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  • Editor: Bernard Kippelen
  • Vol. 19, Iss. S4 — Jul. 4, 2011
  • pp: A900–A907
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Investigation of the strain induced optical transition energy shift of the GaN nanorod light emitting diode arrays

Liang-Yi Chen, Hung-Hsun Huang, Chun-Hsiang Chang, Ying-Yuan Huang, Yuh-Renn Wu, and JianJang Huang  »View Author Affiliations


Optics Express, Vol. 19, Issue S4, pp. A900-A907 (2011)
http://dx.doi.org/10.1364/OE.19.00A900


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Abstract

Strain in the semiconductor light emitting layers has profound effect on the energy band structure and the optical properties of the light emitting diodes (LEDs). Here, we report the fabrication and characterization of GaN nanorod LED arrays. We found that the choice of nanorod passivation materials results in the variation of strain in the InGaN/GaN quantum wells, and thus the corresponding change of light emission properties. The results were further investigated by performing Raman measurement to understand the strain of nanorods with different passivation materials and by calculating the optical transition energy of the devices under the influence of strain-induced deformation potential and the piezoelectric polarization field.

© 2011 OSA

1. Introduction

We previously demonstrated GaN nanorod LED arrays with a nearly constant peak EL(electroluminescent) wavelength under a certain range of injection currents [13

13. C. Y. Wang, L. Y. Chen, C. P. Chen, Y. W. Cheng, M. Y. Ke, M. Y. Hsieh, H. M. Wu, L. H. Peng, and J. J. Huang, “GaN nanorod light emitting diode arrays with a nearly constant electroluminescent peak wavelength,” Opt. Express 16(14), 10549–10556 (2008). [CrossRef] [PubMed]

] and later indicated that the sidewall leakage current can be significantly decreased using a CMP (chemical mechanical polishing) process [14

14. L. Y. Chen, Y. Y. Huang, C. H. Chang, Y. H. Sun, Y. W. Cheng, M. Y. Ke, C. P. Chen, and J. J. Huang, “High performance InGaN/GaN nanorod light emitting diode arrays fabricated by nanosphere lithography and chemical mechanical polishing processes,” Opt. Express 18(8), 7664–7669 (2010). [CrossRef] [PubMed]

]. The reduced sidewall leakage enables us to study the effect of strain relaxation based on the EL spectra without worrying about device self-heating under current injection. In this work, by investigating the optical properties of the GaN nanorod LED arrays, we found that the choice of nanorod passivation materials affects EL emission spectra. Raman measurement was then performed to understand the strain of the nanorods with different passivation materials. And the influence of strain-induced deformation potential and the piezoelectric polarization field to the EL spectra of the devices is analyzed.

2. Experiments

3. Results and disscussion

  • A. Analysis of the electroluminescent spectra

We first analyze the optical properties of the devices at room temperature. In Fig. 2(a)
Fig. 2 EL spectra of the planar LED (a) “Nanorod LED with SiO2“ (b) “Nanorod LED with SOG” (c) at the injection current between 2mA and 20mA. The peak energy position (d) and the peak energy shift (e) of the devices are also plotted.
, the EL spectra of the planar LED shows a 51meV peak energy shift from 2.696eV to 2.747eV as the current increases from 2mA to 20mA. The effect of the energy shift is attributed to the quantum confined stark effect (QCSE) which is mainly resulted from strain induced piezoelectric field in the InGaN/GaN epi-structure. The internal electric field tilts the band-gap of quantum well (QW), which not only causes the separation of electrons and holes but also shrinks the optical transition energy. As we increase the injection current, the increased number of carriers screens the internal electric field, leading to the blue shift of light emission.

  • B. Analysis of the Raman spectra

Figure 4
Fig. 4 Illustration of the vertical force exerted on the sidewall of the nanorods by the passivation material.
illustrates the idea of external induced strain, which the material of the space layer exerts vertical force on the nanorod sidewalls. We suspect that since the PECVD grown SiO2 layer has a sturdier atomic bindings than the SOG, leading to less strain relaxation.

