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Energy Express

  • Editor: Christian Seassal
  • Vol. 20, Iss. S6 — Nov. 5, 2012
  • pp: A812–A821
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Quantitative and depth-resolved deep level defect distributions in InGaN/GaN light emitting diodes

A. Armstrong, T. A. Henry, D. D. Koleske, M. H. Crawford, and S. R. Lee  »View Author Affiliations


Optics Express, Vol. 20, Issue S6, pp. A812-A821 (2012)
http://dx.doi.org/10.1364/OE.20.00A812


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Abstract

Deep level defects in the multi-quantum well (MQW) region of InGaN/GaN light emitting diodes (LEDs) were investigated. InGaN quantum well and GaN quantum barrier defect states were distinguished using bias-dependent steady-state photocapacitance and deep level optical spectroscopy, and their possible physical origin and potential impact on LED performance is considered. Lighted capacitance-voltage measurements provided quantitative and nanoscale depth profiling of the deep level concentration within the MQW region. The concentration of every observed deep level varied strongly with depth in the MQW region, which indicates evolving mechanisms for defect incorporation during MQW growth.

© 2012 OSA

1. Introduction

2. Experiment

InGaN/GaN MQW LEDs emitting at 440 nm were grown on GaN-on-sapphire templates by metal-organic vapor-phase epitaxy (MOVPE). The MQW structure has an n-type GaN layer grown at 1050 °C, followed by a MQW region consisting of five unintentionally doped (UID) 2.5-nm-thick In0.13Ga0.87N QWs grown at 770 °C placed between 7.5-nm-thick Si-doped GaN QBs grown at 850 °C, followed by a 30-nm-thick p-type Al0.15Ga0.85N electron-block layer (EBL) and capped with a 400-nm-thick p-type GaN contact layer. The Si doping target in the QBs was 1 × 1018 cm−3 and 3 × 1018 cm−3 in the n-GaN bulk, and the Mg doping target in the p-layers was 3 × 1019 cm−3. A threading dislocation density of 5.3 × 108 cm−2 was measured from x-ray diffraction (XRD) peak widths [11

11. S. R. Lee, A. M. West, A. A. Allerman, K. E. Waldrip, D. M. Follstaedt, P. P. Provencio, D. D. Koleske, and C. R. Abernathy, “Effect of threading dislocations on the Bragg peakwidths of GaN, AlGaN, and AlN heterolayers,” Appl. Phys. Lett. 86(24), 241904 (2005). [CrossRef]

]. Devices were patterned into 300 μm x 300μm sized mesas using inductively-coupled plasma etching. Ohmic n-type and p-type electrical contacts were formed by evaporating a Ti/Al/Ni/Au and a transparent NiO/Au metal stack, respectively.

DLOS, SSPC, dark capacitance-voltage (CV) and LCV were conducted at room temperature to examine deep level defects in the MQW and n-GaN bulk regions of the LEDs. DLOS was performed with a Boonton 7200 capacitance meter, which has a frequency of 1 MHz, for fast sampling of the photocapacitance transients. LCV was performed with an HP4284A meter at 50 kHz. The lower frequency for LCV measurements was chosen to minimize the in-phase element of the impedance. The difference in the capacitance measured at the two frequencies was small for all bias values, indicating no significant series resistance issues. The LEDs had low leakage at −8 V under all illumination conditions. The phase angle for CV and LCV measurements at 50 kHz remained between −88° and −90° under illumination from −8 – 2 V. The phase angle for DLOS measurements at 1 MHz remained between −88° and −83° under illumination from −8 – 0 V. These phase angles were near the −90° ideal angle for a purely capacitive element, confirming that neither leakage nor series resistance influenced the CV, LCV or DLOS measurements. DLOS and SSPC measure the photocapacitance response from deep level photoemission in depleted regions of the diode upon exposure to sub-band gap, monochromatic illumination. DLOS and SSPC measurements were conducted using broadband illumination from a 150 W Xe arc lamp dispersed through a monochromator using appropriate mode sorting filters to provide a photon energy range of 1.20 – 3.60 eV at 25 meV resolution. The photon flux (ϕ) was calculated from the optical power measured using a Newport 1918-C power meter and a Si photodiode detector divided by the photon energy and the focused beam area. The photon flux varied between 1 – 20 × 1016 cm−2s−1 over the scanned range. The saturated photocapacitance was recorded at each photon energy for SSPC. Inflection points in SSPC spectra occur at the onset of deep level photoemission and approximately indicate the energy of the deep level in the band gap. DLOS determined the spectral variation of the deep level optical cross-section (σo) from the time derivative of the photocapacitance transient at t = 0 s, the time when illumination begins, divided by ϕ. Fitting σo to an appropriate model [12

