GaN-based vertical-cavity surface-emitting lasers (VCSELs) have recently gained increasing attention because of their excellent optical and electrical properties. These include a low threshold current, narrow linewidth, high brightness, and exceptional directionality^[1]. These properties make VCSELs ideal light sources for various applications, including optical communication, three-dimensional sensing, and new boosting virtual reality/augmented reality (VR/AR) systems^[2]. Significant progress has been made in the structural design of blue-GaN-based VCSELs. For example, Zhang et al. designed a blue VCSEL with a lateral optical confinement structure, exhibiting a threshold current of 16 mA and a maximum optical output power of 0.2 mW^[3]. The blue VCSEL designed by Elafandy et al., which utilised birefringent nano-porous distributed Bragg reflectors (DBRs), exhibited a forward voltage of 6 V, differential resistance of 41 Ω, and threshold current density of 59 kA/cm^2[4]. The blue VCSEL developed by Elafandy et al., which employed nanoporous GaN, featured a threshold current density of 42 kA/cm² and a maximum optical output power of 0.17 mW^[5]. Hayashi et al. designed a device with a full-width-at-half-maximum divergence angle of 3.9° for an 8-µm-aperture VCSEL with a curved mirror. This performance was observed when the device was operated at a current that was 1.2 times the threshold current (I_th)^[6]. However, compared with blue GaN-based VCSELs, progress in ultraviolet (UV) AlGaN-based VCSELs has been slow. Leonard investigated a 405 nm VCSEL with a threshold current density of approximately 3.5 kA/cm^2[7]. Zhao et al. found that the threshold current density of a InGaN near-UV LD with the n-side down on a submount was 1.27 kA/cm^2[8]. Yang et al. observed that the threshold current of a ridge waveguide-structure UV LD operating under pulsed conditions was approximately 25 kA/cm^2[9]. Zheng et al. proposed a UV VCSEL structure that employed epitaxial lateral overgrowth to prepare high-quality AlGaN multi-quantum wells (MQWs); this structure exhibited a minimum threshold power density of 0.79 mW·cm^−2[10]. The poor performance of UV VCSELs is caused by their low hole-injection efficiency and electron leakage^[11].

Numerous methods have been proposed to improve the hole injection efficiency. Qiu et al. designed a p-GaN/n-GaN/p-GaN (PNP-GaN) current-spreading layer^[12]. In this design, the thickness of the optically absorptive indium tin oxide (ITO) current-spreading layer can be reduced to decrease internal loss and increase lasing power. Han et al. constructed p-AlGaN/p-GaN hole injection layers (HILs) that improved the electric field within p-GaN and reduced the valence band barrier height of the p-doped electron barrier layer (EBL)^[13]. Polarisation doping based on HIL Al-composition gradient has also been used to improve the hole injection efficiency^[14-16]. Compared to AlGaN layers with a fixed Al composition, those with a graded Al composition along the growth direction facilitate (1) the generation of high-density electrons and holes through polarisation-induced doping and (2) the manipulation of carrier transport behaviour via energy band modulation^[17]. A graded Al composition in p-AlGaN can increase the concentration of polarisation-induced holes and negative-net polarisation charges^[18]. Combining the unique composition of the AlGaN structure with such grading creates a channel for polarisation-induced two-dimensional electron gases (2DEGs)^[19]. The high ionisation energy of Mg acceptors in AlGaN materials results in low p-type conductivity. Hence, polarisation doping is necessary to form a p-type conduction layer. For Ga face growth, n-type conductivity is achieved by increasing the Al content in the growth direction, and p-type conductivity is achieved by decreasing the Al content^[20]. Therefore, the forward resistance and conducting voltage can be reduced by employing polarisation doping to realise p-type conductivity. This minimises a considerable part of the valence-band discontinuity (that is, hole traps).

