Polarization characteristics of semipolar (112̄2) InGaN/GaN quantum well structures grown on relaxed InGaN buffer layers and comparison with experiment

Seoung-Hwan Park; Dhaneshwar Mishra; Y. Eugene Pak; K. Kang; Chang Yong Park; Seung-Hyun Yoo; Yong-Hee Cho; Mun-Bo Shim; Sungjin Kim

doi:10.1364/OE.22.014850

1. Introduction

Nonpolar and semipoalr GaN-based quantum well (QW) structures have received a great deal of attention in recent years for their potential application in blue-green optoelectronic devices because the internal field is expected to be reduced compared to those with the (0001) crystal orientation [1–3]. Also, they show a giant in-plane optical anisotropy in the optical matrix elements [4–6]. This results in a great polarization ratio ρ because a spontaneous emission rate is related to absolute square of the optical matrix element. ρ is defined as (I_y′ − I_x′)/(I_y′ + I_x′) where I is the peak intensity of spontaneous emission rate for x’- and y’-polarizations, respectively, and directly reflects the energy-band structures of emitting layers because the light intensity is mainly determined by the transition between the lowest conduction subband and the topmost valence subband [7]. Among them, the semipolar (112̄2) plane is of special interest because high efficiency green and yellow light-emitting diodes (LEDs) have already been demonstrated on this plane [8, 9]. On the other hand, in the case of a long wavelength region, the lattice mismatch between InGaN wells and the GaN underlayer is large and significant compressive stress in an InGaN quantum well generates defects and deteriorates the performance of the optical devices [10, 11].

Recently, several groups [12–14] proposed a relaxed InGaN underlayer as one way to reduce lattice mismatch. It was shown that the use of ternary InGaN buffer layers resulted in significant changes in polarization properties of green-emitting QW structures [14]. The polarized light source is desirable for backlighting of liquid crystal displays (LCDs) and for improving laser diode (LD) performance by the appropriate selection of waveguide direction using polarized emission [15, 16]. The understanding of physical mechanisms related to this topic will be important for the realization of high efficiency green optoelectronic devices. However, many fundamental properties of (112̄2)-oriented InGaN-based QW structures grown on relaxed In-GaN buffers are not yet well understood because studies based on these structures are in an early developmental stage. In particular, there has been very little work done on partial strain relaxation effects on electronic and optical properties of these QW structures and comparison with experiment.

In this paper, we investigate partial strain relaxation effects on polarization ratio of semipolar (112̄2) InGaN/GaN QW structures grown on relaxed InGaN buffers using the multiband effective-mass theory. We compare these results with those reported experimentally. Here, we consider the free carrier model with the band-gap renormalization. The valence-band structure for the (112̄2) crystal orientation is calculated by using a 6 × 6 Hamiltonian based on the k · p method [1].

2. Theory

The Hamiltonian for an arbitrary crystal orientation can be obtained using a rotation matrix

U = (\begin{matrix} cos θ cos ϕ & cos θ sin ϕ & - sin θ \\ - sin ϕ & cos ϕ & 0 \\ sin θ cos ϕ & sin θ sin ϕ & cos θ \end{matrix}) .

Rotations of the Euler angles θ and ϕ transform the physical quantities from (x, y, z) coordinates to (x′, y′, z′) coordinates. The z-axis corresponds to the c-axis [0001], and the growth axis (defined as the z′-axis) is normal to the QW plane (hkil). The relation between the coordinate systems for vectors and tensors is expressed as

\begin{array}{l} k_{i}^{'} & = & U_{i α} k_{α}, \\ ε_{i j}^{'} & = & U_{i α} U_{j β} ε_{α β}, \\ C_{i j k l}^{'} & = & U_{i α} U_{j β} U_{k γ} U_{l δ} C_{α β γ δ}, \end{array}

where summation over repeated indices is implicit. Then, we obtain a 6 × 6 Hamiltonian for the (112̄2) orientation by using the transformation relation with θ = 56° and ϕ = 0. [17, 18]

