High-efficiency BAlGaN/AlN quantum well structures for optoelectronic applications in ultraviolet spectral region Seoung-Hwan Park∗ Department of Electronics Engineering, Catholic University of Daegu, Hayang, Gyeongsan, Gyeongbuk 712-702, South Korea ∗ [email protected]
Abstract: Light emission characteristics of ultraviolet (UV) Bx Aly Ga1−x−y N/AlN quantum well (QW) structures were using the multiband effective-mass theory. The TE-polarized spontaneous emission is found to be significantly improved owing to the decrease in the latticemismatch between the well and the substrate with the inclusion of boron. However, the spontaneous emission peak begins to decrease when the boron composition exceeds a critical value (x = 0.08 for y = 0.2), which is mainly due to an increase in the heavy-hole effective mass. In addition, in the case of QW structures with higher Al composition (y > 0.5), the light emission is shown to decrease with increasing the boron composition because the characteristic of the topmost valence subband is changed to the crystal-field splitoff hole band. Hence, we expect that Bx Aly Ga1−x−y N/AlN QW structures with y < 0.5 can be used as a TE-polarized light source with a high efficiency. © 2015 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (230.0250) Optoelectronics; (040.4200) Multiple quantum well.
References and links 1. S. Nakamura and G. Fasol, The Blue Laser Diode (Springer, Berlin, 1997). 2. H. Hirayama, Y. Tsukada, T. Maeda, and N. Kamata, “Marked enhancement in the efficiency of deep- ultraviolet AlGaN light-emitting diodes by using a multiquantum-barrier electron blocking layer,” Appl. Phys. Express 3(3), 031002 (2010). 3. T. M. Altahtamouni, J. Y. Lin, and H. X. Jiang, “Optical polarization in c-plane Al-rich AlN/Alx Ga1−x N single quantum wells,” Appl. Phys. Lett. 101(4), 042103 (2012). 4. S.-H. Park and J.-I. Shim, “Carrier density dependence of polarization switching characteristics of light emission in deep-ultraviolet AlGaN/AlN quantum well structures,” Appl. Phys. Lett. 102(22), 221109 (2013). 5. M. Hou, Z. Qin, C. He, J. Cai, X. Wang, and B. Shen, “Effect of injection current on the optical polarization of AlGaN-based ultraviolet light-emitting diodes,” Opt. Express 22(16), 19589 (2014). 6. Y.-H. Lu, Y.-K. Fu, S.-J. Huang, Y.-K. Su, K. L. Wang, M. H. Pilkuhn, and M.-Tao Chu, “Tailoring of polarization in electron blocking layer for electron confinement and hole injection in ultraviolet light-emitting diodes,” J. Appl. Phys. 115(11), 113102 (2014). 7. A. Atsushi Yamaguchi, “Theoretical investigation of optical polarization properties in Al-rich AlGaN quantum wells with various substrate orientations,” Appl. Phys. Lett. 96(15), 151911 (2010). 8. J. E. Northrup, C. L. Chu, Z. Yang, T. Wunderer, M. Kneissl, N. M. Johnson, and T. Kolbe, “Effect of strain and barrier composition on the polarization of light emission from AlGaN/AlN quantum wells,” Appl. Phys. Lett. 100(2), 021101 (2012). 9. T. Takano, M. Kurimoto, J. Yamamoto, and H. Kawanishi, “Epitaxial growth of high quality BAlGaN quaternary lattice matched to AlN on 6HSiC substrate by LP-MOVPE for deep-UV emission,” J. Cryst. Growth 237, 972– 977 (2002).
#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3623
10. S. Gautier, G. Orsal, T. Moudakir, N. Maloufi, F. Jomard, M. Alnot, Z. Djebbour, A. A. Sirenko, M. Abid, K. Pantzas, I. T. Ferguson, P. L. Voss, A. Ougazzaden, “Metal-organic vapour phase epitaxy of BInGaN quaternary alloys and characterization of boron content,” J. Cryst. Growth, 312(5), 641–644 (2010). 11. M. Abid, T. Moudakir, Z. Djebbour, G. Orsal, S. Gautier, A. En Naciri, A. Migan-Dubois, A. Ougazzaden, “Blueviolet boron-based Distributed Bragg Reflectors for VCSEL application,” J. Cryst. Growth 315(1), 283– 287 (2011). 12. X. Li, S. Sundaram, Y. ElGmili, F. Genty, S. Bouchoule, G. Patriache, P. Disseix, F. Rveret, J. Leymarie, J.-P. Salvestrini, R. D. Dupuis, P. L. Voss, A. Ougazzaden, “MOVPE grown periodic AlN/BAlN heterostructure with high boron content,” J. Cryst. Growth (2014), http://dx.doi.org/10.1016/j.jcrysgro.2014.09.030 13. T. Honda, M. Tsubamoto, Y. Kuga, and H. Kawanishi, “Optical Gain in BGaN Lattice-Matched to (0001) 6HSiC,” Mater. Res. Soc. Symp. Proc. 482, 1125–1129 (1997). 14. S. L. Chuang, Physics of Optoelectronic Devices ( Wiley, New York, 1995), Chap. 4. 15. S.-H. Park and S. L. Chuang, “Piezoelectric effects on electrical and optical properties of wurtzite GaN/AlGaN quantum well lasers,” Appl. Phys. Lett. 72, 3103–3105 (1998). 16. D. Ahn, “Theory of non-Markovian optical gain in quantum-well lasers,” Prog. Quantum Electron. 21, 249–287 (1997). 17. S.-H. Park, S. L. Chuang, J. Minch, and D. Ahn, “Intraband relaxation time effects on non-Markovian gain with many-body effects and comparison with experiment,” Semicond. Sci. Technol. 15, 203–208 (2000). 18. K. Shimada, T. Sota, and K. Suzuki, “First-principles study on electronic and elastic properties of BN, AlN, and GaN,” J. Appl. Phys. 84, 4951–4958 (1998). 19. O. Madelung, Semiconductors: Basic Data, 2nd revised ed. (Berlin: Springer, 1996). 20. S.-H. Park, “Optical gain characteristics of non-polar Al-rich AlGaN/AlN quantum well structures,” J. Appl. Phys. 110, 063105 (2011). 21. S.-H. Park, Y.-T. Moon, D.-S. Han, J. S. Park, M.-S. Oh, and D. Ahn, “Light emission enhancement in blue InGaAlN/InGaN quantum well structures,” Appl. Phys. Lett. 99, 181101 (2011).
