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Abstract
In this paper, we investigate the efficiency droop phenomenon in green and blue GaN-based micro-LEDs of various sizes. We discuss the distinct carrier overflow performance in green and blue devices by examining the doping profile extracted from capacitance-voltage characterization. By combining the size-dependent external quantum efficiency with the ABC model, we demonstrate the injection current efficiency droop. Furthermore, we observe that the efficiency droop is induced by injection current efficiency droop, with green micro-LEDs exhibiting a more pronounced droop due to more severe carrier overflow compared to blue micro-LEDs.
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1. Introduction
Nowadays, GaN-based micro-LEDs are widely regarded as one of the fastest-growing technologies all over the world. Recent researches have showed a huge potential for the various applications of micro-LEDs. From wearable display, near-to-eye display such as high-speed 3D/AR/VR display under low current injection to ultra-high definition projectors, high brightness large-scale TV display under high current injection [1–5]. Micro-LED is highly possible to replace the organic-LED (OLED) and liquid crystal display (LCD) technologies in display market in the following years. Currently, the fabrication processes for c-plane GaN-based blue and green micro-LEDs are highly mature. The emission wavelength of is mainly determined by the bandgap energy of the multiple quantum wells active region material, typically InGaN. The bandgap energy can be tuned by controlling the indium content, which directly influences the emission wavelength. As a tiny size light source, micro-LEDs can be applied to neurobiology and optogenetics, also visible light communication (Li-Fi). Under these circumstances, the micro-LED requires even higher current density injection [6–8].
However, for commercial GaN-based micro-LEDs grown on conventional c-plane sapphire substrate, it will suffer severe declined efficiency with increasing current density, known as notorious “efficiency droop” phenomenon. At first, researchers mainly ascribed such a droop to the increasing operating temperature with growing current density, so called “thermal droop” as well. With the deepening of investigation, more mechanisms were proposed with the ABC model to explain the efficiency droop. An early explanation considered the defect-related nonradiative recombination at crystal defects mainly caused the droop [9], called defect-assisted mechanisms. Later on, some literature [10–12] found the spontaneous emission reduction could result in the lower barrier for nonradiative process so that trigger an efficiency droop. Until the Auger recombination coefficient was extracted from the measurement by using different methods [13–16], the Auger recombination mechanism became the most popular explanation in the most papers. Recently, the modified “ABC + f(n)” model was proposed to explain the efficiency droop caused by carrier leakage and overflow [17–20], where f(n) represents the third-order or higher recombination terms.
In this paper, we investigated the blue and green micro-LED efficiency droop based on the carrier overflow analysis. Different carrier overflow situations for blue and green was characterized based on the doping profile extracted from the voltage-capacitance measurement and the m value calculation from the modified series resistance term. Additionally, a refined ABC model incorporating a variable current injection efficiency (CIE) was proposed, based on the EQE and IQE values for blue and green micro-LEDs, respectively.
2. Electrical characterization
Figure 1(a) presents c-plane blue and green GaN-based micro-LED structures, grown using metal-organic chemical vapor deposition on patterned sapphire substrates (PSS), with emission wavelengths of 450 nm and 520 nm, respectively. Figure 1(b) depicts the top-view layouts of the 10 × 10 µm2 blue and green micro-LEDs. The fabrication process in detail can refer to our prior research [21].
Fig. 1. (a) The cross-section diagram of c-plane blue and green micro-LEDs; (b) top-view layouts of the 10 × 10 µm2 blue and green micro-LEDs.
