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Different size InGaN/GaN based micro-LEDs (μLEDs) are fabricated. An extremely high injection level above 16 kA/cm2 is achieved for 10 μm-diameter LED. The lateral current density and carrier distributions of the μLEDs are simulated by APSYS software. Streak camera time resolved photoluminescence (TRPL) results show clear evidence that the band-gap renormalization (BGR) effect is weakened by strain relaxation in smaller size μLEDs. BGR affects the relaxation of free carriers on the conduction band bottom in multiple quantum wells (MQWs), and then indirectly affects the recombination rate of carriers. An energy band model based on BGR effect is made to explain the high-injection-level phenomenon for μLEDs.
© 2015 Optical Society of America
1. Introduction
Although the luminous efficiency has been achieved higher than 300 lm/W, the efficiency droops appear disappointedly in excellent light emitting diodes (LEDs) under high injection level or at high temperature [1,2]. By now still few conventional LEDs can work for current densities of hundreds of A/cm2. The efficiency droop is due to multiple factors, including electron overflow from the active region [3], Auger recombination [1], density-activated defect recombination [4], junction overheating [2], and so on. Many remedies have been reported. Polarization matched barriers and electron blocking layer [3,5], nonpolar LED [6] are supposed to reduce the current overflow by eliminating polarization field. Double heterostructure (DH) active layer [7], improved hole injection [8] are believed to reduce the Auger recombination by lowering the carrier density in the active layer. GaN homogeneous epitaxy on freestanding substrate [9] is an effective route to decrease the junction temperature (Tj) and threading dislocation density. Recently, much attention has been paid to specific small LEDs with chip size of tens micron (μLEDs), which can effectively reduce the droop phenomenon, and endure high current density of even several kA/cm2 [10–16]. The distinct performances of tens micron μLEDs are attributed to uniform current spreading and low junction temperature (Tj) by some groups [2,12,14–16]. However, the maximum endured current density still increases as the size of μLEDs reducing down below the current spreading length and operating under low-duty pulse current. There are few considerations beyond the current spreading and Tj for the high injection performance of small size μLEDs.
It is noted that the concentration of the trapped carriers in QWs would reach 1019 cm−3 with current density above several hundred A/cm2 [17]. Band-gap renormalization (BGR) and band-filling should occur when the carrier concentration is higher than mid 1018 cm−3 [18–20]. It is found that the BGR effect is strengthened with an increase of the biaxial compressive strain [21]. What is more important, the BGR effect can build an additional potential barrier for carriers to inhibit their transferring from high to low energy state, thus leading to efficiency saturation [22]. Band-filling model including localized state, extended state and mobility edge has also been used to investigate the recombination processes under high injection level [19,23,24]. The theories about BGR and band-filling should be useful for understanding the high injection performance of smaller μLEDs.
In this work, different size μLEDs were fabricated using a compatible process with conventional LEDs. Remarkable performances under the injection level of kA/cm2 were achieved for small size μLEDs. Current distributions along the mesa of μLEDs were obtained with simulations by the APSYS version 2008 software package. The dynamic recombination process of carriers for μLEDs was investigated by time-resolved photoluminescence (TRPL) measurements under high excitation power.
2. Experiments
The epitaxial wafer was grown by metal organic chemical vapor deposition (MOCVD) on the sapphire substrate. It was comprised of a nucleation layer, a 2 μm undoped-GaN layer, a 2.5 μm n-GaN layer, a ten-period InGaN(2.2 nm)/GaN(15 nm) multiple quantum wells (MQWs) with light emission wavelength at about 460 nm, and a 230 nm-thick p-GaN layer. The size of the active regions was defined from 300 to 10 μm by conventional photolithography and inductively coupled plasma (ICP) etching. The other detailed fabrication procedures for the EL samples can be found in our previous work [12,13]. The platform of 8 × 8 μLEDs chip array is shown in Fig. 1(a) . The array has a pitch of 1 mm, and the diameters of μLED pillars for each row are the same, while those for different rows downward are decreased in sequence from 300 to 10 μm. The p-pad squares were connected with the μLED pillars by metals.
Fig. 1 (a) The photograph of μLEDs chip array and (b) the schematic structure of μLEDs for the APSYS simulation.
