Auger Recombination in III-Nitride Nanowires and Its Effect on

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Auger Recombination in III-Nitride Nanowires and Its Effect on Nanowire Light-Emitting Diode Characteristics Wei Guo, Meng Zhang, Pallab Bhattacharya,* and Junseok Heo Center for Nanoscale Photonics and Spintronics, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109-2122, United States ABSTRACT: We have measured the Auger recombination coefficients in defect-free InGaN nanowires (NW) and InGaN/GaN dot-in-nanowire (DNW) samples grown on (001) silicon by plasma-assisted molecular beam epitaxy. The nanowires have a density of ∼1
1011 cm-2 and exhibit photoluminescence emission peak at λ ∼ 500 nm. The Auger coefficients as a function of excitation power have been derived from excitation dependent and time-resolved photoluminescence measurements over a wide range of optical excitation power density. The values of C0, defined as the Auger coefficient at low excitation, are 6.1
10-32 and 4.1
10-33 cm6 3 s-1 in the NW and DNW samples, respectively, which are in reasonably good agreement with theoretical predictions for InGaN alloy semiconductors. Light-emitting diodes made with the NW and DNW samples exhibit no efficiency droop up to an injection current density of 400 A/cm2. KEYWORDS: Nitride semiconductor, nanowires, auger recombination, efficiency droop

A

uger recombination in semiconductors is a three-carrier nonradiative recombination process in which the excess energy released by the recombination of an electron-hole pair is transferred by Columbic collisions as kinetic energy of a third free carrier, which is raised in energy deep into the respective band.1 This carrier finally thermalizes back to the band edge, usually by a multiphonon emission process. The probability of the Auger process, given by the Auger coefficient C, decreases with the increase of bandgap of the semiconductor according to (kBT/Eg)3/2 exp (-MEg/kBT) where M is a factor dependent on the carrier effective masses.1 The Auger coefficient should therefore have very low values in wide bandgap semiconductors. In GaN (Eg = 3.42 eV) the expected value of C is ∼10-34 cm6 3 s-1.2-4 In the ternary alloy InGaN emitting in the green wavelength (Eg = 2.2 eV), the expected value of C is ∼10-33-10-32 cm6 3 s-1.2,4 However, measurement of the Auger coefficient in GaN and InGaN by a variety of techniques has yielded values of C in the range of 0.35-2.0
10-30 cm6 3 s-1, which are 2-3 orders of magnitude higher.5-8 Delaney et al9 have identified an interband Auger process having C = 2
10-30 cm6s-1 in InGaN with Eg = 2.5 eV. However, the interband process should be very sensitive to changing bandgap of the material, which is not borne out by data from light-emitting diodes (LEDs). GaN-based LEDs are being developed for application in solid state lighting. To operate at high brightness levels, the LEDs have to be biased with high injection current densities. However, an efficiency rollover, or “droop”, is observed in the devices at elevated injection levels. In fact, in devices with InGaN/GaN multiquantum well (MQW) active region emitting green light (∼500 nm), the onset of droop is observed at current densities as low as 10-20 A/ cm2.10 Several effects have been cited to be responsible for the droop phenomenon, which is persistent in varying degrees in LEDs emitting in the wavelength range of 400-520 nm. Among these, the most prominent ones are Auger recombination, carrier leakage, and defect-related nonradiative recombination. The problem with r 2011 American Chemical Society

ascertaining the most likely cause of droop is the uncertainty in the value of the Auger coefficient C, as outlined above. It is important to note here that calculations of Auger processes are usually done with the assumption of defect-free bulk material with no extraneous effects present. On the other hand, measurement of the Auger coefficient and fabrication of LEDs are done with materials, albeit of the same alloy composition, but with a defect (dislocation) density of 107-1010 cm-2.5-8 It is quite plausible that a “defect-assisted” Auger recombination process with a much higher value of C is experimentally characterized and is operational in the devices. It is therefore important to measure the Auger coefficient in defect-free material. In(Ga)N nanowires can be grown catalyst-free on silicon substrates with density in the range of 108-1011 cm-2 and lengths in the range of a few micrometers depending on the growth time.11-22 The nanowires grow vertically in the wurtzite crystalline form and the In composition of the nanowire can be varied to produce emission in the range of 366-700 nm. Most importantly, extensive structural characterization by several groups,11,13,14,16-18,21,22 including ours,20 indicates that the nanowires are free of extended defects such as dislocations, stacking faults, and twins. It has also been reported that the measured surface recombination velocity in GaN nanowires is very small and ∼103 cm/s.23 We have performed deep level transient spectroscopy (DLTS) measurements on Schottky diodes fabricated on the ensemble of nanowires. Only one dominant electron trap with an activation energy ET = 0.41 eV and a small density 4.8
1012 cm-3 is identified in InGaN nanowires. This deep level has also been identified in bulk InGaN24 and may be related to In segregation (clusters). Dislocation-related deep levels observed in bulk materials24 are found to be absent in the nanowires. Temperature dependent luminescence of the nanowires does not exhibit any blue shift, usually Received: October 18, 2010 Revised: February 1, 2011 Published: March 02, 2011 1434