  • C. Strain relaxation and its correlation with optical transition in the band structure

The wave-number shift of the phonon mode in Raman spectra can be correlated to the biaxial strain ε// following the equation below [15

15. A. G. Kontos, Y. S. Raptis, N. T. Pelekanos, A. Georgakilas, E. Bellet-Amalric, and D. Jalabert, “Micro-Raman characterization of InxGa1−xN/GaN/Al2O3 heterostructures,” Phys. Rev. B 72(15), 155336 (2005). [CrossRef]

].
Δω=ωω0=(2aλ2c13c33bλ)ε||
(1)
Where the ω is the InGaN E2 H mode wave number of the samples, ω0 is the wave number of the strain free InGaN layer, aλ and bλ are phonon deformation potentials, and C13 and C33 are elastic constants. In our case, Δω ( = ω–ω0) can be obtained from Raman measurement. The parameters aλ, bλ, C13 and C33 of the InxGa1-xN are obtained by linearly interpolating the values of InN and GaN assuming x = 0.2 in our epi-structure(see Table 1

Table 1. Parameters employed in the simulation

table-icon
View This Table
). From Eq. (1), the biaxial strain ε// of the planar structure, nanorod with SiO2 and nanorod with SOG are calculated to be −1.37%, −1.33% and −1.22%, respectively.

With the information of the biaxial strain, the band-edge energy and the QCSE induced wavelength shift due to the InGaN/GaN strain can be calculated. At the first thought, the above two mechanisms have opposite effect on the energy band profile. The relaxed strain of the nanorod structure causes the shrinkage of band-edge while the mitigated QCSE results in less tilt of the band structure. The optical transition energy is reduced by the first phenomenon but increased by the second one. As a result, without considering the effect of carrier screening, light emission energy depends delicately on the strain of InGaN/GaN at the low injection current.

To investigate the effect of passivation material on the EL spectrum, we first calculated the band-edge of these three samples and followed by considering QCSE induced optical transition energy shift, both are based on the strain obtained from Raman measurement.

  • (a) Band-edge calculation

To calculate the band-edge, the 6 × 6 k•p method [16

16. S. Ghosh, P. Waltereit, O. Brandt, H. T. Grahn, and K. H. Ploog, “Electronic band structure of wurtzite GaN under biaxial strain in the M plane investigated with photoreflectance spectroscopy,” Phys. Rev. B 65(7), 075202 (2002). [CrossRef]

,17

17. H. H. Huang and Y. R. Wu, “Study of polarization properties of light emitted from a-plane InGaN/GaN quantum well-based light emitting diodes,” J. Appl. Phys. 106(2), 023106 (2009). [CrossRef]

] is applied for obtaining the valence band and the effective mass approximation method [18

18. Y. R. Wu and J. Singh, “Polar heterostructure for multifunction devices theoretical studies,” IEEE Trans. Electron. Dev. 52(2), 284–293 (2005). [CrossRef]

] is employed for the conduction band. The effective mass of GaN and InGaN is listed in Table 1 [19

19. D. Fritsch, H. Schmidt, and M. Grundmann, “Band-structure pseudopotential calculation of zinc-blende and wurtzite AlN, GaN and InN,” Phys. Rev. B 67(23), 235205 (2003). [CrossRef]

]. In this case, we assume that there is no QCSE and the energy band profile is a flat band case. The bandgap is only affected by the strain induced deformation potential and quantum confined effect. The band gap energy Eg of the bulk InGaN is calculated by linearly interpolating the bandgap of GaN (Eg, GaN) and InN(Eg,InN) following the equation by assuming X = 0.2

Eg,GaN(1X)+Eg,InNX
(2)

(b) Calculation of the strain induced piezoelectric field

After obtaining the piezoelectric polarization from strain and meanwhile considering the spontaneous polarization, we can calculate the total charge density from the total polarization. The potential affected by the polarization charges is solved with Schrödinger equation and Poisson equation. Following the Schrödinger equation, the confined charge can be obtained and is then plugged in to the Poisson equation. Once again, the potential determined by Poisson will feedback to the Schrödinger equation until the solution reaches convergence [21

21. Y. R. Wu, M. Singh, and J. Singh, “Gate leakage suppression and contact engineering in nitride heterostructures,” J. Appl. Phys. 94(9), 5826–5831 (2003). [CrossRef]

].

