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Abstract
Micro-LEDs can work under an extremely high injection level and are widely used in high-brightness micro-displays and visible light communication. With the increase of carrier concentration, many-body effects gradually become important factors affecting devices’ characteristics. Considering the effects of carrier scattering, bandgap renormalization, and Coulomb enhancement (CE), changes in the electroluminescence spectra of micro-LEDs are analyzed as the current density increases from 49.2 to 358.2 kA/cm2, the latter representing an ultra-high injection level. Affected by plasma screening, CE decreases below about 150 kA/cm2. After that, polarization screening dominates and effectively alleviates the spatial separation of electrons and holes, which results in CE increases to the maximum injection level of 358.2 kA/cm2. It is established that CE promotes radiative recombination processes. Different from the traditional phenomenon of “efficiency droop”, the enhanced attraction between carriers leads to an abnormal increase of external quantum efficiency at high current density.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the single-particle approximation, the interaction potential is simplified by the mean-field potential. Owing to its simplicity, this approximation is widely used to study the electronic structure of semiconductor [1]. However, the Coulomb interaction cannot be neglected when many carriers are confined in the active region. In particle population inversion systems, such as laser diodes (LDs), many-body effects, including band-gap renormalization (BGR), Coulomb enhancement (CE), and carrier scattering (CS), are considered [2–6]. Previous studies show that BGR effects cause a redshift in the gain spectra [2,4,5], while Coulomb enhancement significantly increases the optical gain [2–5], and carrier collisions broaden the gain spectra [2,6]. Typically, BGR effects are stronger than band filling effects [4,5]. In GaN that is heavily doped with Ge, the rollover of band filling effect to BGR effect is found at high carrier concentration that is above 1019cm-3 [7]. Owing to plasma screening, CE weakens as the carrier concentration increases [2,5,8]. However, for wide band gap materials or in low-dimension systems, CE continues to play an important role even when the device operates at a high injection level [3,8–12]. Localized holes attract free electrons, and strong CE occurs [13,14]. Carrier collisions, including electron-electron (e-e), hole-hole (h-h), electron-hole (e-h), electron-longitudinal optical (LO) phonon (e-LO), and hole-LO phonon (h-LO) scatterings, also dominate in systems with high carrier concentrations [15–18].
In addition to LDs, many-body effects have been considered in systems of light-emitting diodes (LEDs) [19–26]. In applications involving automotive forward lighting, projection display, and general lighting for low cost or flexible functionality, LEDs must perform under high injection levels. However, the efficiency droop becomes increasingly serious as the current density goes up [27]. Hader et al. uses fully microscopic many-body theory to study the efficiency droop mechanism and calculate the radiative loss of LEDs [23]. According to their study, the efficiency droop under high injection level is caused primarily by carrier overflow. In the single-particle approximation, free electrons spread out over the entire quantum well (QW) region. Many of these free carriers undergo non-radiative recombination or leak directly out of the QWs. Considering CE, free electrons are attracted by localized holes, thereby enhancing radiative recombination in the QW region [9,13]. As a result, CE should be taken into consideration when someone optimizes devices’ light output power. Some studies have shown an interplay between CE and polarization field [9,14,26]. The reduction or removal of polarized charges can increase the spatial overlap of electrons and holes, thus strengthens the CE effect. Although many-body effects are well-established from a theoretical perspective, the experimental details of BGR, CE, and CS have yet to be demonstrated clearly.
Micro-LEDs (μLEDs) are reported to operate under extremely high current densities (exceeding tens of kA/cm2) [24,28–30]. Therefore, μLEDs are applied extensively in high-brightness micro-displays [31–33] and visible light communication (VLC) [34,35]. Owing to their small size, μLEDs are also used in devices involving photogenetic neural stimulation [36] and organic pump lasers [37]. In order for future applications, it is necessary to have a thorough understanding of μLEDs’ high-injection characteristics. µLEDs’ outstanding performances are usually explained by their strain relaxation [38,39], uniform current spreading [19,28,40], and low junction temperature [40,41] properties. However, many-body effects, especially CE effects, are seldom discussed.
In this work, a GaN/InGaN multiple quantum well (MQW) µLED with a diameter of 20 μm was fabricated on a GaN substrate, yielding a peak injection current density of 358.2 kA/cm2. Electroluminescence (EL) spectra and light outputs were measured at different injection levels. Combining with simulations, these experiments were analyzed in detail based on many-body effects.