Electron leakage is a critical factor that affects the optoelectronic performance of VCSELs. Although the EBL can prevent electron leakage, discontinuity in the valence band between the EBL and the HIL can hinder hole injection. Lowering the height of the hole potential barrier can improve hole transport to reduce the hole-blocking effect of the EBL^[21-23]. Various EBL designs have been developed to facilitate hole injection, including gradient EBL^[24], superlattice EBL^[25-26], and staircase EBL^[27-28]. The combination of slope-shaped EBL and HIL can also promote carrier injection. However, the growth processes of superlattices and staircase EBLs are complex. Consequently, it is crucial to consider both the influence of the EBL on electron leakage and hole injection, as well as the feasibility of actual production, when designing the EBL.

In this study, we proposed combining the Al-composition gradient HIL structure with the Al-composition gradient EBL in VCSELs to increase hole injection efficiency and decrease electron leakage. Four different structures were designed to verify the influence of this structure on the device performance: a uniform Al-composition HIL and EBL, gradient Al-composition HIL, gradient Al-composition EBL, and hybrid gradient Al-composition HIL and EBL. We investigated the combined effects of polarisation doping and Al composition gradient in the EBL on the carrier concentration, effective barrier height, stimulated emission, and other performance factors. Combining the gradient Al compositions in the HIL and EBL not only improved hole injection efficiency and smoothened the valence band, but also enhanced the ability to prevent electron leakage. This combination significantly increased the stimulated radiative recombination rate in the quantum, resulting in an increase of 17.8% in laser power, and achieved superior optoelectronic performance.

Figure 1 (color online) illustrates the structure of a GaN-based VCSEL. The cavity length thickness d₁ of the GaN-based VCSEL device designed in this study satisfied d₁=λ₀/2n, and the physical thickness d₂ of each DBR layer satisfied d₂=λ₀/4n, where λ₀ is the lasing wavelength of 375 nm, and n is the real refractive index at the lasing wavelength. The GaN-based VCSEL device consisted of 12 pairs of HfO₂/SiO₂ top DBR and 13 pairs of HfO₂/SiO₂ bottom DBR, sandwiching a cavity with a length of 1.5λ. The cavity of VCSEL A was composed of an ITO layer with a thickness of 20 nm, a p-Al_0.12Ga_0.88N layer with a doping concentration of 5×10¹⁹ cm⁻³, a thickness of 144 nm, a p-type Al_0.2Ga_0.8N electron-blocking layer (p-EBL) with a thickness of 20 nm, and a doping concentration of 7×10¹⁹ cm⁻³. The active region consisted of five pairs of GaN (10 nm)/In_0.05Ga_0.95N (6 nm) and an n-Al_0.12Ga_0.88N layer with a doping concentration of 1×10¹⁹ cm⁻³ and thickness of 177 nm. The main difference between VCSEL B and VCSEL A lay in the fraction of Al within the HIL, which was fixed at 0.12 for the former, whereas it uniformly ranged from 0.06 to 0.18 for the latter. VCSEL C differed from VCSEL A in that the original Al composition of 0.2 in the EBL structure was changed to a uniformly graded Al composition ranging from 0.18 to 0.22. Structure D combined the changes in the HIL and EBL from structures B and C, respectively. All the designed VCSELs used SiO₂ layers for hole current and light confinement. The radii of the bottom and top DBRs were 5 and 3 μm, respectively. The width of the annular electrode was 1 μm. A ring-shaped P electrode was placed above the ITO, and a ring-shaped N electrode was placed above the n-AlGaN, both of which achieved Ohmic contacts.

