1 Introduction

The deep-ultraviolet (DUV) laser diode (LD) based on group III nitrides has great potential to be applied to a wide range of applications, such as biological detection, optical data storage, sterilization, secret communication, air purification, and medical treatment [1, 2]. Recent demand for DUV-C spectrum ( less than 280 nm) for nucleic acid destruction and surface disinfection of viruses and pathogens has made it a rapidly developing technology in the decade [3,4,5]. However, deep-ultraviolet laser diodes in this band face many challenges. One of the biggest challenges is that the LD efficiency is very low, the threshold current density is high, resulting in short laser life [6, 7]. The low efficiency is caused by the low hole injection efficiency of DUV LD [8, 9]. The ionization energy of the common p-dopant Mg is about 200 meV in GaN and increases to more than 600 meV in AlN. Such high Mg ionization energy makes it very difficult to dope Mg in the p-type layer with high Al content [10, 11]. This will increase the surface depletion width of the p-type layer and further reduce the hole tunneling efficiency [12]. This problem can be solved by designing new doping methods of wide bandgap semiconductors such as p-AlGaN by electric field or optimizing alloy metals to improve the hole tunneling efficiency at p-type layer interface [13, 14]. It can also be solved by studying the Mg doping distribution [15,16,17] or using the undoped AlInN in the p-cladding layer (p-CL) [18]. Another problem to be solved is that there is a serious electron leakage from the multiple quantum wells (MQWs) to the p-type layer [19, 20]. At present, the most effective way to reduce electron leakage is to insert an electron blocking layer (EBL) between the p-type nitride layer and the active region. However, this layer has become another obstacle to hole transport efficiency. Because the valence band offset at the interface of the EBL forms the barrier to block hole transmission. In addition, when electrons leak from the active region to the p-type region, they combine nonradiatively with holes in the p-type region, which further reduces laser luminous efficiency [21, 22]. Therefore, improving hole injection efficiency and reducing electron leakage are inseparable. It is well known that the interface polarization charge is produced by spontaneous polarization and piezoelectric polarization [23], and the spontaneous polarization charge is related to the composition of Al in AlGaN. In addition, the interface polarization charge also affects the ionization energy [24]. Therefore, adjusting the composition of Al in AlGaN in an effective way can reduce the interface polarization charge. The effective barrier height of the conduction band is increased to reduce electron leakage and the valence band barrier height is further reduced to reduce the hole blocking effect. To reduce the electron leakage and improve the hole injection efficiency, the EBL and the p-type layer must be optimized simultaneously. At present, many new structures of EBL have been proposed to reduce electron leakage and improve device efficiency [25,26,27,28]. However, most of them only improved the EBL. Although the effective EBL can partially weaken the blocking effect on the hole, it cannot solve the problem of low hole energy.

Due to the strong interface polarization effect of p-CL, the hole tunneling efficiency is very low. This study proposes tapered p-CL to introduce the bulk polarization charge to reduce the influence of the polarization electric field, thereby increasing the hole energy. Meanwhile, this paper proposes a triangular EBL to solve the problem that the traditional EBL cannot effectively block the electron leakage and hinder the hole transmission. The results show that the proposed tapered p-CL and triangular EBL can effectively improve the photoelectric characteristics of the laser.

2 The proposed deep-ultraviolet laser diode structure

Figure 1a demonstrates a current-injected DUV LD. The structural parameters of the laser are listed in Table 1. The three laser devices have the same structural parameters except for their different aluminum components in p-CL. The reference p-CL structure has a fixed aluminum component of 0.75 (the energy band diagram is shown in Fig. 1b). The aluminum component of the tapered p-CL structure increases linearly from 0.6 to 0.8, and that of the anti-tapered p-CL structure decreases linearly from 0.8 to 0.6 along the 0001 direction (the energy band diagrams are shown in Fig. 1c, d). The thickness of p-CL for all structures is fixed, i.e., 400 nm. To explore the proposed laser diode structure and compare it with different structures in terms of the photoelectric properties of lasers, PIC3D software was exploited to conduct a simulation. In this simulation software, the radiation recombination coefficient, energy band offset ratio, Auger recombination coefficient, and Shockley–Read–hall (SRH) recombination lifetime are \(0.5 \times 10^{ - 16} m^{3} s^{ - 1}\), 0.58, \(1 \times 10^{ - 46} m^{6} s^{ - 1}\), and 100 ns, respectively [29]. The electrical stimulation of laser is calculated by Poisson equation, drift–diffusion model, current continuity equation, and polarization charge model [30]. The optical simulation of laser is calculated by vector Helmholtz wave equation and Adachi refractive index model [30]. The transfer matrix method and Schrodinger–Poisson self-consistent method are used to calculate the carrier transmission and distribution characteristics. In this simulation, the built-in interface charge is calculated at 40% of the theoretical value [31, 32], the width is 1.5 µm, the cavity length is 534 µm, and the parameter settings in reference [33] is taken for other parameters. The emission wavelength of the laser is about 267 nm, and all the simulations are at room temperature T = 300 K. The lighting principle of the laser is electroluminescence, so the laser can work normally only when a forward biased is applied to the laser.