2. Experiments and simulations
The LED wafer was grown on a c-plane GaN substrate by metal organic chemical vapor deposition (MOCVD). It consisted of a 3 μm layer of undoped GaN, a 2.5 μm layer of n-type GaN, nine periods of In0.08Ga0.92N/GaN MQWs (the thicknesses of well and barrier are 3.7 and 10 nm, respectively), a 20-nm-thick AlGaN electron block layer (EBL), and a 90 nm layer of p-type GaN. The doping concentrations of the n-GaN and p-GaN layers were 5 × 1018 and 8 × 1019 cm−3, respectively. P-type mesas were defined using lithography technology and etched using inductively coupled plasma (ICP). The typical diameter of micro-LED was 20 μm. Indium tin oxide (ITO) was evaporated on the surface of p-type micro-pillars and used for current spreading. The electrodes comprised Cr/Pt/Au metallic multilayers. A SiO2 layer was used for passivation. The structure of the µLED is shown in Fig. 1. I-V measurements under direct current was carried out with an Agilent 4155C semiconductor parameter analyzer. An SSP 6612 LED multiple parameters tester, with a coupled spectrometer and charge-coupled device (CCD) detection system in an integrating sphere, was used to collect Electroluminescence (EL) spectra. The light output power (LOP) was measured with a calibrated Si photodetector. In order to suppress self-heating, a pulsed current was provided by a high-voltage power amplifier (Aigtek ATA 4014) and a function/arbitrary waveform generator (DG 5072, Rigol). The period and duty cycle of the pulse power were set to 10 ms and 0.01%, respectively. The current density in the experimental measurements is ranging from 49.2 to 358.2 kA/cm2.
Fig. 1. (a) Schematic diagram of the 20-μm diameter InGaN/GaN MQW µLED structure. (b) Scanning electron microscope (SEM) image of 20-μm diameter µLED.
The simulations were performed using finite element method (FEM) software (APSYS, Crosslight Software Ltd, Vancouver, Canada) [42]. During our simulation, current density increases from 50 to 360 kA/cm2 at an interval of 10 kA/cm2. We designed a chip structure in APSYS identical to the fabricated structure shown in Fig. 1. The material parameters used in the simulation can be found in Ref. [43]. Band filling effects were activated automatically by increasing the current density. The models relating to the piezoelectric field and temperature were turned on. Current crowding and non-radiative recombination processes were also included in our simulation. Auger recombination coefficients was set as 1 × 10−30 cm6/s [44,45]. Standard drift-diffusion model was used to describe carrier transport processes. The ratio of electrons that fly over QW directly was estimated to be 0.1% [46,47]. For temperatures ≥ 300 K, the well-known effects of donor-acceptor-pair (DAP) recombination on the spectrum can be ignored for narrow-well devices [13]. A uniform indium (In) composition and a polarization screening factor of 0.5 in the QWs were used as the previous work [24,39]. According to the localization landscape theory on the InGaN alloy [48,49], the parameters in the InGaN QWs would bring some errors in APSYS simulation. Considering low In content of 8% in the QWs and high carrier concentration above 1019cm-3, it is reasonable to ignore the alloy fluctuation under ultra-high injection levels [50–52].
The spontaneous emission rate, Rsp(E), was used to characterize many-body effects at high injection levels. The spontaneous emission rate of a μLED at a given energy (Ecv) can be calculated by APSYS according to Ref. [53]. At high injection levels, CS was divided into two categories: carrier–carrier collisions and events involving LO-phonons. Both these processes influenced the optical transition and contributes to spectral broadening. According to Ref. [17], intraband relaxation time, τin, is defined as the inverse of the scattering probability of carriers per unit time. Lorentzian model, which used τin as a significant parameter, was included in APSYS to calculate effects of CS [17]. The change of bandgap Ecv caused by BGR was calculated as ΔEBGR in APSYS according to Ref. [15]. According to Refs. [5] and [54], the spectral power density at a specific energy E was determined by the difference between E and the bandgap Ecv. Consequently, researches on BGR effects focused predominantly on the peak wavelength shift in the spontaneous emission spectrum. A few studies highlighted that the additional potential barrier caused by BGR effects might inhibit the transition of carriers from high to low energy states [19,25]. However, the above conclusion was derived to explain the experimental results and lacked solid theoretical evidence. Typically, theoretical studies on many-body effects showed that BGR effects induced a redshift in the gain spectrum and did not influence the peak gain and spectral width [5,6]. In the Padé approximation [2,15], which incorporated the CE effect, Rsp(E) was modified. The self-consistent MQW model, which removed the restriction of flat-band and coupled the potential with charge density in a self-consistent manner, was used in APSYS except the simulation of Rsp(E) modified by CE. Due to polarization field, the band bending and the spatial separation of electrons and holes along c-axis would weaken CE effects. So the scales of CE effects were drawn from experimental results, and then were used to simulate the light output in APSYS.
