Intersubband transition in lattice-matched BGaN/AlN quantum well structures with high absorption coefficients

Seoung-Hwan Park; Doyeol Ahn; Chan-Yong Park

doi:10.1364/OE.25.003143

1. Introduction

Intersubband (ISB) transitions in semiconductor quantum wells (QWs) has been attracting significant attention because ISB photodetectors present advantages in comparison with interband devices in terms of speed and reproducibility [1]. Among these materials, group III nitride semiconductors are interesting because they show the fastest optical response [2]. Room-temperature ISB absorption in the wavelength range of 1.3–1.55 µm has been reported for GaN/AlGaN and GaN/AlN QW structures [3–7]. However, in the case of the AlN/GaN heterostructures grown on GaN, the lattice-mismatch of 2.5 % is observed, which is large enough to generate structural defects [8] and crack formation [9–11]. Therefore, we need to design GaN-based heterostructures with reduced lattice-mismatch to minimize the formation of structural defects during the epitaxial growth.

Recently, BAlGaN [12] and BInGaN [13] quaternary layers containing boron were proposed as lattice-matched materials to the AlN substrate and the GaN substrate, respectively, because the growth of the lattice-matched quaternary system to AlN or GaN is possible with the inclusion of the small boron. Similarly, the BGaN system was proposed as novel class of materials lattice matched to AlN and SiC substrates [14–16]. In addition, Dreyer et al. [17] reported that the magnitude of the spontaneous polarization for wurtzite BN is estimated to be −2.174 C/m². This value is roughly 25 times larger than that of wurtzite AlN (−0.090 C/m²) [18]. As a result, in a case of boron containing III-nitrides QW structures, a large internal field will be induced in the well. We expect that this gives a positive influence on absorption characteristics of boron containing system because a potential well depth becomes deeper due to the larger internal field, compared to the case with a small internal field. Hence, theoretical studies related to ISB transition in BGaN/AlN QW structures will be important for the design of optoelectronic devices for optical communications.

In this paper, we investigate intersubband absorption characteristics as a function of strain in BGaN/AlN QW structures grown on AlN substrate using an effective mass theory considering the nonparabolicity of the conduction band [19–21]. These results are compared with those of GaN/AlN QW structures. We consider an n-type modulation-doped QW with doping width of L_m=5 Å and the doping density N₃_D in the barrier region at both sides of the well because the lower subbands should be occupied by electrons for intersubband absorption. The sheet carrier density N₂_D in the well was varied from 1 × 10¹⁰ to 5 × 10¹² cm⁻² to investigate doping effect on the absorption coefficient. The donors are assumed to be all ionized. Then, the sheet carrier density N₂_D in the well is given by N₃_D × (2L_m). Here, we neglected effects such as impurity diffusion or impurity absorption.

2. Theoretical model

2.1. Nonparabolicity of conduction band

It has been known that the nonparabolicity of the conduction band should be included for semiconductor heterostructures with high barrier heights and narrow wells or in the case of very high carrier densities [20]. Then, the wave-functions and energy levels are obtained by solving the following Schrödinger equation

- \frac{ℏ^{2}}{2} \frac{d}{d z} (\frac{1}{m (z, E)} \frac{d}{d z} Ψ) + V_{c} (z) Ψ = E Ψ,

where ħ is Planck’s constant divided by 2π and V_c(z) = V (z) + V_ex(z) + V_ϵ(z)−eϕ(z). Here, V (z) is the conduction band edge, V_ex (z) is the exchange-correlation potential, V_ϵ(z) = a_c(ϵ_xx+ϵ_yy+ϵ_yy), ϵ_ii is the strain tensor, a_c is the conduction band deformation potential, and e is the magnitude of electron charge. ϕ(z) is the screening potential induced by the charged carriers, which is obtained by solving the Poisson equation, as discussed below. V_ex (z) is given by [22]

V_{e x} (z) = - {(\frac{9 π}{4})}^{1 / 3} \frac{2}{π r_{s}} [1 + \frac{B}{A} r_{s} \ln (1 + \frac{A}{r_{s}})] \frac{e^{2}}{8 π ϵ_{o} ϵ a^{*}},

where r_s is the dimensionless parameter characterizing electron gas, given by r_s = [(4π/3)a^*3n]^−1/3, a^* = (ϵ(z)/m_e(z))a_B, ϵ(z) is the dielectric constant, and m_e(z) is the parabolic effective mass of the electron. The constants A and B in the calculation are 21 and 0.7734 [22], respectively. Taking the left corner (z₁) of the well as a reference energy, the potential energy in the conduction band is given by

