Study of Predicting the Performance of I-V Curves Through Photoluminescence Spectral Characteristics

Quality of GaN LEDs is closely related to the defects in quantum wells. Effectively evaluating the performance of LEDs is a key step in mass production. Electrical characterization testing is very effective for characterizing the performance of LEDs, and the I-V curve is an important evaluation parameter. In this paper, we analyzed correlation in photoluminescence (PL) spectra and I-V curves among different LEDs and studied the feasibility of using PL to predict and estimate the characteristics of the I-V curves. Firstly, in the experiment, we varied the excitation light power and tested the photoluminescence (PL) spectral characteristics of different samples. Subsequently, I-V tests were conducted on these samples with current injection. The results of the I-V curve tests indicated significant differences among different samples, which were consistent with the PL results. Corresponding carrier transport model was established, and the I-V curves were fitted, resulting in different ideality factors for those samples. The results indicated that samples with lower photoluminescence intensity exhibited a larger ideality factor in the I-V curves. On the contrary, for samples with higher photoluminescence intensity, the resulting ideality factor is smaller, approaching 2. A deeper analysis reveals a negative correlation between the relative strength of the normal peak and the abnormal peak in photoluminescence spectra and the value of the ideality factor. In the future, based on this correlation, photoluminescence-based detection techniques can be used to predict the I-V curve characteristics of LEDs in scenarios where direct current injection is not feasible.

optical communication, and biomedical applications [7], [4], [8], [9], [10], [11].The presence of defects in quantum wells during the LED growth process can have a considerable impact on its light emission characteristics and current transmission properties, ultimately leading to LED malfunction.Various methods are available for defect detection, including XRD, TEM, SEM, XPS, and cathodoluminescence [12], [13], [14].However, these methods are time-consuming and also destructive in some cases.Electroluminescence (EL) and PL tests are also commonly used for LED characterizations.Current injection based EL test can be applied to measure the current-voltage (I-V) curve, but it requires Ohmic contact and the needle probing action reduces efficiency and potentially damage the electrodes.Moreover, in the early stages of wafer production when the electrode structure has not yet been grown, effective I-V curve testing is not possible.In contrast, PL test offers non-contact, non-destructive, and efficient measurements, making it widely applied quality evaluation of multiple quantum wells LED.Meanwhile, the capability of PL for defect detection is also comparable to the aforementioned techniques, with the minimum detectable concentration for point defects being as low as 10 13 cm −3 [15].
Some groups have conducted tests on the emission spectra under both optical injection conditions and electrical injection conditions, including normal samples and defective samples [16], [17], [18], [19].The analysis has shown that the major difference lies in the carrier injection mechanism, while the carrier recombination exhibits certain similarities.Consequently, when structural and impurity defects exist in the quantum wells, anomalies can be observed in the photoluminescence spectra.Similarly, the presence of these defects can also result in abnormal current transport characteristics under electrical injection conditions, thereby causing anomalies in both the emission spectra and the I-V curves.
There have been articles studying the consistency between photoluminescence and electroluminescence.For example, Lian Li et al. investigated correlation between PL spectra and EL spectra under different temperature conditions, demonstrating the similarity in spectral shapes [17].However, few studies have explored the correlation between the I-V curve characteristics under electrical injection and the photoluminescence spectra, which is highly desirable in practical production and testing applications.In our paper, we studied the relationship between the current-injected I-V curves and the PL emission spectra in the presence of defects and validated the feasibility of using PL to evaluate I-V curve characteristics.Firstly, we tested quantum well LEDs on the same wafer and measured their emission spectra under different laser power.Different samples exhibited different intensities.Then, we subjected these samples to current-driven testing to measure I-V curves.The results indicated a transition from resistive characteristics to diode characteristics in the I-V curve among different samples.We established an electrical transport model under current injection conditions and successfully fitted it to the I-V curves.The intensity of the photoluminescence spectra is positively correlated with the ideality factor under electrical injection.Furthermore, we found a negative correlation between the relative intensity of the normal peak and the abnormal peak in the photoluminescence spectra and the value of the ideal factor.Therefore, in the future, LED quality can be evaluated through multiple parameters in PL spectra to estimate the numerical range of the ideality factor in quantum well LEDs.