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Figure 2. Room temperature current-voltage characteristics of InGaN/GaN dot-in-nanowire (DNW) LEDs. The fabricated device is schematically shown in the inset.

Figure 1. (a) Cross sectional SEM and (b) HRTEM images of InGaN nanowires grown on (001) Si. Inset shows the selective area diffraction pattern; (c) HRTEM image of InGaN/GaN DNW sample with 2 nm InGaN dots separated by 20 nm GaN spacers; (d) a TEM image of the interface between GaN and Si substrate where an amorphous layer of SiNx is observed.

attributed to trapping of carriers in localized defects.25 These nanowire samples can therefore provide an excellent platform for the measurement of Auger recombination and the characterization of LEDs made with materials of high optical quality. The large surfaceto-volume ratio of the nanowires not only helps in terminating propagating dislocations, but it also enhances the light extraction efficiency. In the present study, we have investigated Auger recombination in InGaN nanowire (NW) and InGaN/GaN dot-in-nanowire (DNW) samples that emit green light (λ = 500 nm) by excitation power dependent photoluminescence (PL) and excitation power dependent time-resolved PL (TRPL) measurements. Values of C in the range of 10-32-10-34 cm6 3 s-1 depending on excitation, nearly 2 orders of magnitude smaller than those measured and reported earlier, are derived from these measurements. Furthermore, we have characterized LEDs made with the InGaN/GaN NW and DNW samples. No efficiency droop is recorded up to an injection current of 400 A/cm2. These results suggest that the elimination of droop in the nanowire LEDs is related directly to a reduction in defect density (dislocation, clusters, thickness fluctuations in quantum wells), or to a reduction in defect-assisted Auger recombination. The nanowire samples were grown on n-type (001) silicon substrates in a Veeco plasma-assisted molecular beam epitaxy (MBE) system. A detailed description of the growth conditions has been provided by us in an earlier publication.20 To grow InGaN nanowires, 150 nm of GaN nanowire is first grown on the seed Ga droplets before turning on the In flux. The length, diameter, and density of the nanowires are 600 nm, 20-50 nm, and 1-2
1011 cm-2, respectively. Figure 1a,b shows scanning electron microscope (SEM) and high-resolution transmission electron microscope (HR-TEM) images, respectively, of InGaN nanowires. The TEM images, in particular, demonstrate material with low density of treading dislocations, stacking faults, and twins and the c-axis coincident with the direction of growth. Figure 1c shows the HR-TEM image of a DNW sample with multiple InGaN dots (or discs) in a GaN nanowire. The 2 nm

