Photoluminescence enhancement from GaN by beryllium doping

Optical Materials 60 (2016) 398e403

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Photoluminescence enhancement from GaN by beryllium doping rrez a, A. Ramos-Carrazco a, *, D. Berman-Mendoza a, G.A. Hirata b, R. García-Gutie O.E. Contreras b, M. Barboza-Flores a a b

n en Física de la Universidad de Sonora, Hermosillo, Sonora, 83190, Mexico Departamento de Investigacio noma de M Centro de Nanociencias y Nanotecnología, Universidad Nacional Auto exico, Apdo. Postal 2681, C. P. 22800, Ensenada, Baja California, Mexico

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 April 2016 Received in revised form 5 August 2016 Accepted 22 August 2016

High quality Be-doped (Be ¼ 0.19 at.%) GaN powder has been grown by reacting high purity Ga diluted alloys (Be-Ga) with ultra high purity ammonia in a horizontal quartz tube reactor at 1200  C. An initial low-temperature treatment to dissolve ammonia into the Ga melt produced GaN powders with 100% reaction efficiency. Doping was achieved by dissolving beryllium into the gallium metal. The powders synthesized by this method regularly consist of two particle size distributions: large hollow columns with lengths between 5 and 10 mm and small platelets in a range of diameters among 1 and 3 mm. The GaN:Be powders present a high quality polycrystalline profile with preferential growth on the [1011] plane, observed by means of X-ray diffraction. The three characteristics growth planes of the GaN crystalline phase were found by using high resolution TEM microscopy. The optical enhancing of the emission in the GaN powder is attributed to defects created with the beryllium doping. The room temperature photoluminescence emission spectra of GaN:Be powders, revealed the presence of beryllium on a shoulder peak at 3.39 eV and an unusual Y6 emission at 3.32eV related to surface donoracceptor pairs. Also, a donor-acceptor-pair transition at 3.17 eV and a phonon replica transition at 3.1 eV were observed at low temperature (10 K). The well-known yellow luminescence band coming from defects was observed in both spectra at room and low temperature. Cathodoluminescence emission from GaN:Be powders presents two main peaks associated with an ultraviolet band emission and the yellow emission known from defects. To study the trapping levels related with the defects formed in the GaN:Be, thermoluminescence glow curves were obtained using UV and b radiation in the range of 50 and 150  C. © 2016 Elsevier B.V. All rights reserved.

Keywords: Nitrides Phosphors Semiconducting III-V materials

1. Introduction Gallium nitride (GaN) and its alloys have attracted much attention especially for the study of growth, and related structural, electronic and optical properties [1e4]. In the wurtzite form, pure GaN possess a direct band gap (Eg) of 3.45 eV at room temperature, which corresponds to ultraviolet radiation (~360 nm). The semiconductor GaN has been largely used in the areas of optoelectronics, microelectronics and power electronics [5e7]. For optical applications, GaN has been doped with Mg, Eu, Zn, Er and Be [8e12] to improve the luminescence and efficiency trough the incorporation of suitable impurities on the GaN lattice. The gallium nitride doped with beryllium shows potential to obtain a shallow acceptor level for p-type GaN, exhibiting lower

* Corresponding author. Tel.: þ52 6622592156; fax: þ52 6622126649. E-mail address: [email protected] (A. Ramos-Carrazco). http://dx.doi.org/10.1016/j.optmat.2016.08.017 0925-3467/© 2016 Elsevier B.V. All rights reserved.

ionization energy and higher solubility in comparison with the Mg impurity [13]. Therefore, the impurities of beryllium on GaN have produced a shallower acceptor level due to their electronegativity and absence of electrons in d-shell. However, a self-compensation process may occur on GaN:Be due to the occupation of Be atoms on interstitial sites which produce a donor level [14,15]. In last reports, this phenomenon has been related to the migration of the Be atoms on a interstitial site to gallium vacancy and the formation of (Be-Be)Ga donors [16]. Therefore investigation of the Be doping effects is surely justified in relation to the presence of defects that may affect the GaN performance as optoelectronic device. Thermoluminescence (TL) is a very sensitive technique to study defects in the form of shallow and deep trapping levels. It may also provide information about the trapping and recombination mechanisms involved in the radiative recombination of charge carriers with recombination defects centers [17]. In the present work two distinctive deep trapping levels were identified by TL after