II. EXPERIMENTAL DETAILS
The growth of GaN LED on c-plane sapphire substrate was carried out using the metal-organic chemical vapor deposition (MOCVD) technique.The growth sequence started with the deposition of an undoped GaN buffer layer, followed by n-type GaN layer.The active region consisted of an InGaN/GaN multiple quantum wells (MQWs), where the quantum well has a thickness of 3.8 nm and the barrier is 14.3 nm, as shown in Fig. 1.Subsequently, a p-type AlGaN electron blocking layer was grown, and the growth process was completed with the deposition of a p-type GaN layer.Finally, to ensure a solid connection, the electrodes were made in a forked shape, as shown in Fig. 2. The overall size of the chip is 800 µm × 250 µm.A laser with a central wavelength of 408 nm was used for photoluminescence excitation.The diameter of the laser spot was approximately 7 mm.The laser intensity was adjusted by controlling the current.Real-time monitoring of the excitation light power was enabled through the implementation of a beam splitter (BS) and optical power meter, as shown in Fig. 2(a).A long-pass filter (LPF) with a cutoff wavelength of 420 nm was employed to filter out the laser light.The resulting photoluminescence spectra were measured with a spectrometer.I-V test experimental setup is shown in Fig. 2(b).A Keithley 2612B source meter was used as the current source.The current was applied to the positive and negative electrodes of the LED chip with probes.

A. Photoluminescence Spectra
Seven different samples from a wafer were tested.The PL results under different incident light powers are shown in the following Fig. 3.
We ranked these samples and named them as Sample 1 to Sample 7 from lowest to highest PL intensity.These samples are designed as blue LEDs for display applications.Their ideal emission peak is at 450 nm.Apart from 450 nm, all other emission peaks are considered abnormal.It can be observed that, all samples exhibit a 450 nm emission peak, indicating good overall structural uniformity of these samples from one wafer.Except for Sample 7, the spectra exhibit a yellow photoluminescence.Compared with Sample 7, a blue emission peak at 430 nm was also observed especially for Sample 1 and Sample 2. And the shape of the emission spectra of the sample remains consistent with different incident laser power.The emission spectra caused by the defects do not saturate under two different excitation intensities, making it more effective and convenient to evaluate the LED characteristics using PL emission spectra.
We have also plotted the variations of the photoluminescence spectra with respect to the excitation laser power for Sample 4 and Sample 7, as shown in Fig. 4.And it can be observed in Fig. 5, for both normal and abnormal samples, the radiance intensity of photoluminescence increases almost linearly with the increasing incident laser intensity.

B. I-V Curves of Different Sample
I-V curves for the 7 samples under electrical injection are shown in the following Fig. 6.
It can be observed that the I-V curve characteristics vary greatly among different samples.Sample 1 exhibits significant resistive characteristics, while sample 7 shows diode characteristics.I-V curves of other samples falls between sample 1 and sample 7. Furthermore, by comparing them with the photoluminescence spectra, it should be noticed that samples with higher photoluminescence intensity tend to have I-V curves that are closer to the ideal Shockley diode equation curve.

A. Origin and Influence of Defects
The first abnormality in photoluminescence spectral shape is yellow luminescence.Yellow luminescence defect is one  of the most common defects in GaN LEDs.Currently, there are multiple different explanations regarding the cause of the yellow luminescence defect.Some believe that it is caused by impurities related to isolated CN defects or CN-ON defect complexes [20], [21], [22].A few groups believe that deep-level acceptors generated by Ga vacancies are one of the sources of the yellow band defect [23], [24].The origin of the PL bands was also investigated by Evgenii A. Evropeitsev's group through power-dependent experiments with excitations above and below the barrier, and PL from the MQW region was found to increase linearly [25].Others attribute the generation of the yellow band to basal plane dislocations in GaN materials [13], [26].In addition, there have been studies reporting that indium enrichment in GaN is also one of the sources of yellow band defects.TEM technique were used to capture images of the quantum well, as shown in Fig. 7.The black dot-like clusters in the sample are believed to be indium enrichment [27], [28], [29].The enrichment of indium leads to the generation of defects such as misfit dislocations.These dislocations typically act as non-radiative recombination centres and carrier leakage paths, resulting in a decrease in photoluminescence intensity and the emergence of a yellow emission band as shown in Fig. 4.
Meanwhile, we notice a blue spectral emission in Sample 1 and Sample 2. This phenomenon is also considered to be an anomaly, compared to the normal single peak such as sample 7.This anomaly is commonly believed to be associated with V-pit defects, as shown in Fig. 8.The formation of V-shaped pits leads to narrow sidewall quantum wells surrounding every defect, with an effective band gap higher than that of conventional planar quantum wells.Therefore, shorter wavelength emission is observed in inclined quantum wells [30], [31].