3. Results and discussion
Figure 2 shows I-V characteristics of our sample. Under direct current, the reverse current leakage at -7 V is 3 nA and the turn-on voltage is about 2.8 V. Pulsed current is used to suppress self-heating and 20μm LED can reaches the maximum current density of 358.2 kA/cm2. The detailed analysis of I-V curve can be found in our previous work [24].
Fig. 2. I-V curves of 20-μm diameter InGaN/GaN MQW µLED. The black and red dotted lines correspond to operating under direct current and pulsed current, respectively.
The minimum current density of 49.2 kA/cm2 was selected to analyze the many-body effects. At this current density, the average carrier concentration in the MQWs was calculated to be approximately 1 × 1019 cm-3. Figure 3 shows the EL spectra and relative parameters of the μLED for different current densities ranging from 49.2 to 358.2 kA/cm2.
Fig. 3. (a) EL spectrum of 20-μm diameter InGaN/GaN MQW µLED at 358.2 kA/cm2 with the features λp, λL, λR, ΔλL, and ΔλR labeled. (b) Typical EL spectra at different current densities (from 49.2 to 353.3 kA/cm2 with an interval of about 50 kA/cm2). Upper: black arrows indicate the redshift of the peak wavelengths. Bottom: peak intensities are normalized and λp is aligned. (c) From top to bottom, the dependencies of λp, ΔλL, and ΔλR on the current density from 49.2 to 358.2 kA/cm2.
In Fig. 3(a), the EL spectrum corresponding to 358.2 kA/cm2 shows a broad and asymmetric profile. Spline smoothing was used to eliminate random noises in EL spectra. Peak wavelength, λp, is defined as the wavelength that is corresponding to the maximum counts in the smooth curve. Similar to the PL spectra in Ref. [9], the peak wavelength, short-wavelength limit, and long-wavelength limit of the full width at half maximum (FWHM) are denoted by λp, λL, and λR, respectively. Figure 3(b) shows the typical EL spectra at different current densities. The upper panel shows the change in λp, while in the bottom panel, the peak intensity is normalized and λp is moved to the same position. Spectral broadening is clearly observed. Figure 3(c) shows the data for λp, ΔλL, and ΔλR at different injection levels, with λp maintaining an upward trend, which starts from 384.9 nm at 49.2 kA/cm2 and increases to 387.5 nm at 358.2 kA/cm2. There is an obvious platform spanning approximately 150–250 kA/cm2. Initially, ΔλL and ΔλR are approximately 6 nm, with ΔλR growing linearly to reach a maximum of 12.2 nm at 358.2 kA/cm2. However, ΔλL shows three distinct segments: for current densities less than 100 kA/cm2, ΔλL changes similarly to ΔλR; between 100 and 200 kA/cm2, the growth of ΔλL decelerates gradually to zero; for current densities exceeding approximately 200 kA/cm2, ΔλL maintains a steady value of approximately 9 nm. According to the different changes in λp, ΔλL, and ΔλR, these five stages are divided, as shown in Fig. 3(c). In stage I, an obvious red shift occurs, and the spectra broaden symmetrically. In stage II, the redshift of the peak wavelength continues and ΔλL increases slowly. The profile of the spectra gradually become asymmetrical. In stage III, λp is almost unchanged. The growth speed of ΔλL decreases gradually to 0, while ΔλR grows linearly. In stage IV, λp and ΔλL remain stable, while ΔλR grows linearly. In stage V, λp increases again, while ΔλL remains fixed and ΔλR grows linearly.