Light output power (LOP) measurements were performed by a calibrated Si photo-detector while electroluminescence (EL) spectra were collected by a SSP 6612 LED Multiple Parameters Tester with a coupled spectrometer and charge coupled device (CCD) detection system in an integrated sphere. Pulse current was gradually applied on these μLEDs with current densities varying from 0 to 16 kA/cm2. The pulse width is 10 microsecond, and the duty cycle is 0.1%. Time-resolved photoluminescence (TRPL) measurements were performed using a Ti: sapphire laser. The incident wavelength of the doubled-frequency laser was 400 nm with the pulse width of 34 fs, and the repetition rate was 1 kHz. The laser beam diameter is about 1 mm2. The μLED samples prepared for TRPL test were divided to different size regions, in each region the same size μLEDs were arrayed in a 5 mm length square area. Streak camera (c10910 series) was used to collect signal with 1 ps temporal resolution, and test wavelength ranged from 421 to 525.5 nm. The current and carrier distributions of μLEDs were simulated by APSYS package of Crosslight software [25], in which current spreading, strain relaxation and thermal effect were taken into account. The typical structure of μLEDs is shown schematically in Fig. 1(b). The carrier concentration of the n-type GaN layer is 5 × 1018 cm−3, and 3.5 × 1017 cm−3 for the p-type GaN. SRH lifetime is about 58ns, Auger recombination coefficient is about 4 × 10−31cm−6, and band offset ratio is 3/7. Polarization charge density will be automatically generated when the value of screening factor is set from 0.38 to 0.5 according to the strain relaxation in μLEDs measured in Ref [26]. Thermal conductivities of GaN and InGaN used in simulation are 200 W/(m*K) and 80 W/(m*K), respectively. The external temperature is set at 300 K. Other material parameters can be found in [27]. The diameters of the μLED pillars were assigned to 300, 160, 80, 40 and 10 μm, respectively.
3. Results and analyses
Figure 2(a) shows the dependence of the light output power (LOP) on the current density (L-I) for μLEDs with different diameters. The L-I curves show that smaller size μLEDs can endure higher current density. In particular the 10 μm LEDs survive at extremely high current density of 16 kA/cm2. The LOP seems not saturate at so high injection level, while that for 300 μm LEDs are already saturated at the current density of 226 A/cm2. We assume that LEDs operated at saturated current density can be regard as survived LED chips. Below the specific current density, the light output intensity can be enhanced with current density increasing. When the injected current density has approached the specific current density, LEDs would die soon. Figure 2 (b) shows the external quantum efficiency (EQE) curves for 10, 20, 40, 80, 160 and 300 μm LEDs with increased current density. The maxima of each curve have been regard as 1. As sizes of LED chips decrease, efficiency droop can be improved, especially for μLEDs with sizes below 40 μm. The value of efficiency droop is defined as (EQEpeak-EQE200A/cm 2)/EQEpeak. The values of 10 μm and 300 μm LED are 18% and 61%, respectively. Simultaneously, the peak current density (Ipeak) corresponding to EQE maximum increases significantly with the sizes of μLEDs decreasing. The mesa diameter below 40 μm is smaller than the current spreading length [14]. However, the saturated current density increases significantly and the effect of efficiency droop weakens when the diameter is reduced down to 10 μm. There should be some other factors to explain the extremely high current density for smaller μLEDs.
Fig. 2 (a)The dependence of the light output power in EL spectra on the current density for 10, 20, 40, 80, 160 and 300 μm LEDs. (b)The external quantum efficiency (EQE) curves for 10, 20, 40, 80, 160 and 300 μm LEDs with increased current density.
The EL spectra under different current densities are shown in Fig. 3 for the 300 and 10 μm LEDs. Under low injection levels, the peak wavelength blue shifts for both of the two LEDs with current density increasing. The shape and FWHM of the EL spectra are little changed. When the current density is higher than a critical point, the spectra are broadened. The critical points are 56.6 and 318.3 A/cm2 for 300 and 10 μm LEDs, respectively. A later redshift can be observed for the 300 μm LED, while no red shift can be observed for the 10 μm one, as shown in Fig. 3(a) and 3(b). Carrier screening and band filling are usually supposed as the causes for the blueshift with the current density increasing. The blueshift in this injection region is mainly due to carrier screening of polarization field since the QW is formed by the undoped InGaN layer [19]. When the injection level increases to the order of kA/cm2, carrier concentration is above several 1019 cm−3 in QW. At this time, screening effect may be saturated [18], and the blueshift could be attributed to the band filling effect.
