Growth temperature is varied for samples A  C with plasma power unchanged to investigate the impact of substrate temperature on layer properties. Insitu characterization technique viz. the reflection high-energy electron diffraction (RHEED) is used to monitor the growth quality. Surface morphology of the grown layers are investigated through atomic force microscopy (AFM) in tapping mode. High-resolution X-ray diffraction (HRXRD) is used for assessing indium content and crystal quality. Indium composition is calculated from 2 q q measurements by calculating Vegard's law. Both InGaN and GaN layers are considered as relaxed for lattice parameter calculations. Photoluminescence measurements are carried out for evaluating the optical performance of the grown layers using the PL setup, having He-Cd laser source emitting at 325 nm.

Surface morphology
In order to investigate the impact of growth temperatures on the surface morphology of InGaN layers, three sets of samples are grown at substrate temperatures T G ( ) 6001°C (sample A), 5901°C (sample B), and 5801°C (sample C), respectively, while nitrogen flow and forward plasma power are kept at 2 sccm and 300 Watts (table 1). AFM analysis of the samples A  C (figure 3) shows that as growth temperature decreases, V-shaped pits start to diminish and disappear completely at 580°C. The average depth of pits is calculated to be ∼56 nm and ∼12 nm for the samples grown at 600 and 590°C, respectively. Moreover, the width of the pits also decreases at T 590 G =°C, compared to 600°C. This observation is explained in detail as given below. The low dissociation temperature of In-N bonds (∼550°C) leads to dissociation at higher growth temperatures. Dissociated nitrogen atoms transform into nitrogen molecules and evaporate, thus leaving indium atoms on the substrate. Left behind indium facilitates the formation of V-pits. Earlier reported results demonstrate that V-pits are vivid for lower growth temperatures in case of high-temperature growth techniques, such as MOVPE, MOCVD [21,22]. On the contrary, we have observed the opposite trend, i.e., V-pits become more prominent for higher growth temperatures. This apparent contradiction is due to the overall lower growth temperatures of PA-MBE technique. In MOCVD/MOVPE, growth temperatures remain in the range of 700°C -800°C, that is quite higher than the evaporation temperature of metallic indium (∼650°C observed in our case). So, only adsorbed indium atoms are responsible for the formation of V-pits. However, growth temperature in our case varies between 580°C-600°C, which is high enough to dissociate In-N bonds but insufficient to evaporate metallic indium (boiling point: ∼2072°C). So, the formation of V-pits depends on adsorbed and left behind metallic indium, as well. A nominal dissociation rate of In-N bonds at 580°C does not lead to forming any pits on the surface. However, a higher dissociation rate of In-N for sample A, compared to that for sample B leads to early inception and a higher density of pits. This also leads to shallow V-pits in the latter as all the InGaN layers are of the same length.

Indium content and structural quality
In addition to engineering the V-shaped pits in InGaN layers by varying substrate temperatures and III/V ratio, it is also of utmost importance to assess the indium incorporation and crystal quality of the grown structures.
2 w q scan of HRXRD indicates higher indium incorporation with the decrease in growth temperatures, as depicted in figure 4(a). The curves are deliberately upshifted to ease the indexing. Figure 4(b) shows the normalized values of w scan (rocking curve measurements) of the samples, grown at different T G (sample A  C). FWHM values for omega scan are depicted in figure 4(c), with lower values being indicative of good crystal quality. It indicates that 590°C (sample B) is the optimum growth temperature for producing the best crystal quality in our study. Poor crystal quality at low substrate temperatures can be attributed to two major reasons: i) high indium incorporation leads to a higher degree of lattice mismatch and thus, the strain between grown InGaN layers underlying GaN/sapphire substrates. This results in pseudomorphic InGaN layers relaxing beyond critical thickness through forming threading dislocations. FESEM (Field Emission Scanning Electron Microscopy) analysis confirms the thickness of the InGaN layer to be ∼210 nm (figure 5), which is beyond critical thickness. ii) Poor adatom diffusivity at lower temperatures leads to structural defects resulting from grain boundaries. Also, phase segregation at higher indium incorporation results in higher FWHM in rocking curve measurements. On the other hand, higher substrate temperatures give rise to substantial In-N bond dissociation. This leads to degraded crystal quality along with lower indium incorporation, reflected in higher FWHM of rocking curve measurements for sample A T 600 C .

