1 Introduction

The real-world applications, such as water and air disinfection, currency screening, decontamination, photolithography, color display, and even for the disinfection of the SARS-CoV-2 virus, require a narrow UV band spectrum [1,2,3,4,5]. AlGaN-based semiconductor alloys have unique characteristics which make them a promising candidate for the above applications [6, 7]. Due to these remarkable characteristics, the AlGaN-based UV LEDs have been keenly studied in the last two decades [8, 9]. Despite the extensive research, the optoelectronic performance of DUV LEDs is still considerably low. This poor performance of AlGaN-based UV LEDs is due to many factors [8, 10]. High threading dislocation density (TDD) and Auger recombination also severely affect the optoelectronic performance of DUV LEDs. Researchers proposed different DUV structures to enhance the optical characteristics and reducing highly TDD using buffer layers or patterned sapphire substrates [9, 11], p-doped delta-accelerating [12], and quaternary-graded quantum barrier [13]. It is worth noting that electrons have lower effective thermal velocity due to their higher effective mass, so electrons easily overcome the effective potential barrier height (denoted by Φe) of quantum barriers and EBL, resulting in leakage to the p-type layers [14]. Conversely, the holes have lower thermal velocity due to their higher effective mass. For holes, it is difficult to overcome the effective potential barrier height (denoted by Φh) of EBL and quantum barriers. Eventually, the leaked electrons recombine with holes in the p-type layer, leading to non-radiative recombination instead of radiative recombination [14, 15, 16]. Through this, the uneven distribution of carriers occurs, which further stymies the AlGaN-based DUV LEDs performance [17]. To tackle this issue, many sophisticated approaches have been used such as V-shaped EBL [18], W-shaped EBL [19], irregular sawtooth EBL [20], trapezoidal EBL [21], and anti-trapezoidal EBL [22].

Keeping this in mind, we have proposed QLQB and quaternary step-graded EBL and study their effect on the device output. Previously, our group studied the effect of QLQB as well as EBL simultaneously on the carrier leakage [13]. Based on simulation results, it was found that the electron and hole concentrations are remarkably enhanced in our proposed DUV LED. Although our study is theoretical, we expect that experimental implementation is quite simple because many groups fabricated the AlInGaN-based highly efficient layer for DUV LEDs, through many epitaxial technologies such as molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD) [23, 24]. To the best of our knowledge, the effect of QLQB and quaternary step-graded EBL on DUV LEDs has not been reported to date.

2 Device structure and parameters

The AlGaN-based DUV LED denoted as (LED-A) is used as a reference structure in this study. The reference structure (LED A) comprises of a 3-µm-wide electron injector n-Al0.6Ga0.4N layer with doping concentration (Si-doped) of 1 × 1018 cm-3, the active region contains five un-doped Al0.45Ga0.55N (2 nm) QW and six un-doped Al0.56Ga0.44N (12 nm) QB, followed by a 10-nm-thick Al0.6Ga0.4N EBL layer with doping concentration (Mg-doped) of 3 × 1019 cm-3 is used. The hole injector layers, i.e., Al0.4Ga0.6N have a thickness of 50 nm and a doping concentration of 3 × 1019 cm-3 followed by a 50-nm-wide p-contact layer p-GaN with a doping concentration of 3 × 1019 cm-3. The proposed LED denoted as (LED B) is identical to LED A except that the conventional EBL is divided into five layers of AlxInyGazN, each has a thickness of 2 nm. Further, the EBL is step-graded such that the composition value x, y, z for the first EBL is (0.7, 0.02, 0.28), followed by a 10% decrease of Aluminum (Al) composition in the next layer (0.6, 0.02, 0.38) and so on up to five consecutive EBLs and in the last layer composition (x, y, z) of EBL is (0.3, 0.02, 0.68). Change in composition of GaN is related to Al content. Additionally, in the proposed LED, AlInGaN LQB (Al0.56In0.02Ga0.42N) layer is also introduced at the same time instead of ternary Al0.56Ga0.44N. The schematic of LED A is shown in Fig. 1a, while the energy band of LEDs is sketched in Fig. 1b. In Fig. 1b, the black and red lines represent the conduction band of LED A and LED B, respectively. As shown in Fig. 1b the Al content in EBL is constant and the width of EBL is 10 nm in LED A. In LED B, the Al content is decreased step-wise by 10% in every layer and the 10 nm EBL is divided into five layers (each 2 nm thick). It is worth noting that the LQB of conventional LED (AlGaN) is replaced by AlInGaN in the proposed LED.