The spontaneous emission coefficient including the effects of anisotropy on the valence band dispersion is given by [19, 20]

\begin{array}{l} g_{sp} (ω) & = & \sqrt{\frac{μ_{o}}{ε}} 2 (\frac{e^{2}}{m_{o}^{2} ω}) \int_{0}^{2 π} d ϕ_{0} \int_{0}^{\infty} d {k^{'}}_{‖} \frac{{2 k^{'}}_{‖}}{{(2 π)}^{2} L_{w}} \\ \cdot & {| {\hat{e}}^{'} \cdot {M^{'}}_{l m} ({k^{'}}_{‖}, ϕ_{0}) |}^{2} f_{l}^{c} ({k^{'}}_{‖}, ϕ_{0}) (1 - f_{m}^{v}) (k_{‖}^{'}, ϕ_{0})) \\ \cdot & Re L (ω, k_{‖}^{'}, ϕ_{0}), \end{array}

where ω is the angular frequency, μ_o is the vacuum permeability, ε is the dielectric constant, e is the charge of an electron, m_o is the free electron mass, ϕ₀ is the angle between k_x′ and k_y′ wavevectors, k′_‖ is the magnitude of the in-plane wave vector in the QW plane, L_w is the well width, ê′ is a unit vector in the direction of the optical electric field, |M′_lm|² is the momentum matrix element in the strained QW,

f_{l}^{c}

and

f_{m}^{v}

are the Fermi functions for occupation probability by the electrons in the conduction subband states and the valence subband states, respectively. The indices l and m denote the electron states in conduction subband and heavy hole (light hole) subband states, respectively. Also,

E_{l m} (k_{‖}^{'}, \bar{h} ω, ϕ_{0}) = E_{l}^{c} (k_{‖}^{'}, ϕ_{0}) - E_{m}^{v} (k_{‖}^{'}, ϕ_{0}) + E_{g} + Δ E_{S X} + Δ E_{C H} - \bar{h} ω

is the renormalized transition energy between electrons and holes, where E_g is the band gap of the material, and ΔE_SX and ΔE_CH are the screened exchange and the Coulomb-hole contributions [21, 22] to the band-gap renormalization, respectively. Here, h̄ is the Planck constant. The line-shape function is Gaussian for the simplest non-Markovian quantum kinetics and is given in [19] and [20].

The spontaneous emission rate r_spon can be obtained from our calculated spontaneous emission spectrum g_sp by using

r_{spon} (E) = \frac{4 n^{2}}{\bar{h} λ^{2}} g_{sp} (E),

where n is the refractive index of the quantum well and E = 2πch̄/λ with c being the speed of light. The material parameters for GaN and InN used in the calculation were taken from [23] and references in there, except for band-gap. The band-gap expression was obtained from [24]. The parameters for In_xGa_1−xN were obtained from the linear combination between the parameters of GaN and InN except for the band-gap.

3. Results and discussion

Experimental results on semi-polar (112̄2) InGaN/GaN QW structures showed that the polarization switching changing from y′- to x′-polarization occurs at the In composition of about 0.3 for the QW structure with L_w=3 nm under low excitation power [7,25]. The origin of the polarization switching is still not clear. Some groups proposed very large values of the deformation potential D₆ (−8.8, −7.1, and −5.5 eV) to explain polarization switching [7, 26, 27]. However, first-principles calculations and experimental measurements showed much smaller D₆ values of 3.95 and 3.02 eV, respectively [28, 29]. Using these values, the polarization switching was not observed for bulk InGaN under the homogeneous strain. On the other hand, Yan et al. [28] and Roberts et al. [30] suggested that partial strain relaxation is a cause of polarization switching of semipolar InGaN grown on GaN buffer layers because partial strain relaxation has been observed in semipolar InGaN samples [31]. Here, we assume that partial strain relaxation is a cause of polarization switching [32]. First, for comparison with the experiment result for the polarization ratio of green-emitting InGaN/GaN QW structures grown on InGaN suffer layers, we need the value of a partial strain relaxation along y’-axis $(ε_{y^{'} y^{'}}^{0} - ε_{y^{'} y^{'}})$ for the InGaN/GaN QW structure grown on the GaN buffer layer.

Figure 1 shows the polarization ratio as a function of the strain relaxation of $ε_{y^{'} y^{'}} / ε_{y^{'} y^{'}}^{0}$ along [11̄00] (y′-axis) for the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (L_w=3.5 nm) grown on GaN buffer layer with several strain relaxation $ε_{x^{'} x^{'}} / ε_{x^{'} x^{'}}^{0}$ . The polarization ratio is calculated at the carrier density of 2 × 10¹⁹ cm⁻³. The In composition (x=0.34) was selected to give a transition wavelength of about 530 nm. The polarization ratio ρ is defined as (I_y′ − I_x′)/(I_y′ + I_x′) where I is the peak intensity of spontaneous emission rate for x′- and y′-polarizations, respectively. Here, strain component ε_x′x′ was normalized with $ε_{x^{'} x^{'}}^{0}$ , which is a strain component with no strain relaxation. Thus, $ε_{x^{'} x^{'}} / ε_{x^{'} x^{'}}^{0} = 1.0$ means no strain relaxation. Similarly, strain component ε_y′y′ was also normalized with $ε_{y^{'} y^{'}}^{0}$ . Recently, Uchida et al. [14] showed that the polarization ratio is about −0.3 for (112̄2)-oriented 530 nm InGaN/GaN QW structure (L_w=3.5 nm) grown on GaN buffer. Then, we obtain the value of $ε_{y^{'} y^{'}} / ε_{y^{'} y^{'}}^{0} = 0.58$ from the comparison with the experiment.

