III-nitride deep-ultraviolet (DUV) light-emitting diodes (LEDs) have attracted more and more attention due to their potential applications such as the sterilization-medical use and illumination.^[1] However, compared to the GaN-based blue LEDs, the DUV LEDs have much lower external quantum efficiencies due to the high dislocation density, the poor p-type doping, and the low light extraction efficiency.^[2] In general, the structure design strategy can be employed to improve the performance of DUV LEDs.^[3] For example, Hirayama et al. reported that the emission efficiency of DUV LEDs can be significantly enhanced by using the multi-quantum barrier (MQB) electron-blocking layer (EBL).^[4] The improvement can be attributed to the increase of the electron injection efficiency. Liu et al. proposed an AlN-delta-GaN quantum well (QW) structure, which can improve the transverse electric (TE)-polarized surface emission.^[2] For the AlGaN-based LEDs, it is well known that the transverse-magnetic (TM) polarized emission will become dominant with increasing the Al-content due to the different valence band arrangement between AlN and GaN, which will lead to the lower surface light extraction efficiency for the c-axis grown LED structure.^[5,6] Thus, the improvement of TE polarized emission by QW structure designs is important to enhance the light extraction efficiency.

In addition, the type-II QW structure can also be expected to improve the emission efficiency due to the reduction of the effective well width and the enhancement of the optical matrix element, as reported in the literatures.^[7,8] However, most research work is focused on the visible light regime, such as the type-II InGaN/GaNSb QW structure.^[8] In this paper, we investigate the optical properties of the type-II InAlN-AlGaN QW structures with various In-contents in the deep-ultraviolet region. Previous study has reported that the band lineup of the InAlN/AlGaN heterojunction may be switched from type-I lineup to type-II lineup in the certain range of In-content.^[9] Therefore, the type-II lineup structure may be obtained by a reasonable design.

In this study, we first calculate the valence band offset (VBO) and conduction band offset (CBO) for the In_xAl_1−xN/Al_0.59Ga_0.41N heterojunction with various In-contents by the linear interpolation method. Then, TE/TM polarization spontaneous emission spectra of the In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structures are analyzed by studying the optical matrix elements and distribution of carriers. Finally, the polarization ratios versus peak wavelength are shown for the type-II QW structures. In the calculation, the band structures and corresponding wave functions are obtained by solving the Schrödinger–Poisson equations self-consistently.^[10]

In the calculation, the Schrödinger equation is solved by using the effective-mass theory. For obtaining the band structures and wave functions, the block-diagonalized Hamiltonian matrix (H ^v) for the valence band and the single band effective mass Hamiltonian (H ^c) for the conduction band are adopted, which can be respectively expressed as^[10–12]

After obtaining the band structures and wave functions, the spontaneous emission rate ( ) can be calculated as follows:^[16]

The investigated In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N single quantum well (SQW) structure, as shown in the inset of Fig. 1(a), is consist of an n-Al_0.74Ga_0.26N layer, an In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW layer, and a p-Al_0.74Ga_0.26N layer. The well layer includes a 1 nm In_xAl_1−xN layer and a 1 nm Al_0.59Ga_0.41N layer. The barrier layer is a 10 nm Al_0.74Ga_0.26N layer. The carrier concentrations of the n- and p-type layers are set as 1.78×10¹⁸ cm⁻³ and 1.18×10¹⁷ cm⁻³, respectively, which are basically in the range reported in Ref. [18]. The Auger coefficient and the Shockley–Read–Hall (SRH) recombination lifetime are respectively set as 5×10⁻³⁰ cm⁶/s and 10 ns.^[19] Figure 1(a) shows the calculated valence band offsets and conduction band offsets of In_xAl_1−xN/Al_0.59Ga_0.41N with various In-contents. From the figure, it can be observed that a type-II lineup structure occurs in the indium-content range of ∼0.132–0.235. In this indium-content range, the valence band-edge and conduction band-edge of In_xAl_1−xN are both lower than that of Al_0.59Ga_0.41N, as shown in Fig. 1(b).

Fig. 1.

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	Fig. 1. (a) The calculated valence band offsets and conduction band offsets of InxAl1−xN/Al0.59Ga0.41N and (b) the potential profile of the InxAl1−xN–Al0.59Ga0.41N/Al0.74Ga0.26N single quantum well structure. The single quantum well structure is shown in the inset.

Figure 2 shows the TE polarization and TM polarization spontaneous emission spectra of the In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structures with various In-contents at the injection current density of 100 A/cm². For comparison, the spectra of the conventional Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structure are also shown. In order to make the thickness of the well layer of both structures equal, the thickness of the Al_0.59Ga_0.41N well layer is set as 2 nm. For the In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structures, the peak intensities in the spontaneous emission spectrum of TE mode are increased by 47.45%–53.84% as compared to those of the conventional structure. The largest TE mode peak intensity is obtained in the type-II QW structure with , which is basically consistent with the experimental result reported in Ref. [9]. Moreover, it is also observed that the TM polarization spontaneous emission rate of the In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structures is obviously smaller than that of the conventional structure. In order to explain these phenomena, we calculate the optical matrix elements and the carrier distribution.

Fig. 2.