The effects of CS and CE on the spectral shapes are shown in Figs. 4(a) and (b), respectively. Park et al. measured the intraband relaxation time, τin, as 25 fs [16]. An order of 10−14 s was used in the calculation. As the injection level increases, CS becomes stronger, which leads to the decrease of τin. The enhanced CS leads to spectral broadening. The width of the Rsp spectra increases by more than a factor of 2 when τin decreases from 2 × 10−14 to 0.5 × 10−14 s. The CS-induced spectral modifications at the low- and high-energy edges are almost symmetrical. Other than spectrum broadening, strong CS also causes a “blueshift” tendency. Considering the CE effects, many free electrons are attracted by the localized holes [9,13], with these electrons relaxing from high-energy extended states to localized states. Figure 4(b) shows the simulated spontaneous emission spectra with and without CE effects. It is observed that ΔλL shrinks owing to CE effects, while λp also changes in response to the change in the spectral shape. The CE-induced changes in λp are complicated and can be influenced by polarization effects [26], which will be discussed later.
Fig. 4. (a) Spontaneous emission spectra without (black line) and with (red and blue line) CS effects for different values of τin. (b) Spontaneous emission spectra without (black line) and with (red line) CE effects.
It can be concluded from Fig. 4 that ΔλL is affected by CS and CE effects, while ΔλR depends solely on CS effects. The conclusions were used in the processes of parameter fitting and the fitting results are shown in Fig. 5. The τin at different current densities was obtained by fitting ΔλR. Excluding CS-induced spectral broadening, the scaling factors for CE effects were obtained by fitting the experimental ΔλL.
Fig. 5. Experimental and simulated fitting results of (a) ΔλR and (b) ΔλL. (c) Scaling change of the CE effects under different current density.
By fitting the experimental spectrum, at 50 kA/cm2, the τin was determined to be 1.65 × 10−14 s. The basic model, which includes all the factors except many-body effects, is labeled as “base” in Fig. 5. As the current density increases from 50–360 kA/cm2, ΔλR and ΔλL are calculated to increase by 0.33 and 0.41 nm, respectively. This broadening may be attributed to band filling or the increasing of junction temperature. In terms of CS, the specific values of τin at different current densities are achieved by fitting ΔλR. It decreases from 1.65 × 10−14 s at 50 kA/cm2 to 0.74 × 10−14 s at 360 kA/cm2. The change in τin shows that the CS effects become stronger as the injection level increases. After incorporating CS effects into the basic model, the calculated ΔλL exceeds the experimental results. At 50 kA/cm2, the difference was 1.33 nm, dropping to 0.62 nm at approximately 150 kA/cm2, and then rising to 3.01 nm at about 360 kA/cm2. The CE scaling factor was determined to be 0.38, 0.21, and 0.97 at 50, 150, and 360 kA/cm2, respectively. Surrounding particles with opposite charges can screen the effects of CE. The above phenomenon is called “plasma screening”. As the current density increases from 50 kA/cm2 to approximately 150 kA/cm2, plasma screening enhances and thus inhibits CE effects. When the injection level continues to increase, the separation of electrons and holes along c-axis caused by polarization can be relieved. A closer e–h distance enhances CE effects [26]. Overall, the interplay between CE, plasma screening, and polarization results in a change in the CE effects, as shown in Fig. 5(c).
In order to directly show the shift of peak wavelength, Δλp at specific injection level J, which is defined as λp(J)-λp(50 kA/cm2), was used. Considering the many-body effects individually, the dependencies of Δλp on the current density were calculated and are shown in Fig. 6(a). The experimental and simulated λp, which was calculated based on the whole many-body theory, are compared in Fig. 6(b). The current density ranges from 50 kA/cm2 to 360 kA/cm2. In the basic model without many-body effects, a redshift of 0.67 nm is observed (see Fig. 6(a)). This is attributed to the combined effects of increased junction temperature, band filling and polarization screening. Although the pulse current is used throughout the measurements, self-heating is still serious at ultra-high injection levels. The temperature-induced shrinkage of the bandgap results in a redshift of approximately 1.36 nm. In addition, the blueshift caused by band filling and polarization field screening is 0.69 nm. Next, BGR, CS, and CE are added into basic model in turn. Their respective effects on ΔλP were extracted by subtracting the result from the former model. As shown in Fig. 6(a), BGR induces a redshift of 1.74 nm, while the CS effect causes λp to decrease by 0.68 nm. According to Ref. [5], CE can produce a blueshift. The scaling of CE at different current densities were determined from Fig. 5(c). λp increases by approximately 0.62 nm before 150 kA/cm2, and then decreases until 360 kA/cm2. Finally, the simulated λp as a function of current density, combining the basic model totally with BGR, CS and CE effects, are carried out. As shown in Fig. 6(b), the simulated λp conforms well to the experimental one. From 50–150 kA/cm2, λp increases rapidly. The growth rate becomes slow in the range of 150–250 kA/cm2, and then rises again until 360 kA/cm2. The initial increase before 150 kA/cm2 is attributed to BGR and CE effects, whereas the second increase after 250 kA/cm2 is attributed to thermal effect. The slow growth of λp between 150 and 250 kA/cm2 corresponds to the increased contribution of blueshift-inducing components, such as band filling, polarization field screening, and CS and CE effects.