Figure 2 demonstrates the linear current-voltage (I-V) and semi-log current density-voltage (J-V) characteristics of three different sizes: 10 µm (10 × 10 µm2), 30 µm (30 × 30 µm2) and 80 µm (80 × 80 µm2) blue and green micro-LEDs. The I-V characteristics were analyzed by using Keysight (formerly Agilent) B1500 Semiconductor Analyzer, and the voltage step setup was 10 mV. With the same size, the green one indicates a stronger series resistance restricted current capability after 3 V. In Fig. 2 (b), the semi-log curve of the IV data demonstrates the reverse leakage current at reverse bias. The low leakage values, ranging from 10 × 10−13 to 10 × 10−12, can be attributed to the effective sidewall treatment and repair processes employed during fabrication [21]. Both blue and green exhibit a consistent J-V performance within Shockley model region (from 0.001 to 10 A/cm2). The forward voltage at 1 A/cm2 (usually for wearable devices display) is about 2.50 and 2.20 V, at 20 A/cm2 (usually for large-scale display) is about 2.70 and 2.43 V for blue and green device respectively. At least to10 µm device, the current spreading and heat dissipation are much better than a larger device, and therefore the current density injection values are superior at higher bias. With size shrinks down, the series resistance restriction becomes more obvious and especially for green one, which implies the influence from series resistance for 10 µm green device is more severe than 80 µm compared to blue device. The elaborated explanation will be revealed in the series resistance related part.
Fig. 2. (a) The linear representation of the current-voltage relationship (inset displays a semi-log graph of current density-voltage) and (b) the semi-log graph of the current-voltage relationship for blue and green micro-LEDs with dimensions of 80, 30, and 10 µm.
The conventional ohmic series resistance from semiconductor bulk region can be extracted from the traditional Shockley diode Eq. (1), where the I is the device current, Is is the reverse saturation current, q is the electron charge, V is the applied voltage, Rs is the series resistance in bulk region, n is diode ideality factor, k is the Boltzmann constant and T is the absolute temperature. Through Eq. (2), we can calculate the series resistance by plotting the graph of IdV/dI versus I and extracting the curve slope in the linear dependence relation. The IdV/dI represents the product of current (I) and differential resistance (dV/dI) in the I-V curve of the micro-LED, which is calculated using numerical methods, specifically finite differences, to approximate the derivative based on the I-V data. However, Fig. 3(a) shows the curve of blue and green micro-LEDs with the size of 80 and 10 µm, and the results indicate there is no linear dependence of IdV/dI vs. I. The previous research [22] pointed out that the extracted series resistance by this method is not only depending on the bulk region resistance at cryogenic temperatures, but also relying on the space-charge-limited current, which exhibits a quadratic dependence on the applied voltage by Mott-Gurney law [23]. Since at cryogenic temperatures, the radiative recombination process in MQWs region is easily saturated at low carrier injection condition, more electrons overcome the electron blocking layer and accumulated in the p-GaN region. The overflowing electrons can form space charges and generate an internal electric field in P-GaN region. Considering the micro-LED size < 100 µm, the carrier overflow will easier occur at the same current injection level with ordinary LEDs.
Fig. 3. The series resistance extraction: (a) linear dependence of IdV/dI vs. I and (b) quadratic dependence of IdV/dI vs. I for blue and green 80 and 10 µm micro-LEDs respectively.
Figure 3(b) displays the quadratic dependence of IdV/dI vs. I, and the results reveal a better-fitted linear curve of IdV/dI versus square root of the current. When comparing blue and green device in the same size, the green one shows more carrier overflowing than blue one according to the fitted slope and R square value (0.9928 for 80 µm blue, 0.9507 for 80 µm green, 0.9211 for 10 µm blue and 0.8907 for 10 µm green). Similarly when comparing different size with same emission color, the smaller sizes are more carrier overflow dominant. The disagreement of blue and green device may possibly come from two aspects: one is the high-indium component induced intrinsic spontaneous polarization effect in MQWs region, accelerating the overflowing electrons accumulation in p-GaN region, and the other is uneven carrier distribution due to the different epitaxial growth process compared with blue one, which will be discussed in the following capacitance-voltage characterization part. For further study, the IRs term can be replaced by ImRn as shown in Eq. (3) according to [24], in this way the new term is equivalent to all the voltage drop due to carrier overflow and bulk region, and the unit for new “resistance” Rn is ΩA1-m. The m value represents the carrier mechanism, so m come near to 1 means the voltage drop is mainly caused by series resistance in bulk region, and m is smaller than 1 and come near to 0.5 represents the carrier overflow occurs and the space-charge-limited current is dominant in the end. When m become lower than 0.5, that stands for the carrier overflow is increasingly rigorous. Figure 4(a) contrasts the m value of blue and green 80 µm device, indicating the carrier overflow occurs at the beginning, after a temporary rise to 0.733 of green and 0.575 of blue, the m values decline to 0.08 and 0.23 eventually. In addition, the blue one exhibits an observable space charge current limited region from 10 to 300 A/cm2 of injection current density (3 × 1019 to 8 × 1020 cm-3 of carrier concentration). Overall the green one expresses a severer carrier overflow especially after 200 A/cm2, which is compatible with previous analysis.