1.
Introduction
Group III nitride semiconductors, AlN, GaN, InN, and their alloys have been promising materials for their potential electronic and optoelectronic device applications, which include lightemitting diodes (LEDs) and laser diodes (LDs) operating throughout ultraviolet to green visible region [1]. Among them, deep ultraviolet (UV) emitters operating in the 200-340 nm wavelength range based on AlGaN material have been receiving a considerable amount of attention because of many applications such as water purification, biochemical agent detection, medical research/health care, and high-density data storage [2–5]. The performance of AlGaN-based UV LEDs has markedly increased due to the improved quality of high-Al-composition AlGaN layers and also the optimization of LED designs. However, several obstacles still impede further improvement for higher performance UV LEDs [6]. One of the major challenges is the large internal fields induced by the lattice mismatch in the active region. This results in the reduction in the radiative recombination rate and serious electron leakage out of the active region. Also, the design of the active region to give a large transverse electric (TE)-polarized emission is important for high light extraction efficiency because the c-axis polarized light is hard to emit from the surface [7, 8]. On the other hand, the BAlGaN system has been recently proposed as a promising candidate for UV and deep UV applications because the growth of the lattice-matched BAlGaN quaternary system to AlN is possible with the inclusion of the small boron ( < 12 %) [9–12]. The maximum boron contents up to 13 % and 9 % were demonstrated experimentally for BAlN and BGaN, respectively [9, 10]. In addition, the BAlGaN system leads to more degrees of freedom for bandgap engineering of wide band-gap device structures, compared to the ternary materials AlGaN. This means that these systems are promising materials for the use in optoelectronic devices operating in the UV spectral region. However, despite its importance, there has been very little work done on electronic and optical properties of BAlGaN-based quantum well (QW) structures except for estimation of optical gain for BGaN system [13]. In this research, we theoretically investigate light emission characteristics of UV Bx Aly Ga1−x−y N/AlN QW structures using the multiband effective-mass theory and non#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3624
0.30
0.20
(a) x=0.0
0.25
BxAlyGa1-x-yN/AlN y=0.2
Energy (eV)
0.20
HH1
0.10 0.05
-0.05
HH1
0.05
-0.05
HH2
0.1
0.00
-0.20 0.3 0.0
CH1
-0.05
HH2
-0.10
HH2
-0.15 12
0.2
HH1 LH1
CH1
-0.15
k|| (1/Å)
0.10 0.05
-0.10
LH2
-0.10 0.0
LH1
0.00
LH1
(c) x=0.12
0.15
0.10
0.15
0.00
0.20
(b) x=0.06
0.15
N2D=20x10 cm 0.1
0.2
k|| (1/Å)
-2
-0.20 0.3 0.0
0.1
0.2
k|| (1/Å)
0.3
Fig. 1. Valence band structures for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm) with x=0.0, 0.06, and 0.12. The SC solutions are obtained at a sheet carrier density of N2D = 20 × 1012 cm−2 .