The simulations in this study were conducted using Crosslight PICS3D, and appropriate boundary conditions were set to solve the Poisson, drift-diffusion transport^[29], and rate equations and simulate the electrical and optical characteristics of the device^[30]. This model represents a good compromise in terms of efficiency, simplicity, and practical simulation results. In contrast, quantum models based on atomic simulations are more accurate but computationally more burdensome^[31]. The absorption coefficients of the materials in the layer were set as follows to ensure that the simulation and experimental results were consistent: ITO at 4012 cm⁻¹, HIL at 70 cm⁻¹, EBL at 70 cm⁻¹, and n-AlGaN at 5 cm^−1[32]. The ratio of the InGaN/GaN MQW conduction band step to the valence band step was set to 70/30^[33]. The laser operated in a continuous wave mode. The Auger coefficient and Shockley–Read–Hall (SRH) recombination lifetime were set to 2×10⁻³¹ cm⁶s⁻¹ and 1×10⁻⁷ s, respectively^[32]. A polarisation level of 40% was considered to reflect the polarisation-induced charges in modelling the spontaneous and piezoelectric polarisations at the lattice-mismatched interfaces^[34]. The effective index method (EIM) was used to calculate the optical model of the device, which is suitable for complex structures with oxide-limited apertures^[35].

The I-V and L-I curves are shown in Figure 2 (color online). Structures B and D exhibited lower series resistances and threshold voltages than structures A and C. The lasing power of all four structures increased with the injection current. All structures began to exhibit an output at an injection current of 0.35 mA. However, the output power at this point was relatively low. It was not until the injection current reached approximately 0.72 mA, corresponding to a current density of 2.55 kA/cm², that the output power began to increase significantly. Based on the data, the threshold current of structure D was slightly lower than those of structures A, B, and C. When the injection current exceeded 0.75 mA, the output power of all four structures increased significantly. These simulation results indicate that, despite the similarity of the threshold currents for the four structures, their slope efficiencies differ. Structure D exhibited the highest slope efficiency (0.198 W/A), whereas structures A, B, and C had slope efficiency values of 0.183, 0.187, and 0.194 W/A, respectively.

At an injection current of 20 mA, the output power values for structures A, B, C, and D were 2.87, 3.05, 3.24, and 3.38 mW, respectively. Structures B, C, and D exhibited significantly higher output power than structure A. Specifically, structure D exhibited the highest lasing power, which was approximately 17.8% higher than that of structure A. Eqs. (1) and (2) express the threshold current and emission power formulas for VCSELs, respectively:

$ {I_{{\mathrm{th}}}} = \frac{{e{V_{\mathrm{a}}}}}{{{\eta _{\text{a}}}}}(A{N_{{\mathrm{th}}}} + BN_{{\mathrm{th}}}^2 + CN_{{\mathrm{th}}}^3)\quad, $ (1)

$ P={\mathrm{\eta }}_{{\mathrm{d}}}\frac{hv}{e}(I-{I}_{{\mathrm{th}}})P={\mathrm{\eta }}_{{\mathrm{d}}}\frac{hv}{e}(I-{I}_{{\mathrm{th}}})\quad, $ (2)

where e is the electron charge, V_a is the active region volume, η_a is the carrier injection efficiency, A, B, and C are the SRH, radiative, and Auger recombination rates, respectively, η_d is the differential quantum efficiency thickness, hv is the photon energy, I is the operating current, I_th is the threshold current, and P is the emission power. Based on Eqs. (1) and (2), as the carrier injection efficiency increases, the threshold current decreases, and the emission power increases.

Based on the previous analysis, the lasing power has a close relationship with the carrier injection efficiency, whereas the hole injection efficiency has a close relationship with the hole concentration. Hence, the effects of changes in the HIL and EBL on hole concentration were analysed.