12. R. Passler, “Photoionization cross-section analysis for a deep trap contributing to current collapse in GaN field-effect transistors,” J. Appl. Phys. 96(1), 715–722 (2004). [CrossRef]

] that accounts for lattice relaxation of the deep level defect precisely determines the optical ionization energy (Eo) and the Franck-Condon energy (dFC). Uncertainty in fitted values of Eo and dFC are estimated to be 0.05 eV from the spread of values obtained by fitting multiple subsets of DLOS data by excluding data points at the high and low photon energy range. DLOS and SSPC measurements were conducted at reverse bias and fixed photon energy by digitizing photocapacitance transients that were simultaneously sampled at 1 ms and 70 ms using two separate recording instruments. This enables capturing of transients with time constants of a few ms to several seconds. Following each DLOS transient, a filling pulse bias Vf was applied in the dark for a 20 s duration to re-populate deep levels. The deep level density was calculated from LCV [9

9. A. Armstrong, A. R. Arehart, and S. A. Ringel, “A method to determine deep level profiles in highly compensated, wide band gap semiconductors,” J. Appl. Phys. 97(8), 083529 (2005). [CrossRef]

]. Additional LCV details are given in Sect. 4.

3. Deep level characterization

3.1 Distinguishing MQW and n-GaN defects using SSPC

Figure 1
Fig. 1 (a) CV and LCV curves for the LED and (b) apparent space-charge density extracted from the dark CV data. Vth = −1.7 V is indicated, corresponding to the bias point at which V > Vth depletes only the MQW region and V < Vth depletes into the n-GaN bulk.
shows a CV curve and the associated space-charge profile (ρ) that was measured in the dark to determine Vth. The apparent depletion depth (xd) was determined as xd = Aε/C, where ε is the semiconductor relative permittivity and A is the diode area. Here, ε was taken to be 9.3ε0, which is a weighted average over the QWs and QBs in the MQW region. The spatial resolution of ρ was limited by the effective Debye length (LD), which is difficult to define in a MQW region where the free carrier and dopant concentrations vary abruptly over a new nanometers. Applying the usual expression for LD amid a mean background of ~1 × 1018 cm−3 doping in the MQW region gives LD ~3 nm, which is reasonable since QWs nominally spaced 7.5 nm apart are distinct in Fig. 1(b). It was assumed that xd had negligible extension into the p-AlGaN EBL due to the much heavier (~30x) p-type doping relative to the n-type doping in the QBs. Therefore, xd can be interpreted as the depletion depth relative to the edge of the p-AlGaN EBL. QWs 1 – 3 appear as peaks in ρ, and the adjacent n-GaN region appears as a plateau below the MQW region. It is noted that the measured position of the QWs determined by CV agrees with their position relative to the p-AlGaN EBL expected from the MQW periodicity determined from XRD, confirming that the depletion region does not penetrate significantly into the EBL. Figure 1(b) shows that Vth = −1.7 V, such that V > Vth depletes only the MQW region (xd < 57.5 nm) and V < Vth depletes past the MQW and into the n-GaN bulk (xd > 57.5 nm). Therefore, SSPC measurements of this LED at V ≥ −1.7 V reveal only QW and QB deep levels, while deep levels located in the n-GaN bulk are identified by their emergence in SSPC measurements only when V < 1.7 V. Similarly, defect states in the p-AlGaN EBL were not expected to significantly contribute to SSPC spectra at any Vr due to neglible depletion in the EBL relative to the total depletion region.