Fig. 1
figure 1

a Schematics of the LD structure, schematic energy band diagrams of b reference p-CL structure, c tapered p-CL structure and d anti-tapered p-CL structure

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Table 1 Structure parameters of the deep ultraviolet laser
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3 Effect of taper p-cladding layer on hole injection

The polarization-induced charge in the 0001 direction propagates in the form of 3D in p-CL, and it can be expressed as

$$\rho_{\pi } = - \nabla P = \frac{{\sigma_{\pi } \left( {x_{Al} } \right)}}{b},$$
(1)

where \(\nabla P\) is the polarization when the Al component changes; \(\sigma_{\pi } \left( {x_{Al} } \right)\) is the interface binding sheet charge when the Al component changes, and \(b\) is the thickness of p-CL [34]. Therefore, as for the polarization-induced doping effect, the hole accumulation is determined by the thickness of p-CL and the polarization at the Al component gradient interface. The thickness of the three p-CLs is the same, but the polarization at the Al component gradient interface is different. When the Al component in p-CL changes linearly, the layer will produce linear polarization. When the Al content increases linearly from 60 to 80% and decreases linearly from 80 to 60% along this direction, a constant positive polarization charge and a negative polarization charge are generated respectively. This will lead to different polarization-induced charges in the three structures of p-CL, thus affecting the carrier concentration of the laser diode. Since anti-tapered p-CL introduces a negative polarization charge, the value of \(\sigma_{\pi } \left( {x_{Al} } \right)\) decreases, so the value of \(\rho_{\pi }\) also decreases. This makes the hole current density of the structure about 18.8% higher than the reference p-CL LD in Fig. 2 (a). Consistent with these results, the tapered p-CL structure has a lower polarization-induced charge due to the introduction of positive polarization charge, which increases the hole concentration of the structure by about 15.3% in Fig. 2 (b). The hole concentration in the quantum well 2 (QW2) region is about 2.1% higher than that in the quantum well 1 (QW1) region. Since the original hole concentration in QW1 is about 2% higher than that in QW2, the hole concentration in the two quantum wells is more uniform, which is conducive to improving the radiative recombination efficiency of carriers.

Fig. 2
figure 2

Reference p-CL structure, tapered p-CL structure and anti-tapered p-CL structure in the active region (a) hole current density and b logarithmic hole concentration distribution of the

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4 Analysis of the structure with triangular electron blocking layer

4.1 The proposed structure of triangular electron blocking layer

Since EBL with a constant Al composition has a strong interfacial polarization charge, it reduces the conduction band energy lower than the electron quasi-Fermi level is formed at the EBL interface to reduce the efficiency of the EBL. It also forms a parasitic inversion layer to reduce the optical gain of the laser [35]. The valence band offset at the interface of the EBL forms a barrier for blocking hole transmission. The spontaneous polarization effect is caused by the mismatch of lattice constants, which are mainly determined by the aluminum composition. In Fig. 3b, a triangular p-EBL structure (Sample B) is proposed, and the Al composition of the EBL in sample B gradually increases and then decreases along the growth direction. The Al component at the interface of the last quantum barrier/p-EBL gradually increases. This will produce the sheet charge caused by the negative polarization, which decreases the electron accumulation in the last quantum barrier and further suppress the electron leakage. However, EBL cannot be stratified too much, because this will reduce the ability of EBL to block electrons. Therefore, the Al component of the triangular EBL increases linearly from 90 to 98%, and then decreases linearly from 98 to 90%. In this way, a barrier-tip peak layer can be formed in EBL, and the polarization-induced electric field of this layer can well reduce the drift velocity of electrons to improve the electron capture rate and reduce the electron escape of multiple quantum wells. At the interface of the EBL and p-type layer, the Al component of the triangular EBL is gradually reduced, which helps to make the quasi-Fermi level of the hole close to the valence band, thereby reducing the barrier height of the valence band. To analyze the output characteristics of the triangular EBL laser more effectively, the inverse-triangular EBL is also studied in this paper. The change of the Al composition of the structure is opposite to that of the triangular EBL, as shown in Fig. 3a (Sample A). The Al composition of the EBL in sample A gradually decreases and then gradually increases along the growth direction. At present, in each band of light emitting diodes (LED) and laser, the reports on EBL mainly include anti-graded EBL, graded EBL [36], superlattice EBL [25], double tapered EBL [26], anti-tapered EBL, tapered EBL [27], V-type EBL [28] and so on. The graded EBL and the anti-graded EBL are mainly to classify the Al component in the AlGaN material of the laser EBL, and the laser EBL studied in this paper is also AlGaN material. The graded EBL, the anti-graded EBL, the triangular EBL and the inverse-triangular EBL are all optimized by dividing the EBL into two layers. The stratification of EBL will affect the polarization charge at the interface and thus affect the ability of EBL to block electrons. Therefore, comparing the triangular EBL and the inverse-triangular EBL proposed in this paper with the graded EBL and the anti-graded EBL will make the findings more practical. In addition, to make their comparison more reliable, the average Al composition of the four EBLs is the same. As shown in Fig. 3c, the Al composition of the EBL in sample C is first constant at 98% and then constant at 90% along the growth direction. As shown in Fig. 3d, the Al composition of the EBL in sample D is first constant at 90% and then constant at 98% along the growth direction. The four different EBL laser devices have the same structural parameters except for the Al component of EBL, and all of them use the tapered p-CL with high hole concentration.

