overshoot effects of electron on efficiency droop in ingan gan mqw light emitting diodes

Overshoot effects of electron on efficiency droop in InGaN/GaN MQW light-emitting diodes , , Yang Huang, Zhiqiang Liu , Xiaoyan Yi , Yao Guo, Shaoteng Wu, Guodong Yuan, JunXi Wang, Guohong Wang, and Jinmin Li Citation: AIP Advances 6, 045219 (2016); doi: 10.1063/1.4948511 View online: http://dx.doi.org/10.1063/1.4948511 View Table of Contents: http://aip.scitation.org/toc/adv/6/4 Published by the American Institute of Physics AIP ADVANCES 6, 045219 (2016) Overshoot effects of electron on efficiency droop in InGaN/GaN MQW light-emitting diodes Yang Huang,1,2,3 Zhiqiang Liu,1,2,3,a Xiaoyan Yi,1,2,3,a Yao Guo,1,2,3 Shaoteng Wu,1,2,3 Guodong Yuan,1,2,3 JunXi Wang,1,2,3 Guohong Wang,1,2,3 and Jinmin Li1,2,3 R&D Center for Semiconductor Lighting, Chinese Academy of Sciences, Beijing 100083, P R China State Key Laboratory of Solid State Lighting, Beijing 100083, P R China Beijing Engineering Research Center for the 3rd Generation Semiconductor Materials and Application, Beijing 100083, P R China (Received 30 December 2015; accepted 20 April 2016; published online 27 April 2016) To evaluate electron leakage in InGaN/GaN multiple quantum well (MQW) light emitting diodes (LEDs), analytic models of ballistic and quasi-ballistic transport are developed With this model, the impact of critical variables effecting electron leakage, including the electron blocking layer (EBL), structure of multiple quantum wells (MQWs), polarization field, and temperature are explored The simulated results based on this model shed light on previously reported experimental observations and provide basic criteria for suppressing electron leakage, advancing the design of InGaN/GaN LEDs C 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4948511] INTRODUCTION The origin of efficiency droop in InGaN/GaN light emitting diodes (LEDs) remains a topic of active debate.1,2 Although many theories have attempted to explain these experimental observations, including device heating,3 delocalization of carriers,4 Auger recombination,5 and electron leakage,6 there is still no consensus on their underlying physical mechanism Electron leakage is commonly regarded as having an important contribution to the remarkable efficiency loss, especially at high injected current Such leakage is caused by poor hole-injection efficiency,6 an ineffective electron blocking layer (EBL),7,8 non-capture of electrons by quantum wells (QWs),9 and electron escape from the QWs.10 Recently, ballistic and quasi-ballistic transport in electron leakage was investigated for InGaN/GaN LEDs with single double heterostructure (DH) active regions, producing a good agreement with experiments.11,12 Ballistic transport in more complex and significant multiple quantum well (MQW) structures however, which are widely used in InGaN/GaN LEDs, has yet to be studied In this study, we propose a ballistic and quasi-ballistic transport model for random period MQW structures of InGaN/GaN LEDs We build on the preliminary work of Ni et al.,11,12 additionally considering the potential drop in the active region, the In mole fraction of the quantum well, and the temperature The relationships between electron leakage and the period number of the quantum well, the polarization field, the aluminum (Al) mole fraction of EBL, and temperature are analyzed in detail These dependencies can shed light on the previously reported experimental observations and yield the basic criteria for reducing electron leakage THEORETICAL APPROACH FOR BALLISTIC TRANSPORT IN InGaN/GaN MQW LEDs In InGaN/GaN LEDs, electrons across the active region may be captured by the QWs through phonon-mediated or impurity-mediated scattering events; only those electrons falling into QWs a Authors to whom correspondence should be addressed Electronic mail: lzq@semi.ac.cn, spring@semi.ac.cn 2158-3226/2016/6(4)/045219/9 6, 045219-1 © Author(s) 2016 045219-2 Huang et al AIP Advances 6, 045219 (2016) are able to participate in radiative recombination Unscattered electrons may escape the active region, which is called ballistic or quasi-ballistic transport (Fig 1) Electron energies in the n-GaN are distributed in a Fermi-Dirac distribution with an additional kinetic energy (E-Ec) They cross the quantum wells (QWs) and quantum barriers (QBs) over the EBL to p-GaN, with or without energy exchange through interaction with phonons (in which case electron-LO-phonon scattering dominates).13,14 Since the quasi-ballistic transport (scattering with more than one LO phonon in a single QW or QB) is negligible,12 we just consider the electrons experiencing ballistic transport (no