InGaN dots are separated by 20 nm GaN spacers. Figure 1d shows a TEM image of the interface between GaN and Si substrate where an amorphous layer of SiNx is observed. This is probably a consequence of the nitridation during the substratecleaning step before epitaxy.26,27 It may be noticed that no propagating dislocations are observed at the root of the nanowires. Temperature-dependent photoluminescence measurements on both types of samples (NW and DNW) show a slight red shift of the peak emission with increasing temperature in accordance with the Varshni equation.28 No blue shift, usually attributed to carrier localization from defects,29-31 is observed. The LED sample consists of 300 nm Si doped n-type GaN nanowire, followed by an undoped 300 nm InGaN or InGaN/ GaN DNW section with eight dot layers and finally a 150 nm Mgdoped p-type GaN nanowire. The growth temperature for GaN and InGaN are 800 and 550 °C, respectively. The growth rate is ∼300 nm/h. LED fabrication consists of an initial planarization with parylene (an insulator) followed by deposition of 5 nm/ 5 nm Ni/Au and 250 nm indium tin oxide (ITO) as the top p-type ohmic contact. An Al film on the Si substrate forms the n-type ohmic contact. Mesa-etched devices, shown schematically in the inset of Figure 2, have a diameter of 900 μm. The diode IV characteristics exhibit a forward threshold voltage of 5 V and leakage current of 10 μA. Typical current-voltage characteristics of a dot-in-nanowire LED are shown in Figure 2. Auger recombination in the nanowires was characterized by the photoluminescence technique,5 wherein a combination of excitation dependent and time-resolved PL measurements are employed to extract the value of the Auger coefficient, C. Specifically, the measurements were made on an In0.25Ga0.75N NW sample emitting at 500 nm and a DNW sample emitting at 480 nm. The former consists of 200 nm long In0.25Ga0.75N nanowires; the latter consists of 10 periods of 2 nm In0.25Ga0.75N QDs separated by 20 nm GaN spacers. The density of nanowires in both samples is ∼1
1011 cm-2. Although the In mole fraction is the same in the bulk InGaN nanowire and in the InGaN QDs of the DNW sample, the emission wavelength is blue shifted by ∼20 nm due to quantum confinement along the length. Measurements were made with a frequency-doubled modelocked Ti:Sapphire laser (pulse width 130 fs; repetition rate 80 MHz). The photon energy was adjusted to 3.1 eV. The incident beam was focused to a spot of area 1 μm2 with a 27
microscope objective. The PL was analyzed with a Acton spectrometer (resolution 0.05 nm). For the excitation dependent TRPL measurements, the transient light signal was measured by a time-correlated 1435

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Figure 3. Measured room temperature excitation dependent photoluminescence spectra (a) and excitation dependent time-resolved photoluminescence spectra (b) of InGaN NWs. The incident power density (pinc) was varied from 0.1 to 6.0 MW/cm2.

photon counting system equipped with a Hamamatsu high-speed photomultiplier tube. Excitation dependent photoluminescence spectra for the InGaN NW sample are shown in Figure 3a. The emission peak is at 500 nm and the line width (fwhm) is ∼41.4 nm. A significant feature in the data is that the emission peak wavelength remains invariant with excitation power, an observation identical to that for LEDs fabricated with similar nanowires.20 This experimental observation confirms that the strain-induced piezoelectric field and the resulting quantum confined Stark effect are negligible in the nanowires.32,33 Similarly, band-filling effects due to compositional inhomogeneity and alloy disorder, which can cause a red shift with increasing excitation power,34 are also absent. Similar observations were made from the excitation dependent PL data of the DNW sample, not shown here. Therefore, it seems that the strain is negligible in the dots. Excitation dependent timeresolved PL data for the DNW sample are shown in Figure 3b. Again, similar data for the InGaN NW sample are not shown for the sake of brevity. The measured external quantum efficiency (EQE), as a function of carrier density, obtained from the excitation dependent PL data, are shown in Figure 4a,b for the InGaN NW and the InGaN/GaN DNW samples, respectively. The carrier density in these plots are derived from the incident power density as described later. A feature that is immediately observed in both is that the efficiency droop is almost absent. The EQE (ηext) is given by the relation ηext ¼

Bn2 η An - Bn2 þ Cn2

ð1Þ

where A and B are, respectively, the Shockley-Read-Hall (SRH) coefficient and the radiative recombination coefficient. η is the extraction efficiency and is used here as a scaling factor to relate the measured EQE to the internal quantum efficiency (IQE), ηint, to be calculated. The coefficient B is related to ηint via the steady-state relation, ηint = Bn2/G, where G is the carrier

Figure 4. Quantum efficiency as a function of excitation in (a) InGaN NW and (b) InGaN/GaN DNW samples. The data points represent the measured external quantum efficiency and the solid curves represent the calculated internal quantum efficiency using the A-B-C model (see text). The insets show the calculated relation between n and current density J (see text).