Fig. 3 EL spectra measured under different current densities (a) from 0.2 to 282.9A/cm2 for 300μm LED and (b) from 6.4 to 1273.2A/cm2 for 10μm LED. (c)The simulated current density distributions along the mesa diameter neighbor to the last QW of μLEDs with different sizes. The average current density is 200 A/cm2.
On the other hand, lateral current distribution in MQWs should be considered. Figure 3(c) shows simulated current density distribution in the p-GaN layer on top of the last QW, where the average current densities are 200 A/cm2 for all μLEDs. The relative position in the figure refers to the ratio of distances between the left edge and test point to diameters of μLEDs. It is clear that the current density at the sidewall is higher than that in the center of the pillar for all μLEDs. The maximum current density is about 1200 A/cm2 at the sidewall for the 300 μm LED, which is 16 times of that in the center. The maximum is about 240 A/cm2 at the sidewall for the 10 μm LED, while the minimum is 180 A/cm2 in the center. The current spreading is more uniform for the 10 μm LED than the 300 μm one. For small size μLEDs, the surface-volume ratio becomes larger, which will cause the etching damages more significant. However, we use the KOH solution to remove the etching damages, and the calculated current density proportion and carriers proportion in the damaged area is lower than 15% for 10 μm LED. So we think that the damages on the sidewall are not main factor to affect the high injection performance for μLEDs. With the current density increases, the current inhomogeneity would become more serious [28]. It is reasonable to assume that the spectrum will be broadened in case of the current crowding, because the local carrier concentration determines the emission wavelength. When the current density exceeds the critical point, the spectra are broadened as shown in Fig. 3(a) and 3(b). Redshift for the 300 μm LED may be attributed to the self-heating and BGR effects. But due to pulse current being adopted, the self-heating can be avoided. So the significant redshift for 300 μm LED above 127.3 A/cm2 should be mainly due to BGR effect, and the current densities crowded at the sidewall are higher than 1 kA/cm2. However, the redshift cannot be observed for the 10 μm LED even the average current density is higher than 1 kA/cm2. The relationship between LED size and BGR effect will be discussed later.
In the streak camera TRPL measurement, the energy of a single laser pulse is 4 μJ. The excess carrier density in a single QW can be estimated as about 7.3 × 1019 cm−3. The measured signal, F(t) is the convolution of instrument response function (IRF(t)) and real PL intensity, I(t), where t represents time. Although the convolution disturbs the actual time of carrier dynamics, its dynamic process can be observed by the PL spectra evolution. Figure 4 shows the PL spectra evolutions for the 300 and 10 μm LEDs from 8 ps to 1.3 ns. In the initial stage, although the carriers have been injected into the QWs, the PL intensity is weak within the time period of about 100 ps. Before 70 ps, the spectral width is broadened. Then the width is reduced to a minimum before 140 ps, and keeps constant till 2 ns. Due to the energy difference of 0.41 eV between the excitation photons and InGaN band gap, the photogenerated carriers will have excessive energy. The excessive energies are calculated as 86 and 316 meV for hole and electron [20], respectively. The conduction band offset of the InGaN/GaN QWs is about 420 meV, so the electrons will be bounded in MQWs as hot carriers. The initial dark time may be related to the hot carrier relaxation time. It is a bit long because when the carrier concentration increases to more than 1019 cm−3 in QWs, the relaxed time of hot carrier will be extended by two orders compared to that in low carrier concentration bulk [29]. The hot carriers have two channels to relax, either by recombination with holes, or by interaction with phonons. As a matter of fact, the latter is much faster than the former. As such, before the hot carriers well relax enough to the conduction band (CB) bottom and/or occupy some localized states, the carrier radiative recombination rate will not be high. In the relaxation process of the hot electrons, electron-LO phonon scattering and electron-electron collisions would lead to broadened spectra in low energy side as well as a high-energy tail [20]. As time going, low energy states approach more occupied, hence the relaxation rate of the hot carriers to lower energy states decreases, which will lead to more radiation from higher energy levels, i.e. blueshift and narrowing of the spectra. After 140 ps, most of the hot carriers may be relaxed, and the spectral widths become constant. Because the high carrier concentration is above 1019 cm−3 which would induce band filling and BGR effects, more specific recombination mechanism should be further explored.