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exposure of the GaN:Be samples to UV and b-ray source. Until now, most of the emphasis has been placed on the production of high quality epitaxial GaN doped Be layers by the methods of molecular beam epitaxy (MBE) and ion implantation [18,19]. Mostly reports, an emission line with an energy of 3.38 eV followed by two or more phonon replica has been observed in GaN:Be by means of photoluminescence, which are associated with the Be ions [20]. However, GaN polycrystalline and its alloys have demonstrated high potential in applications as phosphor components for solid-state lighting (SSL) and electroluminescent (EL) devices in the form of thin films and powder [21e24]. In particular, the GaN powder is a versatile material for optoelectronics applications due to their flexible form. In the present work, bulk production of high quality Be-doped gallium nitride (GaN:Be) powders have been achieved by means of direct nitriding with ammonia. As main purpose, a close study of the luminescence properties using photoluminescence, cathodoluminescence and thermoluminescence techniques is development for the GaN:Be semiconductor. An optical enhancing with efficiency that exceeds those previously reported in undoped and doped (Si-Mg) GaN powders and their alloys [25e28] is analyzed. To study the trapping levels formed by the beryllium-defects, the TL curves using UV and beta radiation with varied doses are compared. 2. Experimental Be-doped GaN powders were produced using a Ga-Be-NH3 diluted alloy (Be ¼ 0.19 at.%). Using ultra-high purity (UHP) precursors (Ga and Be 99.9995 wt% and ammonia 99.9995 wt%) and highly controlled parameters (temperature, pressure, gas-flow and time) high quality GaN:Be polycrystalline powders were produced in two stages. First, an initial heat treatment for the Ga-Be alloy is realized to form Ga-Be-NH3 diluted alloy. According to the binary alloy phase diagram, Be is soluble in Ga until 19 atomic percent and can form liquid solutions in all proportions at temperatures above 580  C [29]. To prepare Ga-Be alloy, desirable amounts of UHP Ga and Be in an aluminum oxide crucible were placed inside a stainless steel vessel that was fitted to a mechanical shaker (see Fig. 1A). The vessel was tightly closed and heated under vacuum (~103 Torr) from room temperature to 600  C. Then the vessel was filled with high purity ammonia and shaken for several hours (~5 h) in order to produce a highly homogeneous gas-liquid solution. The solution was then poured into an aluminum oxide boat and then placed inside of quartz tube reactor positioned horizontally (see Fig. 1B). The growth method using that horizontal reactor has been

399

previously described in Ref. [24]. For the second stage, the method of doping with beryllium on the gallium nitride is based on the following reaction: 2Ga-Be(l) þ 2NH3(g) / 2GaN:Be(s) þ 3H2(g)

(1)

The quartz tube reactor was evacuated at 103 Torr using a mechanical pump. Then, a flux of ultra high purity N2 was introduced into the quartz tube and the aluminum oxide boat was placed at the entrance of the reactor (<200  C). When the central part of the reactor reached 1200  C, in about 1 h, the vacuum system was closed and a flow of UHP ammonia (~350 sccm) was introduced through the reactor. Once the steady-state conditions were achieved (~30 min), the boat containing the solution was rapidly moved to the middle of the reactor (hot zone, 1200  C) using a magnetic manipulator. The complete reaction of the GaN:Be powders was achieved after 5 h. Subsequently, the aluminum oxide container with the product, a light gray powder (GaN:Be), was moved to the coldest part of the reactor (room temperature) using a magnetic manipulator. Then the ammonia flow was closed and N2 was flowed through the quartz tube. After the product was cooled, the boat was taken out of the reactor. Finally, the GaN:Be powder was ground in a mortar and stored in a vial for further analysis. The crystalline structure of GaN:Be powders was determinated by X-ray diffraction using a X'pert Philips powder diffractometer with CuKa radiation and 2theta scan from 20 to 90 . The morphology of the surface of GaN:Be powders was obtained by a JEOL 5300 electron scanning microscope. High resolution image of the beryllium doped gallium nitride powder was recorded trough a JEOL JEM-2010F transmission electron microscope. The PL measurements were performed by means of a 74 Series Omnichrome He-Cd laser as excitation source, slit width of 100 mm and 1 order of magnitude filter. The PL characterization of the GaN samples was performed at room temperature and low-temperature. The CL spectra were obtained in a JEOL 6300 SEM, operated at an acceleration voltage of 5 kV and a beam current of 300 pA at room temperature. The thermoluminescence curves were acquired in a Risø TL-OSL-DA-15 equipment with a 90Sr-90Y beta radiation source with a dose rate of 0.05 Gy-1. Also, TL curves were obtained using an UV excitation in the range of wavelengths from 200 to 400 nm, which is provided by a Xenon lamp. The TL characterization was performed from 30 to 400  C at a heating rate of 2  Cs1 and exposure doses from 100 to 800 Gy. The glow curves were detected by a photomultiplier tube (9235B ET enterprises) over a wavelength range between 290 nm and 630 nm.