The potential energy in the QW was obtained from the above self-consistently Poisson equation. Again, we applied the 6 × 6 k•p method to calculate the valence band and the effective mass approximation to calculate the conduction band. Finally, the Schrödinger solver was employed to obtain the confined energy state within the tilted QW. The calculated results, by considering both the deformation potential and piezoelectric field, are shown in Fig. 6
Fig. 6 Calculated band gap profiles and the optical transition energy between first energy states within the quantum well of (a) Planar structure (b) Nanorod with SiO2 (c) Nanorod with SOG. The results are obtained by considering both the strain relaxation induced band shrinkage and QCSE.
. The optical transition energy of the nanorod with SOG sample is the highest while the planar one is the lowest.

(c) Correlation between strain and optical transition energy

4.Conclusion

Acknowledgment

This work was supported by the National Science Council in Taiwan under Grant NSC 97-2221-E-002-054-MY3.

References and links

1.

C. H. Chiu, T. C. Lu, H. W. Huang, C. F. Lai, C. C. Kao, J. T. Chu, C. C. Yu, H. C. Kuo, S. C. Wang, C. F. Lin, and T. H. Hsueh, “Fabrication of InGaN/GaN nanorod light-emitting diodes with self-assembled Ni metal islands,” Nanotechnology 18(44), 445201 (2007). [CrossRef]

2.

Y. J. Lee, S. Y. Lin, C. H. Chiu, T. C. Lu, H. C. Kuo, S. C. Wang, S. Chhajed, J. K. Kim, and E. F. Schubert, “High output power density from GaN-based two-dimensional nanorod light-emitting diode arrays,” Appl. Phys. Lett. 94(14), 141111 (2009). [CrossRef]

3.

H. M. Kim, Y. H. Cho, H. Lee, S. I. Kim, S. R. Ryu, D. Y. Kim, T. W. Kang, and K. S. Chung, “High-brightness light emitting diodes using dislocation-free Indium Gallium Nitride/Gallium Nitride multiquantum-well nanorod arrays,” Nano Lett. 4(6), 1059–1062 (2004). [CrossRef]

4.

A. Kikuchi, M. Tada, K. Miwa, and K. Kishino, “Growth and characterization of InGaN/GaN nanocolumn LED,” Proc. SPIE 6129, 36–43 (2006).

5.

M. A. Tsai, P. Yu, C. L. Chao, C. H. Chiu, H. C. Kuo, S. H. Lin, J. J. Huang, T. C. Lu, and S. C. Wang, “Efficiency enhancement and beam shaping of GaN–InGaN vertical-injection light-emitting diodes via high-aspect-ratio nanorod arrays,” IEEE Photon. Tech. L. 21(4), 257–259 (2009). [CrossRef]

6.

M. Y. Ke, C. Y. Wang, L. Y. Chen, H. H. Chen, H. L. Chiang, Y. W. Cheng, M. Y. Hsieh, C. P. Chen, and J. J. Huang, “Application of nanosphere lithography to LED surface texturing and to the fabrication of nanorod LED arrays,” IEEE J. Sel. Top. Quant. 15(4), 1242–1249 (2009). [CrossRef]

7.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: The quantum-confined stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984). [CrossRef]

8.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007). [CrossRef]

9.

H. J. Chang, Y. P. Hsieh, T. T. Chen, Y. F. Chen, C. T. Liang, T. Y. Lin, S. C. Tseng, and L. C. Chen, “Strong luminescence from strain relaxed InGaN/GaN nanotips for highly efficient light emitters,” Opt. Express 15(15), 9357–9365 (2007). [CrossRef] [PubMed]

10.