V (z) = {\begin{array}{l} | e | F_{z}^{b} (z - z_{1}) + Δ E_{c}, & z \leq z_{1} \\ | e | F_{z}^{w} (z - z_{1}), & z_{1} < z \leq z_{2} \\ | e | F_{z}^{b} (z - z_{2}) + Δ E_{c}, & z_{2} < z \end{array}

where z₂ is the right corner of the well, ΔE_c is the conduction band offset, and F_z is the internal field due to the piezoelectric polarization P^PZ and the spontaneous polarization P^SP in the well (superscript w) and the barrier (superscript b). The electric fields in the well and the barrier are

\begin{array}{l} F_{z}^{w} = \frac{L_{b}}{ϵ_{b} L_{w} + ϵ_{w} L_{b}} (P_{b} - P_{w}) \\ F_{z}^{b} = - \frac{L_{w}}{ϵ_{b} L_{w} + ϵ_{w} L_{b}} (P_{b} - P_{w}) \end{array}

where L_w and L_b are the well width and the barrier width, respectively, and ϵ_w and ϵ_b are dielectric constants in the well and the barrier, respectively. Here,

P_{w} = P_{w}^{P Z} + P_{w}^{S P}

and

P_{b} = P_{b}^{P Z} + P_{b}^{S P}

are total polarizations in the well and the barrier, respectively. The effect of nonparabolicity is incorporated into eq. (1) simply by making the effective mass a function of the energy E. That is, the effective mass is given by [23]

m (z, E) = m_{e} (z) (1 + \frac{E - V_{c} (z)}{E_{g} (z)}),

where E_g (z) is the band gap energy.

2.2. Self-consistent calculation

The self-consistent band structures and wave functions are obtained by iteratively solving the Schrödinger equation for electrons and Poisson’s equation [24,25]. The total potential profile is

V_{c} (z) = V_{c w} (z) - | e | ϕ (z),

where V_cw (z) = V (z) + V_ex (z) + V_ϵ(z) and ϕ(z) satisfies the Poisson equation

\frac{d}{d z} (ϵ (z) \frac{d}{d z}) ϕ (z) = - e [N_{D}^{+} (z) + n (z)] .

The electron concentration, n(z), is related to the wave functions of the l-th conduction subband by

n (z) = \frac{k T m_{e} (z)}{π ℏ^{2}} {\sum_{l} | f_{l} (z) |}^{2} \ln (1 + e^{[E_{f c} - E_{c l} (0)] / k T})

where m_e is the effective mass of electrons, l is the quantized subband index for the conduction band, E_fc is the quasi-Fermi levels of the electrons, respectively, E_cl (0) is the quantized energy level of the electrons, and f_l (z) is the envelope functions in the conduction band. The Fermi level is obtained from the charge neutrality condition:

\int_{- L / 2}^{L / 2} ρ (z) d z = 0,

where L is the total length of the quantum well structure, i.e, L = L_w + 2L_b. The potential ϕ(z) is obtained by integration [24]:

ϕ (z) = - \int_{- L / 2}^{z} E (z^{'}) d z^{'},

where

E (z) = \int_{- L / 2}^{z} \frac{1}{ϵ (z)} ρ (z^{'}) d z^{'} .

Eq. (1) leads to nonlinear eigenvalue problem because energy E appears in all the terms. i.e., H(E)Ψ = EΨ, which cannot be solved by conventional diagonalization routines. Instead, eigenvalues are obtained by scanning for energies E_i with det([H(E_i)] − E_i[I]) = 0, where [I] is the unity matrix [21]. Also, the wavefunctions corresponding to any particular E_i can be found by the following linear eigenproblem,

([H (E_{i})] - E_{i} [I]) f_{i} = λ f_{i} .

One of eigenvalues obtained from eq. (12) will be almost zero and the eigenvector corresponding to it is actually the eigenfunction corresponding to E_i.