With this distinction in mind, Fig. 2(a)
Fig. 2 (a) SSPC spectra as a function of applied bias. Arrows mark the onset of individual deep levels, found by distinct changes in slope. Onsets at 1.60 eV, 2.05 eV, 2.60 eV and 2.70 eV evident at V = Vth are assigned to deep levels in the MQW region. The 3.25 eV onset that occurs only when V < Vth is assigned to a deep level in the n-GaN bulk. (b) DLOS spectrum taken at −1.7 and −8 V.
presents the SSPC spectra of the LED measured at V = −1.7 V (Vf = 2 V), corresponding to xd ~57 nm, and V = −8 V (Vf = −4 V), corresponding to xd ~100 nm. A Vf of 2 V was used to refill deep levels in the MQW region, and a Vf of −4 V was used to refill deep levels only in the n-GaN bulk. The evolution of the SSPC spectra as a function of V, i.e. xd, provides insight into the location of the observed defects. Before considering variation in SSPC spectra with bias, it is important to realize that the magnitude of ΔC can depend on the spectral intensity of the lamp for the case of thermal carrier re-capture in the depletion region [17

17. P. Blood and J. W. Orton, The Electrical Characterization of Semiconductors: Majority Carriers and Electron States (Academic, London, 1990), Chap. 7.

]. However, this effect impacts all deep levels equally for a given Vr, so the SSPC line shape is unaffected. Reduced carrier re-capture with increasing Vr did not significantly influence the SSPC results in this study, as it is shown below that the primary impact of Vr on the SSPC spectra is to reduce ΔC.

The −1.7 V SSPC spectrum revealed four deep levels, observed by their photoemission onsets (i.e. distinct changes in the slope of ΔC) at 1.60 eV, 2.05 eV, 2.60 eV and 2.70 eV, and all of the associated defects are located in the MQW region because V = Vth. Sensitivity to the QWs at V = −1.7 V was verified by the peak at 2.85 eV in the SSPC spectrum, which arises from near-band-edge absorption by In0.13Ga0.87N. The −8 V SSPC spectrum evidenced an emergent deep level onset at 3.25 eV that is immediately attributed to the n-GaN bulk because it appears only for V < Vth. Table 1

Table 1. Summary of Deep Level Defect Location and Properties Listed by Vr Value Used for DLOS Analysis

table-icon
View This Table
summarizes the characteristics and location of these deep level defects as determined from SSPC and DLOS analyses described in section 3.2.

3.2. Deep level characterization using DLOS

Considering first the DLOS spectrum taken at V = −1.7 V that was particular to the MQW region, the spectral variation of σo between 1.2 – 2.1 eV and 2.7 – 2.9 eV that correspond to the SSPC onsets at 1.60 eV and 2.70 eV SSPC, respectively, were well fit to the theoretical model to determine Eo values of 1.62 (dFC = 0.32 eV) and 2.76 eV (negligible dFC), respectively. These Eo values are referenced to the conduction band minimum (Ec) because the associated ΔC were positive. The sizeable dFC value for the Ec – 1.62 eV level is consistent with an SSPC onset energy less than Eo due to phonon-assisted photoemission and indicates significant lattice coupling of the corresponding defect center.

4. Depth dependence of deep level density

Having determined the location of deep level defects, the LCV technique was used to quantitatively profile their depth distribution. The density of defects within a particular layer of the MQW region or adjacent n-GaN bulk can be determined from the difference in V (ΔV) required to achieve the same xd (and therefore C) with deep levels fully occupied or empty of electrons [19

19. S. D. Brotherton, “Measurement of deep-level spatial distributions,” Sol. St. Elec. 19(4), 341–342 (1976). [CrossRef]

]. This voltage shift is illustrated in the inset of Fig. 1(a). From the Poisson equation, V depends on xd as
V+Vb=qε0xdxNd(x)xnt(x)dx,
(2)
where q is the Coulomb charge, Vb is the built-in voltage, nt is the density of occupied defects, and Nd is the spatially ionized shallow donor density. It is assumed in Eq. (2) that the deep level is sufficiently deep in the band gap to be fully occupied throughout the entire depletion region in the absence of light at the measurement temperature (> 1eV for 293 K) and thus. In this case, the ΔV required to reach xd when defects are emptied by illumination (nt = 0) compared to when the defects are fully occupied (nt = Nt) is
ΔV=qε0xdxnt(x)dx.
(3)
Once the location (QW versus QB) of a given deep level defect is known from DLOS, Nt can be determined for individual QWs, individual QBs, and the n-GaN bulk using LCV. Thus, LCV measurements of an LED quantify Nt(xd) to provide nanoscale depth resolution of the defect distribution in the MQW region.