Fig. 3
figure 3

Schematic of the a inverse-triangular EBL structure (Sample A), b triangular EBL structure (Sample B), c anti-graded EBL structure (Sample C), and d graded EBL structure (Sample D)

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4.2 Optical characteristic

The optical confinement factor \(\Gamma\) of the laser can be expressed as:

$$\Gamma = \frac{{\int_{ - d/2}^{d/2} {n_{r} \left| {E(z)} \right|^{2} dz} }}{{\int_{ - L/2}^{L/2} {n_{r} \left| {E(z)} \right|^{2} dz} }},$$
(2)

where \(d\) is the thickness of the active region, \(n_{r}\) is the refractive index, \(E(z)\) is the electric field, and \(L\) is the whole length of the laser [37]. The estimation results of the near-field optical distribution and the real refractive index of the four EBL structures are shown in Fig. 4. The optical confinement factor of sample B reaches 43.59%, which is 117% higher than that of sample A. Such a large increase is attributed to the real refractive index of sample B can better limit the light to the active region. This also indicates that the triangular EBL of sample B can effectively reduce the optical leakage to improve the optical properties of the laser.

Fig. 4
figure 4

Real refractive index (left axis), and near-field optical distribution (right axis) for Sample A, Sample B, Sample C, and Sample D

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4.3 Energy band analysis

To further explore the physical implications behind the improvement of the optical properties of sample B, the energy band diagrams of the four EBL structures are estimated, and the results are shown in Fig. 5. Their ability to restrict electrons can be characterized by the effective barrier height of the conduction band (\(\phi_{e}\)). The effective conduction band barrier height of \(\phi_{e}\) is the difference between the conduction band (Ec) and the quasi-Fermi levels of electrons (Efe) at the interface between the EBL and the p-type layer. Sample B achieves the highest \(\phi_{e}\)(about 437.28 meV), thus this structure has the strongest ability to restrict electrons and can effectively reduce electron leakage. Meanwhile, the binding of holes can be characterized by the height of the valence band barrier (\(\phi_{h}\)). The effective valence band barrier height of \(\phi_{h}\) is the difference between the valence band (Ev) and the quasi-Fermi levels of holes (Efh) at the interface between the EBL and the p-type layer. Usually, the hole concentration depends on the effective density of states of the holes and the height of the valence band barrier. In general, the lower the effective barrier height of the valence band is, the higher the concentration of holes. The height of the valence band barrier is \(\phi_{{\text{h}}} = \Delta E_{V} - kT \times \ln \left( {p/N_{V} } \right)\), where \(\Delta E_{V}\) is the potential energy difference of the valence band; \(k\) is the Boltzmann constant; \(T\) is the carrier temperature; \(p\) is the regional hole concentration, and \(N_{V}\) is the effective density state of the hole [38, 39]. The potential energy difference is proportional to the effective barrier height. Therefore, the lower potential energy difference, the lower effective barrier height of the valence band, the higher hole concentration. Sample B achieves the lowest effective barrier height (about 137.38 meV), so this structure has the weakest binding capacity to holes and can effectively increase the hole injection. This is consistent with the results of the optical confinement factor calculated in Fig. 4. It is the increase in carrier concentration that leads to the enhancement of optical properties.