Fig. 1
figure 1

Schematic of a LED A b Energy band rectangular LQB, step-graded EBL of both structures

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The LED structures have been numerically simulated using SiLENSeTM 5.14. SiLENSeTM is based on the 1D drift-diffusion model by considering some specific properties like threading dislocation density, low efficiency of the wurtzite materials, and strong piezoelectric polarization. The electron and hole fluxes calculated using a self-consistent (SC) solution of the drift-diffusion transport and Poisson equations. The carrier wave functions are determined by solving the Schrödinger wave equation. The main characteristics of the SiLENSe tool are energy band profile, carrier concentration, radiative recombination rate, emission spectrum, carrier flux, and IQE. IQE is computed as [25].

$$\eta_{IQE} = \eta_{inj } .\frac{{R_{rad} }}{{R_{rad } + R_{SRH } + R_{Aug} }}$$

where ηIQE is the IQE, ηinj is the injection quantum efficiency, RSRH is the SRH recombination radiative, Rrad is recombination rate, while RAug is the Auger recombination rate. The defects that contribute to SRH recombination rate are computed as [26].

$$R_{SRH} = (\frac{{\tau_{n}^{tot} }}{n} + \frac{{\tau_{p}^{tot} }}{p})^{ - 1} .\left[ {1 - { }exp^{{\left( { - \frac{{F_{n} - F_{p} }}{kT}} \right)}} } \right]$$

where, the \({\tau }_{n}^{tot}, {\tau }_{p}^{tot}\) shows the electrons and holes lifetime, and n, p, Fn, and Fp are the electron and hole concentration at quasi-Fermi level, respectively. The non-radiative lifetime is calculated by [25].

$$\tau_{n,p}^{tot} = \left( {\frac{1}{{\tau_{n,p}^{def} }} + \frac{{f_{n,p} }}{{\tau_{n,p}^{dis} }}} \right)^{ - 1}$$

where, \(\tau_{n,p}^{dis}\) is non-radiative lifetime due to some defects such as impurities and vacancies. Similarly, the relation for the total recombination rate inside the LED QWs is written as

$$R = An + Bn^{2} + Cn^{3}$$

where \(n, A,B,C\) are the carrier concentration, SRH recombination coefficient, radiative recombination coefficient, and Auger recombination coefficient.

The overall area of the LED chips are 300 µm × 300 µm. Other parameters used in this work are the band offset ratio of conduction and valence band, i.e., 0.7/0.3, Auger Coefficient, i.e., 2.5 × 10-30 cm6 s-1. Shockley–Read–Hall (SRH) lifetime, i.e., 10 ns [27]. Electron and hole mobility of 100 cm2/V.s and 10 cm2/V.s, respectively, is employed while the operating temperature is set at 300 K. Some important parameters used in simulations are listed in Table 1. The remaining parameters of the materials and complete explanation of the simulation model are given elsewhere [27,28,29].

Table. 1 Important Materials Parameters used in Simulations Package [27, 28]
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3 Results and discussion

Figure 2 presents the IQE profile for both LEDs. The peak IQE of LED A and LED B is ~37% and ~54%, respectively. The IQE of LED B is increased by 48% as compared to LED A. Interestingly, the efficiency droop is severely decreased up to ~3% in LED B, while LED A exhibits ~52% droop at 200 A/cm2. The amelioration in IQE and  decline in efficiency droop are quite clear in our proposed structure. So, it is evident that the optical characteristics of LED B (proposed structure) are improved markedly as compared to LED A.