Fig. 1 Polarization ratio as a function of the strain relaxation of $ε_{y^{'} y^{'}} / ε_{y^{'} y^{'}}^{0}$ along [11̄00] (y′-axis) for the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (L_w=3.5 nm) grown on GaN buffer layer with several strain relaxation $ε_{x^{'} x^{'}} / ε_{x^{'} x^{'}}^{0}$ .

Download Full Size | PDF

Figure 2 shows the polarization ratio as a function of In composition of InGaN buffer and comparison with experimental data for the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (L_w=3.5 nm) grown on InGaN buffers. The experimental data were taken from [14]. Here, $ε_{x^{'} x^{'}} / ε_{x^{'} x^{'}}^{0}$ was fixed to be 0.2 for all cases because the polarization ratio is its weak function. We assume that the strain relaxation ratio $(ε_{y^{'} y^{'}}^{0} - ε_{y^{'} y^{'}}) / ε_{y^{'} y^{'}}^{0}$ is linearly proportional to the difference of lattice constants between the well and the substrata. For example, values of $(ε_{y^{'} y^{'}}^{0} - ε_{y^{'} y^{'}}) / ε_{y^{'} y^{'}}^{0}$ used in the calculation are 0.65 and 0.72 for cases grown on InGaN buffers with In compositions of 0.05 and 0.10, respectively. Here, in the case of the QW structure grown on GaN buffer layer (y=0.0), $ε_{y^{'} y^{'}} / ε_{y^{'} y^{'}}^{0} = 0.58$ was used in the calculation of the in-plane optical ratio, as shown in Fig. 1. The absolute of the polarization ratio gradually decreases with increasing In composition in InGaN buffer layer and change its sign for the QW structure grown on InGaN buffer layer with a relatively larger In composition. We know that theoretical results are in good agreement with the experiment. To understand behavior of the polarization ratio by the partial strain relaxation effects, we need to calculate the peak intensities of spontaneous emission rate in addition to the electronic and optical properties such as valence band structrues and optical matrix elements for QW structures with different In compositions in the buffer layers. In particular, the polarization ratio is directly related to states constituting the topmost valence subband at the Γ point of the valence band structures because the light intensity is mainly determined by the transition between the lowest conduction subband and the topmost valence subband.

Fig. 2 Polarization ratio as a function of In composition of InGaN buffer and comparison with experimental data for the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (L_w=3.5 nm) grown on InGaN buffers. The experimental data were taken from [14].