Using this method, Nt(x) was calculated for the deep levels using Eq. (3) by performing sequential LCV scans at selected deep-level-dependent photon energies. For example, [Ec – 1.62 eV] (brackets indicate the density of the deep level defect) was measured from ΔV under 2.10 eV illumination relative to the dark CV. Referring to Fig. 2(a), at 2.10 eV, only the Ec – 1.62 eV is optically stimulated. Likewise, [Ec – 2.11 eV] was calculated from ΔV under 2.60 eV illumination relative to 2.10 eV illumination, and [Ec – 2.76 eV] was calculated from ΔV under 2.85 eV relative to 2.60 eV illumination. A net Nt was calculated for the remaining defect states at Ec – 2.73 eV and 3.25 eV from ΔV at 3.30 eV illumination relative to ΔV at 2.85 eV.

5. Conclusions

Acknowledgments

References and links

1.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, D. D. Koleske, M. H. Crawford, S. R. Lee, A. J. Fischer, G. Thaler, and M. A. Banas, “Effect of dislocation density on efficiency droop in GaInN/GaN light-emitting diodes,” Appl. Phys. Lett. 91(23), 231114 (2007). [CrossRef]

2.

S. F. Chichibu, A. Uedono, T. Onuma, B. A. Haskell, A. Chakraborty, T. Koyama, P. T. Fini, S. Keller, S. P. Denbaars, J. S. Speck, U. K. Mishra, S. Nakamura, S. Yamaguchi, S. Kamiyama, H. Amano, I. Akasaki, J. Han, and T. Sota, “Origin of defect-insensitive emission probability in In-containing (Al,In,Ga)N alloy semiconductors,” Nat. Mater. 5(10), 810–816 (2006). [CrossRef] [PubMed]

3.

H. Yamada, K. Iso, M. Saito, H. Masui, K. Fujito, S. P. DenBaars, and S. Nakamura, “Compositional Dependence of Nonpolar m-Plane InxGa1-xN/GaN Light Emitting Diodes,” Appl. Phys. Express 1, 041101 (2008). [CrossRef]

4.

J. Hader, J. V. Moloney, and S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 99(18), 181127 (2011). [CrossRef]

5.

T. Mukai, M. Yamada, and S. Nakamura, “Characteristics of InGaN-Based UV/Blue/Green/Amber/Red Light-Emitting Diodes,” Jpn. J. Appl. Phys. 38(Part 1, No. 7A), 3976–3981 (1999). [CrossRef]

6.

B. Monemar and B. E. Sernelius, “Defect related issues in the “current roll-off” in InGaN based light emitting diodes,” Appl. Phys. Lett. 91(18), 181103 (2007). [CrossRef]

7.

L. Rigutti, A. Castaldini, and A. Cavallini, “Anomalous deep-level transients related to quantum well piezoelectric fields in InyGa1−yN/GaN-heterostructure light-emitting diodes,” Phys. Rev. B 77(4), 045312 (2008). [CrossRef]

8.

L. Rigutti, A. Castaldini, M. Meneghini, and A. Cavallini, “Photocurrent spectroscopy evidence for stress-induced recombination centres in quantum wells of InGaN/GaN-based light-emitting diodes,” Semicond. Sci. Technol. 23(2), 025004 (2008). [CrossRef]

9.

A. Armstrong, A. R. Arehart, and S. A. Ringel, “A method to determine deep level profiles in highly compensated, wide band gap semiconductors,” J. Appl. Phys. 97(8), 083529 (2005). [CrossRef]

10.

A. Armstrong, M. H. Crawford, and D. D. Koleske, “Quantitative and depth-resolved investigation of deep-Level defects in InGaN/GaN heterostructures,” J. Electron. Mater. 40(4), 369–376 (2011). [CrossRef]

11.

S. R. Lee, A. M. West, A. A. Allerman, K. E. Waldrip, D. M. Follstaedt, P. P. Provencio, D. D. Koleske, and C. R. Abernathy, “Effect of threading dislocations on the Bragg peakwidths of GaN, AlGaN, and AlN heterolayers,” Appl. Phys. Lett. 86(24), 241904 (2005). [CrossRef]

12.

R. Passler, “Photoionization cross-section analysis for a deep trap contributing to current collapse in GaN field-effect transistors,” J. Appl. Phys. 96(1), 715–722 (2004). [CrossRef]

13.