Markovian model. Here, we consider the free carrier model with the band-gap renormalization. We assume that a BAlGaN/AlN QW structure is grown on a thick AlN buffer layer. The self-consistent (SC) solutions are obtained by solving the Schr¨odinger equation for electrons, the block-diagonalized 3 × 3 Hamiltonian for holes, and Poisson’s equation iteratively [14, 15]. The non-Markovian spontaneous emission spectrum gsp (ω ) used in the calculation was taken from [16, 17]. The material parameters for BN used in the computations are given in Table 1. The material parameters for GaN and AlN used in the calculation were taken from [20] and references in there, except for band-gap. The parameters for Bx Aly Ga1−x−y N are obtained from the linear combination between the parameters of BN, AlN, and GaN. On the other hand, several material parameters for BN such as the energy parameters (Δ2 =Δ3 ) accounting for spin-orbit interactions, valence band effective-mass parameters, and the spontaneous polarizaiton constant are not well known. We assumed its parameters to be equal to those of AlGaN as a first approximation in the case of a lack of published data. The top most valence band is determined by the crystal-field split-off energy (Δcr ) and Δ2 . We expect that the characteristic of the top most valence subband of BAlGaN QWs will be mainly affected by the crystal-field split-off energy because of its large value (333 meV). Also, valence band effectivemass parameters and spontaneous polarizaiton constant affect the effective mass of the top most valence subband and the matrix element, respectively. Thus, in the case of high B content BAlGaN QWs, their electronic and optical properties will be affected by these parameters. However, we believe that overall tendency given in this paper will not changed because the boron composition used in the calculation is relatively small. 2.
Results and discussion
Figure 1 shows the valence band structures for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm) with x=0.0, 0.06, and 0.12. The SC solutions are obtained at a sheet carrier density of N2D = 20 × 1012 cm−2 . The symbols HHn, LHn, and CHn denote the n-th heavy-hole, light-hole, and crystal-field splitoff hole subbands, respectively. The characteristic of the topmost valence subband is observed to be HH1, irrespective of the boron composition. On the other hand, the crystal-field splitoff hole subband is shifted upward with the inclusion of the boron. Also, the heavy-hole effective mass for the topmost valence band is found to increase significantly with increasing boron composition. For example, the heavy-hole effective masses #227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3625
Table 1. Physical parameters for BN material used in the calculation.
0.3
BN 2.534 4.191 0.27 -0.85 -19.2 -14.0 3.9 -3.32 -4.3
Parameters Elastic stiffness constant [18] (1011 dyn/cm2 ) C11 C12 C13 C33 C44 Conduction band effective mass [19] me /mo Dielectric constant(ε0 ) [19] ε Energy parameter (eV) Eg [19] Δcr [18] 1.0
(a) BxAlyGa1-x-yN/AlN Lw=2.5 nm, y=0.2
2
|M|
Strain (%)
x=
0.2
0.5
0.0 0.06 0.12
0.1
0.0 -0.5 -1.0
TE (c1-v1)
0.1
0.2
k|| (1/Å)
0.3
BxAlyGa1-x-yN/AlN Lw=2.5 nm, y=0.2
-1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -4.5
-1.5
0.0 0.0
(b)
-2.0
-5.0
Internal field (MV/cm)
Parameters ˚ Lattice constant [18] (A) a c Piezoelectric constant [18] (C/m2 ) e13 e33 Deformation potentials [18] (eV) D1 D2 D3 D4 D5
-5.5
0.00 0.03 0.06 0.09 0.12
Boron composition
Fig. 2. (a) Optical matrix element and (b) strain and internal field in the well as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm).
for BAlGaN/AlN QW structures with x=0.0 and 0.12 are 1.75m0 and 2.97m0 , respectively. This will give a significant influence on the quasi-Fermi level separation, as discussed below. For the heavy-hole effective mass, we consider the parabolic band fitted to the lowest subband of the exact band structure. The effective mass is determined so that, for a given carrier density and quasi-Fermi level for holes, the carrier density and the quasi-Fermi level agree with those of the exact band structure. Hence, the effective mass of the fitted parabolic band reflects an averaged density of states for a given carrier density. Figure 2 shows (a) optical matrix element and (b) strain and internal field in the well as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm). The SC solutions are obtained at a sheet carrier density of N2D = 10 × 1012 cm−2 . The matrix element for the conventional AlGaN/AlN QW structure is nearly independent of the k|| . On the other hand, in the case of the BAlGaN/AlN QW structure with a relatively high boron composition (x=0.1), it rapidly decreases when the in-plane wave vector exceeds 0.1. This can be explained by the fact that the dominant characteristic of the topmost valence subband changes #227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3626
BN 98.2 13.4 7.4 107.7 38.8 0.752 5.06 5.2 0.333
Spontaneous emission coefficient (1/cm)
5000
4000
6000
(a)
x=
TE
y=0.2
3000
0.0 0.02 0.06 0.10 0.12
(b)
5000
BxAlyGa1-x-yN/AlN Lw=2.5 nm
y=0.2
4000 3000
0.4
2000 2000 1000
1000
0 280
300
320
340
Wavelength (nm)
0
0.6
0.00 0.03 0.06 0.09 0.12
Boron composition
Fig. 3. (a) Spontaneous emission coefficients for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2) with several x values and (b) peak intensities as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures with several y values.