Fig. 1. Schematic diagrams of the two heating systems of GaN:Be powders growth. A) Small reactor utilized to form the Ga-Be melt and B) Horizontal furnace used to synthesize the GaN:Be powder.

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400

XRD Intensity (arb .u.)

(1011)

the quality crystalline (FWHM ¼ 0.17 ) of these powders, is similar to that reported on GaN:Er applied in thin films technology [11].

GaN:Be

3.2. Electron microscopy (1010)

(0002)

(2020) (1012)

(1120)

(2022) (1013) (1122) (2021) (0004)

30

40

50

60

70

80

2 Theta (°) Fig. 2. X-ray diffractogram pattern of wurzite crystalline structure obtained from the GaN:Be powder.

3. Results and discussion 3.1. Structure Fig. 2 shows XRD diffractograms of beryllium doped GaN powders, obtained by direct nitridation with ammonia. The XRD peaks have been indexed using the PDF card # 76e0703 concluding that the resulting GaN:Be powders presents a wurtzite hexagonal structure. There are not others crystalline phases present such as oxides, pure metals or other nitrides, which also demonstrates the high quality control from this method to synthesize doped GaN crystallites. The crystallographic planes (101 0), (0002) and (101 1) were marked as main XRD peaks of the corresponding GaN phase with interplanar distances of 2.7 Å, 2.5 Å and 2.4 Å. In addition, other secondary planes of the GaN with a lower intensity were also indexed. By means of the Scherrer equation (t ¼ 0.9l/bcosq) [30] the crystallite size of GaN:Be powders was calculated using the full width at half maximum (FWHM) of the highest intensity obtained on the plane (101 1). As a result, an average crystallite size of 50 nm approximately was computed for the doped GaN. In comparison with others dopants reported on gallium nitride,

SEM images of GaN powders synthesized in this work are shown in Fig. 3(A). The morphologies of doped gallium nitride crystallites are irregular polyhedra presenting mainly hollow columns with lengths of 5e10 mm and platelets with a diameter size distribution between 1 and 4 mm, as shown in Fig. 3(B) and (C), respectively. Other smaller structures with different formations such as semispheres and plates are also present with a lower distribution on the GaN:Be powder. It should be mentioned that all structures are the combination of the smaller crystallites obtained in the nitride powder. The powder sample was prepared for transmission electron microscopy (TEM) by sonication in isooctane alcohol. Fig. 4-(A) shows a high resolution TEM image of GaN powders doped with beryllium. The diffraction patterns show a typical hexagonal shape consisting of three crystal orientations corresponding to the crystallographic planes (101 0), (0002) and (101 1), as presented in Fig. 4-(B). Using the software Digital Micrograph, the interplanar distances of 2.68 Å, 2.58 Å and 2.38 Å corresponding to the previously discussed planes were computed.

3.3. Raman scattering From Fig. 5, the Raman spectrum showing the peaks at about 143, 533, 567 and 738 cm1 corresponding to the EL2, A1 (TO), EH2 and E1 (LO) modes of GaN with a wurtzite structure were obtained for the GaN:Be powder [31]. The EH2 phonon peak is obtained when the incident beam laser is perpendicular to the c-plane of the GaN crystalline structure. In comparison with the doped GaN:Mg, the presence of atomic oscillation creates a local vibrational mode (LVM) has been previously reported. The LVM is associated with the atomic weight of the element, which is higher than the impurity. However, even with the fact that Be lighter than Mg atom, the GaN:Be powders only shows the typical Raman frequencies for pure GaN [32], which also is consistent with the not presence of pure metals and oxides in the Raman spectrum.