Download Full Size | PDF

Figure 3 shows valence band structures along k_x′ and k_y′ of the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (x=0.34, L_w=3.5 nm) grown on In_yGa_1−yN buffer layer with (a) y=0.0, (b) 0.05, and (c) 0.10. The naming of the subbands for the QW structure follows the dominant composition of the wave function at the Γ point in terms of the |X′〉, |Y′〉, and |Z′〉 bases. The components $P_{m}^{i = (X^{'}, Y^{'}, Z^{'})}$ of each wave function are given by $P_{m}^{X^{'}} = 〈 {g^{'}}_{m}^{(3)} | {g^{'}}_{m}^{(3)} 〉 + 〈 {g^{'}}_{m}^{(6)} | {g^{'}}_{m}^{(6)} 〉$ , $P_{m}^{Y^{'}} = (〈 {g^{'}}_{m}^{(1)} + {g^{'}}_{m}^{(2)} + {g^{'}}_{m}^{(1)} + {g^{'}}_{m}^{(2)} 〉 + 〈 {g^{'}}_{m}^{(4)} + {g^{'}}_{m}^{(5)} | {g^{'}}_{m}^{(4)} + {g^{'}}_{m}^{(5)} 〉) / 2$ , $P_{m}^{Z^{'}} = (〈 {g^{'}}_{m}^{(2)} - {g^{'}}_{m}^{(1)} | {g^{'}}_{m}^{(2)} - {g^{'}}_{m}^{(1)} 〉 + 〈 {g^{'}}_{m}^{(4)} - {g^{'}}_{m}^{(5)} | {g^{'}}_{m}^{(4)} - {g^{'}}_{m}^{(5)} 〉) / 2$ . Here, $ε_{x^{'} x^{'}} / ε_{x^{'} x^{'}}^{0}$ was fixed to be 0.2 for all cases. We know that states constituting the topmost valence subband at the Γ point are predominantly |X′>-like for QW structures grown on InGaN buffer layers with relatively small In compositions. On the other hand, the QW structure grown on the In-GaN buffer layer with a relatively larger In composition (x=0.1) shows that states constituting the topmost valence subband at the Γ point are predominantly |Y′>-like. Thus, in the case of the QW structure grown on the InGaN buffer layer with a relatively larger In composition, optical matrix element and spontaneous emission rate for y’-polarization are expected to be dominant, as discussed below. Also, the average hole effective mass slightly increases for the QW structure grown on the InGaN buffer layer. For example, the average hole effective masses are 1.08 and 1.27 m_o at the carrier density of 2 × 10¹⁹ cm⁻³ for QW structures grown on GaN and InGaN (x = 0.10) buffer layers, respectively. Here, hole effective masses are averaged in the k_x′ -k_y′ plane because they show anisotropy in the QW plane for general crystal orientation. To estimate the magnitude of the hole effective mass, we consider the parabolic band fitted to the lowest subband of the exact band structure.

Fig. 3 Valence band structures along k_x′ and k_y′ of the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (x=0.34, L_w=3.5 nm) grown on In_yGa_1−yN buffer layer with (a) y=0.0, (b) 0.05, and (c) 0.10.

Download Full Size | PDF

Figure 4 shows optical matrix elements for x′- and y′-polarizations of the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (x=0.34, L_w=3.5 nm) grown on In_yGa_1−yN buffer layer with (a) y=0.0, (b) 0.05, and (c) 0.10. Here, the notation k_‖ means that the optical matrix elements were averaged in k_x′ -k_y′ QW plane because they depend on the angle ϕ between k_x′ and k_y′ wavevectors. In the case of the QW structure grown on the InGaN buffer layer with a relatively smaller In composition, the x′-polarized matrix element is dominant at the band-edge (k_‖ = 0) and rapidly decreases with increasing k_‖. However, the y′-polarized matrix element rapidly increases with increasing k_‖ and becomes similar to the x′-polarized matrix element at a large k_‖. On the other hand, in the case of the QW structure grown on the InGaN buffer layer with a relatively larger In composition (x = 0.10), the y′-polarized matrix element becomes dominant at the band-edge.

Fig. 4 Optical matrix elements for x′- and y′-polarizations of the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (x=0.34, L_w=3.5 nm) grown on In_yGa_1−yN buffer layer with (a) y=0.0, (b) 0.05, and (c) 0.10.

Download Full Size | PDF

Figure 5 shows spontaneous emission rate for x′- and y′-polarizations of the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (x=0.34, L_w=3.5 nm) grown on InyGa_1−yN buffer layer with (a) y=0.0, (b) 0.05, and (c) 0.10. The spontaneous emission rate is calculated at the carrier density of 2 × 10¹⁹ cm⁻³. Here, the spontaneous emission rate was averaged in k′_x-k′_y QW plane. In the case of the QW structure grown on GaN buffer layer, the spontaneous emission rate for the x′-polarization is shown to be larger than that for the y′-polarization. On the other hand, with increasing In composition in the InGaN subsrate, the spontaneous emission rate for the y′-polarization gradually increases while that for x′-polarization gradually decreases due to the decrease in a matrix element at the band-edge (k_‖ = 0). Thus, the absolute value of the polarization ratio decreases with increasing In composition in the InGaN buffer layer and changes its sign for the QW structure with a relatively larger In composition (x > 0.07). For example, polarization ratios are −0.3 and 0.1 for QW structures grown on InGaN buffer layers with 0.0 and 0.1, respectively.

Fig. 5 Spontaneous emission rate for x′- and y′-polarizations of the (112̄2)-oriented In_xGa_1−xN/GaN QW structures (x=0.34, L_w=3.5 nm) grown on InyGa_1−yN buffer layer with (a) y=0.0, (b) 0.05, and (c) 0.10.