from the HH band to the CH band for higher states above k|| =0 because the energy spacing between the HH and the CH bands is reduced with increasing boron composition, as shown in Fig. 1. On the other hand, in the case of the conventional AlGaN/AlN QW structure, the HH band characteristic of the topmost valence subband at band-edge remains unchanged even at higher states. Also, the matrix element at the band-edge (k|| = 0) is found to increase rapidly with increasing boron composition. For example, the normalized optical matrix elements at the zone center are 0.05 and 0.18 for QW structures with x = 0.0 and 0.12, respectively. This can be explained by the fact that the spatial separation between the electron and the hole wave functions in the well is reduced because the internal field in the well decreases with increasing boron composition. Also, the decrease in the internal field is originated from the reduction in the lattice mismatch between the well and the substrate with the inclusion of the boron. Here, the well is lattice-matched to the substrate near x=0.09. Figure 3 shows (a) spontaneous emission coefficients for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2) with several x values and (b) peak intensities as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures with several y values. Spontaneous emission spectra are obtained at a sheet carrier density of N2D = 20 × 1012 cm−2 . The peak wavelength of the conventional AlGaN/AlN QW structure with the Al composition of 0.2 is shown to be about 315 nm. It is shifted to the short wavelength with increasing boron composition because of the increase in the bandgap energy. We know that the spontaneous emission peak of BAlGaN/AlN QW structures is found to be greatly improved with the inclusion of the boron. In particular, in the case of y=0.2, the light intensity of the QW structure with x=0.08 is about twice larger than the conventional QW structure. However, the spontaneous emission peak begins to decrease when the boron composition exceeds a critical value, for example, x=0.08 for y=0.2. The decrease in the spontaneous emission peak is related to the decrease in the quasi-Fermi level separation, as discussed below. Also, the critical value rapidly decrease with increasing Al composition. In the case of QW structures with higher Al composition (y = 0.6), the light emission is reduced with the inclusion of the boron. This is related to the fact that the characteristic of the topmost valence subband is changed to the crystal-field splitoff hole band with the inclusion of boron. Thus, the TM-polarized light emission is enhanced with increasing boron composition, although not shown here. Figure 4 shows potential profile and the wave functions (C1 and HH1) at zone center for
#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3627
7
(b) x=0.06
(a) x=0.0
0.25
(c) x=0.12
6
(d)
ΔEfc
0.20
5
Energy (eV)
C1
C1
C1
3 BxAlyGa1-x-yN/AlN
2
Lw=2.5 nm, y=0.2
1 HH1
HH1
0
HH1
ΔEfc+ΔEfv
0.10 0.05
ΔEfv
0.00 -0.05
-1 -2
ΔEfc+ΔEfv (eV)
0.15
4
0
30 60 90 0
Position (Å)
30 60 90 0
Position (Å)
30 60 90
Position (Å)
-0.10 0.00 0.05 0.10
Boron composition
Fig. 4. Potential profile and the wave functions (C1 and HH1) at zone center for cases with (a) x=0.0, (b) 0.06, and (c) 0.12 and (d) quasi-Fermi level separation as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (Lw =2.5 nm).
cases with (a) x=0.0, (b) 0.06, and (c) 0.12 and (d) quasi-Fermi level separation as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (Lw =2.5 nm). Here, the quasiFermi-level separation ΔE f c (ΔE f v ) is defined as the energy difference between the quasi-Fermi level and the ground-state energy in the conduction band (the valence band). The quasi-Fermilevel separation is obtained at the sheet carrier density of N2D = 20 × 1012 cm−2 . In the case of the conventional QW structure, a large spatial separation between electron and hole wave functions is observed in the QW structure because of the large internal field. On the other hand, a spatial separation between electron and hole wavefunctions is reduced due to the decrease in the internal field increasing boron composition, which results in the increase in the optical matrix element, as shown in Fig. 2. However, the quasi-Fermi-level separation is observed to decrease rapidly with increasing boron composition. Thus, we know that the decrease in the spontaneous emission peak observed for the case with high x values is mainly due to the decrease in the quasi-Fermi level separation. The reduction in the quasi-Fermi level separation can be explained by the fact that the heavy-hole effective mass around the topmost valence band greatly increases with increasing boron composition. Hence, we expect that BAlGaN/AlN QW structures with small boron compositions below critical values can be used as a light source with a high efficiency in UV region.
3.
Conclusion
In summary, light emission characteristics of UV BAlGaN/AlN QW structures were using the multiband effective-mass theory and non-Markovian model. The matrix element at the bandedge is found to increase rapidly with increasing boron composition. Thus, the QW structures show much larger light intensity than the conventional QW structure. However, the spontaneous emission peak shows a maximum at the critical value (x= 0.08 for y=0.2) and begins to decrease when the boron composition is further increased. In particular, in the case of QW structures with higher Al composition (y > 0.5), the light emission is shown to be reduced with the inclusion of #227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3628
the boron because the characteristic of the topmost valence subband is changed to the crystalfield splitoff hole band. Hence, we expect that Bx Aly Ga1−x−y N/AlN QW structures with small boron compositions for y < 0.5 can be used as a TE-polarized light source with a high efficiency in UV region.
Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012R1A1B3000476) and partially by the Industrial Strategic technology development program, 10041878, Development of WPE 75% LED device process and standard evaluation technology funded by the Ministry of Knowledge Economy (MKE, Korea).