Fig. 4. (a) m-value extraction for green and blue 80 µm micro-LEDs; (b) doping profile calculation via capacitance-voltage measurement by using Eq. (4)–(6) for green and blue 80 µm micro-LEDs.
The carrier transport mechanism can be reflected in capacitance-voltage measurements, showing the depletion region width and doping profile for blue and green micro-LEDs, respectively. The C-V characterization was performed at a frequency of 1 MHz with an AC voltage of 20 mV at room temperature. For blue micro-LED, we set the voltage range as -30 - 3 V, and for green micro-LED, we set the voltage range as -30 - 0 V. this setup ensures that the dependency of doping concentration and depletion region width for blue and green devices is adequately demonstrated in both zero bias and reverse bias regions. The capacitance and doping profile can be calculated as
Figure 4 (b) indicates the depletion region length is valued at 25.5 nm at -0.4 V for green one and 27 nm at 1.7 V for blue one. Dual x-axes are illustrated: voltage positioned at the top and depletion width at the bottom. The correlation between voltage and depletion width can be expressed using Eqs. (4) and (5). Since the different C-V range for each, it can be confirmed that the depletion range of green one is smaller than that of blue one at zero bias, resulting from a higher Si doping concentration [25]. It should be emphasized that the activated carrier concentration within the n-region is considerably greater than that in the p-region. However, the EBL serves to confine electrons within the active region and block electrons from escaping the active region to p-region [26,27]. The C-V characterization focuses on the reverse bias region, and under this condition the EBL effectively blocks the flow of electrons to p-region and affects the depletion width distribution. But when the micro-LED is under high forward bias, the electric field is directed in the same direction as flow of carriers. The carrier concentration in the active region increases significantly, leading to an increase of carrier overflow. Consequently, owing to the influence of the EBL, the depletion region is predominantly constrained to the n-region and the MQWs at reverse bias [24], thus the apparent doping profile can be estimated as Si donor concentration in n-region. With the increase of reverse voltage bias, the depletion region width becomes larger along the direction to n-region. The donor concentration is estimated as 2.50 × 1019 cm-3 and 1.75 × 1019 cm-3 for green and blue respectively. Importantly, the green one exhibited a more obvious abrupt junction characteristic due to the uneven carrier distribution in the depletion width of 40 to 50 nm, opposite with a linearly graded junction characteristic of blue one. This is probably thanking to a better quality of lightly Si doped n--GaN layer and superlattice structure (SLS) under MQWs region [28]. To be more specific, many V-pits are introduced during the low temperature InGaN/GaN SLS growth process, serving as low energy level for carrier localization. On the one hand, the V-pits truly prevent the carrier diffusion to dislocation centers and reduce the non-radiative recombination probability under low current injection [29]. However on the other hand, the uneven carrier distribution will create severer carrier overflow under high current injection.