Fig. 6. (a) Simulated peak wavelength shifts to one at 50 kA/cm2, Δλp under different injection level based on different models: base, BGR, CS and CE. (b) The experimental and simulated λp as a function of current density, where the simulation combines the basic model with BGR, CS and CE effects.
Next, the important roles of various many-body effects in determining the light output power of the μLED under high injection levels were simulated. The quantity d(logL)/d(logI), that is, the slope of the logL−logI curves, was analyzed based on the ABC model described in Ref. [28]. Here, L is the LOP of the µLED, and I is the corresponding current. The value of d(logL)/d(logI) is approximately 1 when radiative recombination dominates. In contrast, if the nonradiative recombination relating to defects (i.e., Shockley–Read–Hall (SRH) recombination) dominates, then d(logL)/d(logI) is approximately 2. Meanwhile, d(logL)/d(logI) can decrease owing to carrier leakage and Auger recombination to a value below 1. Figures 7(a) and (b) show the experimental and simulated d(logL)/d(logI) curves, respectively. In our previous work [24], SRH recombination, many-body effects, carrier leakage, and Auger recombination were used to explain experimental d(logL)/d(logI) curves. Hader et al. reported that density-activated defect recombination (DADR) occurs at high injection levels, gradually becoming saturated at ultra-high levels [22,55]. As a result of DADR, SRH recombination dominates at high injection levels.
Fig. 7. Impact of many-body effects on EL intensities at different current densities: (a) experimental d(logL)/d(logI) curve, (b) simulated d(logL)/d(logI) curve, (c) experimental EQE curve, and (d) simulated EQE curve.
In this study, the d(logL)/d(logI) curve corresponding to the influence of many-body effects was calculated quantitatively, as presented in Fig. 7(b). SRH recombination model was activated in the basic model. Because there is a lack of factors that compensate for SRH recombination enhancement, the d(logL)/d(logI) curve continues to increase for current densities up to 230 kA/cm2. The d(logL)/d(logI) has a peak value of 1.61, which is higher than the experimental result. When CS effects are considered, the peak of the slope reduces to 1.42. The effect of CS on slope reduction may be analogous to Auger recombination, which yields a slope of approximately 0.7. When both CS and CE effects are considered, the peak of the slope reduces to 1.27. This is almost identical to the experimental value of 1.26. Scaling factors of CE were adopted based on the data shown in Fig. 5(c); CE enhances radiative recombination and decreases d(logL)/d(logI). The experimental external quantum efficiency (EQE) was also simulated, as shown in Fig. 7(d). The EQE decreases with increasing current density up to about 100 kA/cm2, as shown in Fig. 7(c). Efficiency droops are common in GaN/InGaN MQW LEDs. Carrier leakage and Auger recombination are considered to be the main origins for this [56,57]. According to our simulation, the abnormal increase of EQE with increasing current density after 150 kA/cm2 should be attributed to CE effects. In the basic model or base + CS model, EQE curves show no abnormalities. There are some differences between the experimental EQE curve and simulated one by the model of base + CS + CE. The simulated EQE maximum point is the start point, while the experimental one is at about 275 kA/cm2. The current density of simulated EQE minimum point is about 40 kA/cm2 larger than that of the experimental one. The simulated EQE curve shows monotonously increase in the current density range of 150-360 kA/cm2. However, the EQE saturates at 200 kA/cm2 and decreases after 300 kA/cm2 in the experiment. It is a big approximation to set the Auger coefficient as a constant of 1×10−30 cm6/s [44,45]. Auger coefficient may be larger than the real one under the current density from 50 kA/cm2 to 100 kA/cm2. CE will compensate more Auger recombination to make the EQE reach extremes, which causes the less EQE and higher current density. The Auger coefficient may be smaller than the real one when the current density increases above 300 kA/cm2. Auger recombination cannot exceed the CE, which makes simulated EQE increase monotonously. The Auger recombination variation in the 50-360 kA/cm2 can also explain the difference between the d(logL)/d(logI) curves in Fig. 7(a) and 7(b). Another attribution to EQE differences may be carrier leakage. The ratio of electrons that fly over QW directly was estimated to be 0.1% [46,47]. It will be not accurate when the QWs become nearly full under extremely high current injection [58]. It is obvious that when the carrier leakage increases both the d(logL)/d(logI) slope and EQE will decreases. If the Auger coefficient and carrier leakage can be adjusted to the current density, the above differences between the experiment and simulation will become small in Fig. 7.