#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3629
Abstract: Light emission characteristics of ultraviolet (UV) Bx Aly Ga1−x−y N/AlN quantum well (QW) structures were using the multiband effective-mass theory. The TE-polarized spontaneous emission is found to be significantly improved owing to the decrease in the latticemismatch between the well and the substrate with the inclusion of boron. However, the spontaneous emission peak begins to decrease when the boron composition exceeds a critical value (x = 0.08 for y = 0.2), which is mainly due to an increase in the heavy-hole effective mass. In addition, in the case of QW structures with higher Al composition (y > 0.5), the light emission is shown to decrease with increasing the boron composition because the characteristic of the topmost valence subband is changed to the crystal-field splitoff hole band. Hence, we expect that Bx Aly Ga1−x−y N/AlN QW structures with y < 0.5 can be used as a TE-polarized light source with a high efficiency. © 2015 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (230.0250) Optoelectronics; (040.4200) Multiple quantum well.
References and links 1. S. Nakamura and G. Fasol, The Blue Laser Diode (Springer, Berlin, 1997). 2. H. Hirayama, Y. Tsukada, T. Maeda, and N. Kamata, “Marked enhancement in the efficiency of deep- ultraviolet AlGaN light-emitting diodes by using a multiquantum-barrier electron blocking layer,” Appl. Phys. Express 3(3), 031002 (2010). 3. T. M. Altahtamouni, J. Y. Lin, and H. X. Jiang, “Optical polarization in c-plane Al-rich AlN/Alx Ga1−x N single quantum wells,” Appl. Phys. Lett. 101(4), 042103 (2012). 4. S.-H. Park and J.-I. Shim, “Carrier density dependence of polarization switching characteristics of light emission in deep-ultraviolet AlGaN/AlN quantum well structures,” Appl. Phys. Lett. 102(22), 221109 (2013). 5. M. Hou, Z. Qin, C. He, J. Cai, X. Wang, and B. Shen, “Effect of injection current on the optical polarization of AlGaN-based ultraviolet light-emitting diodes,” Opt. Express 22(16), 19589 (2014). 6. Y.-H. Lu, Y.-K. Fu, S.-J. Huang, Y.-K. Su, K. L. Wang, M. H. Pilkuhn, and M.-Tao Chu, “Tailoring of polarization in electron blocking layer for electron confinement and hole injection in ultraviolet light-emitting diodes,” J. Appl. Phys. 115(11), 113102 (2014). 7. A. Atsushi Yamaguchi, “Theoretical investigation of optical polarization properties in Al-rich AlGaN quantum wells with various substrate orientations,” Appl. Phys. Lett. 96(15), 151911 (2010). 8. J. E. Northrup, C. L. Chu, Z. Yang, T. Wunderer, M. Kneissl, N. M. Johnson, and T. Kolbe, “Effect of strain and barrier composition on the polarization of light emission from AlGaN/AlN quantum wells,” Appl. Phys. Lett. 100(2), 021101 (2012). 9. T. Takano, M. Kurimoto, J. Yamamoto, and H. Kawanishi, “Epitaxial growth of high quality BAlGaN quaternary lattice matched to AlN on 6HSiC substrate by LP-MOVPE for deep-UV emission,” J. Cryst. Growth 237, 972– 977 (2002).
#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3623
10. S. Gautier, G. Orsal, T. Moudakir, N. Maloufi, F. Jomard, M. Alnot, Z. Djebbour, A. A. Sirenko, M. Abid, K. Pantzas, I. T. Ferguson, P. L. Voss, A. Ougazzaden, “Metal-organic vapour phase epitaxy of BInGaN quaternary alloys and characterization of boron content,” J. Cryst. Growth, 312(5), 641–644 (2010). 11. M. Abid, T. Moudakir, Z. Djebbour, G. Orsal, S. Gautier, A. En Naciri, A. Migan-Dubois, A. Ougazzaden, “Blueviolet boron-based Distributed Bragg Reflectors for VCSEL application,” J. Cryst. Growth 315(1), 283– 287 (2011). 12. X. Li, S. Sundaram, Y. ElGmili, F. Genty, S. Bouchoule, G. Patriache, P. Disseix, F. Rveret, J. Leymarie, J.-P. Salvestrini, R. D. Dupuis, P. L. Voss, A. Ougazzaden, “MOVPE grown periodic AlN/BAlN heterostructure with high boron content,” J. Cryst. Growth (2014), http://dx.doi.org/10.1016/j.jcrysgro.2014.09.030 13. T. Honda, M. Tsubamoto, Y. Kuga, and H. Kawanishi, “Optical Gain in BGaN Lattice-Matched to (0001) 6HSiC,” Mater. Res. Soc. Symp. Proc. 482, 1125–1129 (1997). 14. S. L. Chuang, Physics of Optoelectronic Devices ( Wiley, New York, 1995), Chap. 4. 15. S.-H. Park and S. L. Chuang, “Piezoelectric effects on electrical and optical properties of wurtzite GaN/AlGaN quantum well lasers,” Appl. Phys. Lett. 72, 3103–3105 (1998). 16. D. Ahn, “Theory of non-Markovian optical gain in quantum-well lasers,” Prog. Quantum Electron. 21, 249–287 (1997). 17. S.-H. Park, S. L. Chuang, J. Minch, and D. Ahn, “Intraband relaxation time effects on non-Markovian gain with many-body effects and comparison with experiment,” Semicond. Sci. Technol. 15, 203–208 (2000). 18. K. Shimada, T. Sota, and K. Suzuki, “First-principles study on electronic and elastic properties of BN, AlN, and GaN,” J. Appl. Phys. 84, 4951–4958 (1998). 19. O. Madelung, Semiconductors: Basic Data, 2nd revised ed. (Berlin: Springer, 1996). 20. S.-H. Park, “Optical gain characteristics of non-polar Al-rich AlGaN/AlN quantum well structures,” J. Appl. Phys. 110, 063105 (2011). 21. S.-H. Park, Y.-T. Moon, D.-S. Han, J. S. Park, M.-S. Oh, and D. Ahn, “Light emission enhancement in blue InGaAlN/InGaN quantum well structures,” Appl. Phys. Lett. 99, 181101 (2011).