2.3. Intersubband absorption spectrum

The intersubband absorption coefficient for the intersubband transition between the ground state (E₁) and the first excited state (E₂) is given by [24]

α (ℏ ω) = (\frac{ω}{n_{r} c ϵ_{o}}) \frac{{| μ_{21} |}^{2} (Γ / 2)}{{(E_{2} - E_{1} - ℏ ω)}^{2} + {(Γ / 2)}^{2}} (N_{2} - N_{1}),

where ω is the angular frequency, c is the speed of light, o is the vacuum permittivity, Γ is the linewidth, n_r is the refractive index, and

μ_{21} = 〈 f_{2} | e z | f_{1} 〉 = \int f_{2}^{*} (z) e z f_{1} (z) d z

is the intersubband dipole moment and N₁ is the number of electrons per unit volume in the ith subband, which is given by

N_{i} = \frac{k T m_{e}}{π ℏ^{2} L_{w}} \ln (1 + e^{[E_{f c} - E_{i}] / k T}) .

Here, we used Γ/2 = 26 meV [26]. The material parameters for BN, GaN, and AlN used in the calculation are summarized in Table. I. In present, a deformation potential for BN is not well known. We assumed its parameter to be equal to that of GaN as a first approximation. The parameters for B_xGa₁₋_xN are obtained from the linear combination between the parameters of BN and GaN except for the band-gap energy. For that, we used $E_{g} (x) = x E_{g}^{B N} + (1 - x) E_{g}^{G a N} - C x (1 - x)$ with the bowing parameter C. However, there exists an uncertainty in the bowing parameters. For example, Ougazzaden et al. [36] reported the value of C= 9.2 eV while Kadys et al. [38] reported 4.0 eV. Here, we used the value of C= 9.2 eV. The influence of this uncertainty on the calculation results will be discussed in the below.

Table 1. Physical parameters for BN, GaN, and AlN materials used in the calculation.

View Table

3. Results and discussion

Figure 1 shows (a) strain as the function of B content for B_xGa₁₋_xN/AlN QW structure grown on AlN substrate and intersubband transition wavelengths λ₂₁ for (b) GaN/AlN and (c) lattice-matched B_xGa₁₋_xN/AlN (x=0.115) QW structures. The dashed lines are guideline for the zero strain (ϵ = 0) and the intersubband transition wavelength of 1.55 µm in the conduction band, respectively. The intersubband transition wavelength was obtained at a sheet carrier density of N₂_D = 1 × 10¹¹cm⁻². The absolute value of strain rapidly decreases with increasing boron content and becomes zero at a B content of x=0.115. That is, B_xGa₁₋_xN (x=0.115)/AlN QW structure is lattice-matched to AlN substrate. We see that the intersubband transition wavelength for both QW structures rapidly increases with increasing well width. The increasing rate of the wavelength for the QW structure with thick barrier width (L_b=30 Å) is shown to be smaller than that for the QW structure with thin barrier width (L_b=20 Å). Thus, the well width to give the intersubband transition wavelength of 1.55 µm increases with increasing barrier width. In the case of the lattice-matched BGaN/AlN QW structures, the wavelength of 1.55 µm for telecommunication applications are obtained at L_w=25 Å for L_b=20 Å and L_w=30 Å for L_b=30 Å, respectively. On the other hand, in the case of the conventional GaN/AlN QW structures, they are L_w=17 Å for L_b=20 Å and L_w=18 Å for L_b=30 Å, respectively. Well widths for the lattice-matched BGaN/AlN QW structures are much larger than those for the conventional GaN/AlN QW structures.

Fig. 1 (a) Strain as the function of B content for B_xGa₁₋_xN/AlN QW structure grown on AlN substrate and intersubband transition wavelengths λ₂₁ for (b) GaN/AlN and (c) lattice-matched B_xGa₁₋_xN/AlN (x=0.115) QW structures.

Download Full Size | PDF

Figure 2 shows (a) internal field as a function of B content for B_xGa₁₋_xN/AlN QW structures grown on AlN substrate and potential profiles and wave functions for the first two subbands (C1 and C2) in the conduction band of (b) GaN/AlN and (c) lattice-matched B_xGa₁₋_xN/AlN (x=0.115) QW structure. The absolute value of the internal field decreases with increasing boron content and becomes zero at x=0.04. The dashed line is guideline for the zero internal field. However, it begins to increase with sign change when the boron content exceeds x=0.04. Well and barrier widths (Å) for lattice-matched BGaN/AlN and conventional GaN/AlN QW structures are set to give the intersubband transition wavelength of 1.55 µm. Well and barrier widths (L_w, L_b) for BGaN/AlN and GaN/AlN QW structures are (25, 20) and (18, 30), respectively. For both QW structures, we observe that the two subbands are confined in the well and there exist a larger internal field in the well. However, the lattice-matched BGaN/AlN has much larger internal field and potential well depth than the conventional GaN/AlN QW structure. For example, internal fields for BGaN/AlN and GaN/AlN QW structures are 10.9 and 6.8 MV/cm, respectively. Also, the effective potential well depths for BGaN/AlN and GaN/AlN QW structures are about 2.5 and 5.0 eV, respectively. As a result, the former exhibits larger carrier confinement than the latter.