Optical properties
Since we try to engineer V-shaped pits in the active region of InGaN-based LEDs; it is of prime importance to evaluate the role of growth parameters on the optical properties of these samples. Photoluminescence (PL) measurements are carried out using a He-Cd laser with an emission wavelength of 325 nm. Room temperature PL (RT-PL) spectra of the samples (figure 6(a)) demonstrate red-shifting of peak emission wavelength with the decrease in growth temperatures, confirming higher indium incorporation. Inset of figure 6(a) plots the variation in peak emission wavelength and FWHM of PL spectra, calculated by fitting the spectra with Lorentzian equations. Higher FWHM of the spectra, indicates a higher degree of indium inhomogeneity with higher indium incorporation. In order to find out about non-radiative recombination processes in the samples, temperature-dependent PL (TDPL) is conducted and fitted with the basic Arrhenius equation [23], I T Here, I T ( ) and I 0 ( ) are the spectrally integrated PL intensities at temperatures T and minimum possible temperature (10 K in our setup). C 1 and C 2 are fitting parameters; E A1 and E A2 are the activation energies  corresponding to non-radiative recombination. Figure 6(b) depicts fitted curves and the inset shows activation energies of non-radiative recombination processes. The highest activation energy for non-radiative recombination for sample B makes the growth temperature 590°C as the most suitable for our work, as also confirmed by HRXRD analysis. Figure 7(a) illustrates the variation of FWHM for PL spectra with measurement temperatures, which arises due to the presence of radiative defect states in the bandgap. It can be inferred from the highest variation in FWHM of PL spectra from sample C T 580 C  that lower growth temperatures result in a higher density of radiative defects. One of the most vital parameters for optoelectronic devices is internal quantum efficiency (IQE), defined as ratio of emitted photons to injected carriers in the active region. IQE from PL measurements is found out as the ratio I I 300 0 , ( ) ( ) / which is plotted in figure 7(b) for samples A  C. Variation of IQE can be attributed to crystal quality of the samples, which is greatly dependent on growth temperatures, as discussed before. 590°C is once again appeared to be the ideal growth temperature in the study. V-pits would only contribute to enhancing optical properties after the growth of QW structures. In our samples, sidewalls of V-pits contain higher Indium composition with lower bandgap [21,24,25], thus facilitating nonradiative recombination of carriers through threading dislocations. We acknowledge that there's a plenty of scopes to improve growth quality of InGaN planar/nanowires, which is not at per the current state-of-the-art. Based on observations, we believe that relatively poor crystal quality can be attributed to the plasma source and leaky metal line for carrying pure nitrogen gas to the plasma generator.

Defects in InGaN nanowires
NWs are one dimensional semiconductor structure whose diameter varies between a few nanometers to few tens of nanometers. Due to the dimensional constrains, the carriers are free to move in only the axial direction. In the recent past, a lot of research is being conducted on NWs by various research groups across the globe due to their unique advantages. Strain-induced threading dislocations and compositional pulling in planar InGaN structures pose a daunting challenge for solving the 'green gap'. Recently, InGaN NWs are receiving huge interest due to superior crystal quality. Unlike the planar structure, the nanowires could be grown on any substrates without having any lattice strain. The smaller dimension also facilitates better compositional homogeneity, viz. minimum compositional pulling across the length. Moreover, a high surface-to-volume ratio facilitates efficient light extraction. The reduced internal electric field due to the absence of lattice-strain improves optical quality. These attractive traits indeed stimulated a revolution of optical research with NWs that open a new doorway towards solving the 'green gap' through InGaN NWs. Despite all the merits, the impact of defects in InGaN NWs is not widely investigated in the higher wavelength regime ( 520 l > nm). In this work, we have carried out a detailed optical investigation of InGaN NWs, targeting the higher wavelength regime.

Sample preparation
We have prepared three sets of InGaN NWs, grown on the c-plane sapphire substrates. We initially grow ∼200 nm GaN NWs on sapphire substrate at high temperatures (∼885°C), followed by growth of ∼350 nm long InGaN NWs, as shown schematically in the figure 8. Growth parameters for GaN NWs are kept same for all the samples. During InGaN NW growth, Gallium flux is reduced, and indium flux is introduced while keeping nitrogen flux unchanged. We have grown three sets of samples with substrate temperatures T G ( ) during InGaN NWs growth as 625, 600, and 580°C, designated as sample A, B, and C, respectively. Nitrogen rich growth condition (V/III 2.5 > ) is maintained by keeping forward plasma power ∼475 Watts and flow of nitrogen flux as ∼3.5 sccm (standard cubic centimeter per minute). Pressure of the growth chamber for above nitrogen flow remains at 3 10 5 -Torr for growing all the samples. Details of nanowire growth can be found in other works of the group [26,27,68].

FESEM and HRTEM analysis
In order to determine growth rate, NW density, and their degree of coalescence, we have performed FESEM measurements. Figure 9 depicts bird-view (45°tilted) and top-view of the NWs, which demonstrates that NWs become thicker from sample A  C, and they are even clearly visible to be joined in sample C. Trend in the degree of coalescence can be understood from the top-view that is found to be increasing with decrease in T . G This happens because of the group-III adatoms traverse along the sidewalls (m-plane) to reach to top surface (cplane) of nanowires, where they react with active nitrogen. This phenomenon can be attributed to lesser sticking coefficient of m-plane than c-plane in III-nitrides [33][34][35], enabling axial growth of nanowires. Figure 10 shows growth mechanism of III-nitride nanowires schematically. The growth rate of the NWs is determined to be 4 > nm/min from bird-view FESEM imaging for all the samples. Bright-field HRTEM measurements are done to determine the indium content in a single nanowire from calculations of lattice parameters. Figure 11 depicts inter-planar distance and indium incorporation of different regions in the NW from all the samples B, which are calculated using Vegard's law, d xd xd 1 .

InGaN GaN InGaN
where x being the indium composition. It is considered that the NWs are strain-free for determining lattice parameters. The presence of indium atoms, having the highest atomic number (51), compared to Gallium and Nitrogen, appear darker in bright-field HRTEM images. One can get an idea of indium inhomogeneity from the scattered distribution of dark patches. HRTEM images are processed using Gatan's digital micrograph software for calculations, which show variation in indium composition across the NWs. To further solidify our assessment, we conducted STEM radial linescans at different locations of a NW from sample B, which also show variation in indium concentration, depicted in figures 12(a)-(d). Counts for a respective material on STEM plots depend on the actual concentration of atoms and their sensitivity during detection. We repeated our HRETM and STEM analysis for nanowires from all the samples and achieved the same conclusion i.e., presence of indium inhomogeneity.