1.
Introduction
Group III nitride semiconductors, AlN, GaN, InN, and their alloys have been promising materials for their potential electronic and optoelectronic device applications, which include lightemitting diodes (LEDs) and laser diodes (LDs) operating throughout ultraviolet to green visible region [1]. Among them, deep ultraviolet (UV) emitters operating in the 200-340 nm wavelength range based on AlGaN material have been receiving a considerable amount of attention because of many applications such as water purification, biochemical agent detection, medical research/health care, and high-density data storage [2–5]. The performance of AlGaN-based UV LEDs has markedly increased due to the improved quality of high-Al-composition AlGaN layers and also the optimization of LED designs. However, several obstacles still impede further improvement for higher performance UV LEDs [6]. One of the major challenges is the large internal fields induced by the lattice mismatch in the active region. This results in the reduction in the radiative recombination rate and serious electron leakage out of the active region. Also, the design of the active region to give a large transverse electric (TE)-polarized emission is important for high light extraction efficiency because the c-axis polarized light is hard to emit from the surface [7, 8]. On the other hand, the BAlGaN system has been recently proposed as a promising candidate for UV and deep UV applications because the growth of the lattice-matched BAlGaN quaternary system to AlN is possible with the inclusion of the small boron ( < 12 %) [9–12]. The maximum boron contents up to 13 % and 9 % were demonstrated experimentally for BAlN and BGaN, respectively [9, 10]. In addition, the BAlGaN system leads to more degrees of freedom for bandgap engineering of wide band-gap device structures, compared to the ternary materials AlGaN. This means that these systems are promising materials for the use in optoelectronic devices operating in the UV spectral region. However, despite its importance, there has been very little work done on electronic and optical properties of BAlGaN-based quantum well (QW) structures except for estimation of optical gain for BGaN system [13]. In this research, we theoretically investigate light emission characteristics of UV Bx Aly Ga1−x−y N/AlN QW structures using the multiband effective-mass theory and non#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3624
0.30
0.20
(a) x=0.0
0.25
BxAlyGa1-x-yN/AlN y=0.2
Energy (eV)
0.20
HH1
0.10 0.05
-0.05
HH1
0.05
-0.05
HH2
0.1
0.00
-0.20 0.3 0.0
CH1
-0.05
HH2
-0.10
HH2
-0.15 12
0.2
HH1 LH1
CH1
-0.15
k|| (1/Å)
0.10 0.05
-0.10
LH2
-0.10 0.0
LH1
0.00
LH1
(c) x=0.12
0.15
0.10
0.15
0.00
0.20
(b) x=0.06
0.15
N2D=20x10 cm 0.1
0.2
k|| (1/Å)
-2
-0.20 0.3 0.0
0.1
0.2
k|| (1/Å)
0.3
Fig. 1. Valence band structures for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm) with x=0.0, 0.06, and 0.12. The SC solutions are obtained at a sheet carrier density of N2D = 20 × 1012 cm−2 .
Markovian model. Here, we consider the free carrier model with the band-gap renormalization. We assume that a BAlGaN/AlN QW structure is grown on a thick AlN buffer layer. The self-consistent (SC) solutions are obtained by solving the Schr¨odinger equation for electrons, the block-diagonalized 3 × 3 Hamiltonian for holes, and Poisson’s equation iteratively [14, 15]. The non-Markovian spontaneous emission spectrum gsp (ω ) used in the calculation was taken from [16, 17]. The material parameters for BN used in the computations are given in Table 1. The material parameters for GaN and AlN used in the calculation were taken from [20] and references in there, except for band-gap. The parameters for Bx Aly Ga1−x−y N are obtained from the linear combination between the parameters of BN, AlN, and GaN. On the other hand, several material parameters for BN such as the energy parameters (Δ2 =Δ3 ) accounting for spin-orbit interactions, valence band effective-mass parameters, and the spontaneous polarizaiton constant are not well known. We assumed its parameters to be equal to those of AlGaN as a first approximation in the case of a lack of published data. The top most valence band is determined by the crystal-field split-off energy (Δcr ) and Δ2 . We expect that the characteristic of the top most valence subband of BAlGaN QWs will be mainly affected by the crystal-field split-off energy because of its large value (333 meV). Also, valence band effectivemass parameters and spontaneous polarizaiton constant affect the effective mass of the top most valence subband and the matrix element, respectively. Thus, in the case of high B content BAlGaN QWs, their electronic and optical properties will be affected by these parameters. However, we believe that overall tendency given in this paper will not changed because the boron composition used in the calculation is relatively small. 2.
