Deep Ultraviolet BGaN Quantum Dot structures

— This research studies boron-containing quantum dot (QD) structures that emit the ultraviolet. Ternary and quaternary lattice-matched structure: , , , , , , , and and their TE and TM gain spectra, spontaneous emission, spontaneous polarization, and piezoelectric polarization have been examined in these structures. They have high TE and TM spectra under reducing boron content in the QD or barrier layer. The total polarization decreases for the Al-containing systems, which is preferred. Binary systems emit at 199nm, while the quaternary can have a peak wavelength near 235nm. Elongating of the wavelength to 290nm is possible with with high gain at a few boron contents.


I. INTRODUCTION
The ultraviolet (UV) region covers the 10-400 nm wavelength range and enters various applications. For example, non-thermal technology is the most used for food to protect and prolong its shelf life [1]. The deep ultraviolet (DUV) radiation can efficiently kill viruses and bacteria, so they are used in bio-medicine, water, and air purification. Other applications include high-density storage data, medical health care, fluorescence spectroscopy, photolithography [2,3], and optical lithography with improved resolution [4]. These subwavelengths obtained by semiconductor structures, such as and GaN, crystals can work in infrared and visible regions [5].
AlGaN-based light-emitting diodes have gained significant importance in the UV region and especially in the DUV. Although increasing AlGaN devices performance due to the quality development and devices optimization, it still suffers from higher performance improvement obstacles [3]. It's lattice-mismatched with AlN and GaN substrates cause an internal field in the active region, reducing the carrier recombination as the electrons and holes are spatially separating by this field [6]. So, the required carrier density for optical gain increases for two reasons: first, the leakage by the internal field. Second, the effective hole mass is heavier than the conventional zinc blende crystals such as GaAs and InP. Then, the oscillator strength is degrading, and the emission wavelength is redshifted [7].
AlGaN suffers from poor emission efficiency in the TE mode, the favoring mode in the conventional light-emitting diodes [8]. At high Al content (x ≥ 0.25), the topmost valence band is the crystal field split-off hole band, a P_zorbital-like band. Then AlGaN emits in a TM mode which is perpendicular to the c-axis [9].
There are many treatments; the non-(0001) structures (the 0001 is the z-axis or the c-axis in the wurtzite crystals) which can expect to be zero field orientation [7], Kim et al. have enhanced the efficiency by sidewall emission to extract TM DUV light from MQW [9]. There is another development of AlGaN yield by removing the lattice mismatching as closely as possible by using boron [10].
Boron-based devices are proved as a candidate promising for UV and DUV applications. The lattice matching is possible for the structure of these devices with small boron content (<12%). It experimentally demonstrates that up to 9 and 13% boron contents for BGaN and BAlN, respectively, have lattice matching to AlN. Bandgap engineering for the quaternary is possible for wide bandgap BAlGaN structures [2,10].
Park and Ahn have shown that BAlGaN can work as a UV source with high efficiency and reduced strain [3]. They also have investigated the TM emission increment from this structure [8]. Park refers that boron in BAlGaN QW improves the TE spontaneous emission [2]. Park et al. have compared the emission characteristics from polar (c-plane) and nonpolar (a-plane) BInGaN QW and show that they have higher emission characteristics than InGaN structures [11]. This research studies BGaN, BAlGaN, BInGaN QDs and obtaining high TE and TM gain and spontaneous emission at 199-290nm wavelengths. The result is important in LED work which is not attaining with quantum well (QW) counterpart.

II. BORON-BASED QD STRUCTURES
Many BGaN-based structures have been examined in this work. They are BGaN, BAlGaN, and BInGaN. The parameters were calculated by the following relation [12], In order to account for shape imperfections and random distribution in QDs during their production, the inhomogeneous broadening of the QDs spectrum must be considered. Thus, the optical gain and the spontaneous emission rate can be defined by [13,14,15], The terms c f and v f are the respective quasi-Fermi distribution function for the conduction and valence bands, respectively, c F and v F are the quasi-Fermi levels of the conduction valence bands. For accurate calculations, take into account the contributions of both the WL and QD layers to the definition of the global quasi-Fermi levels. | ̂ ⃗ | is the momentum matrix element for electron-heavy hole transition energy. The scripts ́ are the free mass of electrons, the free space permittivity, the light speed, the material background refractive index, the optical transition energy, and the overlap between envelope functions of the QD electron and hole states, respectively.  For accurate calculations, consider the contributions of both the barrier have been considered, the WL, and the QD layers, That was contributed in definition of the global quasi-Fermi levels of the conduction c F , and valence bands v F . They were determined from the surface carrier density per QD layer as follows [13]; hh The sum of the spontaneous polarization in the structure, which is at equilibrium, and the piezoelectric polarization P  that results from strain-induced polarization is the total macroscopic polarization (P) of the solid in the absence of external fields. The piezoelectric polarization is proportional to the strain ϵ in the linear regime [19], The equation (14) specifies the piezoelectric tensor components (using Voigt notation). Since the (0001) axis is the growth direction of both bulk materials and nitride superlattices, the polarization is considering along this direction. The piezoelectric polarization is simply expressing as [19], where is the equilibrium value of the lattice constant , and and are the piezoelectric coefficients. The polarization induced by a shear strain related to the piezoelectric tensor, e 15 , will be ignored in this study.