Optical characterizations
In order to check optical properties of the NWs, PDPL and TDPL analysis have been carried out using a He-Cd laser of spot-size 80 mm. TDPL is conducted in order to achieve qualitative assessment of non-radiative recombination, where laser power is kept at 10 mW and measurement temperatures are varied from 10 to 300 K. Red-shift of emission peak (∼512  ∼577 nm) in TDPL spectra at 10 K (figure 13) demonstrates higher indium incorporation in sample A  C due to low dissociation energy of InGaN. Single dominant peak from B and C    refer to higher carrier confinement in these samples. Whereas sample A displays multiple peaks as temperature changes, indicating lesser degree of confinement. Typically, PL intensity decreases with decrease in temperature due to enhanced non-radiative recombination due to increased carrier mobility. However, insets show that for sample B and C, PL intensity increases at 25 K, compared to that at 10 K, eventually decreasing from 40 K onwards. This can be justified with the fact that higher confinement in samples B and C leads to the formation of excitons at low temperatures (10 K), thus preventing all the carriers from recombining and emitting photoresponse. At 40 K, these excitonic bonds dissociate, and carriers then participate in emitting light, thus increasing the rising trend. Beyond 40 K, non-radiative recombination activates due to higher carrier mobility, leading to decrease PL intensity. In the case of sample A, lesser carrier confinement doesn't facilitate exciton formation. Thus, all the excited carriers take part in photoemission from the very beginning. Integrated PL intensity thus decreases in sample A from 10 K itself. For attaining comparative idea about non-radiative defects, PL intensity spectra at each temperature are integrated over a wavelength range (300-800 nm) and fitted using the equation [23].
Here, I T ( ) and I 0 ( ) are the integrated PL intensity at temperatures T and the lowest temperature (10 K in our setup), respectively. i is the number of non-radiative recombination channels. The fitting parameters E Ai and C Di represent activation energy of non-radiative recombination and defect density, respectively. Fitted values of E Ai and C Di for all the samples are listed in table 2, which shows an increasing trend as T G decreases. Highest values of E Ai and C Di (E A1 and C D1 in the table 2) are the defining parameters of optical properties. Increased C D1 signifies a rise in defect density that can be attributed to the poor crystal quality as growth temperature decreases. Increase in activation energy E A1 ( ) signifies a higher degree of carrier confinement with an increase in indium incorporation. So, the degree of carrier confinement is higher for samples B and C compared to sample A, reconfirming our analysis from figure 13.
Observing varying degrees of carrier confinement from TDPL spectra analysis and visualization from HRTEM and STEM line scans, a physical model is developed (figure 14) to explain PL response from the NWs, taking all physical processes during PL measurements into consideration. The simplified model contains two local potential minima in the conduction band, a deep and a shallow one, for representing the varying degree of carrier confinement due to indium phase segregation. Valence band has similar local potential minima for holes, identical to conduction band at the same position, which is not incorporated to maintain the simplicity of the schematic. As PL measurements are done in steady-state, we further described the model with coupled differential rate equations and solved them analytically to determine steady-state response of the NWs. Interpretations from our model can be applied to samples with any number of local potential minima.
Here, the laser source is illustrated to irradiate both the potential minima. carrier generation rate, carrier density, a radiative and non-radiative lifetime for deep local potential minima are denoted as g , d n ,  Figure 13. TDPL spectra of (a) sample A (T 625 G results in higher Indium incorporation. Single dominant peak in sample B and C show higher confinement in them, compared to sample A (T 625 G =°C). Reproduced from [65]. © IOP Publishing Ltd. All rights reserved. Table 2. Fitting parameters and E A for NW ensemble from different samples. Reproduced from [65]. © IOP Publishing Ltd. All rights reserved. In order to assess the nature of recombination at varying degrees of carrier density, we have carried out PDPL measurements on NW ensemble from all the samples as depicted in figure 15. Up to 10 mW laser power is applied in accordance with the capability of our PL setup. Measurements are performed at 10 K to eliminate the chance of carrier mobility to make our interpretation simple. PDPL spectra show that NW ensemble from sample B and C show no shift in the wavelength axis with variation in laser power, indicating high confinement.  Contrary to this observation, sample A displays a blue-shift in the emission peak with an increase in laser power, re-confirming less degree of carrier confinement as observed from TDPL analysis. This can be well explained from the physical model of figure 14. At low laser power excitation, carriers initially fill up the deep local minima due to higher confinement. Upon applying high laser power, carriers saturate the deep minima and start filling up the shallow local potential minima, showing a blue-shift of the peak emission ( 524 l~to 512 nm). Shoulder in the TDPL and PDPL spectra from samples B and C indicate indium phase segregation at higher indium incorporation.
Rate of change in excess carrier density in both the potential minima during PL measurements in the time duration of t d can be written as, Rest of the terms in the equations are already explained before. carrier generation rates g d and g s depend on excitation laser power density P. In simple term, P accounts for the density of impinging photon density onto NWs. We can assume that carriers are not spatially mobile due to the negligible thermal energy of carriers at 10 K, i.e., .
where B rad is the recombination co-efficient and n d s , 0 is the equilibrium carrier density before irradiation in the respective local potential minima. At low excitation laser power radiative lifetime r d s , that is given as, here s is the carrier capture crosssection by defect center, N T is the non-radiative defect density and V th is the thermal velocity of carriers.
Here, G is the proportionality constant. As r d s , t remains unchanged for low access carrier accumulation, equation (7) implies that upon the presence of significant defect density, integrated PL intensity varies sub linearly with laser power density i.e., I P , Carrier recombination paths after excitation are explained with the help of a schematic in figure 16. Carrier source contains all the excited carriers after laser irradiation, which then recombine into the carrier sink through the means of fast radiative and slow non-radiative recombination process. Intermediate halt by defects in the process of non-radiative recombination is pictured as 'intermediate carrier storage'. SRH, being a slow recombination process, results in saturation of the defect states when high density of excited carriers is accumulated in the sample. Carrier-induced defect saturation for InGaN quantum well based LEDs is studied in detail in section 6. SRH lifetime after defect saturation is expressed as, is the free defect density participating in SRH recombination. Also, radiative lifetime keeps decreasing with an accumulation of high carrier density. Thus, equation (6) dictates that at high accumulated carrier density, integrated PL intensity increases super linearly with laser power density i.e., I P ,   In figure 17(a), sample A displays that fitting parameter F 1 until low laser power, indicating dominant radiative recombination. However, at high input power, the curve shows sub-linear relation i.e., F 1.
< This can be attributed to the fact that at higher laser power, carriers saturate lower energy states and start filling the higher energy states. Since sample A has the lowest confinement, carriers with higher energy have a higher chance of spatial spreading, rate of recombination decreases at high laser power, thus bringing sub-linear nature in figure 17(a). In case of sample B and C, the plot shows sub-linearity at low injection, indicating dominating non-radiative recombination due to higher non-radiative defect density than sample A, as discussed from TDPL spectra analysis. However, interestingly at high laser power density, I versus P shows super-linearity F 1.22 ( ) for sample B while still being sub-linear for sample C. We can justify this observation with the concept of defect saturation and carrier localization. High input laser power induces the accumulation of a huge number of carriers in sample B, facilitated by a higher degree of confinement, which also saturates non-radiative defects. These two effects result in super-linearity in the figure 17(b), as discussed above in detail. In contrary, as sample C has the highest degree of defects, high laser irradiation cannot saturate them  F µ Indication of different recombination processes with F is described in the text. Reproduced from [65]. © IOP Publishing Ltd. All rights reserved. even after having high carrier confinement. Thus, sub-linearity nature prevails across the entire laser power density range, as depicted in the figure 17(c).