Fig. 3. SEM images of beryllium doped gallium nitride powders grown by direct nitriding. A) Plane view of the GaN powder, B) Hollow GaN:Be columns and C) GaN:Be platelets.

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PL Intensity (arb. u.)

9.0x10

401

5

Y6

GaN GaN:Be

373 nm 3.32 eV

6.0x10

5

3.0x10

5

Be 3.39 eV

YL band

Y4

370 nm 3.35 eV

0.0 350

400

450

500

550

Wavelength (nm) Fig. 6. Photoluminescence spectra of GaN:Be powders (Y6 line and Be-related emission) and undoped GaN (Y4 line) powders at room temperature.

3.4. Photoluminescence 3.4.1. Room temperature Fig. 6 exhibits room-temperature PL spectra of undoped GaN powders with an emission peak around 370 nm (3.35 eV). This kind of high-energy transition, known as Y4 line is unusually found in undoped GaN, which is related to an exciton bounded to structural defects at the surface. The calculated FWHM of the Y4 peak is around 126 meV and is associated to the interactions between the excitation source and the crystalline lattice impurities [33]. Also, room-temperature PL spectrum of Be-doped GaN powders showing an ultraviolet (UV) emission around 373 nm (3.32eV) is presented in Fig. 6. In comparison with the undoped GaN sample, the main peak on the GaN:Be spectrum is related with the Y6 line that corresponds to surface donor-acceptor-pair (DAP). The Y6 line has been reported for the undoped GaN and its origin has been associated with the shallow donor and acceptor located on the sample surface [34]. Also, the luminescence band related with the BeGa acceptor is present at 3.39 eV on the left side of the Y6 peak [35]. It is important to mention that the luminescence intensity of these doped GaN powders was one order of magnitude higher than the brightest emission of our undoped GaN previously reported

Intensity (arb. u.)

4x10

3x10

2x10

4

E

GaN:Be

H 2

4

4

E1 (TO) 1x10

4

A1 (TO) E

E1 (LO)

L

400

600

-1

800

1.6x10

6

1.2x10

6

Room Temp. He Temp. (10K)

1000

Raman shift (cm ) Fig. 5. Raman spectra of the GaN:Be powder at room temperature.

DAP 3.17 eV Y6

8.0x10

Be

LO phonon 3.1 eV

365 nm 3.39 eV

358 nm 3.46 eV

5

Y2 362 nm 3.42 eV

Y1 350

4.0x10

355

360

365

370

Wavelength (nm)

5

0.0 350

2

200

3.4.2. Low temperature From Fig. 7, it can be observed the photoluminescence emission spectrum of GaN:Be powders at room and low temperature (10 K). As discussed before, the Y6 emission located at 3.32 eV and the transition due to Be doping at 3.39 eV were obtained at room temperature. However, as the temperature decreases the PL spectra shows two different transitions with energies of 3.17 eV and 3.10 eV related with donor acceptor pair and longitudinal optical (LO) phonon replica, respectively [25]. From the inset in Fig. 7, the shoulder of beryllium at the left side of the Y6 emission disappears as the temperature decreases while two Yi emissions (Y1 and Y2) with a weaker intensity were observed [37,38]. Also, the emission from defects known as yellow luminescence band (YL) was observed in both spectra. From PL results, a temperature dependence of the emission in the GaN:Be powder is observed. Since the beryllium produces an energetic level at 3.39 eV, near to the conduction band of the GaN, the decrease of the thermal energy affects the promotion of free electrons to this high energy transition. In comparison with our previous reports related to GaN powders, the defects created by beryllium doping suppress a peak emission at 3.47 eV which is related with a donor bound exciton in the undoped GaN powder [25].

PL Intensity (arb. u.)

Fig. 4. High resolution TEM image of a GaN:Be crystallite. A) Three interplanar distances identified from the TEM image and B) Characteristic crystallographic planes obtained on GaN:Be powder.

[25]. Additionally, the emission from defects known as yellow luminescence band (YL) was observed in the GaN:Be spectrum with a peak centered at 530 nm approximately (2.34 eV) [36].

YL band 400

450

500

550

600

650

700

Wavelength (nm) Fig. 7. Photoluminescence spectra of the GaN:Be powder at room temperature and low-temperature (10 K).