3. Optical characterization
Figure 5 shows the peak wavelength shift range and full width at half maximum (FWHM) broaden tendency for 80 µm green and blue devices. The green one peak wavelength shifts from 523.8 nm at 1.5 A/cm2 to 507.3 nm at 746.9 A/cm2, totally 16.5 nm shifting range. As for blue one, the range is 7.9 nm, which is from 464.0 nm at 2.3 A/cm2 to 456.1 nm at 414.1 A/cm2. The emission wavelength blue shift of micro-LEDs results from the screening effect with increasing current injection of the strain-induced piezoelectric field in GaN-based materials [30], also known as quantum-confined Stark effect (QCSE). Due to the high indium component in MQWs of green micro-LEDs, the intrinsic piezoelectric field is larger than blue one. Low current injection is not enough to screen the piezoelectric field and saturate the blue shift, so the shift range is wider than blue one. Meanwhile, indium-rich active areas play an important role of reducing the effective active volume in MQWs region, since more indium atoms are incorporated into active MQWs, and the inhomogeneity generates the indium clustering. Such a deterioration leads to a shorter depletion width and an easier saturation of radiative recombination [31], so the carrier concentration or injection current density value at peak EQE of green device should be smaller than blue one, and also the carrier overflowing should become severe at higher current density injection, consistent with the m value extraction results and C-V analysis aforementioned. The shutoff of blue shift means the piezoelectric field is fully screened, and the subsequent red shift is due to the thermal production under high current density. The broadening of FWHM is the well-known band filling effect. With the increase of carrier concentration, the excitons cannot occupy the lower energy state and much higher energy states will occur, accompanied with the FWHM broadening. Our green and blue devices exhibit almost equal broadening range as 10.8 nm, since the different exciton lifetime of blue and green can be neglecting at room temperature [32]. The larger FWHM value for green device can be attributed to higher indium composition fluctuation and indium clustering aforesaid [30].
Next we will concentrate on the EQE/IQE characterization with ABC model analysis. Different size (80, 50, 30, 10, and 6 µm) of green and blue micro-LEDs are Al-wire bonded without any packaging process, and the integrating sphere spectrometer system is used for measuring the light output power and calculating the EQE with Eq. (7), where the P is light output power, h is the Planck constant, and ν is the central frequency of the emission photons, I is injection current and e is electron charge respectively. The numerator represents the total number of emission photons from active region and the denominator represents the total number of injected electrons. Figure 6(a) and (b) demonstrates the EQE results of green and blue one respectively, and the insets are the current density at peak EQE shifting with various sizes for each. The specific peak EQE values and droop ratios are shown in Fig. 6(c) and (d). For green micro-LEDs, the peak EQE is 23.9% at 3.1 A/cm2 of 80 µm, 23.1% at 4.0 A/cm2 of 50 µm, 22.38% at 4.7 A/cm2 of 30 µm, 20.3% at 9.1 A/cm2 of 10 µm and16.7% at 20 A/cm2 of 6 µm. Since the first available data of 6 µm appears at 20 A/cm2, we believe the current density at peak EQE would be slightly smaller than 20 A/cm2. For blue micro-LEDs, the peak EQE is 25.4% at 14.1 A/cm2 of 80 µm, 21.9% at 22.0 A/cm2 of 50 µm, 17.1% at 50.0 A/cm2 of 30 µm, 17.7% at 65.0 A/cm2 of 10 µm and 14.2% at 83.3 A/cm2 of 6 µm. The efficiency droop is alleviated with size shrinks for both. With the size growing for both green and blue, the current density at peak EQE drops. According to the ABC model formula shown in Eq. (8), the current density should be proportional to $\sqrt {\textrm{A}/\textrm{C}} $, where the ηLEE represents the light extraction efficiency (LEE), ηinj represents the CIE, A, B and C are related to the nonradiative Shockley-Read-Hall (SRH) recombination, radiative recombination and Auger recombination respectively. Regarding the Auger recombination coefficient C is size-independent under low current injection (<100 A/cm2), the current density at peak EQE will grows up when size scales down, since the SRH recombination coefficient A is enhanced from the aggravated mesa sidewall surface recombination [33–35].
Fig. 6. The EQE results for (a) green and (b) blue micro-LEDs respectively, and the insets are the shift of current density at peak EQE for each; (c) and (d) are peak EQE values and EQE droop ratio for green and blue.