Fig. 2 (a) Internal field as a function of B content for B_xGa₁₋_x N/AlN QW structures grown on AlN substrate and potential profiles and wave functions for the first two subbands (C1 and C2) in the conduction band of (b) GaN/AlN and (c) lattice-matched B_xGa₁₋_x N/AlN (x=0.115) QW structure.

Download Full Size | PDF

Figure 3 shows (a) intersubband dipole moment between the first two subbands in the conduction band and (b) quasi-Fermi level separation ΔE_fc as a function of carrier density for lattice-matched B_xGa₁₋_xN/AlN (x=0.115) and GaN/AlN QW structures with the intersubband transition wavelength of 1.55 µm. The inset shows a square of the product of the wavefunctions as a function of the position (z) for the first two subbands ( $Ψ_{c_{1}}$ and $Ψ_{c_{2}}$ ) in the conduction band. Here, the quasi-Fermi-level separation ΔE_fc is defined as the energy difference between the quasi-Fermi level and the ground-state energy in the conduction band. That is, ΔE_fc = E_fc−E_c₁ where E_c₁ is the ground state in the conduction band. The dipole moments for both BGaN−/AlN and GaN/AlN QW structures are nearly independent of the carrier density. However, the lattice-matched BGaN/AlN QW structure shows larger dipole moment than the conventional GaN/AlN QW structure. For example, they are 7.0 and 6.0×10⁻²⁹C · m, respectively, for BGaN/AlN and GaN/AlN QW structures. This can be explained by the fact that the asymmetry of the wavefunction for the first excited state is enhanced due to the triangular shape of the potential well by the large internal field in the BGaN/AlN QW structure. The overlap between wave functions for the ground state and the first excited state is enhanced for the BGaN/AlN QW structure, as shown in the inset. The BGaN/AlN QW structure also show larger quasi-Fermi-level separation than the GaN/AlN QW structure. As a result, we expect that the BGaN/AlN QW structure will exhibit larger absorption coefficient than the GaN/AlN QW structure.

Fig. 3 (a) Intersubband dipole moment between the first two subbands in the conduction band and (b) quasi-Fermi level separation ΔE_fc as a function of carrier density for lattice-matched B_xGa₁₋_xN/AlN (x=0.115) and GaN/AlN QW structures with the intersubband transition wavelength of 1.55 μm. The inset shows a square of the product of the wave-functions as a function of the position (z) for the first two subbands ( $Ψ_{c_{1}}$ and $Ψ_{c_{2}}$ ) in the conduction band.

Download Full Size | PDF

In Fig. 4, we plotted intersubband absorption spectra as a function of the sheet carrier density for lattice-matched B_xGa₁₋_xN/AlN (x=0.115) and GaN/AlN QW structures with the intersubband transition wavelength of 1.55 μm. The solid lines in Fig. 4(b) show results for the case with the bowing parameter of C=4.0 eV. BGaN/AlN QW structures with C=4.0 eV show slightly smaller intersubband absorption coefficients and a small blue shift of the wavelength, compared to those with C=9.2 eV. That is, we observe that the overall tendency is not changed significantly with C=4.0 eV. The BGaN/AlN QW structure shows much larger intersubband absorption coefficients than the conventional GaN/AlN QW structure, irrespective of the sheet carrier density. This can be explained by the fact that the BGaN/AlN QW structure has larger intersubband dipole moment and quasi-Fermi-level separation than the conventional GaN/AlN QW structure. We note that, in present, there exist substantial technological difficulties in growing BGaN epilayers with boron content exceeding 5–7 %. For example, boron contents of up to 5 % were reported for chemical vapor deposition (CVD) and molecular beam epitaxy (MBE) growth [37, 38]. Also, up to 7 % were reached using ion implantation [39]. However, with the current progress in BGaN epilayer growth, we expect that the BGaN/AlN QW structure could be obtained with B content as high as 11.5 % in a future.