scattering in the QWs or QBs) and the quasi-ballistic transport (scattering with one LO phonon in a single QW or QB) For ballistic or quasi-ballistic transport, the percentage of electrons leaking is given by12  +∞ f (E) ∗ N (E) ∗ Q (E) dE E P = limit +∞ , (1) f (E) ∗ N (E) dE where f(E) and N(E) are the Fermi-Dirac distribution function and the conduction band density of states in the n-GaN, respectively We assume that the electrons traverse only in the direction normal to the heterointerface, which would very slightly overestimate the escape probability, especially at high injected current At a given energy E, the probability of ballistic or quasi-ballistic transport Q(E) is proportional to exp(−t/τsc),11,12 where t is the transit time and τsc is the electron-LO-phonon scattering time We can consider Q(E) in the QW or QB under the two transport cases under a flatband approximation i w (E) Qifree Ballistic case (no scattering) −Lw = exp( ) ν E + ∆Ec + nwell ∗ ωph ∗ τwell sc i i b (E) = exp( Qfree −Lb ), ν E + ∆Ec + nbarri ∗ ωph ∗ τbarri sc i (2) w (E) where iw and ib denote the ith QW and ith QB in MQWs starting from n-GaN, respectively; Qifree ib barri well and Qfree (E) are the Q(E) without scattering; τsc and τsc are the electron-LO-phonon scattering time of the corresponding QW or QB; nwell and nbarri refer to the total phonons absorbed by the i i electron from n-GaN to the corresponding QW and QB (negative values represent the emission of phonons); Lw and Lb are the width of the QW and QB; ∆Ec is the conduction band offset between n-GaN and the QB or QW; and ωph(≈ 88mev) is the LO phonon energy The velocity of electrons can be written as  ν (E) = ∗ E/me, (3) where me is the effective electron mass ii Quasi-ballistic transport with one phonon emission FIG Schematic illustration of ballistic or quasi-ballistic transport of electrons under the flatband approximation in InGaN/GaN LEDs 045219-3 w (E) = Qiem Huang et al  Lw AIP Advances 6, 045219 (2016) −x ( ) ) ∗ ( ∗ well well + 1) ∗ ω well ν E + ∆Ec + (nwell + 1) ∗ ω ∗ τ ν E + ∆E + (n c ph ph ∗ τem sc i i exp exp  −(Lw − x) dx ν E + ∆Ec + nwell ∗ ωph ∗ τwell sc i Lb i b (E) = Qem exp ν E+ −x ∗ ∗ barri barri ν E + (ni + 1) ∗ ωph ∗ τbarri + 1) ∗ ωph ∗ τsc em (nbarri i exp −(Lb − x) dx, ν E+ ∗ ωph ∗ τbarri sc (4) nbarri i barri where τwell em and τem are the phonon emission times in QWs and QBs, respectively iii w (E) = Qiabs Quasi-ballistic transport with one phonon absorption  Lw −x exp ν ( E + ∆Ec + (nwell − 1) ∗ i exp  i b (E) = Qabs ν E+ ωph ∗ τwell sc ∗ ν ( E + ∆Ec + (nwell − 1) ∗ i ) ∗ ωph ∗ τwell abs −(Lw − x) dx ν E + ∆Ec + nwell ∗ ωph ∗ τwell sc i Lb exp ) (nbarri i exp −x ∗ ∗ barri barri ν E + (ni − 1) ∗ ωph ∗ τbarri − 1) ∗ ωph ∗ τsc abs ν E+ −(Lb−x) dx, ∗ ωph ∗ τbarri sc nbarri i (5) barri where τwell abs and τabs are the phonon absorption times in QWs and QBs, respectively In accordance with above analysis, the total percentage of leakage electrons is described by 3(2∗num−1)  +∞ f (E) ∗ N (E) ∗ Qj (E) dE j j=1 Elimit P=  +∞ f (E) ∗ N (E) dE (0 num−1 ) Qj (E) = Qi w Qi b ∗ Qi w Q = ib j ib Qfree , i=1 ib ib Qabs or Qem Qi w w w w = Qifree , Qiabs or Qiem Elimit = max{−nbarri ∗ ωph, −nwell num ∗ ωph + φEBL − q ∗ V , 0}, i (6) where ‘3(2∗num−1)’ is the number of possible transport processes and ‘num’ is the period number of MQWs in the active region Qj (E) gives the probability of the jth transport process, which implies that electrons pass the last quantum barrier and EBL via thermionic emission due to the barrier layer j being thinner than the electron mean free path Elimit is the lower energy limit of the integral for the j jth transport process Only when the kinetic energy is above Elimit can electrons flow over the EBL in the jth transport process φEBL is the EBL barrier height and V is the potential drop across the active region Although informative, the flatband approximation deviates significantly from the real band structure of InGaN/GaN LEDs In particular, the potential drop of the built-in field of the PN junction, the polarization field, and the applied voltage lead to band bending in QWs and QBs As a result, electrons will be accelerated or decelerated depending on the direction of the net electric field, further affecting the probability of ballistic or quasi-ballistic transport To verify the potential distribution in QWs and QBs, energy band simulation was performed via APSYS of crosslight In Fig 2, the conduction band at different drive voltages is illustrated Based on the simulated result, the turn-on voltage of the LED is around 2.8V As the applied voltage approaches 3V, the quasi-flatband condition is approached Further increasing injection