Fabrication and characterization of InGaN LEDs
In this section, we present the fabrication of InGaN MQW based LEDs, followed by extensive electrical and optical characterizations. Description of the heterostructure and device design are provided in section 5.2. Fabrication steps, challenges faced, and ways to overcome them are detailed in section 5.3. Detailed experimental findings of the devices are discussed and analyzed in section 5.4.

Motivation
Despite the recent significant progress, InGaN/GaN LEDs still suffer from various efficiency degradations, i.e., internal quantum efficiency (IQE) degrades with an increase in emission wavelength, driving current, and operating temperatures. These are termed as 'green gap', 'efficiency droop', and 'thermal droop'. Especially thermal droop has become a major research topic due to the requirement of LEDs working efficiently in various environmental conditions. Several works have attributed the self-heating induced performance degradation to the carrier overflow, increased non-radiative recombination of carriers in the active region, joule heating etc [28,29]. However, exact phenomena for different operating conditions are still under debate. Additionally, low leakage current during reverse bias is also an essential criterion for device reliability [30], effective electrostatic discharge [31], and device degradation [32,33], which is observed to rise substantially as a result of self-heating. Generally, the heating of LEDs impacts carrier generation rate, dominant recombination processes, and the transport mechanism of carriers. At forward bias, current versus voltage (I-V) characteristics of LEDs are primarily governed by these physical processes. Thus, it is of prime importance to understand the effect of selfheating on I-V characteristics in order to completely understand its adverse impact and to eventually achieve maximum utilization of LEDs. In an attempt to emulate the impact of self-heating, we have established the fabrication process flow of green LEDs on standard MOCVD grown InGaN/GaN MQW based heterostructure. The established fabrication process flow will be applied to our PA-MBE grown heterostructures in order to compare performance parameters with standard samples and enhance device quality, which is an ongoing work in our group. Fabricated devices are then subsequently subjected to high temperatures during temperaturedependent current versus voltage (T-I-V) measurements in order to determine major carrier kinetics at temperatures under forward and reverse bias regions. Challenges faced during fabrication are also discussed in brief. Another motivation of carrying out LED fabrication is investigating carrier-induced defect saturation (observed in section 4), which is described in detail in section 6. Figure 18(a) shows the description of the standard MOCVD grown LED heterostructure consisting of a ∼5 mm thick silicon doped n-GaN with a doping concentration of ∼5 × 10 18 cm −3 . The active region is undoped and is composed of 10 nos. of quantum wells with ∼3 nm thickness each, separated by ∼14.5 nm thick barrier layer. The quantum well layer is made of InGaN with ∼25% indium composition, whereas the barrier layer is GaN. For the electron blocking layer (EBL), ∼30 nm thick Al 0.2 Ga 0.8 N is then grown for better confinement of injected electrons in the active region. ∼360 nm thick Mg-doped p-GaN layer with a doping concentration of ∼5 × 10 17 cm −3 is then grown over the EBL layer. Since the hole has less mobility, a ∼200 nm thick highly conductive indium tin oxide (ITO) is deposited on top-GaN to be acting as hole spreading layer in order to prevent current crowding near the contact. The active region of the LED structure consists of a cylindrical mesa structure containing all the above-mentioned layers. Sidewalls of the structures are then covered with a passivation layer to mitigate the adverse effects of dangling bonds. The passivation of the layer also serves two purposes: acting as contact pads for p-contacts and preventing electrical short between n-GaN and p-GaN layers. Device operation relies on horizontal carrier injection. p-contact is designed as circular in order to mitigate the current crowding caused by slow holes, by having equal distribution of electric fields.