Fig. 4 Intersubband absorption spectra as a function of the sheet carrier density for lattice-matched B_xGa₁₋_xN/AlN (x=0.115) and GaN/AlN QW structures with the intersubband transition wavelength of 1.55 μm. The solid lines in Fig. 4(b) show results for the case with the bowing parameter of C=4.0 eV.

Download Full Size | PDF

4. Conclusion

In conclusion, optical absorption properties of lattice-matched BGaN/AlN QW structures grown on AlN substrate were investigated considering the nonparabolicity of the conduction band. These results were compared with those of GaN/AlN QW structures. We found that the BGaN/AlN QW structure has larger intersubband dipole moment and quasi-Fermi-level separation than the conventional GaN/AlN QW structure. This is mainly due to the fact that the overlap between wave functions for the ground state and the first excited state and the carrier confinement were enhanced for the BGaN/AlN QW structure. As a result, The BGaN/AlN QW structure shows much larger intersubband absorption coefficients than the conventional GaN/AlN QW structure. Hence, we expect that the lattice-matched BGaN/AlN QW structure can be used for telecommunication applications at 1.55 μm with the high absorption coefficient.

Funding

This work was supported by the ICT R&D program of MSIP/IITP [1711028311, Reliable crypto-system standards and core technology development for secure quantum key distribution network] and partially supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2015R1D1A1A01057110).

References and links

1. D. Ahn and S. L. Chuang, “Intersubband optical absorption in a quantum well with an applied electric field,” Phys. Rev. B 35(12), R4149–R4151 (1987) [CrossRef]

2. D. Ahn and S. L. Chuang, “Calculation of linear and nonlinear intersubband optical absorptions in a quantum well model with an applied electric field,” IEEE J. Quantum Electron. 23(12), 2196–2204 (1987). [CrossRef]

3. N. Suzuki and N. Iizuka, “Feasibility study on ultrafast nonlinear optical properties of 1.55-μ m Intersubband transition in AlGaN/GaN quantum wells,” Jpn. J. Appl. Phys. 36(8A), L1006 (1997). [CrossRef]

4. C. Gmachl, H. M. Ng, S.-N. G. Chu, and A. Y. Cho, “Intersubband absorption at λ ∼ 1.55μ m in well- and modulation-doped GaN/AlGaN multiple quantum wells with superlattice barriers,” Appl. Phys. Lett. 77(23), 3722–3724 (2000). [CrossRef]

5. C. Gmachl, H. M. Ng, and A. Y. Cho, “Intersubband absorption in degenerately doped GaN/Al_x Ga₁₋_x N coupled double quantum wells,” Appl. Phys. Lett. 79(11), 1590–1592 (2001). [CrossRef]

6. K. Kishino, A. Kikuchi, H. Kanazawa, and T. Tachibana, “Intersubband transition in (GaN)^m/(AIN)ⁿ superlattices in the wavelength range from 1.08 to 1.61 μ m,” Appl. Phys. Lett. 81(7), 1234–1236 (2002). [CrossRef]

7. N. Iizuka, K. Kaneko, and N. Suzuki, “Near-infrared intersubband absorption in GaN/AlN quantum wells grown by molecular beam epitaxy,” Appl. Phys. Lett. 81(10), 1803–1805 (2002). [CrossRef]

8. S.-H. Park and D. Ahn, “Intersubband energies in strain-compensated InGaN/AlInN quantum well structures,” AIP Advances 6(1), 015014 (2006). [CrossRef]

9. H. Akabli, A. Almaggoussi, A. Abounadi, A. Rajira, K. Berland, and T. G. Andersson, “Intersubband energies in Al₁₋_y In_y N/Ga_1−i In_x N heterostructures with lattice constant close to a_GaN,” Superlat. Microstruct. 52(1), 70–77 (2012). [CrossRef]

10. X.Y. Liu, T. Aggerstam, P. Jänes, P. Holmström, S. Lourdudoss, L. Thylénc, and T.G. Andersson, “Investigation of intersubband absorption in GaN/AlN multiple quantum wells grown on different substrates by molecular beam epitaxy,” J. Cryst. Growth 301, 457–460 (2007). [CrossRef]