Download Full Size | PDF

4. Conclusion

In summary, partial strain relaxation effects on polarization ratio of semipolar (112̄2) In-GaN/GaN QW structures grown on relaxed InGaN buffers were investigated using the multi-band effective-mass theory. The absolute of the polarization ratio gradually decreases with increasing In composition in InGaN buffer layer and change its sign for the QW structure grown on InGaN buffer layer with a relatively larger In composition. Theoretical results are in good agreement with the experiment. This can be explained by the fact that, with increasing In composition in the InGaN subsrate, the spontaneous emission rate for the y′-polarization gradually increases while that for x′-polarization decreases.

Acknowledgments

This work is supported by the Samsung Advanced Institute of Technology in Samsung Electronics Co., Ltd. under the Technology Collaboration program.

References and links

1. S.-H. Park and S. L. Chuang, “Crystal-orientation effects on the piezoelectric field and electronic properties of strained wurtzite semiconductors,” Phys. Rev. B 59, 4725–4737 (1999). [CrossRef]

2. S.-H. Park, “Crystal orientation effects on electronic properties of wurtzite GaN/AlGaN quantum wells with spontaneous and piezoelectric polarization,” Jpn. J. Appl. Phys. 39, 3478–3482 (2000). [CrossRef]

3. P. Waltereit, O. Brandt, A. Trampert, H. T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, and K. H. Ploog, “Nitride semiconductors free of electrostatic fields for efficient white light-emitting diodes,” Nature 406, 865–868 (2000). [CrossRef] [PubMed]

4. B. Rau, P. Waltereit, O. Brandt, M. Ramsteiner, K. H. Ploog, J. Puls, and F. Henneberger, “In-plane polarization anisotropy of the spontaneous emission of M-plane GaN/(Al,Ga)N quantum wells,” Appl. Phys. Lett. 77, 3343–3345 (2000). [CrossRef]

5. Y. Zhao, Q. Yan, D. Feezell, K. Fujito, C. Van de Walle, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Optical polarization characteristics of semipolar (303̄1) and ( $\bar{3031}$ ) InGaN/GaN light-emitting diodes,” Opt. Express 21, A53–A59 (2012). [CrossRef]

6. L. Schade and U. T. Schwarz, “Energy offset between valence band anti-crossing and optical polarization switching in semipolar InGaN quantum wells,” Appl. Phys. Lett. 102, 232101 (2013). [CrossRef]

7. M. Ueda, M. Funato, K. Kojima, Y. Kawakami, Y. Narukawa, and T. Mukai, “Polarization switching phenomena in semipolar In_x Ga_1−xN/GaN quantum well active layers,” Phys. Rev. B 78, 233303 (2008). [CrossRef]

8. H. Sato, H. Hirasawa, H. Asamizu, N. Fellows, A. Tyagi, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “High Power and High Efficiency Semipolar InGaN Light Emitting Diodes,” J. Light Visual Environ. 32, 107–110 (2008). [CrossRef]

9. H. Sato, R. B. Chung, H. Hirasawa, N. Fellows, H. Masui, F. Wu, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Optical properties of yellow light-emitting diodes grown on semipolar (112̄2) bulk GaN substrates,” Appl. Phys. Lett. 92, 221110 (2008). [CrossRef]

10. M. Funato, M. Ueda, D. Inoue, Y. Kawakami, Y. Narukawa, and T. Mukai, “Experimental and theoretical considerations of polarization field direction in semipolar InGaN/GaN quantum wells,” Appl. Phys. Express 3, 071001 (2010). [CrossRef]

11. J. Nishinaka, M. Funato, and Y. Kawakami, “Anisotropic lattice relaxation in non-c-plane InGaN/GaN multiple quantum wells,” J. Appl. Phys. 112, 033513 (2012). [CrossRef]

12. M. J. Kappers, T. J. Badcock, R. Hao, M. A. Moram, S. Hammersley, P. Dawson, and C. J. Humphreys, “On the origin of blue-green emission from heteroepitaxial nonpolar a-plane InGaN quantum wells,” Phys. Status Solidi C 9, 465–468 (2012). [CrossRef]

13. I. L. Koslow, M. T. Hardy, P. S. Hsu, P.-Y. Dang, F. Wu, A. Romanov, Y.-R. Wu, E. C. Young, S. Nakamura, J. S. Speck, and S. P. DenBaars, “Performance and polarization effects in (112̄2) long wavelength light emitting diodes grown on stress relaxed InGaN buffer layers,” Appl. Phys. Lett. 101, 121106 (2012). [CrossRef]