LED Heterostructure
2 w q scan of HRXRD analysis, performed on the heterostructure shows a sharp GaN (0002) peak along with multiple satellite peaks ( figure 18(b)). It indicates crystalline perfection and sharp interfaces in between quantum wells and barriers in the active region. The angular spacing between satellite peaks, 2 p q is determined to be 0.52°. Hence, the MQW period (sum of well and barrier thicknesses) L t t cos 2 .
17.77 B o q = Room temperature PL spectra of the heterostructure is depicted in figure 19. The peak emission wavelength is obtained as ∼512.5 nm for 12 mW of incident laser power. Broad peak, centered at ∼440 nm can be attributed to have been manifested from sub-bandgap dopant states due to Mg and Si from p-GaN and n-GaN regions, respectively [36, 37].

Fabrication steps
The detailed fabrication flow is shown in figure 20, illustrating each step. The heterostructure is annealed at 520 o C for 10 min in a furnace under Nitrogen ambience for ITO to make ohmic contact with p-GaN. After patterning with lithography technique and etching ITO with diluted HCl, mesa structures with a diameter of ∼60 mm and depth of ∼1 mm are then made using inductively coupled plasma (ICP) etching, where Ar, Cl 3 , and BCl 3 flow are maintained at 20, 40, and 40 sccm, respectively for 400 s. Pause during ICP etching is given after every 100 s in order to avoid the hardening of the photoresist due to overheating. Photoresist is used as a mask during ICP etching for defining patterns, which is hard-baked long enough at adequate temperature to enhance hardening and adhesion of the resist. In the case of planar LEDs, ICP etching technique introduces profuse defects on the surface. This is even critical for micro-LEDs with a device dimension of few tens of micrometers. Thus, it has been a common practice to passivate the sidewalls of etched III-nitride LED structures with SiN x or SiO x . Blanket of SiO 2 of thickness 200 nm is then deposited as passivation layer using plasma-enhanced chemical vapor deposition technique (PECVD) and is etched by photolithography technique. It also serves the purpose of isolating each mesa pattern and making contact pad for p-contact. 350 nm thick Titanium/Aluminum (Ti/Al) metal stack is then deposited for n and p contact using electron gun (e-gun) deposition technique. For finding out emission properties of the fabricated LEDs, electroluminescence (EL) spectra and optical output power versus injected current (L-I) is investigated, as depicted in figure 21. EL spectra shows peak emission at ∼513 nm for an applied current of 1 mA ( figure 21(a)). L-I characteristics of LED ( figure 21(b)) show prominent signature of carrier induced efficiency droop beyond ∼35 kA cm −2 . External quantum efficiency (EQE) shows highest value of 24.9% at a current value of 0.4 mA. T-I-V measurements are conducted for a temperature range of RT    It is essential to understand carrier kinetics during and after turn-on of the device. We attempt to do so through with a schematic of band-diagram under forward and reverse bias conditions, as shown in figure 23. Defect states in the active region are also shown in the schematic. Forward current of a diode is expressed as [38], Here, V A is applied forward bias, q is the electronic charge, h is the ideality factor, K is the Boltzmann's constant.
Operating temperature is T (Kelvin), I 0 is the temperature-dependent reverse saturation current. R s is the series  resistance and I R . s is the voltage drop across R , s dominant at high forward bias. Current flow in a diode is result of carrier recombination (radiative or non-radiative). Forward leakage current before turn-on voltage (∼1 V) results from the carriers hopping through the defect states and recombining non-radiatively, as shown in figure 23(a). Inset of the figure 22 shows in semi-log plot that forward leakage current increases with temperatures due higher thermal generation of carriers. However, at 120 o C and beyond, slope of forward leakage current decreases owing to higher resistance at higher temperatures. This occurs because of higher carrier-carrier scattering. It has been demonstrated by various research works that radiative recombination rate decreases at high temperatures [39,40]. But in our case, turn-on voltage has decreased at higher temperatures. We attribute this to enhanced phonon-assisted SRH recombination at higher temperatures. T-I-V characteristics of figure 22 show that forward current of LED increases exponentially after turn-on, conforming to the equation (8). Series resistance comes into effect at higher forward bias, bringing linearity in current values. As shown in figure 22, current increases sub-linearly after turn-on at higher temperatures, denoted as region A. We attribute this to lesser carrier mobility at higher temperatures due to increased carrier-carrier scattering, resulting in lesser carrier mobility. On the other hand, we observe a significant increase in forward current for higher temperatures at higher bias, denoted as region B. Significant increase in current of region B is explained with the help of carrier recombination rate in the following paragraph.  A and B) can be observed at high temperatures after turn-on. Inset depicts I-V before turn-on, which shows variation in slope with temperature, indicating different transport phenomena at different temperatures. Reproduced from [66]. © IOP Publishing Ltd. All rights reserved.   [41]. Auger recombination rate varies with carrier density as n , 3 µ with contrast to radiative recombination, which depends on carrier density as n 2 µ [42]. So, Auger recombination becomes effective at high forward bias. Carrier leakage from one side to another is also an adverse effect of high carrier injection. Recombination of minority carriers then happens in the bulk region instead of quantum well. However, recombination rate depends on carrier density as, R n p . µ [43], where electron and hole density are n and p, respectively. Since carrier density in quantum wells is orders of magnitude after turn-on bias due to enhanced confinement [43], significant increase of region B can only be justified through enhanced Auger recombination.
Carrier kinetics at high forward bias and high temperatures are illustrated in figure 23(b). Rate of Auger recombination can be expressed as, R C n p C p n . . . . .