Results and discussion
Figure 1 shows the valence band structures for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm) with x=0.0, 0.06, and 0.12. The SC solutions are obtained at a sheet carrier density of N2D = 20 × 1012 cm−2 . The symbols HHn, LHn, and CHn denote the n-th heavy-hole, light-hole, and crystal-field splitoff hole subbands, respectively. The characteristic of the topmost valence subband is observed to be HH1, irrespective of the boron composition. On the other hand, the crystal-field splitoff hole subband is shifted upward with the inclusion of the boron. Also, the heavy-hole effective mass for the topmost valence band is found to increase significantly with increasing boron composition. For example, the heavy-hole effective masses #227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3625
Table 1. Physical parameters for BN material used in the calculation.
0.3
BN 2.534 4.191 0.27 -0.85 -19.2 -14.0 3.9 -3.32 -4.3
Parameters Elastic stiffness constant [18] (1011 dyn/cm2 ) C11 C12 C13 C33 C44 Conduction band effective mass [19] me /mo Dielectric constant(ε0 ) [19] ε Energy parameter (eV) Eg [19] Δcr [18] 1.0
(a) BxAlyGa1-x-yN/AlN Lw=2.5 nm, y=0.2
2
|M|
Strain (%)
x=
0.2
0.5
0.0 0.06 0.12
0.1
0.0 -0.5 -1.0
TE (c1-v1)
0.1
0.2
k|| (1/Å)
0.3
BxAlyGa1-x-yN/AlN Lw=2.5 nm, y=0.2
-1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -4.5
-1.5
0.0 0.0
(b)
-2.0
-5.0
Internal field (MV/cm)
Parameters ˚ Lattice constant [18] (A) a c Piezoelectric constant [18] (C/m2 ) e13 e33 Deformation potentials [18] (eV) D1 D2 D3 D4 D5
-5.5
0.00 0.03 0.06 0.09 0.12
Boron composition
Fig. 2. (a) Optical matrix element and (b) strain and internal field in the well as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm).
for BAlGaN/AlN QW structures with x=0.0 and 0.12 are 1.75m0 and 2.97m0 , respectively. This will give a significant influence on the quasi-Fermi level separation, as discussed below. For the heavy-hole effective mass, we consider the parabolic band fitted to the lowest subband of the exact band structure. The effective mass is determined so that, for a given carrier density and quasi-Fermi level for holes, the carrier density and the quasi-Fermi level agree with those of the exact band structure. Hence, the effective mass of the fitted parabolic band reflects an averaged density of states for a given carrier density. Figure 2 shows (a) optical matrix element and (b) strain and internal field in the well as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2, Lw =2.5 nm). The SC solutions are obtained at a sheet carrier density of N2D = 10 × 1012 cm−2 . The matrix element for the conventional AlGaN/AlN QW structure is nearly independent of the k|| . On the other hand, in the case of the BAlGaN/AlN QW structure with a relatively high boron composition (x=0.1), it rapidly decreases when the in-plane wave vector exceeds 0.1. This can be explained by the fact that the dominant characteristic of the topmost valence subband changes #227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3626
BN 98.2 13.4 7.4 107.7 38.8 0.752 5.06 5.2 0.333
Spontaneous emission coefficient (1/cm)
5000
4000
6000
(a)
x=
TE
y=0.2
3000
0.0 0.02 0.06 0.10 0.12
(b)
5000
BxAlyGa1-x-yN/AlN Lw=2.5 nm
y=0.2
4000 3000
0.4
2000 2000 1000
1000
0 280
300
320
340
Wavelength (nm)
0
0.6
0.00 0.03 0.06 0.09 0.12
Boron composition
Fig. 3. (a) Spontaneous emission coefficients for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2) with several x values and (b) peak intensities as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures with several y values.