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402

3.5. Cathodoluminescence

3.6. Thermoluminescence 3.6.1. TL stimulated with UV radiation TL glow curves were determined for Beryllium doped GaN powders by plotting the integrated TL intensity as function of the UV excitation wavelength (200 nme400 nm). From Fig. 9-(A), two main TL glow curves are depicted in the range of 30e150  C and 300e400  C. However, the main peak recorded in this glow curve is centered at 100  C which can be associated with shallow trapping levels produced in the GaN:Be powders. In comparison, the peak located after the 350  C indicates the formation of deep trapping levels in this sample. Also, the increase of the wavelength radiation affects directly the TL intensity of GaN:Be powders. This effect may be explained by recalling that the glow curves were performed using a Xenon lamp with a monochromator which select the wavelength with a limited optical power density. In all cases, a small shift position on the main peak towards lower temperatures as function of the TL intensity is observed which has been attributed to the activation of the trapping levels due to the increment of the optical power density at 400 nm. For the undoped GaN powder, the thermoluminescence measurements exposed under the same UV irradiation conditions presents negligible response.

CL Intensity (arb. u.)

3x10

4

CL emission from GaN:Be powders UVL

UVL

Y6

2x10

4

1x10

4

Y6

Be 350

360

370

380

390

Wavelenght (nm)

YL

0

400

500

600

700

Wavelenght (nm) Fig. 8. Cathodoluminescence spectrum of the GaN:Be powder showing three main emissions at room temperature.

2

4.0x10

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2

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200 nm 250 nm 300 nm 350 nm 400 nm

100

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Temperature (°C) 1.2x10

3

(B)

TL Intensity (arb. u.)

Fig. 8 presents the CL spectrum of the gallium nitride powder doped with beryllium measured at room temperature. Two well defined transitions of high energy and a yellow luminescence band of low intensity were obtained on the GaN:Be powder. From the inset, it can be observed that the Be peak is located at the left side of the Y6 emission, close to 3.39 eV. However, an ultraviolet (UVL) emission at 3.26 eV [39] domains the luminescence of GaN:Be powders obtained by means of the CL technique. In contrast with other reported GaN powders [40], the doped gallium nitride from this work does not require an annealing treatment to produce an UV luminescence. Also, the UVL transition is comparable with the band-edge emission reported for GaN:Eu using a similar doping method [41]. In our previous reports regarding of doped GaN:Mg, the emission at 3.26 eV was also obtained with a magnitude 50% lower than the UVL on the GaN:Be [25]. It is clear that the emission spectra of the GaN:Be powder presents a dependence in their optical response with respect to the excitation source such as a photon beam for PL and an electron beam for CL spectra. The stimulation of the UVL emission suggests a shallow acceptor level related with the defects formed by beryllium doping, which was only excited using a high energy beam.

TL Intensity (arb. u.)

(A) 6.0x10

8.0x10

2

4.0x10

2

50

100 Gy 200 Gy 400 Gy 800 Gy

100

150

200

250

300

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Temperature (°C) Fig. 9. Thermoluminescence glow curve of GaN:Be powders: A) exposed to ultraviolet radiation at different wavelengths and B) exposed to beta radiation at different doses.

3.6.2. TL stimulated with b radiation In Fig. 9-(B) the TL glow curve obtained from the stimulation under b radiation for GaN: Be powder is shown. In comparison with the TL spectra obtained with UV excitation, these emissions are in the range of 50e200  C with a maximum at 90  C approximately. Also, the TL intensity increase is congruent in comparison to the increments in radiation dose. Furthermore, the spectra obtained when samples are stimulated with b in GaN:Be are considerably higher than the measured with UV radiation. In comparison with the TL glow curve with UV excitation, a shift position on the principal peaks from 90  C to 100  C as function of the dose was obtained. From TL results, a similar behavior of the glow curve using UV light and b irradiation was found. Since b-rays are highly energetic compared to UV photons, the TL glow curve of the GaN:Be sample presents an intensity enhancement as the radiation dose increases in the shallow trapping levels. It is important to recall that the YL emission can be directly associated with the glow curves since the detection was performed over a wavelength range between 290 nm and 630 nm. However, this emission is independent of the incorporation of the Be atoms since the YL band is related not to a specific impurity but to some native defect [34]. In comparison with the optically stimulated thermoluminescence, the different behavior as a function of wavelength for the two TL transitions is due to the material response to the excitation of the xenon lamp. The depth of penetration of light in this measurement approximates the tens of nanometers which would produce a superficial characterization of the material. Therefore, the density of defects on the surface of the GaN:Be powders rules the optical activation at high temperatures while low temperatures not contribute significantly. In the other hand, beta radiation