Figure 8 shows schematic illustrations of many-body effects. Blue solid balls and red hollow balls represent the electrons and holes, respectively. Figure 8(a) illustrates carrier scattering processes. As shown in Fig. 8(a-1), electrons at j and j’ collide with each other and scatter into holes at i and i’. The formation of a hole at i during optical transition is intercepted by the above scattering process. Meanwhile, optical transition of an electron at j may also be intercepted by the collision of holes at i and i’ (shown in Fig. 8(a-2)). As is shown in Fig. 8(a-3) and (a-4), some phonon-assisted scattering processes can lead to similar results. As a result of carrier scattering, optical transition with a specific energy of Ecv can be broadened. Lorentzian model is used to approximate the broadening line shape. Due to the interception of optical transition, CS also have a certain influence on the spontaneous emission rate. Figure 8(b) shows that the effective bandgap for optical transitions shrinks as a result of BGR effects. Ecv decreases to Ecv’, which leads to obvious redshift as demonstrated in Fig. 6(a). Figure 8(c) illustrates the effects of CE on carrier distribution in QW with and without polarization field. Due to the effect of polarization, band bending occurs in well and results in the separation of carriers along z-axis. Since the effective mass of hole is much larger than electron, hole is more likely to fix in the local area. While electrons in the x-y plane spread randomly, as seen in Fig. 8(c-1) and 8(c-3). The distribution of carriers in x-y plane can be changed by CE effects. The attraction force between carriers increases the spatial overlap of electrons and holes, which enhances radiative recombination, as shown in Fig. 8(c-2) and 8(c-4). When polarization field is effectively screened as shown in Fig. 8 (c-3) and 8(c-4), the separation of carriers along z-axis can be eliminated. In Fig. 8(c-4), closer distance enhances the attraction between electrons and localized holes, and leads to further enhancement of CE effects.
Fig. 8. Schematic illustrations of CS, BGR and CE effects: (a) Schematic illustration of CS effects for electron-electron, hole-hole, electron-LO phonon and hole-LO phonon scattering. (b) Schematic illustration of BGR effects and their effects on emission spectra shift. (c) Schematic illustration of CE effects on carrier distribution in QW.
4. Summary
A GaN/InGaN µLED with a diameter of 20 μm was fabricated on a GaN substrate. EL spectra were measured from 49.2 to 358.2 kA/cm2. The width and the peak wavelength of the EL spectra, and the light output power were analyzed. Many-body effects, including CS, BGR, and CE, were discussed individually and used to demonstrate EL behaviors under ultra-high injection levels. The broadening of the EL spectra is due to the CS effect, while CE causes the low-wavelength edge of the spectra to shrink. Redshift of the spectral features is caused primarily by BGR and the junction temperature increasing. This redshift overwhelms blueshifts induced by band filling, polarization field screening, and the CS and CE effects. Due to the interplay between CE, plasma screen and polarization, the influence of CE effects drops before about 150 kA/cm2, and then increases until about 360 kA/cm2. The enhanced CE leads to abnormal phenomena in the d(logL)/d(logI) and EQE curves.
Funding
National Key Research and Development Program of China (2016YFB0400100); National Natural Science Foundation of China (61674005, 61927806); Science and Technology Planning Project of Guangdong Province (2016B010111001); Science and Technology Planning Project of Henan Province (161100210200).
Disclosures
The authors declare no conflicts of interest.
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