A. Armstrong, A. R. Arehart, B. Moran, S. P. DenBaars, U. K. Mishra, J. S. Speck, and S. A. Ringel, “Impact of carbon on trap states in n-type GaN grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 84(3), 374–376 (2004). [CrossRef]

14.

P. B. Klein, J. A. Freitas Jr, S. C. Binari, and A. E. Wickenden, “Observation of deep traps responsible for current collapse in GaN metal–semiconductor field-effect transistors,” Appl. Phys. Lett. 75(25), 4016–4018 (1999). [CrossRef]

15.

A. Hierro, D. Kwon, S. A. Ringel, M. Hansen, J. S. Speck, U. K. Mishra, and S. P. DenBaars, “Optically and thermally detected deep levels in n-type Schottky and p+-n GaN diodes,” Appl. Phys. Lett. 76(21), 3064–3066 (2000). [CrossRef]

16.

E. Gür, Z. Zhang, S. Krishnamoorthy, S. Rajan, and S. A. Ringel, “Detailed characterization of deep level defects in InGaN Schottky diodes by optical and thermal deep level spectroscopies,” Appl. Phys. Lett. 99(9), 092109 (2011). [CrossRef]

17.

P. Blood and J. W. Orton, The Electrical Characterization of Semiconductors: Majority Carriers and Electron States (Academic, London, 1990), Chap. 7.

18.

J. L. Lyons, A. Janotti, and C. G. Van de Walle, “Carbon impurities and the yellow luminescence in GaN,” Appl. Phys. Lett. 97(15), 152108 (2010). [CrossRef]

19.

S. D. Brotherton, “Measurement of deep-level spatial distributions,” Sol. St. Elec. 19(4), 341–342 (1976). [CrossRef]

20.

P. M. Petroff, R. C. Miller, A. C. Gossard, and W. Wiegmann, “Impurity trapping, interface structure, and luminescence of GaAs quantum wells grown by molecular beam epitaxy,” Appl. Phys. Lett. 44(2), 217–219 (1984). [CrossRef]

21.

T. Akasaka, H. Gotoh, T. Saito, and T. Makimoto, “High luminescent efficiency of InGaN multiple quantum wells grown on InGaN underlying layers,” Appl. Phys. Lett. 85(15), 3089–3091 (2004). [CrossRef]

22.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001) InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008). [CrossRef]

OCIS Codes
(300.6470) Spectroscopy : Spectroscopy, semiconductors
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: June 22, 2012
Revised Manuscript: August 17, 2012
Manuscript Accepted: August 17, 2012
Published: September 13, 2012

Citation
A. Armstrong, T. A. Henry, D. D. Koleske, M. H. Crawford, and S. R. Lee, "Quantitative and depth-resolved deep level defect distributions in InGaN/GaN light emitting diodes," Opt. Express 20, A812-A821 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S6-A812