Furthermore, there is a reduced size-dependence for green compared to blue one, which is attributed to the smaller surface recombination velocity due to the increased carrier localization from the higher indium component. The prior literature reported such a crossover occurs at 10 µm [36], which means when micro-LED size scales down to 10 µm or smaller, the peak EQE of green one should be higher than blue one. In our case, an obvious crossover occurs at 30 µm. Considering we used ALD (atom layer deposition) Al2O3 passivation layer rather than sputtered Al2O3 layer in [34] (other fabrications and structures are almost the same, such as ITO current spreading layer and electrodes contact), the sidewall damage repair would be better. It is well-known that the surface recombination strongly depends on the surface-to-volume ratio, so that the proportion of surface recombination will rapidly increase when the micro-LED size shrinks, especially below 10 µm [33]. Appropriate sidewall treatment and passivation can repair the most sidewall damage induced by dry etching process and reduce the proportion of surface recombination. In addition, 10 µm is also a remarkable size in our case because both of green and blue exhibit a better EQE performance i.e. favorable peak EQE value and low EQE droop ratio of 10 and 6 µm, indicating the effectiveness of sidewall repair by using ALD Al2O3 passivation layer. Plus the current crowding is suppressed effectively for small sizes by using ITO current spreading layer [37], since the heat accumulation plays an essential role to efficiency droop.
A huge difference is shown in the insets that the current densities of different size at peak EQE for blue one are much bigger than green one. The general observed trends are in agreement with the discussion in C-V characterization and blue shift part. That is indium clustering resulting in shorter depletion width and an easier saturation of radiative recombination, which indicates the radiative recombination coefficient B of green one should be smaller than blue one as well. Besides, the current density at peak EQE of 80 µm also corresponds to the largest m-value mentioned above, which is about 3 to 5 A/cm2 for green one and 10 to 14 A/cm2 for blue one, revealing the carrier overflowing greatly impacts on the EQE performance. A quantitative analysis with ABC model will be demonstrated in the following paragraphs.
4. Current injection efficiency droop
Before we move further step, the widely acknowledged efficiency droop mechanisms of GaN-based LEDs should be summarized. The most popular explanation should be the Auger recombination theory proposed by Lumileds and Nakamura et al. [13,38], which is a nonradiative process that the electron-hole recombination transfer the excess energy to other carriers, subsequently excited to a higher energy state rather than emit photons. The Auger recombination will be dominant at high current density, contributing to the efficiency droop. The other latest widely accepted explanation is carrier leakage mechanism. Carrier leakage or electron overflow [17,18,39] refers to electrons escaping from the active region and combining with holes in p-GaN region. Under higher current density injection, the leakage or overflow become severer since the EBL can hardly suppress the high energy carriers from MQWs. To account for this mechanism, a “ABC + f(n) model” was proposed by Dai et al. [40], where the f(n) represents the contribution of carrier overflow. The f(n) is supposed to include another third-order recombination coefficient or other higher than third-order recombination coefficients. Higher order recombination terms involved, the more noticeable decline trends of IQE droop showed. However, very little research investigated the CIE variation trend in carrier leakage model, most of the literature assumed the CIE as 100% over a wide current density range. Apparently, a certain fraction of carriers possess the higher energy than barriers when considering the Fermi-Dirac distribution of free carriers in MQWs, and the carrier overflow through EBL happens over the MQWs active region, leading to a decreasing CIE with growing current density. Overall, the carrier overflow may not only contain the third-order recombination term or higher, but also gradually worsen the CIE with increasing current density.
Next, the efficiency droop phenomenon of blue and green 80 µm micro-LEDs will be discussed, combining with the carrier overflowing and CIE droop aforementioned. Figure 7 demonstrates the experimental IQE, theoretical IQE and CIE values of blue and green devices. The experimental IQEs are extracted from the EQE values shown in Fig. 7 by using the room-temperature reference-point method (RTRM). The IQE shows similar tendencies with EQE as expecting. To our surprise, IQE values for both blue and green are approximately 90%, indicating our micro-LEDs are improved with well-designed ITO current spreading layer, hydroxide sidewall treatment and subsequently ALD Al2O3 passivation. The detailed fabrication can refer to [21]. The theoretical IQE curves are fitted by assuming the CIE is 100% in the range of ultra-low current density level (smaller than the current density at