generation rate. The carrier density n can be derived from the measured TRPL data in the high excitation regime, where Rγµ n due to phase space filling,35 using the relation: n = G(t1 - t2)/ [1 - L(t1)/L(t2)] where L(t) is the spectrally integrated photoluminescence intensity at time t, and t1 and t2 are two times in the initial decay of the time-resolved PL signal. The generation rate G is related to the incident power Pinc, the absorption coefficient R, and the photon energy by G = Pinc(1 - R)R/A hν where A is the incident excitation area and R is the surface reflectivity of the sample. To measure the absorption coefficient of the nanowire samples, the InGaN nanowires were embedded in a polydimethylsiloxane (PDMS) matrix and the silicon substrate was removed by dry etching. Transmission measurements as a function of wavelength were then made on this sample and a control sample consisting of the PDMS matrix only. A value of R = 0.78
105 cm-1 is derived for λ = 500 nm. The value of R is calculated to be ∼0.04 by Fresnel’s law in which the effective refractive index of the nanowire-air composite nInGaN effective = 1.5 is calculated by the Maxwell-Garnett equation36 with a nanowire fill factor of 40%. Thus knowing the values of G, n, and ηint (equal to ηext/η) for each excitation power density, the values of B are calculated using B = ηintG/n2 and then fitted with B = B0/ (1 þ n/n*)35 where B0 and n* are the fitting parameters. The values of A and C are then iteratively obtained by fitting ηint as a function of excitation power density with the measured PL and TRPL data. It has been theoretically shown37 that at high excitation, the Auger recombination rate RAuger attains a subcubic carrier density dependence C = C0/(1 þ n/n*), where C0 is the Auger coefficients at low injection. The fits to the measured EQE data with eq 1 are shown with the solid lines in Figure 4a,b. The insets to Figure 4a,b show the calculated relation between n and current density J (= qd(An þ Bn2 þ Cn3), where d is the thickness of the active region). The calculated values of the Auger 1436

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Figure 5. Auger recombination coefficient in (a) nanowire, and (b) dotin-nanowire samples from photoluminescence data plotted as a function of injection carrier density.

coefficients C in the high excitation regime, where Auger recombination dominates, are shown in Figure 5a,b for the NW and DNW samples, respectively. From a fit of the data of Figure 5 with the subcubic dependence on n we derive C0 = 6.1
10-32 and 4.1
10-33 cm6 3 s-1 for the NW and DNW samples, respectively. The corresponding values of n* are 1.23
1019 and 1.62
1019 cm-3, respectively. The lower value of C0 in the DNW sample seems to agree with the data of David and Grundmann,35,38 where a smaller Auger coefficient was measured in InGaN quantum wells compared to those in bulk InGaN. Similar observations have also been made with InGaAs/InP bulk and quantum well materials39 and suggest that the discrete states in a quantum confined system are responsible for a smaller rate of Auger transitions. It is important to note that for both types of nanowire samples, the value of C0 is more than an order of magnitude smaller than those measured in quantum wells and quantum dots40 emitting at ∼400-500 nm. The negligible droop observed in the quantum efficiency data of Figure 4 is believed to be a direct consequence of reduced Auger recombination. It is therefore apparent that in the nanowires, wherein the defect density is negligible (or much smaller than those in InGaN quantum well, quantum dots, or bulk material grown on foreign substrate), the measured Auger coefficient is much closer to the calculated values assuming an intraband Auger process. Electroluminescence spectra from the DNW LEDs measured under cw biasing conditions shown in the inset of Figure 6a are characterized by an emission peak at 520 nm. The spectra show multiple peaks, as in the case of PL data, which can be attributed to dots of varying indium compositions in the ensemble contained in the mesa-etched region. Light-current characteristics were measured under pulsed bias conditions (pulse width 1 ms, duty cycle 0.1%) to minimize Joule heating effects. The duty cycle was varied until two sets of data coincided, confirming that such effects are minimized. Measured characteristics are shown in Figure 6a. The corresponding EQE data are plotted in Figure 6b. It is evident that no efficiency droop occurs up to 400 A/cm2. Some important insights can be gained from the results obtained in this study. It is evident that the Auger recombination

Figure 6. (a) Measured light-current characteristics of NW and DNW light-emitting diodes at room temperature; inset shows a typical electroluminescence spectrum of a DNW LED. (b) Normalized external quantum efficiency as a function of injection current density derived from the data in (a).