Fig. 4 Temporal changes of the PL spectra for (a) 300 μm and (b) 10 μm LEDs from 8 ps to 1.3 ns. The peaks are connected by short dash lines.
Time resolved peak intensities and peak wavelengths of the PL spectra are extracted from the streak camera images for 300, 160, 80, 40 and 10 μm LEDs, as shown in Fig. 5 . The time resolved peak intensity curve in Fig. 5(a) includes a rising edge and a falling edge. The rising edges are terminated at about 140 ps. The slope of the rising edge increases with the size of μLED decreasing. Correspondingly, the decay rate also increases with the size of the μLEDs decreasing in the rest time of 2 ns. The exception is the falling edge for the 10 μm LED, in which the initial decay rate is slower than those of the other larger size μLEDs, while the global falling edge decays most rapidly in the time of 2 ns. In Fig. 5(b), the time resolved peak wavelengths show blueshift first, and then nearly constant for μLEDs within 2 ns. The turning points are marked by circles. It is observed that the blueshift is smaller for smaller size μLEDs, and has less shift time as well. But the blueshift of 10 μm LEDs take longer time, also as shown in Fig. 5(b). The time of 2 ns is too short to show the whole dynamics process of the photogenerated carriers. Figure 5(c) shows the peak wavelength change within 50 ns scale. The peak wavelengths blue shift first before 3.6 ns, and then keep constant till 7 ns, and red shift eventually. More clearly, there are trenches at about 3.2 ns for all the μLEDs. By expanding the time scale in the test, it is found that the blueshift time is prolonged. Due to the instrument response, the PL peak intensities are usually appeared in the initial 5-8% of the time scale. The spectra evolution seems prolonged at the initial stage with the time scale increasing. After the initial 5-8% of the time scale, the data is influenced weakly by instrument response for all time scales. It is useful to get more information about carrier dynamics by magnifying the time scale, as shown in Fig. 5(c). For example, the trenches are not clear as a brief process in 2 ns time scale while highlighted in the larger one.
Fig. 5 Time resolved (a) peak intensities, (b) peak wavelengths of the PL spectra taken from the streak camera images for 300, 160, 80, 40 and 10 μm LEDs with the time scale of 2 ns, and (c) peak wavelengths with the time scale of 50 ns.
In order to explain the above results, a model of carrier dynamics is developed, referring to Ref [24], as shown in Fig. 6 . The model includes a schematic band diagram,possible paths of carrier transport and recombination in InGaN QW under high injection level. When the laser pulse illuminates the MQWs of μLEDs, photogenerated electrons with excessive energy become hot carriers in the QWs. The localized states are almost empty at this time. As mentioned above, electron-phonon and electron-electron scattering lead to carrier relaxation to the states on the CB bottom as free carriers. And then free carriers on CB bottom may also relax to some localized states. Electron-electron, electron-LO phonon interactions of hot carriers cause the broad spectra and more emission at low energy side.