peak EQE). Based on the previous m value analysis, the carrier overflow is far from dominant in this range, so we can simply regard the CIE in this range as a reference value of 100%. Under this circumstance, the ABC model coefficient for blue one is A = 5.5 × 108 s-1, B = 2.2 × 10−10 cm3s-1, and C = 1 × 10−32 cm6s-1, and for green one is A = 3.5 × 107 s-1, B = 8.0 × 10−11 cm3s-1, and C = 1 × 10−32 cm6s-1. It is worth noting that A of blue one is much higher than green one. The reasons may come from the MQWs active region and surface recombination of sidewall. For one aspect, the indium-rich clusters in active region leads to the carrier localization, and these clusters can keep the injection carriers away from the epitaxy defects which serve as SRH nonradiative recombination centers under low current injection [29,41]. For another, the surface recombination rate of green micro-LEDs is much smaller than blue, thus the surface recombination of green can be alleviated [36]. Lower B of green also originates from the high-indium component, since the indium clustering results in a reduced active volume in active region and an easier saturation of radiative recombination, i.e. lower radiative recombination coefficient B. Moreover, Auger recombination coefficients (∼1 × 10−32 cm6s-1) of blue and green are set as approximately equal to each other, while Piprek et al. [42] reported that the Auger coefficient needs to be larger than 1 × 10−31 cm6s-1 to contribute to IQE droop. It is likely that the CIE droop induced by carrier overflow becomes dominant for IQE droop instead of Auger recombination in our case. The CIE is experimental IQE divided by theoretical IQE, which exhibits a declining trend from low carrier concentration to high. At low current injection, the CIE remains to 100% due to the well-coincided curves of experimental and theoretical IQE. Some critical points of a definite current density or carrier concentration are demonstrated in the graph. The CIE of blue one declines from 76% to 34% from 100 to 1500 A/cm2, and the green one declines from 63% to 30% from 100 to 1500 A/cm2.
Fig. 7. The theoretical IQE fitted by ABC model, experimental IQE extracted from room-temperature reference-point method (RTRM) based on the EQE results in Fig. 6, and CIE trends for (a) green and (b) blue 80 µm micro-LEDs respectively.
In order to further explore the relationship between CIE attenuation and current density of green and blue micro-LEDs, the S parameters were analyzed and demonstrated in Fig. 8. It is believed that the S parameter at each forward bias varies with the dominant carrier recombination process. When S ≥ 2, the tunneling or surface leakage current and nonradiative recombination from lattice defects are dominant; when S≈1, the radiative recombination is dominant; when S < 1, the carrier leakage by overflowing from MQWs is dominant [43]. The S parameters are calculated from Eq. (9):
where L stands for light output power, and I represents the injection current. From Fig. 8, it can be observed that when S≈1, the current density values are corresponding to the EQE peak position aforementioned, and the CIE stay around 100% and undergo a decline after that position. Besides, the carrier overflowing of green happens earlier than blue, which could be a solid explanation for the lower current density at peak EQE of green micro-LEDs. Overall, green micro-LEDs experience more severe carrier overflow compared to blue ones. This is reflected in the experimental IQE and CIE values, where blue micro-LEDs outperform green micro-LEDs at current densities up to 1500 A/cm2.Fig. 8. Semi-log plot of S parameter (dlog(L)/dlog(I)) and CIE versus current density of green and blue 80 µm micro-LEDs.
5. Conclusion
In conclusion, the clear evidence from electrical and optical characterization points that the efficiency droop comes from the carrier overflowing for both green and blue. The high EQE and over 90% IQE value at low current injection indicate the sidewall damage is relatively suppressed and the non-radiative recombination defects are diminished by using ALD passivation especially for 10 µm micro-LEDs. Carrier overflowing leads to a decrease in current injection efficiency, which in turn results in a quantum efficiency droop. The proofs represent the green micro-LEDs exhibit a severer and earlier carrier overflow with current density growing up than blue micro-LEDs through the m value and s parameter analysis, which accounts for the higher EQE droop ratio and lower current density value at peak EQE position.
Funding
Shenzhen Science and Technology funding ((JSGG20180507183058189, JSGG20180508152033073); Shenzhen Peacock Team funding (KQTD20170810110313773); Science and Technology Planning Project of Guangdong Province (2017B010114002).
Acknowledgments
The authors would like to thank Shenzhen Sitan Technology, Nanosystem Fabrication Facility (NFF) and E-pack Lab in HKUST for technical support to accomplish the fabrication and characterization in this work. The authors would also like to thank Prof. Jr-Hau He from CityU of Hong Kong for their valuable discussion.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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