Enhanced Light Emission from Type-II Red InGaN/GaNSb/GaN Quantum-Well Structures

Electronic and optical properties of type-II InGaN/GaNSb/GaN quantum-well (QW) structures are investigated by using the multiband eective mass theory for potential applications in red light-emitting diodes. e heavy-hole eective mass around the topmost valence band is not aected much by the insertion of the GaNSb layer, and the optical matrix elements are greatly increased by the inclusion of the GaNSb layer in the InGaN/GaN QW structure. As a result, the type-II InGaN/GaNSb/GaN QW structure shows a much larger emission peak than the conventional type-I QW structure owing to the decrease in spatial separation between electron and hole wavefunctions, in addition to the reduction of the eective well width. It is also observed that the In content in InGaN well can be signicantly reduced for the type-II QW structure with a large Sb content, compared to that for the type-I QW structure.


Introduction
III-nitride-based white light-emitting diodes (LEDs) have received much attention for their tremendous potential for energy-e cient general illumination applications [1][2][3].
ey have been usually fabricated by using InGaN/GaN quantum wells (QWs) as InGaN has a direct band gap covering the entire visible spectrum. So far, blue and green InGaN/GaN LEDs have been improved greatly although the e ciency of green LEDs is still inferior to that of blue LEDs. On the other hand, emission in the red wavelength range typically exhibits much lower quantum e ciency because higher In content and relatively thicker QWs are necessary. [4] e high In content in the QW region leads to the large piezoelectric (PZ) and spontaneous (SP) polarization elds [5,6], which signi cantly reduce the internal quantum efciency of the QW owing to a larger spatial separation between electron and hole wavefunctions.
As a method to reduce the internal eld e ect, type-II QW structures have been studied by several research groups. e structures considered include the type-II InGaN/GaNAs QW [7,8], the type-II InGaN/ZnGeN 2 QW [9], and the type-II InGaN/ZnSnN 2 /GaN QW [10,11]. In addition, the type-II InGaN/GaNSb/GaN QW was proposed to improve the internal quantum e ciency of the InGaN/GaN QW structure for the blue wavelength range [12]. On the other hand, in the case of the red wavelength range, there has been no work reported on the optical properties of the type-II QW structures combining InGaN and GaNSb.
In this paper, we theoretically investigate the electronic and optical properties of the type-II QW structure combining In x Ga 1−x N and GaN 1−y Sb y as one way of improving the internal quantum e ciency of the red In x Ga 1−x N/GaN QW structure. e multiband e ective mass theory is utilized to calculate the optical properties of these InGaN/ GaNSb/GaN QW structures. e nite di erence method (FDM) is implemented in Fortran codes to calculate the valence-band structures. ese results are compared with those of the conventional red InGaN/GaN QW structure. e self-consistent (SC) band structures and wavefunctions are obtained by solving the Schrödinger equation for electrons, the 3 × 3 Hamiltonian for holes, and the Poisson's equation iteratively [13,14]. e non-Markovian free-carrier model with bandgap renormalization to calculate the spontaneous emission spectrum g sp (ω) is taken from [15] and [16]. e bandgap energy of GaN 1−y Sb y used in the calculation is obtained by E GaNSb and E GaN g are bandgap energies of GaSb and GaN, respectively, and C is the bowing parameter. Here, we assume that the unknown parameters of GaNSb are same as those of GaN as a first approximation. e material parameters for GaN and InN used in the calculation are taken from [17] and references therein. Figure 1 shows potential energy profiles where Figure 1(a) is for the type-I In x Ga 1−x N/GaN QW structure and Figure 1(b) is for the type-II In x Ga 1−x N/GaN 1−y Sb y /GaN QW structure. e wavefunctions of the first conduction subband (C1) and the first valence subband (HH1) at the zone center are also shown. e well width of the type-I InGaN/GaN QW structure is fixed as L w = 3 nm. e sum of the left (L w1 ) and right (L w2 ) side well widths of the type-II InGaN/GaNSb/GaN QW structure is also selected to be 3 nm. e thickness and the Sb content of the GaNSb layer are set to be 1 nm and 0.04, respectively. e In contents in In x Ga 1−x N wells are selected to give a transition energy corresponding to a wavelength of 640 nm, which are 0.47 and 0.45 for the type-I and type-II QW structures, respectively.