from the HH band to the CH band for higher states above k|| =0 because the energy spacing between the HH and the CH bands is reduced with increasing boron composition, as shown in Fig. 1. On the other hand, in the case of the conventional AlGaN/AlN QW structure, the HH band characteristic of the topmost valence subband at band-edge remains unchanged even at higher states. Also, the matrix element at the band-edge (k|| = 0) is found to increase rapidly with increasing boron composition. For example, the normalized optical matrix elements at the zone center are 0.05 and 0.18 for QW structures with x = 0.0 and 0.12, respectively. This can be explained by the fact that the spatial separation between the electron and the hole wave functions in the well is reduced because the internal field in the well decreases with increasing boron composition. Also, the decrease in the internal field is originated from the reduction in the lattice mismatch between the well and the substrate with the inclusion of the boron. Here, the well is lattice-matched to the substrate near x=0.09. Figure 3 shows (a) spontaneous emission coefficients for Bx Aly Ga1−x−y N/AlN QW structures (y=0.2) with several x values and (b) peak intensities as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures with several y values. Spontaneous emission spectra are obtained at a sheet carrier density of N2D = 20 × 1012 cm−2 . The peak wavelength of the conventional AlGaN/AlN QW structure with the Al composition of 0.2 is shown to be about 315 nm. It is shifted to the short wavelength with increasing boron composition because of the increase in the bandgap energy. We know that the spontaneous emission peak of BAlGaN/AlN QW structures is found to be greatly improved with the inclusion of the boron. In particular, in the case of y=0.2, the light intensity of the QW structure with x=0.08 is about twice larger than the conventional QW structure. However, the spontaneous emission peak begins to decrease when the boron composition exceeds a critical value, for example, x=0.08 for y=0.2. The decrease in the spontaneous emission peak is related to the decrease in the quasi-Fermi level separation, as discussed below. Also, the critical value rapidly decrease with increasing Al composition. In the case of QW structures with higher Al composition (y = 0.6), the light emission is reduced with the inclusion of the boron. This is related to the fact that the characteristic of the topmost valence subband is changed to the crystal-field splitoff hole band with the inclusion of boron. Thus, the TM-polarized light emission is enhanced with increasing boron composition, although not shown here. Figure 4 shows potential profile and the wave functions (C1 and HH1) at zone center for
#227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3627
7
(b) x=0.06
(a) x=0.0
0.25
(c) x=0.12
6
(d)
ΔEfc
0.20
5
Energy (eV)
C1
C1
C1
3 BxAlyGa1-x-yN/AlN
2
Lw=2.5 nm, y=0.2
1 HH1
HH1
0
HH1
ΔEfc+ΔEfv
0.10 0.05
ΔEfv
0.00 -0.05
-1 -2
ΔEfc+ΔEfv (eV)
0.15
4
0
30 60 90 0
Position (Å)
30 60 90 0
Position (Å)
30 60 90
Position (Å)
-0.10 0.00 0.05 0.10
Boron composition
Fig. 4. Potential profile and the wave functions (C1 and HH1) at zone center for cases with (a) x=0.0, (b) 0.06, and (c) 0.12 and (d) quasi-Fermi level separation as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (Lw =2.5 nm).
cases with (a) x=0.0, (b) 0.06, and (c) 0.12 and (d) quasi-Fermi level separation as a function of the boron composition for Bx Aly Ga1−x−y N/AlN QW structures (Lw =2.5 nm). Here, the quasiFermi-level separation ΔE f c (ΔE f v ) is defined as the energy difference between the quasi-Fermi level and the ground-state energy in the conduction band (the valence band). The quasi-Fermilevel separation is obtained at the sheet carrier density of N2D = 20 × 1012 cm−2 . In the case of the conventional QW structure, a large spatial separation between electron and hole wave functions is observed in the QW structure because of the large internal field. On the other hand, a spatial separation between electron and hole wavefunctions is reduced due to the decrease in the internal field increasing boron composition, which results in the increase in the optical matrix element, as shown in Fig. 2. However, the quasi-Fermi-level separation is observed to decrease rapidly with increasing boron composition. Thus, we know that the decrease in the spontaneous emission peak observed for the case with high x values is mainly due to the decrease in the quasi-Fermi level separation. The reduction in the quasi-Fermi level separation can be explained by the fact that the heavy-hole effective mass around the topmost valence band greatly increases with increasing boron composition. Hence, we expect that BAlGaN/AlN QW structures with small boron compositions below critical values can be used as a light source with a high efficiency in UV region.
3.
Conclusion
In summary, light emission characteristics of UV BAlGaN/AlN QW structures were using the multiband effective-mass theory and non-Markovian model. The matrix element at the bandedge is found to increase rapidly with increasing boron composition. Thus, the QW structures show much larger light intensity than the conventional QW structure. However, the spontaneous emission peak shows a maximum at the critical value (x= 0.08 for y=0.2) and begins to decrease when the boron composition is further increased. In particular, in the case of QW structures with higher Al composition (y > 0.5), the light emission is shown to be reduced with the inclusion of #227126 - $15.00 USD (C) 2015 OSA
Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3628
the boron because the characteristic of the topmost valence subband is changed to the crystalfield splitoff hole band. Hence, we expect that Bx Aly Ga1−x−y N/AlN QW structures with small boron compositions for y < 0.5 can be used as a TE-polarized light source with a high efficiency in UV region.
Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012R1A1B3000476) and partially by the Industrial Strategic technology development program, 10041878, Development of WPE 75% LED device process and standard evaluation technology funded by the Ministry of Knowledge Economy (MKE, Korea).
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Received 18 Nov 2014; revised 30 Jan 2015; accepted 30 Jan 2015; published 5 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003623 | OPTICS EXPRESS 3629