Fig. 5
figure 5

Calculated energy band diagrams for Sample A, Sample B, Sample C, and Sample D in the EBL

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4.4 Carrier distribution

The calculation of the band diagram based on band theory shows that sample B can improve the height of the conduction band barrier and reduce the height of the valence band barrier. The electron current density and hole current density can reflect the carrier injection efficiency more clearly. Figure 6a, b illustrates the electron current density and hole current density in the active region of the four samples, and Fig. 6c shows their stable values. The electron current density in this region represents the degree of electron leakage. The higher the electron current density, the more electron leakage to the p-type region. On the contrary, the hole current density in this region represents the degree of hole injection. The higher the hole current density, the better the hole injection efficiency. The increase of electron current density of sample B is consistent with the analysis results of the triangular EBL laser, which is related to the specific Al component energy band of triangular EBL. However, the improvement of hole current density is attributed to the higher hole tunneling efficiency tunneling though the triangular EBL. The p-CL in the 0001 direction has the polarization-induced electric field \(E_{PZ + SP}\) opposite to the electric field \(E_{ex}\) generated by the external bias, which reduces the hole drift velocity. Therefore, it is necessary to screen the polarization-induced field in the EBL. The net energy obtained by the hole entering the quantum wells through the EBL is \(\Delta E = E\left( {\text{s}} \right) + \int\limits_{0}^{l} {E(p)dx}\), where \(E\left( s \right)\) represents the difference of electric field on both sides of the EBL; \(E\left( p \right)\) is the coupling electric field of \(E_{ex}\) generated by the external bias voltage and the polarization-induced electric field \(E_{PZ + SP}\); \(l\) is the thickness of the EBL [40]. Therefore, to increase the hole energy, the coupling electric field \(E\left( p \right)\) needs to be increased, which can be realized by introducing a bulk polarization charge into the EBL to partially compensate for the \(E_{PZ + SP}\). The EBL with a gradient Al component can sense the bulk polarized charge in Fig. 3. Thus, the coupling electric field \(E\left( p \right)\) will increase, further improving the net energy \(\Delta E\) of the hole. The calculated results of the electric field intensity of the four structures are shown in Fig. 7a. The triangular EBL has the lowest electric field, which makes the hole current density of sample B about 20.56% higher than that of sample A (Fig. 6b, c). This indicates that the use of triangular EBL laser can not only reduce electron leakage, but also improve hole injection efficiency. The results are consistent with the energy band calculation results in Fig. 4, further indicating that the triangular EBL laser can improve the height of the conduction band barrier to increase the electron current density and reduce the height of the valence band barrier to increase the hole current density. Based on this, the radiative recombination rate of sample B is about 113% higher than that of sample A (Fig. 7b). This provides additional evidence for the excellent photoelectric properties of sample B. The radiative recombination rate of sample C and sample D in the second quantum well is also improved, but the uneven distribution in the two quantum wells is not conducive to the photoelectric properties of the laser.

Fig. 6
figure 6

a Electron current density, b hole current density and c their stable values for Sample A, Sample B, Sample C, and Sample D

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Fig. 7
figure 7

a Electric field and b radiative recombination rate for Sample A, Sample B, Sample C, and Sample D

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4.5 Output characteristics

The output characteristics of the four EBLs are calculated in Table 2. It can be seen from the results that the threshold current can be reduced by the EBL with a gradual change of aluminum composition; the effect of triangular EBL is better, especially in increasing the output power of the laser. The slope efficiency (SE) of sample B reaches 3.243 W/A. Compared with structure A, the threshold current of structure B decreased from 28.58 mA to 17.65 mA, which decreased by 38.24%, and the output power increased from 133.6 mW to 169.8 mW, which increased by 27.09%. Meanwhile, the threshold voltage is also reduced, which can prolong the service life and luminous efficiency of the laser. This is achieved by the fact that the triangular EBL structure can match the upper and lower lattices and reduce the net polarization charge at the interface; thus, it increases the height of the conduction band barrier and reduces the height of the valence band barrier, further improving the carrier concentration of the laser.

Table 2 Output characters of LDs for Sample A, Sample B, Sample C, and Sample D
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5 Conclusion

In this work, tapered p-CL and triangular EBL structures are proposed to improve the carrier concentration and further improve the performance of the DUV LD. The introduction of the bulk polarization charge enables the tapered p-CL structure to effectively improve the hole concentration, thus reducing the polarization-induced charge and improving the hole accumulation. The triangular EBL structure forms a barrier-tip peak layer in EBL, and the polarization-induced electric field of this layer can reduce the drift velocity of electrons. At the EBL interface, the Al component is gradually reduced, which helps to make the quasi-Fermi level of the hole close to the valence band, thus reducing the height of the valence band barrier and further reducing the energy loss in the hole tunneling process. The results show that the optical confinement factor of the laser is increased by about 117%, and the radiation recombination rate is increased by about 113%. The threshold current is decreased by 38.24%, and the output power increased by 27.09%. The proposed methods and reported physical devices in this work are very useful for the development of deep-ultraviolet laser diodes.