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References

  1. M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, D. D. Koleske, M. H. Crawford, S. R. Lee, A. J. Fischer, G. Thaler, and M. A. Banas, “Effect of dislocation density on efficiency droop in GaInN/GaN light-emitting diodes,” Appl. Phys. Lett.91(23), 231114 (2007). [CrossRef]
  2. S. F. Chichibu, A. Uedono, T. Onuma, B. A. Haskell, A. Chakraborty, T. Koyama, P. T. Fini, S. Keller, S. P. Denbaars, J. S. Speck, U. K. Mishra, S. Nakamura, S. Yamaguchi, S. Kamiyama, H. Amano, I. Akasaki, J. Han, and T. Sota, “Origin of defect-insensitive emission probability in In-containing (Al,In,Ga)N alloy semiconductors,” Nat. Mater.5(10), 810–816 (2006). [CrossRef] [PubMed]
  3. H. Yamada, K. Iso, M. Saito, H. Masui, K. Fujito, S. P. DenBaars, and S. Nakamura, “Compositional Dependence of Nonpolar m-Plane InxGa1-xN/GaN Light Emitting Diodes,” Appl. Phys. Express1, 041101 (2008). [CrossRef]
  4. J. Hader, J. V. Moloney, and S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett.99(18), 181127 (2011). [CrossRef]
  5. T. Mukai, M. Yamada, and S. Nakamura, “Characteristics of InGaN-Based UV/Blue/Green/Amber/Red Light-Emitting Diodes,” Jpn. J. Appl. Phys.38(Part 1, No. 7A), 3976–3981 (1999). [CrossRef]
  6. B. Monemar and B. E. Sernelius, “Defect related issues in the “current roll-off” in InGaN based light emitting diodes,” Appl. Phys. Lett.91(18), 181103 (2007). [CrossRef]
  7. L. Rigutti, A. Castaldini, and A. Cavallini, “Anomalous deep-level transients related to quantum well piezoelectric fields in InyGa1−yN/GaN-heterostructure light-emitting diodes,” Phys. Rev. B77(4), 045312 (2008). [CrossRef]
  8. L. Rigutti, A. Castaldini, M. Meneghini, and A. Cavallini, “Photocurrent spectroscopy evidence for stress-induced recombination centres in quantum wells of InGaN/GaN-based light-emitting diodes,” Semicond. Sci. Technol.23(2), 025004 (2008). [CrossRef]
  9. A. Armstrong, A. R. Arehart, and S. A. Ringel, “A method to determine deep level profiles in highly compensated, wide band gap semiconductors,” J. Appl. Phys.97(8), 083529 (2005). [CrossRef]
  10. A. Armstrong, M. H. Crawford, and D. D. Koleske, “Quantitative and depth-resolved investigation of deep-Level defects in InGaN/GaN heterostructures,” J. Electron. Mater.40(4), 369–376 (2011). [CrossRef]
  11. S. R. Lee, A. M. West, A. A. Allerman, K. E. Waldrip, D. M. Follstaedt, P. P. Provencio, D. D. Koleske, and C. R. Abernathy, “Effect of threading dislocations on the Bragg peakwidths of GaN, AlGaN, and AlN heterolayers,” Appl. Phys. Lett.86(24), 241904 (2005). [CrossRef]
  12. R. Passler, “Photoionization cross-section analysis for a deep trap contributing to current collapse in GaN field-effect transistors,” J. Appl. Phys.96(1), 715–722 (2004). [CrossRef]
  13. A. Armstrong, A. R. Arehart, B. Moran, S. P. DenBaars, U. K. Mishra, J. S. Speck, and S. A. Ringel, “Impact of carbon on trap states in n-type GaN grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett.84(3), 374–376 (2004). [CrossRef]
  14. P. B. Klein, J. A. Freitas, S. C. Binari, and A. E. Wickenden, “Observation of deep traps responsible for current collapse in GaN metal–semiconductor field-effect transistors,” Appl. Phys. Lett.75(25), 4016–4018 (1999). [CrossRef]
  15. A. Hierro, D. Kwon, S. A. Ringel, M. Hansen, J. S. Speck, U. K. Mishra, and S. P. DenBaars, “Optically and thermally detected deep levels in n-type Schottky and p+-n GaN diodes,” Appl. Phys. Lett.76(21), 3064–3066 (2000). [CrossRef]
  16. E. Gür, Z. Zhang, S. Krishnamoorthy, S. Rajan, and S. A. Ringel, “Detailed characterization of deep level defects in InGaN Schottky diodes by optical and thermal deep level spectroscopies,” Appl. Phys. Lett.99(9), 092109 (2011). [CrossRef]
  17. P. Blood and J. W. Orton, The Electrical Characterization of Semiconductors: Majority Carriers and Electron States (Academic, London, 1990), Chap. 7.
  18. J. L. Lyons, A. Janotti, and C. G. Van de Walle, “Carbon impurities and the yellow luminescence in GaN,” Appl. Phys. Lett.97(15), 152108 (2010). [CrossRef]
  19. S. D. Brotherton, “Measurement of deep-level spatial distributions,” Sol. St. Elec.19(4), 341–342 (1976). [CrossRef]
  20. P. M. Petroff, R. C. Miller, A. C. Gossard, and W. Wiegmann, “Impurity trapping, interface structure, and luminescence of GaAs quantum wells grown by molecular beam epitaxy,” Appl. Phys. Lett.44(2), 217–219 (1984). [CrossRef]
  21. T. Akasaka, H. Gotoh, T. Saito, and T. Makimoto, “High luminescent efficiency of InGaN multiple quantum wells grown on InGaN underlying layers,” Appl. Phys. Lett.85(15), 3089–3091 (2004). [CrossRef]
  22. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001) InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett.92(5), 053502 (2008). [CrossRef]

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