= +
Here, n and p are electron and hole density, respectively. Auger recombination coefficient, involving two electrons with one hole and two holes with one electron are C n and C , p respectively [44]. In Auger process, electron-hole pair recombine and the excess energy transfers to nearby electron or hole. After receiving excess energy, electron or hole get to an excited state and eventually thermalizes to a lower energy state through phonons. Figure 24 depicts mechanism of direct and indirect Auger recombination without and with involvement of phonons, respectively. Higher temperatures increase phonon density in crystals, resulting in higher coefficient of phonon-assisted Auger recombination, as shown by various researchers for InGaN based quantum well structures [45,46]. Additionally, high density of injected carriers at higher forward bias facilitates Auger recombination due to n 3 µ dependence. Hence, Auger recombination rate increases with higher forward bias and temperature. For a particular bias, high temperatures result in higher current because of enhanced carrier generation as per the relation, n T E K T .exp 2 .
Here, n i is intrinsic carrier density, T is the operating temperature (Kelvin), K is the Boltzmann's constant and bandgap of the material is denoted as E g [47,48]. Figure 25 shows semilog plot of T-I-V characteristics of green LED under reverse bias till 10 V with temperature range of 25°C-200°C. Breakdown voltage was measured to be ∼12.9 V. Various research works show that reverse leakage current of LEDs increases exponentially as we increase temperature from RT. However, inset of figure 25 shows that leakage current doesn't increase too much until 60°C (region II) and it shows exponential increase from 80°C and beyond, denoted as region I. We believe the reason behind this trend comes from the fact that carriers get trapped in the quantum wells and sufficient thermal energy is needed for them to get out and be collected by contacts. Slight increase in leakage current at lesser temperature can be attributed to the carriers at the edge of depletion being swept away by enhanced electric field under reverse bias. At high reverse bias (4.5 V) and high temperatures (160°C), leakage current deviates from linearity. This can be attributed to the fact that in addition to thermally generated carriers, valence band electrons of p-side tunnel to the n-side through sub-bandgap defect states through band-to-band hopping. It happens at higher reverse bias owing to narrow barrier height at higher reverse bias. Carrier dynamics under reverse bias is schematically depicted in figure 26. Hence, it can be inferred from our analysis on carrier kinetics that upon heating of LEDs, Auger recombination can be attributed as the dominant non-radiative recombination process under high carrier- injection, while SRH recombination is prominent at low carrier-injection. A similar investigation in reverse bias brought light into the requirement of carrier emitting from deep quantum wells for leakage current to increase with temperature.

Defect dynamics in InGaN LEDs
Non-radiative defects present in the active region of LEDs play a deterministic role in determining the performance of these devices. Yet, the behavior of the defects during device operation demands serious attention in order to apprehend carrier dynamics in these devices. Although defect saturation has been investigated previously for various semiconductor materials [49,50], it is not explored in GaN/InGaN photonic systems.
Our work in section 4 shows that carrier induced defect saturation blocks part of the non-radiative channel, thus enhancing optical emission ( p l ∼ 551 nm) from InGaN nanowires. However, detailed mechanism and direct observation of defect saturation is still lacking in optoelectronic devices. Understanding such phenomena can provide us a more accurate description of the system and a clear view of the logical approach to maximize device performance. Moreover, conventional resistance-capacitance RC circuit to represent the active region of LED needs serious revision in the light of defect saturation, which only takes carrier accumulation in the quantum Figure 25. Reverse current versus 1000/Temperature characteristics at applied reverse bias. Two trends of increment in current are seen, mentioned as region I and II. Inset shows reverse leakage current versus applied bias at different temperatures. Reproduced from [66]. © IOP Publishing Ltd. All rights reserved. Figure 26. Hopping of valence electrons through defect states in the depletion region at high reverse bias is depicted. Hollow and solid red balls represent holes; solid black balls are conduction band electrons. Thermal generation of electron-hole pairs and their eventual transport is also illustrated with arrow marks. Reproduced from [66]. © IOP Publishing Ltd. All rights reserved. wells (QWs) into account. This has motivated us to establish a solid theoretical background on carrier dynamics in defects and its experimental validation in InGaN MQW based LEDs [51,52].