11. R. Butté, J.F. Carlin, E. Feltin, M. Gonschorek, S. Nicolay, G. Christmann, D. Simeonov, A. Castiglia, J. Dorsaz, H.J. Buehlmann, S. Christopoulos, G. Baldassarri Hoger von Hogersthal, A.J.D. Grundy, M. Mosca, C. Pinquier, M.A. Py, F. Demangeat, J. Frandon, P.G. Lagoudakis, J.J. Baumberg, and N. Grandjean, “Current status of AlInN layers lattice-matched to GaN for photonics and electronics,” J. Phys. D 40(20), 6328 (2007). [CrossRef]

12. R. Butté, E. Feltin, J. Dorsaz, G. Christmann, J.F. Carlin, N. Grandjean, and M. Ilegems, “Recent progress in the growth of highly reflective nitride-based distributed Bragg reflectors and their use in microcavities,” Jpn J. Appl. Phys. 44(10), 7207 (2005). [CrossRef]

13. S. Watanabe, T. Takano, K. Jinen, J. Yamamoto, and H. Kawanishi, “Refractive indices of B_x Al₁₋_x N (x = 0–0.012) and B_y Ga₁₋_y N (y = 0–0.023) epitaxial layers in ultraviolet region,” Phys. Stat. Sol. (C) 0, 2691–2694 (2003) [CrossRef]

14. 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, and A. Ougazzaden, “Metal-organic vapour phase epitaxy of BInGaN quaternary alloys and characterization of boron content,” J. Cryst. Growth , 312(5), 641–644 (2010). [CrossRef]

15. T. Honda, M. Shibata, M. Kurimoto, M. Tsubamoto, J. Yamamoto, and H. Kawanishi, “Band-gap energy and effective mass of BGaN,” Jpn. J. Appl. Phys. 39(4B), 2389 (2000). [CrossRef]

16. A. Ougazzaden, S. Gautier, T. Moudakir, Z. Djebbour, Z. Lochner, S. Choi, H. J. Kim, J.-H. Ryou, R. D. Dupuis, and A. A. Sirenko, “Bandgap bowing in BGaN thin films,” Appl. Phys. Lett. 93(8), 083118 (2008). [CrossRef]

17. A Kadys, J MickevicȈius, T Malinauskas, J JurkevicȈius, M Kolenda, S Stanionyté, D Dobrovolskas, and G Tamulaitis, “Optical and structural properties of BGaN layers grown on different substrates,” J. Phys. D: Appl. Phys. 48(46), 465307 (2015). [CrossRef]

18. C. E. Dreyer, J. L. Lyons, A. Janotti, and C. G. Van de Walle, “Band alignments and polarization properties of BN polymorphs,” Appl. Phys. Express 7, 031001 (2014). [CrossRef]

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

20. C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50(12), 8663–8674 (1994). [CrossRef]

21. J. M. Li, Y. W. Lu, X.X. Han, J.J. Wu, X.L. Liu, Q.S. Zhu, and Z.G. Wang, “Theoretical investigation of intersubband transition in Al_x Ga₁₋_x N/GaN/Al_y Ga₁₋_y N step quantum well,” Physica E 28(4), 453–461 (2005). [CrossRef]

22. V. D. Jovanović, Z. Ikonić, D. Indjin, P. Harrison, V. Milanovic, and R. A. Soref, “Designing strain-balanced GaN/AlGaN quantum well structures: Application to intersubband devices at 1.3 and 1.55 mu m wavelengths,” J. Appl. Phys. 93(6), 3194–3197 (2003). [CrossRef]

23. M. Helm, Intersubband Transitions in Quantum Wells: Physics and Device Applications I, H.C. Liu and F. Capasso, eds., (Academic, 2000).

24. J. Radovanović, V. Milanović, Z. Ikonić, D. Indjin, V. Jovanović, and P. Harrison, “Optimal design of GaN-AlGaN Bragg-confined structures for intersubband absorption in the near-infrared spectral range,” IEEE J. Quant. Electron. 39(10), 1297–1304 (2003). [CrossRef]

25. S. L. Chuang, Physics of Optoelectronic Devices (Wiley, 1995).

26. 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(24), 3103–3105 (1998). [CrossRef]

27. S.-H. Park, Y.-T. Lee, and D. Ahn, “Spontaneous polarization and piezoelectric effects on intraband relaxation time in a wurtzite GaN/AlGaN quantum well,” Appl. Phys. A 71, 589–592 (2000). [CrossRef]

28. 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). [CrossRef]

29. H. P. Maruska and J. J. Tietjen, “The preparation and properties of vapor-deposited single-crystalline GaN’,” Appl. Phys. Lett. 15, 327–328 (1969). [CrossRef]

30. V. Bougrov, M. E. Levinshtein, S. L. Rumyantsev, and A. Zubrilov, in Properties of advanced semiconductor Mmterials GaN, AlN, InN, BN, SiC, SiGe, M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, eds. (Wiley, 2001), pp. 1–30.