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produces a TL response with a greater depth of penetration into the nitride making different signal curves. In this case the defects created in the nitride present a different distribution compared with the surface. However, establishing the accurate type of defects produced in the powders may involve a more detailed work using computer glow curve deconvolution (CGCD) and fitting processes that are far from the scope and objectives of the present work. 4. Conclusions Bulk production of high quality, beryllium doped gallium nitride powders have been successfully achieved by using a direct nitriding technique. The GaN:Be powder consists of highly crystalline large hollow columns and platelets with a wurtzite like structure. The different optical responses of the doped GaN powder were characterized using photoluminescence, cathodoluminescence and thermoluminescence spectroscopies. A high luminescence band at around 373 nm (Y6 line emission) with an efficiency that exceeds those previously seen in undoped GaN powders was obtained at room temperature by optical excitation. An emission at 3.39 eV associated with beryllium incorporation is obtained by doping GaN. A dependence of temperature decreasing (10 K) on the PL spectrum was observed. In particular, the absence of the Y6 line and the Be related emission and the appearance of two emissions at 3.17 eV and 3.1 eV. A dominant ultraviolet emission at 3.26 eV on the GaN:Be powder was obtained by means of CL. The results of CL present a barely visible yellow band emission, however, the YL band shows higher sensitivity when is optically stimulated. The results of thermoluminescence measurements under UV and beta irradiation display a main peak centered at 100  C which proves radiation resistance without losing their optical properties. Therefore, there results suggest that this material is a good candidate to replace ZnS in electroluminescent devices. Acknowledgements The authors gratefully acknowledge the facilities provided by Universidad de Sonora (UNISON) and Centro de Nanociencias y Nanotecnología (CNyN-UNAM). This Research has been partially supported by CONACYT (project 102671). References [1] J. Park, J.S. Ha, S.K. Hong, S.W. Lee, M.W. Cho, T. Yao, H.W. Lee, S.H. Lee, S.K. Lee, H.J. Lee, Heteroepitaxial growth of GaN on various powder compounds (AlN, LaN, TiN, NbN, ZrN, ZrB2, VN, BeO) by hydride vapor phase epitaxy, Electron. Mater. Lett. 8 (2012) 135e139. [2] X. Zeng, B. Han, X. Wang, J. Shi, Y. Xu, J. Zhang, J. Wang, J. Zhang, K. Xu, Comparison of morphology, structure, and optical properties of GaN powders prepared by Ga2O3 nitridation and gallium nitridation, J. Cryst. Growth 367 (2013) 48e52. [3] B. Monemar, Bound excitons in GaN, J. Phys. Condens. Matter 13 (2001) 7011e7026. [4] H. Fang, L.W. Sang, L.B. Zhao, S.L. Qi, Y.Z. Zhang, X.L. Yang, Z.J. Yang, G.Y. Zhang, Luminescent properties in the strain adjusted phosphor-free GaN based white light-emitting diode, App. Phys. Lett. 93 (2008) 261117. [5] F.A. Ponce, D.P. Bour, Nitride-based semiconductors for blue and green lightemitting devices, Nature 386 (1997) 351e359. [6] P. Ramesh, S. Krishnamoorthy, S. Rajan, G.N. Washington, Fabrication and characterization of a piezoelectric gallium nitride switch for optical MEMS applications, Smart Mater. Struct. 21 (2012) 094003. [7] Y. Jiang, Q.P. Wang, K. Tamai, T. Miyashita, S. Motoyama, D.J. Wang, J.P. Ao, Y. Ohno, GaN MOSFET with Boron Trichloride-based dry recess process, J. Phys. Conf. Ser. 441 (2013) 012025. [8] L. Cheul-Ro, S. Kyeong-Won, Y. Jeong-Mo, C. Dae-Kyu, A. Haeng-Keun, The effect of p-GaN: Mg layers on the turn-on voltage of p-n junction LED, J. Cryst. Growth 222 (2001) 459e464.

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