Theory
This subsection establishes the theory of defect saturation from the band diagram of quantum well structures, numerically calculated by solving Schrödinger and Poisson equations self-consistently. A simple p-i-n heterostructure, having InGaN QW of 3 nm width with high indium composition (25%) is considered for the study. Energy eigen-values and wave functions for electrons and holes in the QW are calculated, taking the first bound state as the dominant energy state. Figure 27(a) shows distribution of wavefunctions for electrons and holes under the carrier density of 10 25 m −3 ( n p D = D ). Higher effective mass results in higher confinement for holes, leading to higher hole density in the QW. Figures 27(b), (c) depict energy profiles of valence (E v ) and conduction band (E c ) for the carrier density of 10 25 and 10 28 m −3 . Both the band edges show a downward shift at high carrier injection. This enhances confinement for electrons; whereas, holes show a decreasing trend of confinement, as reflected in figure 27(d). Carriers of the first energy state accumulate mostly in the middle of the QW, thus showing maximum effect in that region.
Spatially integrated carrier capture coefficients for electrons and holes by mid-gap defects are calculated to determine system dynamics. Mid-bandgap defect density of N 10 m | | µ Y [53]. This results in C n increasing and C p decreasing with increase in carrier density. Higher effective mass of holes makes C p lower than C n at any carrier density, as shown in    [54]. Upon solving these set of differential rate equations, we obtain density of saturated defects, taking various values of emission time .  ( ) by defects. While C n increases with injected carrier density, C p shows decreasing trend. Reprinted with permission from [51]. Copyright (2021) American Chemical Society. Figure 29. Transition of electrons (red balls and red arrows) and holes (white balls and blue arrows) among different energy levels after injection, as described in the text. Reprinted with permission from [51]. Copyright (2021) American Chemical Society. of escape time, degree of defect saturation increases with higher rate of injected carriers. However, no emission of carriers from defects leads to saturation of all the defects at even lower injection rate. Time dynamics of n t and p t is shown in figure 30 = ps are considered for the calculations. As can be observed, electrons are likely to saturate the defects, as compared to holes. Higher capture coefficient of electrons can be ascribed to this phenomenon.

Model
Capacitance versus voltage (CV) measurement is a common technique to characterize semiconductor/oxide interfaces by assessing trapped charge by defects. We thus employ CV technique to interpret carriers, trapped in the mid-bandgap defects. In this subsection, we establish the equivalent RC circuit model of LEDs to understand CV behavior of the devices.
The conventionally active region of LED is represented with an RC circuit model, Accumulation of carriers in the QW and band-to-band transition path are represented as the capacitance (C d ) and resistance (R d ), respectively [55,56]. Non-radiative recombination is not captured by these typical models. In this process, carriers are captured by mid-bandgap defects, followed by recombination with carriers of opposite charge. Our calculations of the previous subsection indicate saturation of defects by injected carriers at a steady state, especially by electrons due to lower effective mass. In order to reflect this effect, we propose a correction entity in the conventional RC model by adding a capacitance and resistance, connected in parallel, correlating to the SRH process. As radiative and non-radiative processes occur parallelly, the correction entity is added in parallel with the typical model, as shown in figure 31 with a dotted box. Here, C nr and R nr represent carrier capture by defects and eventual recombination, respectively. Contact resistance is being accounted as R .
s The effective resistance of the active region is, R R R .
t being the radiative and  non-radiative recombination lifetime, respectively. Upon simplification, corresponds to the loss of carriers during recombination processes. This Negative capacitance is interpreted as the inductive behavior of LED at higher forward bias [55,57]. Lifetime ( ) t w depends on angular frequency w as, 2 ( ) wt ) [58]. In case of input signal with higher frequencies, carriers must recombine faster. This leads to lesser lifetime for carriers. The equation, shown below is the expression for capacitance after correction.

Experimental
Details of heterostructure and fabrication process flow of green InGaN LEDs along with their optical characterizations can be found in section 5. The non-radiative recombination rate is less dominant than the radiative one in standard GaN/InGaN LEDs. Hence, low-frequency CV measurements are carried out to probe the defect saturation with forward bias ranging from 0 to 5 V and traversed back. AC signal has a peak-to-peak voltage of 10 mV, and the applied frequencies are 100 kHz, 200 kHz, 500 kHz, and 1 MHz. GV measurements are carried out simultaneously to identify the nature of device conductance at different biases and frequencies. In order to probe carrier kinetics at reverse bias CV measurements have also been done under reverse bias ranging from 0 to 10 V and traversed back. Frequency values are chosen as same as that used in forward bias.