VI. RESULTS AND DISCUSSION
The parameters of the calculations are shown in Table 1. In this section, The results of boron-containing QD structure were presented, and they grouping depending on their QD layer structure. Figure 1 shows the TE and TM gain modes for at some boron mole fractions. The TE spectra are higher than that of TM by three orders. All the spectra are peaked at 199nm. Reducing x (boron)-mole fraction by one order increases the gain by three orders. The spontaneous emission spectra are a picture of the gain spectra. High TE (and TM) is of central importance in LED applications compared to its QW counterpart and promising in UV QD LED. Figure 2 shows the possibility of increasing spectra by more reduction in the boron mole-fraction. The QD spectra are still at the same peak wavelength despite the change of mole fraction, which refers to the main effect of the barrier that has a wide bandgap as a comparison with to that of QD. Figure 3 shows the polarization effect of QD structure. At 0.15 boron mole-fraction, the pizoelectric polarization changes from positive to negative due to strain effect at this mole fraction. Note that, works (and this work) are not go this fraction [2]. Figure 4 studies QD structure. It shows the effect of adding boron to the barrier layer. A few boron mole fractions in the barrier still give similar results when the alone is the barrier in both spectrum height at wavelength. Higher boron content in the barrier reduces the spectrum. In Figure 5, AlGaN have been examined as a barrier layer for BGaN QD structure. However, BGaN emits at 199nm at all of the above structures, Figure 5 shows the increasing peak gain and a slight blue shift with increasing Al-mole fraction in the barrier layer of BGaN/AlGaN QD structure attributed to the wider bandgap of AlN, which controls the transitions. Al-barrier controlling of the emission wavelength is also with other QD structures not containing boron [20]. Figure 6 examines QD structure and shows the possibility of increasing gain by reducing boron mole-fraction. TE gain is increased by one order while TM mode is doubling. Figure 7 shows the effect of Al composition on the QD layer in QD structure. Increasing Al content reduces the spectra. Increasing the Al content by 0.001 reduces the TE gain by three times. A similar result is also shown [2,8] for BAlGaN QWs. Figure 8 shows the polarization when adding a few Al molefraction. As comparison with Figure 3 (for ), the spontaneous polarization was increased for the Alcontaining structure, and then the total polarization is reduced for this structure which is preferred. Figure 9 shows the QD structure at different boron content in the barrier layer where their emission wavelength is 200nm. Reducing the boron content (increasing Al) in the barrier increases the peak gain. Figure 10 examines BInGaN/AlN QD structure. The effect of adding indium instead of aluminum exhibits a spectrum with a peak at the same wavelength. However, it becomes higher. BInGaN/AlN QD structure is increased by four orders in both TE and TM compared with BAlGaN/AlN QD structure in Figure 6. Figure 11 shows the polarization of BInGaN, which is not different from BAlGaN. In addition to exploring the boron-based QD structures in the UV region, BInGaN/AlGaN is examined in Figure 12 and shows interesting results. Adding Ga to the AlN barrier changes the emission wavelength from 199 into 290nm with a high TE gain while absorption for TM mode under few reductions of boron content in the QD. Continuing examination of the AlGaN barrier, Figure 13 shows the emitted wavelength is made shorter with the increasing of boron in the QD, which is also shown in [2,8,11] for QWs due to growing bandgap with boron composition [21]. In both figures 12 and 13, the gain changes from positive to negative, i.e., gain due to high transparency point of these structures which means that a high carrier density must be used to attain gain. Figure 14 shows an increment in the absolute value of polarization for BInGaN/AlGaN compared with BInGaN/AlN QD structures.

C. BInGaN structures
Then, the research has examined the addition of boron to the barrier layer. Figure 15 shows BInGaN/BAlN QD structure where the structure emits near 222nm by controlling boron composition in the barrier. Better TE and TM gain values are obtaining. Figure 16 gives another example of the BInGaN/BALN QD structure emitting possibility, which emits near 235nm by adjusting boron content in the QD and barrier layers. Reducing boron fraction reduces gain.

VII. CONCLUSIONS
Boron-based QD structures emit at ultraviolet were examined theoretically . Ternary and quaternary lattice  matched structure:  ,  ,  , , , , and . TE and TM gain spectra, spontaneous emission, spontaneous polarization, and piezoelectric polarization were experienced in these structures, and high spectra result from reducing boron content. The total polarization is few at 0.15 boron mole-fraction. Binary systems were emitted at 199nm. Higher boron content in the barrier reduces the spectrum. spectrum was increased by four orders compared to the corresponding Al structure.
was emitted near 222nm by controlling boron in the barrier with good TE and TM gain.
. The structure can have a peak wavelength near 235nm. Elongating wavelength to 290nm is possible with with high yield appearing at few boron.

Disclosers:
The authors declare that there is no conflict of interest.