makes the 045219-4 Huang et al AIP Advances 6, 045219 (2016) FIG Energy band of the simulated InGaN/GaN LED at different applied voltages band gradually shift upward due to voltage saturation The net potential drop at different applied voltages within QWs and QBs, expressed as ∆Vwell and ∆Vbarrier, are exhibited in Fig At the working voltage, the build-in field of the PN junction is compensated by the applied voltage Thus, the net potential drop in QWs and QBs, which is primarily driven by the polarization charge, have almost the same absolute values with opposite directions It is therefore reasonable to approximate that the ∆Vwell and ∆Vbarrier are constant within the entire active region and that ∆Vwell equals to ∆Vbarrier Due to the opposite directions of the net potential drop in QWs and QBs, electrons are accelerated within QWs and decelerated within QBs Because ∆Vwell = ∆Vbarrier = ∆V, (7) the average increment of velocity in QWs and QBs, in contrast to the flatband approximation, is  ¯ = ∆ν ¯ well = ∆ν ¯ barrier = ∗ ∗ q ∗ ∆V (8) ∆ν me ¯ must be added to ν (E) in equations (2)-(5) to account Hence, the average increment of velocity ∆ν for the potential drop in the active region Except for the last barrier, the QB and QW are generally deposited in pairs The direction of potential in the last barrier however is opposite of the other barriers, as exhibited in Fig Thus we classify the net voltage drop in MQWs into two parts: the last barrier and the remainder For calculation convenience, we take the net voltage drop in the MQWs except the last barrier as determining the velocity variation of electrons, while the net potential drop in the last barrier, named FIG Potential drop in QWs and QBs at different applied voltages based on the band simulations presented in Fig 045219-5 Huang et al AIP Advances 6, 045219 (2016) Vb, is taken as equivalent to a reduction of the effective height of the EBL It is therefore necessary to correct equation (6) as j Elimit = max{−nbarri ∗ ωph , −nwell num ∗ ωph + φEBL−q ∗ Vb, 0} i (9) DISCUSSION To date, research on carrier leakage of InGaN/GaN LEDs are scattered in experiment and theory,6,8,11,15 limiting their application Here, on our ballistic transport model, we systematically analyze the properties of InGaN/GaN LEDs electron leakage To eliminate carrier leakage, an AlGaN layer is typically inserted between MQWs and p-GaN as an EBL The Al fraction in the AlGaN layer is a crucial parameter in EBL design The percent electron leakage (electron leakage current divided by the total current) as a function of φEBL under the flatband approximation is calculated and shown in Fig In the quantum wells, we used a well well phonon scattering time (τwell sc ), phonon emission time (τem ), and phonon absorption time (τabs ) of 0.009 ps, 0.01 ps, and 0.1 ps, respectively, for room temperature calculations In the quantum barbarri riers, we used a phonon scattering time (τbarri sc ), phonon emission time (τem ), and phonon absorption barri 16 time (τabs ) of 0.05 ps, 0.055 ps, and 0.55 ps, respectively As shown in Fig 4, our calculated results for one QW (i.e., a single DH structure) are identical to that of Ni et al.12,17 under the same conditions the simulated result of the MQW structure with three periods of 3-nm-thick QWs and 7.5-nm-thick QBs also has been presented in Fig In these two structures, the percent leakage current decreases monotonically with increasing Al content in the EBL, confirming that EBL design is an effective means of suppressing carrier leakage Compared to the other QBs, the last barrier has an opposite potential drop As we know, the direction of piezoelectric polarization in the EBL (AlGaN) is opposite to that of a QW (InGaN); unlike other barriers, the last barrier has its deposited upper layer of EBL Therefore, when the applied voltage is above a certain value under working conditions, the net potential drop in the last barrier will have the opposite sign Though the compensation of Vb for the electron blocking barrier can lead to high electron leakage, increasing the Al content in the EBL may effectively inhibit this effect, as seen in Fig However, the potential drop Vb is not only relevant to the width of the last barrier, but also to the aluminum composition in EBL As a result, incrementally increasing the Al fraction in the EBL is not going to reduce overflow current unless further details are investigated The acceleration or deceleration of electrons in the electric field of the active region has been analyzed above We note that the built-in potential of the PN junction is compensated by the applied voltage, and that the applied voltage saturates with increasing