coefficient is at least 2 orders of magnitude smaller in InGaN nanowires of high optical quality and having a low density of surface and volume defects. No efficiency droop is observed in LEDs made with the same nanowires up to high injection current densities. Carrier leakage from the active region is a factor that can cause efficiency droop in LEDs. Such leakage includes both fly over injected carriers that are not captured and hot carriers in the active region that are lost by thermionic emission. Carrier leakage is not present in the nanowire LEDs. The similarity in the nature of the results from the nanowire and dot-in-nanowire (where leakage is a possibility) LEDs suggests that leakage cannot be a significant factor contributing to efficiency droop. It is quite likely that the nature and density of bulk and surface defects, both structural and electronic, would be very different in the active region of the NW and DNW LEDs. Again, the similarity in the output characteristics of both devices suggests that such defects are probably not a dominant contributor to efficiency droop. Therefore, it seems that the most probable cause of efficiency droop observed in state-ofthe-art multiquantum well LEDs is a defect-assisted Auger recombination process, which is absent in the nanowire LEDs due to a smaller density of such defects. In conclusion, we have measured the Auger recombination coefficients in defect-free InGaN nanowires and InGaN/GaN dotin-nanowire samples, grown catalyst-free on (001) silicon, by performing excitation-dependent PL and TRPL measurements. The measured values of the coefficient C0 are ∼10-33 cm6 3 s-1, which are much smaller than the earlier measured values of ∼10-30 10-31 cm6 3 s-1 in InGaN/GaN quantum wells and bulk InGaN samples that have a defect density of 107-109 cm-2. We believe that a defect-assisted Auger recombination process operative in these materials account for the large value of C. Electroluminescence 1437

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Nano Letters measurements made on LEDs fabricated with InGaN nanowire and InGaN/GaN dot-in-nanowire samples show no evidence of efficiency droop up to current densities of 400 A/cm2.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] Phone: 734-763-6678. Fax: 734763-9324.

’ ACKNOWLEDGMENT The work was supported by KAUST under Grant N012509-00. ’ REFERENCES (1) (a) Bhattacharya, P. Semiconductor Optoelectronic Devices, 2nd ed; Prentice Hall: Englewood Cliffs, NJ, 1996. (b) Piprek, J. Optoelectronic devices: advanced simulation and analysis; Springer: New York, 2005. (2) Piprek, J. Semiconductor Optoelectronic Devices: Introduction to Physics and Simulation; Academic Press: San Diego, CA, 2003. (3) Hader, J.; Moloney, J. V.; Pasenow, B.; Koch, S. W.; Sabathil, M.; Linder, N.; Lutgen, S. Appl. Phys. Lett. 2008, 92, No. 261103. (4) Bertazzi, F.; Goano, M.; Bellotti, E. Appl. Phys. Lett. 2010, 97, No. 231118. (5) Shen, Y. C.; Mueller, G. O.; Watanabe, S.; Gardner, N. F.; Munkholm, A.; Krames, M. R. Appl. Phys. Lett. 2007, 91, No. 141101. (6) Zhang, M.; Bhattacharya, P.; Singh, J.; Hinckley, J. Appl. Phys. Lett. 2009, 95, No. 201108. (7) Meneghini, M.; Trivellin, N.; Meneghesso, G.; Zanoni, E. J. Appl. Phys. 2009, 106, No. 114508. (8) Laubsch, A.; Sabathil, M.; Baur, J.; Peter, M.; Hahn, B. IEEE Trans. Electron Devices 2010, 57, 79. (9) Delaney, K. T.; Rinke, P.; Van de Walle, C. G. Appl. Phys. Lett. 2009, 94, No. 191109. (10) Yang, Y.; Cao, X. A.; Yan, C. IEEE Trans. Electron Devices 2008, 55, 1771. (11) Bertness, K. A.; Roshko, A.; Sanford, N. A.; Barker, J. M.; Davydov, A. V. J. Cryst. Growth 2006, 287 (2), 522–527. (12) Cerutti, L.; Ristic, J.; Fernandez-Garrido, S.; Calleja, E.; Trampert, A.; Ploog, K. H.; Lazic, S.; Calleja, J. M. Appl. Phys. Lett. 2006, 88 (21), No. 213114. (13) Kishino, K.; Kikuchi, A.; Sekiguchi, H.; Ishizawa, S. Proc. SPIE 2007, 6473, 64730T–1. (14) Calleja, E.; Risti
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