Figure 3 (color online) illustrates the effects of the different gradient Al fractions of the HIL and EBL on the hole injection efficiency. Figure 3(a) shows the radial hole concentration at an injection current of 20 mA. Compared to structure A, when structure B introduced polarisation doping, it exhibited a significant increase in hole concentration in the active region. Furthermore, while blocking electron leakage, the traditional EBL prevents hole injection^[36]. In addition to improving p-type conductivity, the polarisation-induced-graded p-type AlGaN layer facilitates electron blocking without introducing additional barrier carriers to hole injection. It also provides extended flexibility in graded-refractive-index design, which is applicable to UV lasers^[37]. Under the condition of an unchanged average Al composition, the gradient Al composition of the HIL reduces the abrupt hole barrier at the HIL/EBL interface, thereby weakening the hindrance effect on hole injection. Modifying the EBL in structure C significantly impedes electron leakage and facilitates hole injection. This is because it reduces the abrupt potential barrier at the interface between the HIL and the EBL. Moreover, inhibition of electron leakage is advantageous for hole injection. With the introduction of both polarisation doping and a modified EBL, structure D exhibited the highest hole concentration in the active region. This is attributed to the low ionisation energy of Mg within GaN and the strong interface polarisation charge of AlGaN compounds. The introduction of polarisation doping enables the incorporation of a bulk polarisation charge to increase the hole concentration. Furthermore, because the unshielded polarisation charges at the interfaces are positive, they electrostatically contribute to the appearance of parasitic hole-blocking layers. Therefore, hole injection into the active region is restricted because of the thermionic emission from the hot electrons. However, improving the EBL to address electron leakage issues also alleviate this problem, further suppressing unintentional hole-blocking layers and improving hole injection efficiency.

The hole concentration previously mentioned was determined under dynamic equilibrium conditions. This indicates that at the same injection current and operating temperature, the active region of structure D accumulates more holes than structures A, B, and C. Thus, a higher hole injection efficiency is obtained in structure D, facilitating population inversion and satisfying the threshold conditions for stimulated emissions.

Figure 3(b) depicts the radial hole current density for each structure at an injection current of 20 mA. The radial hole current density across the active region and p-type spacer layers is higher in structures B, C, and D than in structure A. This demonstrates that polarisation doping improves the ionisation efficiency of Mg dopants, increasing the hole concentration. The longitudinal hole current densities in both the active region and p-type spacer layers of structure D were the highest among all the structures. This further confirms that the combination of gradient Al composition in the HIL and an EBL that effectively blocks electron leakage results in an increased number of holes being injected into the active region, increasing injection efficiency.

Figure 4(a) (color online) shows the electron concentration distribution for each structure. A significant electron leakage was observed even in structure A with the EBL. This is caused by the interface polarisation charges between the last quantum barrier and the EBL, as well as between the HIL and the EBL. The influence of the EBL on hole and electron transport is primarily attributed to the parasitic inversion layer formed by interface polarisation charges and the impact of the active region on the confined carrier density in the EBL. The introduction of polarisation doping and the transition of the EBL to a gradient Al composition resulted in a significant increase in the electron concentration in the active region. Moreover, the combination of these two factors resulted in the highest electron concentration in the active region. This is because the increased hole concentration generated by polarisation doping reduces electron leakage, and the HIL acts as a natural electron barrier to enhance the effective barrier for electrons.

Figure 4(b) (color online) shows the electron current density distribution on the p-side of each structure. The electron current density exhibited a stair-step trend in the active region, caused by the transport of electrons among the QWs. In each QW, electrons and holes recombined to emit light. Therefore, as electrons passed through each QW, some electron-hole pairs recombined, resulting in a decrease in the electron current density. Electrons injected from the n-type layer into the active region recombined with the holes in the QWs. However, several electrons also spilled over to the p-type layer without undergoing recombination with the holes in the QWs, which is defined as electron leakage. Therefore, the electron current density in the p-type layer can be used to assess the extent of electron leakage. The electron leakage density was significantly lower in structure D, indicating the lowest electron spillover from the active region to the p-type layer (Figure 4(b)). Structures B and C exhibited lower electron leakage densities in the p-type layer compared to structure A. This suggests that structures B and C can also reduce electron leakage. The reduction in the electron leakage density in the p-type layer also suppresses the nonradiative recombination between electrons and holes, increasing the concentration of holes injected into the active region.

Figure 5 (color online) shows the stimulated recombination rates in the active region for the different structures. The stimulated radiation recombination rates of structures B, C, and D were all higher than that of structure A. This is closely related to the increased hole-injection efficiency and enhanced ability to block electron leakage. More electron-hole pairs did not undergo nonradiative recombination in the HIL; instead, radiative recombination occurred in the active region. In structure D, the stimulated radiation recombination rate significantly increased near the EBL QW, indicating that more holes were consumed because of the stimulated radiation recombination in the QW.