current at high injection via the Shockley equation (SE) Hence, the polarization field dominates the band bending in QWs and QBs under operating conditions From Fig 2, we obtain the potential drop ∆V ≈ 0.14V, of the FIG Calculated ratio of electron leakage current to total current as a function of EBL barrier height (φEBL) under the flatband approximation for two different designed active region structures 045219-6 Huang et al AIP Advances 6, 045219 (2016) FIG Calculated ratio of overflow electron current to total current vs the net voltage drop in the last barrier Vb with varying aluminum content in the EBL same order of magnitude as the reported polarization potential18,19 the average increment of velocity ¯ = 2.965 × 105 m, near the electron saturation velocity of GaN calculated in QWs and QBs is ∆ν 20 (∼3 × 10 m/s) Ignoring the velocity saturation effect, we display the dependence of the percent electron leakage current on the potential drop ∆V in Fig 6(a) Similar to previous reports, we find that the polarization field accounts for the promotion of ballistic or quasi-ballistic transport, or carrier leakage In some publications,21,22 the dependence of luminescence efficiency on In composition of the quantum well was observed, and the difference in polarization field was hypothesized to be the main cause Nevertheless, as showed in Fig 6(a), with the same potential drop, the calculated electron leakage current increases monotonically with increasing In mole fraction in QWs, resulting in more luminescence efficiency loss That indicates that the In composition dependence of electron velocity in QWs with different conduction band offsets also contributes to the luminescence difference That suggests that the electron leakage resulting from ballistic transport could explain the efficiency difference between LEDs of different wavelengths To better evaluate the effect of the velocity increment due to the polarization field on electron leakage current, we introduce a concept of gain ratio, a relative scale of electron leakage current, defined as Gain Ratio = (electron leakage current / total current)∆V (electron leakage current /total current)∆V=0 (10) The gain ratio as a function of ∆V is presented in Fig 6(b) It demonstrates that the polarization field plays a more important role in electron leakage for LEDs with lower indium compositions For this reason, enough attention should be paid to the polarization effect on short wavelength LEDs FIG (a) Calculated ratio of electron leakage current to total current and (b) calculated gain ratio vs potential drop ∆V in QBs and QWs with varying In mole fraction 045219-7 Huang et al AIP Advances 6, 045219 (2016) despite their low field intensity, especially where carrier leakage is concerned However, neglecting the velocity saturation effect we may overestimate the electron overflow in InGaN/GaN LEDs, and for MQWs with high In compositions, even the possibility of negative differential mobility should be considered The luminescence of LEDs is strongly dependent on the number of quantum wells in MQW structures because they affect the injection efficiency and distribution of carriers Optimization of the period number of MQW is therefore necessary for improving InGaN/GaN LEDs’ performance In Fig 7, we compare the electron leakage in structures with different periods of MQWs and Al concentrations in the EBL Without an EBL (no Al in the EBL), the ratio of leakage current drops dramatically as the period number of MQWs increases in our calculation Furthermore, the lower the concentration of aluminum in the EBL, the higher the leakage current As the aluminum concentration approaches 8%, the ratio of leakage current is nearly invariant with increasing MQW period number Thus, with low aluminum content in the EBL, the electron leakage is controlled by both the EBL barrier height φEBL and the MQW period number For structures with a high-Al-content EBL, however, the influence of the period number on leakage is not as significant Hence, when EBLs with low aluminum content are required for enhancement of hole injection, it is optimal to moderately increase the quantity of QWs; when QWs are sparse and uncontrolled, increasing the Al content of the EBL is ideal While superficially it appears that the electron leakage current in high-period-number MQWs is unremarkable (Fig 7), we must stress that the phonon scattering time (τbarri sc = 0.05ps) used in our simulation is relatively short compared to experimentally measured values (approximately 5ps),23 which would significantly improve the electron leakage current However, for comparison purposes, the phonon scattering time illustrated in Fig is used