N. Thillosen, K. Sebald, H. Hardtdegen, R. Meijers, R. Calarco, S. Montanari, N. Kaluza, J. Gutowski, and H. Lüth, “The state of strain in single GaN nanocolumns as derived from micro-photoluminescence measurements,” Nano Lett. 6(4), 704–708 (2006). [CrossRef] [PubMed]

11.

Y. H. Sun, Y. W. Cheng, S. C. Wang, Y. Y. Huang, C. H. Chang, S. C. Yang, L. Y. Chen, M. Y. Ke, C. K. Li, Y. R. Wu, and J. J. Huang, “Optical properties of the partially strain relaxed InGaN/GaN light-emitting diodes induced by p-type GaN surface texturing,” IEEE Electron Device Lett. 32(2), 182–184 (2011). [CrossRef]

12.

S. H. Park, D. Ahn, and S. L. Chuang, “Electronic and optical properties of a- and m-plane wurtzite InGaN–GaN quantum wells,” IEEE J. Quantum Electron. 43(12), 1175–1182 (2007). [CrossRef]

13.

C. Y. Wang, L. Y. Chen, C. P. Chen, Y. W. Cheng, M. Y. Ke, M. Y. Hsieh, H. M. Wu, L. H. Peng, and J. J. Huang, “GaN nanorod light emitting diode arrays with a nearly constant electroluminescent peak wavelength,” Opt. Express 16(14), 10549–10556 (2008). [CrossRef] [PubMed]

14.

L. Y. Chen, Y. Y. Huang, C. H. Chang, Y. H. Sun, Y. W. Cheng, M. Y. Ke, C. P. Chen, and J. J. Huang, “High performance InGaN/GaN nanorod light emitting diode arrays fabricated by nanosphere lithography and chemical mechanical polishing processes,” Opt. Express 18(8), 7664–7669 (2010). [CrossRef] [PubMed]

15.

A. G. Kontos, Y. S. Raptis, N. T. Pelekanos, A. Georgakilas, E. Bellet-Amalric, and D. Jalabert, “Micro-Raman characterization of InxGa1−xN/GaN/Al2O3 heterostructures,” Phys. Rev. B 72(15), 155336 (2005). [CrossRef]

16.

S. Ghosh, P. Waltereit, O. Brandt, H. T. Grahn, and K. H. Ploog, “Electronic band structure of wurtzite GaN under biaxial strain in the M plane investigated with photoreflectance spectroscopy,” Phys. Rev. B 65(7), 075202 (2002). [CrossRef]

17.

H. H. Huang and Y. R. Wu, “Study of polarization properties of light emitted from a-plane InGaN/GaN quantum well-based light emitting diodes,” J. Appl. Phys. 106(2), 023106 (2009). [CrossRef]

18.

Y. R. Wu and J. Singh, “Polar heterostructure for multifunction devices theoretical studies,” IEEE Trans. Electron. Dev. 52(2), 284–293 (2005). [CrossRef]

19.

D. Fritsch, H. Schmidt, and M. Grundmann, “Band-structure pseudopotential calculation of zinc-blende and wurtzite AlN, GaN and InN,” Phys. Rev. B 67(23), 235205 (2003). [CrossRef]

20.

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amaro, and I. Akasaki, “Quantum-confined stark effect due to piezoelectric fields in GaInN strained quantum wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]

21.

Y. R. Wu, M. Singh, and J. Singh, “Gate leakage suppression and contact engineering in nitride heterostructures,” J. Appl. Phys. 94(9), 5826–5831 (2003). [CrossRef]

22.

A. D. Bykhovski, B. L. Gelmont, and M. S. Shur, “Elastic strain relaxation and piezoeffect in GaN-AlN, GaN-AlGaN and GaN-InGaN superlattices,” J. Appl. Phys. 81(9), 6332–6338 (1997). [CrossRef]

23.

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III–V nitrides,” Phys. Rev. B 56(16), R10024–R10027 (1997). [CrossRef]

24.

A. S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron Dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973). [CrossRef]

25.