The wall-plug efficiency (WPE) is a key parameter for evaluating the performance of VCSELs. Figure 6 (color online) shows the relationship between the WPE and the injection current. Compared to structure A, all the other structures exhibited improved WPE, consistent with the analysis of the variation in the applied voltage and laser power with the injection current. The WPE initially increased rapidly before gradually decreasing as the current increased. When the current reached the threshold, the photons generated by electron-hole radiation recombination in the active region offset the lost photons. As the current increased, the efficiency of radiation recombination further increased, resulting in a rapid increase in the WPE. With a further increase in the current, the radiation recombination of carriers in the active region reached saturation. A further increase in the current caused overflow and nonradiative recombination of carriers in the active region, resulting in a decrease in the WPE. Therefore, the WPE initially increased rapidly and then decreased gradually. Structure D exhibited the highest WPE, highlighting the advantages of energy and high efficiency.

To illustrate the underlying reasons for the enhancement of hole concentration in the MQW and the suppression of electron leakage in the hole-injection layer, we present band diagrams for the active region, EBL, and hole-injection layer of each structure (Figure 7, color online). We defined the effective barrier height for carriers by considering the energy difference between the quasi-Fermi level of electrons and the conduction band as the electron barrier height and the energy difference between the quasi-Fermi level of holes and the valence band as the hole barrier height. First, the electron barrier heights for the structures were 141, 172, 190, and 193 meV, and the changes in these heights were analysed. A lower electron barrier height facilitates the escape of electrons from the active region to the p-type region, whereas a higher electron barrier height causes less electron leakage. Because of significant changes in the material composition near the electronic barrier layer, piezoelectric and polarisation effects are comparatively strong, resulting in band bending^[38]. Band bending leads to a significant separation of the wave functions of holes and electrons, not only weakening the confinement of electrons in the active region but also limiting the injection of holes from the p-type layer^[39].

Compared with structure A, the electron barrier height in structure B significantly increased after introducing polarisation doping. This is because the polarisation doping introduces bulk polarisation charges that can shield the polarisation-induced electric field in the QWs, reducing the quantum-confined Stark effect (QCSE). A decrease in the strength of the polarisation-induced electric field in the QW can increase the overlap of the electron-hole wavefunctions. The reduced QCSE is conducive to the stimulated radiative recombination of electrons and holes. The electron barrier height in structure C was also higher than that in structure A, indicating that the EBL structure could reduce electron leakage more effectively. Structure D had the maximum electron barrier height, indicating its superior ability to block electron leakage. This is consistent with the analysis of the electron concentration and electron current density distributions previously discussed.

Subsequently, the variation in the hole barrier height was analysed. The hole barrier heights for the structures were 170, 156, 167, and 147 meV, respectively. Structures B, C, and D had lower hole barrier heights than structure A. Specifically, structure D eliminated the abrupt barrier between the EBL and the HIL by changing the Al compositions of the EBL and HIL. This smoothens the valence band and facilitates hole injection, consistent with the previous analysis of the hole concentration and hole current density distributions.

We designed a GaN-based UV VCSEL structure and thoroughly investigated the combined effects of the gradient Al composition in the HIL and Al-composition gradient EBL on the device performance. Our results indicate that under the condition of a constant average Al composition in each structure, polarisation doping can introduce bulk polarisation charges to shield the polarisation-induced electric field in the QWs, reduce the QCSE, improve the hole injection efficiency, and enhance the ionisation efficiency of Mg dopants, thereby increasing the hole concentration. Furthermore, implementing an Al composition gradient in the EBL on this basis eliminates the abrupt hole barrier at the interface between the hole-injection layer and the EBL, smoothening the valence band. Moreover, the ability to block electron leakage is improved, suppressing unintentional hole-blocking layers. This approach effectively optimises the hole injection efficiency, increases the stimulated radiation recombination rate in the QW, decreases the threshold voltage, and achieves superior optoelectronic performance.