Fig. 2
figure 2

Internal quantum efficiency as a function of current density

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Figure 3 illustrates quantitatively the number of electrons and holes at 80 A/cm 2. The electron concentration in a region of LED B is increased by 25% as compared to LED A as shown in Fig. 3a. It is worth noting that in the last quantum well the electron large concentration shows the high capability of electron confinement. Likewise, the holes in the MQWs for LED B are increased by 15% as compared to LED A, as shown in Fig. 3b. Thus, these results show that the LED B confine carriers in the active region effectively.

Fig. 3
figure 3

Carriers’ concentration in MQWs a Electron, b hole at 80 A/cm2

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The enhancement in the carriers’ concentrations in the MQWs leads to a decrease in the electron leakage and encourages the hole transport into MQWs. To verify this, the electron and hole current density as a function of position are plotted in Fig. 4a and b, respectively. The electron current density, for LED B, in p-type layers is lesser than LED A due to increased Φe [30]. Conversely, the hole transport for LED B is 4.3 times greater than LED A as shown in Fig. 4b. Thus, the number of electrons is remarkably improved in the proposed structure as previously mentioned. It is principally because of the lower band-bending at the LQB and EBL interface due to lattice match, which leads to less carrier leakage in the proposed LED.

Fig. 4
figure 4

a [Electron Current Density], b [Hole Current Density] in both LEDs at 80 A/cm2

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To explore the further reason for the amelioration of IQE in the proposed LED, the radiative recombination rate of both LEDs is investigated. Figure 5 shows the radiative recombination rate at 80 A/cm2. The electron-hole pairs radiative recombination for LED B is enormously increased by 55% as compared to LED A. So, the elevation in radiative recombination is assigned to more electron-hole pairs confinement in the active zone which is explained above.

Fig. 5
figure 5

Radiative recombination rates in the MQWs of both LEDs

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Magnified radiative recombination rate leads to the high emission intensity of DUV LED. Figure 6 presents the emission spectra of LEDs at the current density of 80 A/cm2. The peak intensity of LED B is increased as compared to LED A. Peak emission spectra are around ~277 nm which are in the range of DUV LEDs [6]. A very minute blueshift is assigned to the reduction of quantum confinement stark effect in the proposed structure.

Fig. 6
figure 6

Spontaneous emission spectrum for both LEDs

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Figure 7 illustrates the band profile of both LEDs at 80 A/cm2. The Φe and Φhfor electron and hole in LED A are ~334 meV and ~345 meV, respectively. Inversely, in LED-B the Φe and Φh are ~443 meV and ~336 meV, respectively, indicating the better ability of electron confinement as well as hole transport into the MQWs region as shown in Fig. 7. It is due to the decrease of lattice mismatching leading to a lowering in polarization. It is highly believed that the above band-gap engineering is possible due to our proposed LED structure. In Fig. 3, 4, 5, and 7, the position (x-axis) is with reference to the device structure shown in Fig. 1a.

Fig. 7
figure 7

Energy band profile a Conventional EBL structure (LED A), b LQB and step-graded EBL structure (LED B) at 80 A/cm2

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4 Conclusion

This study reported the effect of AlInGaN-based LQB and step-graded EBL on the optoelectronic behavior of AlGaN-based DUV LEDs. The results indicated that our approach improved the recombination of electron-hole pairs in the active region because of the elevation of potential barrier height of the conduction layer, which effectively suppressing the leakage of electrons. It is also attributed to the reduction of the induced polarization field, which is associated with lattice matching of epi-layers. Quantitively, the electron and hole concentrations are increased by 25% and 15% as compared to conventional LED. The IQE is enhanced by 48% while the efficiency droop is decreased from 52% to 3% in the proposed LED. So, not only the IQE is ameliorated but also the efficiency droop is stifled remarkably as compared to LED A. Therefore, we highly trust that this approach provides a feasible guideline to the researchers for achieving high IQE as well as near-droop-free efficient AlGaN-based DUV LEDs.