V. Y. Davydov, V. V. Emtsev, A. N. Goncharuk, A. N. Smirnov, V. D. Petrikov, V. V. Mamutin, V. A. Vekshin, S. V. Ivanov, M. B. Smirnov, and T. Inushima, “Experimental and theoretical studies of phonons in hexagonal InN,” Appl. Phys. Lett. 75(21), 3297–3299 (1999). [CrossRef]

OCIS Codes
(230.3670) Optical devices : Light-emitting diodes
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: March 7, 2011
Revised Manuscript: June 3, 2011
Manuscript Accepted: June 3, 2011
Published: July 1, 2011

Virtual Issues
Optics in LEDS for Lighting (2011) Optics Express

Citation
Liang-Yi Chen, Hung-Hsun Huang, Chun-Hsiang Chang, Ying-Yuan Huang, Yuh-Renn Wu, and JianJang Huang, "Investigation of the strain induced optical transition energy shift of the GaN nanorod light emitting diode arrays," Opt. Express 19, A900-A907 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A900


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References

  1. C. H. Chiu, T. C. Lu, H. W. Huang, C. F. Lai, C. C. Kao, J. T. Chu, C. C. Yu, H. C. Kuo, S. C. Wang, C. F. Lin, and T. H. Hsueh, “Fabrication of InGaN/GaN nanorod light-emitting diodes with self-assembled Ni metal islands,” Nanotechnology 18(44), 445201 (2007). [CrossRef]
  2. Y. J. Lee, S. Y. Lin, C. H. Chiu, T. C. Lu, H. C. Kuo, S. C. Wang, S. Chhajed, J. K. Kim, and E. F. Schubert, “High output power density from GaN-based two-dimensional nanorod light-emitting diode arrays,” Appl. Phys. Lett. 94(14), 141111 (2009). [CrossRef]
  3. H. M. Kim, Y. H. Cho, H. Lee, S. I. Kim, S. R. Ryu, D. Y. Kim, T. W. Kang, and K. S. Chung, “High-brightness light emitting diodes using dislocation-free Indium Gallium Nitride/Gallium Nitride multiquantum-well nanorod arrays,” Nano Lett. 4(6), 1059–1062 (2004). [CrossRef]
  4. A. Kikuchi, M. Tada, K. Miwa, and K. Kishino, “Growth and characterization of InGaN/GaN nanocolumn LED,” Proc. SPIE 6129, 36–43 (2006).
  5. M. A. Tsai, P. Yu, C. L. Chao, C. H. Chiu, H. C. Kuo, S. H. Lin, J. J. Huang, T. C. Lu, and S. C. Wang, “Efficiency enhancement and beam shaping of GaN–InGaN vertical-injection light-emitting diodes via high-aspect-ratio nanorod arrays,” IEEE Photon. Tech. L. 21(4), 257–259 (2009). [CrossRef]
  6. M. Y. Ke, C. Y. Wang, L. Y. Chen, H. H. Chen, H. L. Chiang, Y. W. Cheng, M. Y. Hsieh, C. P. Chen, and J. J. Huang, “Application of nanosphere lithography to LED surface texturing and to the fabrication of nanorod LED arrays,” IEEE J. Sel. Top. Quant. 15(4), 1242–1249 (2009). [CrossRef]
  7. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: The quantum-confined stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984). [CrossRef]
  8. M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007). [CrossRef]
  9. H. J. Chang, Y. P. Hsieh, T. T. Chen, Y. F. Chen, C. T. Liang, T. Y. Lin, S. C. Tseng, and L. C. Chen, “Strong luminescence from strain relaxed InGaN/GaN nanotips for highly efficient light emitters,” Opt. Express 15(15), 9357–9365 (2007). [CrossRef] [PubMed]
  10. N. Thillosen, K. Sebald, H. Hardtdegen, R. Meijers, R. Calarco, S. Montanari, N. Kaluza, J. Gutowski, and H. Lüth, “The state of strain in single GaN nanocolumns as derived from micro-photoluminescence measurements,” Nano Lett. 6(4), 704–708 (2006). [CrossRef] [PubMed]