14. K. Uchida, S. Miyoshi, K. Yamane, N. Okada, K. Tadatomo, and N. Kuwano, “Evaluation of {112̄2} Semipolar multiple quantum wells using relaxed thick InGaN layers with various in compositions,” Jpn. J. Appl. Phys. 52, 08JC07 (2013). [CrossRef]

15. K. Okamoto, T. Tanaka, M. Kubota, and H. Ohta, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46, L820–L822 (2007). [CrossRef]

16. M. Kubota, K. Okamoto, T. Tanaka, and H. Ohta, “Temperature dependence of polarized photoluminescence from nonpolar m-plane InGaN multiple quantum wells for blue laser diodes,” Appl. Phys. Lett. 92, 011920 (2008). [CrossRef]

17. S.-H. Park, “Crystal orientation effects on electronic properties of wurtzite InGaN/GaN quantum wells,” J. Appl. Phys. 91, 9904–9908 (2002). [CrossRef]

18. K. Nishizuka, M. Funato, Y. Kawakami, S. Fujita, Y. Narukawa, and T. Mukai, “Efficient radiative recombination from <112̄2>-oriented In_x Ga_1−xN multiple quantum wells fabricated by the regrowth technique,” Appl. Phys. Lett. 85, 3122–3124 (2004). [CrossRef]

19. D. Ahn, “Theory of non-Markovian optical gain in quantum-well lasers,” Prog. Quantum Electron. 21, 249–287 (1997). [CrossRef]

20. 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). [CrossRef]

21. W. W. Chow, S. W. Koch, and M. Sergent III, Semiconductor-Laser Physics (Springer, Berlin, 1994), p. 168.

22. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1993), p. 195.

23. 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, 1175–1182 (2007). [CrossRef]

24. 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). [CrossRef]

25. H. Masui, H. Asamizu, A. Tyagi, N. F. DeMille, S. Nakamura, and S. P. DenBaars, “Correlation between optical polarization and luminescence morphology of (112̄2)-oriented InGaN/GaN quantum-well structures,” Appl. Phys. Express 2, 071002 (2009). [CrossRef]

26. H. H. Huang and Y. R. Wu, “Light emission polarization properties of semipolar InGaN/GaN quantum well,” J. Appl. Phys. 107, 053112 (2010). [CrossRef]

27. W. G. Scheibenzuber and U. T. Schwarz, “Polarization switching of the optical gain in semipolar InGaN quantum wells,” Phys. Status Solidi B 248, 647–651 (2011). [CrossRef]

28. Q. Yan, P. Rinke, M. Scheffler, and C. G. Van de Walle, “Strain effects in group-III nitrides: Deformation potentials for AlN, GaN, and InN,” Appl. Phys. Lett. 95, 121111 (2009). [CrossRef]

29. R. Ishii, A. Kaneta, M. Funato, Y. Kawakami, and A. A. Yamaguchi, “All deformation potentials in GaN determined by reflectance spectroscopy under uniaxial stress: definite breakdown of the quasicubic approximation,” Phys. Rev. B 81, 155202 (2010). [CrossRef]

30. C. Roberts, Q. Yan, M.-S. Miao, and C. G. Van de Walle, “Confinement effects on valence-subband character and polarization anisotropy in (112̄2) semipolar InGaN/GaN quantum wells,” J. Appl. Phys. 111, 073113 (2012). [CrossRef]

31. A. Tyagi, F. Wu, E. C. Young, A. Chakraborty, H. Ohta, R. Bhat, K. Fujito, S. P. DenBaars, S. Nakamura, and J. S. Speck, “Partial strain relaxation via misfit dislocation generation at heterointerfaces in (Al,In)GaN epitaxial layers grown on semipolar (112̄2) GaN free standing substrates,” Appl. Phys. Lett. 95, 251905 (2009). [CrossRef]

32. S.-H. Park, D. Mishra, Y. E. Pak, C. Y. Park, S.-H. Yoo, Y.-H. Cho, M.-B. Shim, S. Hwang, and S. Kim, “Partial strain relaxation effects on polarization anisotropy of semipolar (112̄2) InGaN/GaN quantum well structures,” Appl. Phys. Lett. 103, 221108 (2013). [CrossRef]

Polarization characteristics of semipolar (112̄2) InGaN/GaN quantum well structures grown on relaxed InGaN buffer layers and comparison with experiment

Abstract

1. Introduction

2. Theory

3. Results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (4)

Optics Express