31. I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94, 3675–3696 (2003). [CrossRef]

32. O. Madelung, Semiconductors: Basic Data 2nd revised ed (Springer, 1996).

33. M. Suzuki, T. Uenoyama, and A. Yanase, “First-principles calculations of effective-mass parameters of AlN and GaN,” Phys. Rev. B 52, 8132–8139 (1995). [CrossRef]

34. V. W. L. Chin and T. L. Tansley, and Osotchan, “Electron mobilities in gallium, indium, and aluminum nitrides,” J. Appl. Phys. 75, 7365–7372 (1994). [CrossRef]

35. A. Polian, M. Grimsditch, and I. Grzegory, “Elastic constants of gallium nitride,” J. Appl. Phys. 79, 3343–3344 (1996). [CrossRef]

36. G. Martin, A. Botchkarev, A. Rockett, and H. Morkoç, “Valence-band discontinuities of wurtzite GaN, AlN, and InN heterojunctions measured by x-ray photoemission spectroscopy,” Appl. Phys. Lett. 68, 2541–2543 (1996). [CrossRef]

37. A. Ougazzaden, S. Gautier, T. Moudakir, Z. Djebbour, Z. Lochner, S. Choi, H. J. Kim, J.-H. Ryou, R. D. Dupuis, and A. A. Sirenko, “Bandgap bowing in BGaN thin films,” Appl. Phys. Lett. 93, 083118 (2008). [CrossRef]

38. S. Gautier, G. Patriarche, T. Moudakir, M. Abid, G. Orsal, K. Pantzas, D. Troadec, A. Soltani, L. Largeau, O. Mauguin, and A. Ougazzaden, “Deep structural analysis of novel BGaN material layers grown by MOVPE,” J. Cryst. Growth 315, 288–291 (2011). [CrossRef]

39. A. Kadys, J. Mickevičius, T. Malinauskas, J. Jurkevičius, M. Kolenda, S. Stanionytė, D. Dobrovolskas, and G. Tamulaitis, “Optical and structural properties of BGaN layers grown on different substrates,” J. Phys. D: Appl. Phys. 48, 465307 (2015). [CrossRef]

40. A. Y. Polyakov, M. Shin, M. Skowronski, D. W. Greve, R. G. Wilson, A. V. Govorkov, and R. M. Desrosiers, “Growth of GaBN ternary solutions by organometallic vapor phase epitaxy,” J. Electron. Mater. 26, 237–242 (1997). [CrossRef]

Parameters	BN	GaN	AlN
Lattice constant (Å)
a	2.534 [27]	3.1892 [28]	3.112 [28]
Energy parameter (eV)
E _g	5.5 [29]	3.438 [30]	6.158 [30]
Conduction band effective mass
m_e/m_o	0.752 [31]	0.2 [32]	0.33 [32]
Dielectric constant(ϵ₀)
ϵ	5.06 [31]	10.0 [33]	8.5 [33]
Elastic stiffness constant (10¹¹ dyn/cm²)
C ₁₁	98.2 [27]	39.0 [34]	39.8 [33]
C ₁₂	13.4 [27]	14.5 [34]	14.0 [33]
C ₁₃	7.4 [27]	10.6 [34]	12.7 [33]
C ₃₃	107.7 [27]	39.8 [34]	38.2 [33]
Piezoelectric constant (×10⁻¹²m/V)
d ₃₁	0.297 [27]	−1.7 [35]	−2.0 [35]
Spontaneous polarization constant (C/m²)
P_SP	−2.174 [17]	−0.029 [18]	−0.081 [18]

Intersubband transition in lattice-matched BGaN/AlN quantum well structures with high absorption coefficients

Abstract

1. Introduction

2. Theoretical model

2.1. Nonparabolicity of conduction band

2.2. Self-consistent calculation

2.3. Intersubband absorption spectrum

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (4)

Tables (1)

Equations (15)

Optics Express