B. Analysis of LED I-V Curve Characteristics
As indicated by the previous experimental results and theoretical analysis, when defects cause the abnormal photoluminescence, the corresponding I-V (current-voltage) curve under injection conditions will also exhibit anomalies.Under optical injection conditions, we can use integrated light intensity to describe the defect characteristics of different samples.Similarly, under electrical injection, we need to establish a model to describe the characteristics of the I-V curves.For an ideal diode, its I-V curve follows the characteristics of Shockley's diode equation [29], [30] as shown in ( Where I 0 represents the reverse saturation current, q equals 1.6 × 10 −19 C, k equals 1.38 × 10 −23 J/K, T represents the temperature 298 K in the experiment, and n represents the ideality factor.I represents current and U represents voltage.
However, in abnormal samples, it is evident that those curves no longer fit well.Therefore, we need to modify this model to account for the deviations.The tunneling and carrier leakage effect caused by defects in GaN LEDs has been studied by some groups [6], [32], [33], [34], [35], [36].In these cases, during current injection, small resistance pathways are formed at the defect sites.So we modified the I-V model, as depicted in Where R represents the magnitude of the resistance.a and b represent current coefficients.When the value of a U R is larger, it indicates that the impedance characteristics are close to that of a resistor.Conversely, if the value is smaller, it indicates that the characteristics are closer to those of an ideal diode.To further simplify the model, we can express it as (3) The ideality factor n can be calculated using Based on the measured I-V curves, polynomial fitting was performed based on (3) mentioned above.The results of the values of a, b, c, and n for different samples are shown in the following Table I.
The R 2 is over 92%, indicating the goodness of fit of the fitting model to the actual data.The fitting has some errors because the defect concentrations in the transition between the defect region and the normal region gradually shift, rather than simply being in parallel.In addition, the ideality factor n value varies in different voltage ranges.However, for the sake of convenient comparison, each sample needs to be represented by a single n value.So the fitting will also introduce some errors.The fitting errors do not affect the overall trend of the predictive results.It can be observed that the ideality factor n decreases gradually from sample 1 to sample 7, indicating that the I-V curves are approaching the normal characteristics of LED diode.As confirmed by TEM and PL, there are some In-cluster and V-pit defects in the devices.Additionally, there may be point defects in MQWs that could also lead to yellow luminescence.These defects can provide tunneling and leakage paths [37], [38], [39].In that case, the main transport mechanism is associated with carrier tunneling and current leakage, rather than thermal diffusion, which will lead to high ideality factors [37], [38], [39], [40], [41].