in this paper unless otherwise specified The temperature in the active region of InGaN/GaN LEDs varies with working current and circumstance The performance of LEDs at various temperatures varies considerably Both the temperature dependence of the electron-LO-phonon scattering time and the band offset (φEBL and ∆Ec) make the ballistic or quasi-ballistic transport sensitive to temperature The correlation between electron-LO-phonon scattering time and temperature can be simply expressed as.24 Θ τ =τ∞ ∗ exp( ), T (11) where T is the average temperature of MQWs,τ∞ is the scattering time at the temperature of infinite, and the characteristic temperature is defined as Θ= wph , kB (12) FIG Calculated ratio of electron leakage current to total current vs the period number of MQWs of InGaN/GaN LEDs with different EBLs 045219-8 Huang et al AIP Advances 6, 045219 (2016) FIG Calculated ratio of electron leakage current to total current vs the temperature of MQWs where kB is the Boltzmann constant For LO-phonon scattering in GaN or InGaN, Θ ≈ 1020K The relationship between temperature and band gap (or the band offset) is not discussed here, as they are addressed elsewhere.25 The percentage of electron leakage current at temperatures ranging from 1K to 500K is presented in Fig There is a maximum overflow current at approximately 200K, below which the ratio of leakage current is almost constant From that point to higher temperatures, the ratio significantly decreases Our model explains this behavior At low temperatures, the impact of temperature on the band offset is dominant,26 and increasing temperature leads to low φEBL; at high temperatures, the scattering time becomes shorter and the strong scattering hinders ballistic transport.24 Recently, an anomalous temperature-dependence of electroluminescence intensity in GaN-based LEDs was reported.27–30 It was found that when temperature is decreased to around 200 K, the EL intensity rises, as expected from the improved quantum efficiency However with a further decrease in temperature, the EL intensity falls dramatically That phenomenon was explained by reduced carrier capture by QWs at low temperature,27–29 or by the low ionization rate of magnesium (Mg) in p-GaN at low temperature.30 In our simulation, Fig reveals that the electron non-capture is much stronger at low temperature due to the weaker electron-LO-phonon scattering, which leads to the weak EL intensity below 200k, but it does not grow worse with a further fall in temperature, indicating that the weak EL intensity is nearly temperature-independent over the low temperature range (below 200 K) The measured EL intensity however further decreases at lower temperatures Given these considerations, the Mg freeze-out in p-GaN at low temperature must also be considered for this intensity decrease Therefore, both proposed mechanisms are responsible for the anomalous temperature-dependence of electroluminescence intensity at low temperature CONCLUSIONS In this work, an analytic model of ballistic and quasi-ballistic transport for InGaN/GaN MQW LEDs is proposed The dependence of electron overflow on the polarization field, Al mole fraction in the EBL, and temperature were investigated, providing new design rules for InGaN/GaN LEDs Several lingering issues however, including the relationship between the potential drop in the last barrier and the Al mole fraction in the EBL, and he influence of electron velocity saturation in MQWs on ballistic transport, should be further investigated ACKNOWLEDGEMENTS This work was supported by the National High Technology Program of China (Grant No.2013A A03A101) and the National Natural Science Foundation of China (Grant No.61306051 and No.61306050) 045219-9 Huang et al AIP Advances 6, 045219 (2016) J Cho, E F Schubert, and J K Kim, Laser & Photonics Reviews 7(3), 408–421 (2013) J Piprek, physica status solidi (a) 207(10), 2217–2225 (2010) X A Cao and S D Arthur, Applied Physics Letters 85(18), 3971 (2004) S F Chichibu, A Uedono, T Onuma, B A 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(2016) Overshoot effects of electron on efficiency droop in InGaN/ GaN MQW light- emitting diodes Yang Huang,1,2,3 Zhiqiang Liu,1,2,3,a Xiaoyan Yi,1,2,3,a Yao Guo,1,2,3 Shaoteng Wu,1,2,3 Guodong Yuan,1,2,3... INTRODUCTION The origin of efficiency droop in InGaN/ GaN light emitting diodes (LEDs) remains a topic of active debate.1,2 Although many theories have attempted to explain these experimental observations,... period MQW structures of InGaN/ GaN LEDs We build on the preliminary work of Ni et al.,11,12 additionally considering the potential drop in the active region, the In mole fraction of the quantum well,