Fig. 6 Energy band diagram of conduction band for possible paths of carrier transport and recombination in TRPL
As the hot carriers concentration decreases, phonon assisted recombination is weakened, and higher energy levels are occupied on the CB bottom. So the peak wavelengths of PL spectra blue shift, which are shown in Fig. 5(b) and 5(c). Due to the presence of high concentration free carriers in QWs, BGR happens at this moment, which will hinder carriers’ relaxation to low energy level. The compressive strain can enhance the BGR effect in InGaN QWs [21], and the strain will be relaxed when the size of μLEDs decreases, especially for 10 μm LEDs. Thus the small size μLEDs have more free carriers relaxed to the localized states, and long wavelength emissions begin playing roles, which lead to the slight blue shift in the early stage in Fig. 5(b) and 5(c). When the hot carriers are fully relaxed, the concentration of free carriers begins to decrease. Then BGR is distinctly weakened as the free carriers decrease, which will lead to the peak wavelength blueshift again. Weaker BGR effects cause the localized states filled rapidly, which will lead to the peak wavelength redshift. Those changes of peak wavelengths like trenches, as shown in Fig. 5(c). The PL intensities increase sharply when the localized states are occupied rapidly. Due to the weaker BGR effect, the transition to localized states is more rapid for smaller size μLEDs [22]. So the slope of the rising edge increases with the size of μLED decreasing in Fig. 5a. The PL intensities approach their maxima when the sum of the radiative recombination rate for the free carriers on the CB bottom and localized ones is the largest. These recombination components make the initial part fall rapidly after the peak intensity. Because the small size μLEDs have a faster recombination rate for weaker BGR effect, the initial part of the failing edge drops more rapidly. When the free carrier’s concentration is reduced further, they would relax to the localized states rather than recombine with holes. Then, recombination of localized states plays a dominant role. So the decay rate is almost reduced to a constant in the rest time of 2 ns. In Fig. 5(a), the 10 μm LED doesn’t have the initial part with rapid rate at the failing edge. It may be due to the weakest BGR effect in 10 μm LED. The free carriers on the CB bottom will easily transit to the localized states. The free carrier concentration on the CB bottom will be lower than those for larger size µLEDs. Due to the scarce of transitions from the CB bottom to the valence band, the decay rate will be the lowest one in all the samples at initial decay stage. It is also the reason why the blueshift time of peak wavelength prolongs for 10 μm LEDs in Fig. 5(b). At last, when the carriers are also depleted in CB bottom levels and shallow localized states, the redshift will happen because the deep localized states play the dominant role gradually, as shown in Fig. 5(c).
In TRPL measurement, the lifetime of 10 μm LED is about 2 times lower than that of 300 μm LED. So the carrier concentration in QWs for 300 μm LED is about 3 times of that for 10 μm LED under the same current injection. The carrier concentration in QWs is about 1020 cm−3 somewhere under current density of several kA/cm2 for both 10 and 300 μm LEDs. The junction temperature is calculated above 450 K. The microsecond-width current pulse means that the carriers in the QWs are in dynamic equilibrium. Some injected carriers are free on the CB bottom and others are localized in QWs, similar to the above hot carriers fully relaxed stage in TRPL under high injection level. Although the nonradiative losses and/or electron leakage are supposed heavily under this injection level by now, the small size μLEDs can still work well. So they are not fatal under extremely high injection level. The weaker BGR effects due to the uniform current spreading and strain relaxation may lead to the excellent performance for small size μLEDs. Further reducing the size to nanometer, the nano LEDs will show strain free when the diameter reaches to 140 nm [28], the BGR effect will decrease more. However, the effects of thermal dissipation and space charge limiting will prevent the improvement of the high injection level performance of nano LED [29]. So μLEDs can be served as one of the most potential candidates for kA/cm2 order current injection devices in the future, which will be applied in the high power density illumination and visible light communication.
4. Conclusion
In summary, the GaN-based μLEDs with different size are fabricated. Tens micron μLEDs can work well under the injection level of kA/cm2. Current distributions along the mesa and the carrier distributions in quantum wells (QWs) of μLEDs are simulated by the APSYS software package. TRPL measurements show that under high injection level, the strain relaxed μLEDs have a faster recombination rate in all wavelength range because of weaker BGR effect. The BGR effect inhibits the free carriers transferring from CB bottom to localized states in QWs, thus leading to efficiency saturation. Tens micron LEDs are the potential candidates for kA/cm2 class current injection devices in the future.
Acknowledgments
This work was supported by projects of National Key Basic Research Special Foundation of China under Nos. TG2011CB301905, TG2013CB328705 and Natural Science Foundation of China under Nos. 61334009, 60876063, 61076012. This work was also supported by Guangdong Innovative Research Team Program (No. 2009010044). The authors are grateful to Prof. Weikun Ge from the Hong Kong University of Science and Technology for his useful discussion and English polishing.
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