C. Feasibility of I-V Characterization Using PL
By quantitatively generating a certain type of defect such as point defects [42] and measuring the abnormality of photoluminescence spectra and the corresponding ideality factor under these conditions, a quantitative correlation between the defects concentration and PL/ I-V performance could be established.Here, due to the coexistence of multiple types of defects, including structural and point defects, our aim is to establish a correlation between PL and I-V performance.We obtained the photoluminescence spectra of different samples as show in Fig. 3.We also obtained the I-V curves and ideality factor of these samples.Therefore, we plotted the correlation between ideality factor n and integrated photoluminescence intensity of the 7 samples under different excitation power.The results are shown in the following Fig. 9.
It can be observed that the integrated intensity of photoluminescence (PL) from different samples shows a positive correlation with their ideality factor n.
It is difficult to establish a direct mathematical relationship between the ideality factor n and the integrated intensity due to the error in the fitting model.We describe the leakage current caused by defects in the form of parallel resistance.This approximate model itself has errors.Defects of low concentration only result in recombination in deep energy levels, leading to the yellow band phenomenon.Defects of high concentration directly cause breakdown.However, there is no clear boundary between the two, but rather a gradual accumulation process.When the ideality factor n is small, slight fluctuations in its value correspond to significant attenuation of photoluminescence intensity.However, when the ideality factor n is large, the changes in its value result in relatively smaller variations in the photoluminescence intensity.This finding is of significant importance for estimate the value range of the ideality factor through photoluminescence.
Similarly, there is another characteristic in the photoluminescence spectra that is also related to the ideality factor, such as the relative intensity of the normal and abnormal emission peaks.In our LED quantum well structure, the normal emission peak is around 450 nm, while the shifted blue and yellow emission peaks are considered as abnormal peaks.We compared the relative PL intensities at around 430 nm, 470 nm, and 450 nm with incident laser power of 0.0329 mW, and found that the greater the ideality factor, the greater the relative intensity of the abnormal emission peak compared to the normal emission peak, as illustrated in Fig. 10.This can be easily understood since the more normal emission intensity there are, the more ideal the quantum well structure is, and the more it behaves like an ideal Schottky diode, leading to a smaller ideality factor.
We believe that in GaN MQWs, many defects can result in a similar correlation between PL emission characteristics and I-V characteristics.V-pit defects generally traverse multiple layers of the quantum well region [30], [43].Research indicates that blue emission is notably strongest around the V-pit defects, while the yellow emission is enhanced within the defects themselves [43].Point defects such as gallium vacancies, nitrogen vacancies, interstitials, antisite defects, and complex defects can alter the band structure, causing electron-hole recombination to occur at different energy levels and creating carrier leakage path.This leads to the yellow luminescence, distinct from typical luminescence [21], [22], [23], [24], [30], [31], [39], and decrease of PL intensity.Both defects in the barriers and wells will influence the photoluminescence spectra [30].Similarly, under conditions of electrical injection, these defects can result in trap-assisted tunneling and carrier leakage, disrupting the ideal Shockley diode model and increasing the ideality factor [37], [38], [39], [40], [41].We believe that this negative correlation between PL intensity and the ideality factor applies to a wider range of LEDs, and other electrical properties can be extended to predicted, for example, the ideality factor is somewhat related to the forward voltage [40].However, the rate at which the ideality factor increases with the decrease in PL intensity may vary based on different structures, doping, and other variations in LED design and fabrication.
In practical applications, we can first test small batch samples for photoluminescence (PL) and current-voltage (I-V) curve characteristics.By doing so, we obtain the integrated intensity, relative intensity of the normal peak, and the fitted ideality factor for the corresponding samples.Then, we can plot the variation of the ideality factor with integrated intensity and the variation of the ideality factor with relative intensity of the normal peak.This correlation primarily arises from defects within the quantum well structure, therefore, so this correlation theoretically holds true regardless of the presence of electrodes.For other LEDs, the I-V curves and ideality factors can generally be estimated within their corresponding value ranges based on their respective PL emission spectra characteristics.And PL characteristics can also be used to predict the I-V performance of LEDs that have not yet been fully fabricated.

IV. CONCLUSION
This paper investigates the feasibility of using photoluminescence spectral characteristics to estimate the range of ideality factor values under electrical injection.Firstly, we collected photoluminescence spectra and I-V curves for seven different samples.There were significant differences between the results of different samples, indicating that there were defects in the LEDs.Through TEM and FIB technology, we found that the main defects were the enrichment of V-pit and In-cluster.To explore the direct relationship between photoluminescence and I-V curve characteristics under electrical injection conditions, we modified the I-V curve model of LED and fitted the I-V curves.We found that there was a negative correlation between the ideal factor value and the integrated intensity of the photoluminescence spectrum, as well as the relative intensity of the normal emission peak to the abnormal emission peak.In the future, based on this regularity, we can preliminarily estimate and evaluate the ideality factor of the I-V curve under electrical injection based on the photoluminescence spectral characteristics.

Fig. 4 .
Fig. 4. PL spectra of sample 4 and sample 7 with incident power ranging from 0.00296 mW to 0.329 mW.

Fig. 9 .
Fig. 9. Correlation between the ideality factor n and integrated photoluminescence intensity under incident power of 0.0329 mW.

Fig. 10 .
Fig. 10.Correlation between the ideality factor n and relative intensity of the abnormal emission peak compared to the normal emission peak under incident power of 0.0329 mW.

TABLE I I
-V CURVE CHARACTERISTIC PARAMETERS