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	Fig. 2. (a) TE polarization and (b) TM polarization spontaneous emission spectra of the InxAl1−xN–Al0.59Ga0.41N/Al0.74Ga0.26N QW structures and the conventional Al0.59Ga0.41N/Al0.74Ga0.26N QW structure at the injection current density of 100 A/cm2.

Figures 3(a) and 3(b) show the optical matrix elements as a function of the in-plane wave vector k_t for the In_0.15Al_0.85N–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structure and the conventional Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structure, where c1 is the lowest conduction sub-band and v1, v2, and v3 are the top three valence sub-bands. Note that v1–v3 are obtained by using the upper Hamiltonian. For the c1–v1 transition, the TE polarization optical matrix elements ( ) of both structures are almost the same. However, for the c1–v2 and c1–v3 transitions, the of the conventional structure is far larger than that of the In_0.15Al_0.85N–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structure in the vicinity of the point. In addition, the TM polarization optical matrix elements ( ) of the conventional structure for these transitions are also larger, especially for the c1–v1 transition. Figure 3(c) shows the product of the Fermi–Dirac distribution functions of electron ( ) and hole . It can be seen that the product of the type-II QW structure is larger than that of the conventional QW structure for the c1–v1, c1–v2, and c1–v3 transitions. According to formula (4), the spontaneous emission rate is proportional to the optical matrix element and . Thus, the larger peak intensity in the TE polarization spontaneous emission spectrum for the type-II lineup structure can be attributed to the larger product of and the approximately equal for the c1–v1 transition. Meanwhile, the larger TM polarization peak intensity of the conventional structure can be mainly attributed to the larger for the c1–v1 transition.

Fig. 3.

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	Fig. 3. (a) TE-polarized optical matrix elements ( ), (b) TM-polarized optical matrix elements ( ), and (c) the product of Fermi–Dirac distribution functions of electron and hole as a function of the in-plane wave vector kt for the In0.15Al0.85N–Al0.59Ga0.41N/Al0.74Ga0.26N QW structure and the conventional structure.

Figure 4 shows the TE-polarized and TM-polarized optical matrix elements and at the point for the In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structures with different In-contents. From Fig. 4(a), it can be observed that the TE-polarized optical matrix element with increasing the In-content firstly decreases slightly and then increases for the c1–v1 transition, and decreases for the c1–v2 and c1–v3 transitions. Moreover, the for the c1–v1 transition is far smaller than that for the c1–v2 and c1–v3 transitions. However, for , the trend is completely opposite as shown in Fig. 4(c). Thus, the change of the peak intensity for the TE mode with In-content as shown in Fig. 2(a) can be attributed to the combined effect of and for these transitions. For the TM polarization, the optical matrix element for the c1–v1 transition is much larger as compared to that for the c1–v2 and c1–v3 transitions as shown in Fig. 4(b). And for the c1–v1 transition decreases with increasing In-content, which will lead to the reduction of the TM polarization spontaneous emission rate. Thus, the change of the TM polarization spontaneous emission rate with In-content can be mainly attributed to the reduction of for the c1–v1 transition.

Fig. 4.

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	Fig. 4. (a) TE-polarized and (b) TM-polarized optical matrix elements and (c) at the point for the InxAl1−xN–Al0.59Ga0.41N/Al0.74Ga0.26N QW structures with different In-contents.

Finally, one shows the TE polarization total spontaneous emission rate ( ) and the polarization ratio as a function of peak wavelength of the In_xAl_1−xN–AlGaN/Al_0.74Ga_0.26N QW structures ( , 0.15, 0.17, 0.2, 0.23) and the conventional structure at the current density of 100 A/cm² in Fig. 5. The polarization ratio is defined as .^[20] Here, and denote the TE-polarized and TM-polarized . The total spontaneous emission rate can be obtained by the formula . It can be seen that the TE-polarized of the In_xAl_1−xN–AlGaN/Al_0.74Ga_0.26N QW structures first increases and then decreases with increasing the In-contents due to the combined effect of and as discussed above. In addition, the absolute value of polarization ratio for the conventional structure is much larger than that for the In_xAl_1−xN-AlGaN/Al_0.74Ga_0.26N QW structures, which indicates the strong TM mode emission. By replacing the AlGaN well layer with In_xAl_1−xN–AlGaN layer, the degree of polarization of the DUV LEDs can be much reduced and TE polarized emission can be significantly enhanced.

Fig. 5.

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	Fig. 5. (a) The TE polarization total spontaneous emission rate ( ) and (b) polarization ratio as a function of peak wavelength for the InxAl1−xN–AlGaN/Al0.74Ga0.26N QW structures ( , 0.15, 0.17, 0.2, 0.23) and the conventional structure at the current density of 100 A/cm2.

In summary, we have investigated the optical properties of the type-II lineup In_xAl_1−xN–Al_0.59Ga_0.41N/Al_0.74Ga_0.26N QW structures with various In-contents by using the effective mass theory. As compared to the conventional structure, the type-II lineup structure has much larger TE polarization spontaneous emission rate due to the larger product of and the approximately equal for the c1–v1 transition. In addition, the TE-polarized of the In_xAl_1−xN-AlGaN/Al_0.74Ga_0.26N QW structures has a maximal value in the range of –0.23 at the injection current density of 100 A/cm². It can be attributed to the combined effect of and for the c1–v1, c1–v2, and c1–v3 transitions.