Results and discussions
In order to validate the concept of defect saturation, we solve the equation (13) numerically and attempt to match it with experimental CV data of fabricated LEDs. Following expressions lay down the relations of C d and C , nr respectively.
where, w and A are the width of QW and cross-section area of the device, respectively. f V ( )is the filling factor of defects by carriers. q is the electronic charge and n is the excess carrier density in the QW. Considering the same p-i-n heterostructure used in section 5, voltage dependent carrier density n V n n V 0 ( ) ( ) = + and current I V ( ) are solved self-consistently using the expressions, The evolution of calculated carrier density in QW and resultant current with forward-bias can be observed from figure 32, as found from the calculations. Current initially increases exponentially around turn-on bias. However, it later follows a linear profile owing to the significant effect of R s at higher currents. QW carrier density initially increases, resulting in an increase in forward current. After reaching saturation, carrier density then starts to descend. An increase in carriers in QW can be linked to carrier injection in the active region to turn on the device. Beyond certain forward bias, the recombination rate increases so much that it surpasses the carrier injection rate. This leads to descendance of the QW carrier density. Loss of charge from QWs with bias results in negative capacitance, as discussed in subsection 6.2.
In equation (16), equilibrium carrier density in the QW is n 0 and ideality factor is denoted as , h V T is the thermal voltage. In equation (17), r V ( )is the fraction of carriers that recombine. Filling factor of defects is  [55,56,60,61]. Capacitance increases at lower bias owing to accumulation of carriers in the QWs. bleeRadiative recombination results in decrease in capacitance, leading to 1st gaussian like peak during turn-on. Defect-saturation leads to 2nd peak in CV curves at higher forward bias. Carrier capture rate in the QW is much higher compared to that at the defect energy level. This results in defect-saturation related peak to appear at higher bias. Capacitance plunges after 2nd peak, indicating significant recombination rate eventually leading to negative capacitance. During the measurement, carrier density profile tries to follow  the applied AC signal. 1st peak is observable at all the frequencies since radiative recombination is a fast process. Defects are slow to respond, thus, defect-saturation related 2nd peak is not observed for high frequencies ( 1 MHz), as depicted in figure 34(a). The left shift of both the capacitance peaks at lower frequencies is due to an increase in lifetime, thus leading to a higher accumulation of carriers in the active region and lower turn-on voltage. At higher bias regime, CV response shows hysteresis, as shown in the inset of figure 34(a). Backward sweep (i.e., 5  0 V) gives lower capacitance than that at forward sweep (i.e., 0  5 V). This comes from the fact that maximum defects are already saturated at 5 V, thus increasing the probability of radiative recombination at a backward sweep, which is faster than SRH process. Hysteresis is not observable at lower bias as degree of defect saturation is not significant. Figure 34(b) shows GV response of the LED, which illustrates increasing conductivity after turn-on voltage. As shown in the inset oof figure 34(b), capacitive nature of LED at lower bias regime results in higher conductance with increasing frequencies. Inductive nature at higher bias regime results in higher conductance with lesser frequencies. Inductive nature of LED is reflected as enhanced negative capacitance in higher bias regime, as indicated in figure 34(a).
We have also determined CV response under forward bias by numerically solving the equations (13)-(17) for different defect densities at 500 kHz, while considering non-radiative lifetime being inversely proportional to defect density, as plotted in figure 35. Two peaks in CV curves are apparent, with defect-saturation related peak (2nd peak) being dominant at lower frequencies and higher bias. CV peak (1st peak), at lower bias corresponds to the carrier accumulation in the QWs; bias value at the peak is the turn-on voltage. While the first peak subsides, the second peak rises with increased defect density. The rise in the second peak can be related to a higher degree of defect saturation at a particular bias for increased defect density. Subsiding of the first peak is attributed to the faster recombination of injected carriers due to the higher SRH rate, thus hindering carrier accumulation in QWs. Less degree of carrier accumulation in QWs leads to higher turn-on bias. We can infer  that low-frequency CV measurements could assess defects in the active region of InGaN LEDs by comparing the values of defect-saturation related peak. Figure 36 depicts the measured CV behavior of the green LED under reverse bias at different frequencies. It is evident that the frequency of AC signal has a strong influence on the capacitance values through the entire range of reverse bias. The initial decline in capacitance value at lower bias can be attributed to the loss of carriers from edges of the active region. Following this, increase, and saturation of capacitance occurs, probably due to carriers in the barrier layers being trapped in QWs. Lower frequencies lead to lower capacitance at higher bias. This observation can be attributed to the Poole-Frenkel mechanism. Electrons from the p-side valence band populate the sub-bandgap defects and emit in this process, ultimately tunneling to the conduction band of the n-side. Carrier capture by defects is a slow process with a timescale in the range of microseconds for GaN/InGaN based LEDs [62,63]. Carrier density varies continuously through tunneling to cope up with the AC bias. At high frequencies, carriers do not get enough time to tunnel for reflecting the AC profile, resulting in higher capacitance. Moreover, inadequate flushing out of trapped carriers during the very short time periods leads to saturation of the defect states at high reverse bias. This results in lesser tunneling or higher capacitance during the reverse sweep from high to low bias, leading to hysteresis in the CV characteristics at 1 MHz. AC signal with lower frequencies lets the carriers have enough time to emit and be captured by defects, enhancing the Poole-Frenkel tunneling. Lower capacitance is thus obtained at lower frequencies without significant hysteresis.  Lower frequencies result in higher rate of defect-assisted tunneling, leading to lower capacitance. Initial dip in capacitance is due to carriers in the active region being pulled away with reverse bias. Reprinted with permission from [67] © The optical Society.

Conclusion
To summarize, we have tried to shed light into our works on assessing non-radiative defects in InGaN-based grown samples and fabricated LEDs through various characterization techniques e.g., CV, HR-XRD, SEM, TEM, PL, AFM etc. We then tried to analyze the measurement results by developing and simulating analytical models. Analysis of all the works are explained in section 3-6. In sections 3 and 4, we developed growth recipe for InGaN planar and nanowire samples of good optical quality. Our work on growth of bulk InGaN layers brings us to the conclusion that density and depth of V-pits on InGaN layers can be tuned by optimizing growth temperature and III-V ratio. We conclude from the work on InGaN NWs that defect saturation can improve optical outputs from NWs by utilizing carrier-localization in Indium-rich regions. In sections 5 and 6, we focused on assessing carrier dynamics through defect states in InGaN LEDs under reverse and forward bias. Temperature-dependent current-voltage measurements of LEDs show that Auger recombination prevails at high forward bias and high temperatures. We also developed the theory of carrier-induced defect saturation in InGaN LEDs and demonstrated it through CV measurements. We believe that our findings are valuable to the research community across the globe, working on InGaN-based photonic devices. Understanding carrier dynamics through defects will really be helpful for us to improve growth recipe of heterostructures and optimize fabrication process steps. This will facilitate in mitigating the age-old problem of 'green gap'. The knowledge buildup and analytical models in our work can further be exploited for understanding properties on other material-based photonic devices.