Results and Discussion
In the case of the conventional type-I QW structure, a large spatial separation between electron and hole wavefunctions is observed due to the large internal field. On the other hand, a spatial separation between electron and hole wavefunctions in the type-II InGaN/GaNSb/GaN QW structure is greatly reduced, compared to that of type-I QW structure.
us, we expect that the optical transition probability will be greatly improved with the inclusion of the GaNSb layer, as discussed in the following. Figure 2 shows the valence-band structures where e heavy-hole effective mass around the topmost valence band is not affected much by the GaNSb layer. e overall shapes of the valence-band structures for both cases are similar to each other. However, the energy spacing between the first two subbands and the third two subbands of the type-II QW structure is slightly smaller than that of the type-I QW structure. matrix element of the type-II InGaN/GaNSb/GaN QW structure is shown to be smaller than that of the conventional type-I QW structure. However, at the higher sheet carrier density, the type-II InGaN/GaNSb/GaN QW structure shows a larger matrix element than the conventional type-I QW structure because the reduction effect in the built-in potential by the carrier screening is dominant for the type-II QW structure. Figure 4 shows TE-polarized spontaneous emission spectra (Figure 4(a)) and peak intensities as a function of sheet carrier density (Figure 4(b)) for type-I InGaN/GaN and type-II InGaN/GaNSb/GaN QW structures. TE-polarized spontaneous emission spectra are obtained at a sheet carrier density of 20 × 10 12 cm − 2 .
e peak wavelengths of both QW structures are shown to be approximately 640 nm. e type-II InGaN/GaNSb/GaN QW structure shows a larger emission peak than the conventional type-I QW structure in the investigated range of sheet carrier densities although the matrix element of the type-II InGaN/GaNSb/GaN QW structure is smaller than that of the conventional type-I QW structure in the range of low sheet carrier densities owing to a small screening effect. is is mainly because the density of states k ‖ /(πL eff w ) for the type-II QW structure is enhanced owing to the reduction of the effective well width, L eff w . e effective well width is given by wherem v w1 and m c w2 are hole and electron effective masses for wells, respectively [18].
In particular, in the range of higher sheet carrier densities, the peak intensity of the type-II InGaN/GaNSb/ GaN QW structure is much larger than that of the conventional type-I QW structure owing to an increased matrix element. Also, the peak intensities of both QW structures rapidly increase with increasing sheet carrier density. e increasing rate of the peak intensity for type-II QW structure is larger than that for type-I QW structure. If the Sb content in GaNSb is increased, the In content in InGaN well can be significantly reduced, as discussed in the following. Figure 5 shows the potential energy profile for the type-II In x Ga 1−x N/GaN 1−y Sb y /GaN QW structure with x = 0.3 and y = 0.08 ( Figure 5(a)) and TE-polarized spontaneous emission spectra of both type-I and type-II QW structures ( Figure 5(b)). e inset in Figure 5(b) shows the TE-polarized optical matrix element for the type-II In x Ga 1−x N/ GaN 1−y Sb y / GaN QW structure (x = 0.3, y = 0.08). e SC solutions are obtained at a sheet carrier density of 20 × 10 12 cm − 2 . e thickness of the GaNSb layer is set to be 1 nm as in Figure 1, but the Sb content of the GaNSb layer is changed from 0.04 to 0.08. With this change, the transition wavelength of 640 nm is obtained at an In content of 0.3 in the InGaN well. is value is much smaller than that for the type-I In x Ga 1−x N/GaN QW structure (x = 0.47). In addition, we observe that the type-II InGaN/GaNSb/GaN QW structure still has a much larger emission peak than the conventional type-I QW structure even for the case of smaller In content. On the other hand, the emission peak of the type-II In x Ga 1−x N/GaN 1−y Sb y /GaN QW structure (x = 0.3, y = 0.08) is slightly smaller than that of the type-II In x Ga 1−x N/GaN 1−y Sb y /GaN QW structure (x = 0.45, y = 0.04) because the former has a smaller optical matrix element than the latter owing to the reduced overlap between electron and hole wavefunctions.

Summary
In summary, electronic and optical properties of type-II red InGaN/GaNSb/GaN QW structure have been investigated by using the multiband effective mass theory. Optical matrix elements for the type-II InGaN/GaNSb/GaN QW structures are greatly increased owing to the screening effect with increasing sheet carrier density. e type-II InGaN/GaNSb/ GaN QW structures show much larger emission peaks than the conventional type-I QW structure in an investigated range of sheet carrier densities because the density of states for the type-II QW structure is enhanced owing to the reduction of the effective well width. Also, we have observed that the In content in InGaN well can be significantly reduced with increasing Sb content in the GaNSb layer.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest. Advances in Condensed Matter Physics 5