  11. Y. H. Sun, Y. W. Cheng, S. C. Wang, Y. Y. Huang, C. H. Chang, S. C. Yang, L. Y. Chen, M. Y. Ke, C. K. Li, Y. R. Wu, and J. J. Huang, “Optical properties of the partially strain relaxed InGaN/GaN light-emitting diodes induced by p-type GaN surface texturing,” IEEE Electron Device Lett. 32(2), 182–184 (2011). [CrossRef]
  12. S. H. Park, D. Ahn, and S. L. Chuang, “Electronic and optical properties of a- and m-plane wurtzite InGaN–GaN quantum wells,” IEEE J. Quantum Electron. 43(12), 1175–1182 (2007). [CrossRef]
  13. C. Y. Wang, L. Y. Chen, C. P. Chen, Y. W. Cheng, M. Y. Ke, M. Y. Hsieh, H. M. Wu, L. H. Peng, and J. J. Huang, “GaN nanorod light emitting diode arrays with a nearly constant electroluminescent peak wavelength,” Opt. Express 16(14), 10549–10556 (2008). [CrossRef] [PubMed]
  14. L. Y. Chen, Y. Y. Huang, C. H. Chang, Y. H. Sun, Y. W. Cheng, M. Y. Ke, C. P. Chen, and J. J. Huang, “High performance InGaN/GaN nanorod light emitting diode arrays fabricated by nanosphere lithography and chemical mechanical polishing processes,” Opt. Express 18(8), 7664–7669 (2010). [CrossRef] [PubMed]
  15. A. G. Kontos, Y. S. Raptis, N. T. Pelekanos, A. Georgakilas, E. Bellet-Amalric, and D. Jalabert, “Micro-Raman characterization of InxGa1−xN/GaN/Al2O3 heterostructures,” Phys. Rev. B 72(15), 155336 (2005). [CrossRef]
  16. S. Ghosh, P. Waltereit, O. Brandt, H. T. Grahn, and K. H. Ploog, “Electronic band structure of wurtzite GaN under biaxial strain in the M plane investigated with photoreflectance spectroscopy,” Phys. Rev. B 65(7), 075202 (2002). [CrossRef]
  17. H. H. Huang and Y. R. Wu, “Study of polarization properties of light emitted from a-plane InGaN/GaN quantum well-based light emitting diodes,” J. Appl. Phys. 106(2), 023106 (2009). [CrossRef]
  18. Y. R. Wu and J. Singh, “Polar heterostructure for multifunction devices theoretical studies,” IEEE Trans. Electron. Dev. 52(2), 284–293 (2005). [CrossRef]
  19. D. Fritsch, H. Schmidt, and M. Grundmann, “Band-structure pseudopotential calculation of zinc-blende and wurtzite AlN, GaN and InN,” Phys. Rev. B 67(23), 235205 (2003). [CrossRef]
  20. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amaro, and I. Akasaki, “Quantum-confined stark effect due to piezoelectric fields in GaInN strained quantum wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]
  21. Y. R. Wu, M. Singh, and J. Singh, “Gate leakage suppression and contact engineering in nitride heterostructures,” J. Appl. Phys. 94(9), 5826–5831 (2003). [CrossRef]
  22. A. D. Bykhovski, B. L. Gelmont, and M. S. Shur, “Elastic strain relaxation and piezoeffect in GaN-AlN, GaN-AlGaN and GaN-InGaN superlattices,” J. Appl. Phys. 81(9), 6332–6338 (1997). [CrossRef]
  23. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III–V nitrides,” Phys. Rev. B 56(16), R10024–R10027 (1997). [CrossRef]
  24. A. S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron Dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973). [CrossRef]
  25. V. Y. Davydov, V. V. Emtsev, A. N. Goncharuk, A. N. Smirnov, V. D. Petrikov, V. V. Mamutin, V. A. Vekshin, S. V. Ivanov, M. B. Smirnov, and T. Inushima, “Experimental and theoretical studies of phonons in hexagonal InN,” Appl. Phys. Lett. 75(21), 3297–3299 (1999). [CrossRef]

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