**1. Introduction**

Vertical-cavity surface-emitting lasers (VCSELs) exhibit several advantages over edge-emitting lasers (LDs), including high-speed direct modulation, circular mode profile, low threshold current, etc. [1–3]. Recently, although GaAs-based VCSELs that emit red or infrared light have been commercialized and applied to various products, it is still hoped that VCSELs will not only cover the red area, but also the blue and green spectrum region, thus constituting the ternary color of light for illumination, display and communication of the next generation [4]. As wide-bandgap materials, the bandgap width of gallium nitride (GaN) and its alloy materials are continuously adjustable from 0.7 eV to 6.2 eV, covering near-red, green, blue, and ultraviolet. They have become the main material for manufacturing short-wavelength light-emitting diodes (LEDs) and LDs. Recently, the GaN-based materials have been applied to VCSELs and achieved important progress [5]. Universities and research institutes such as National Chiao-Tung University [6], Nichia Corporation [7], University of California, Santa Barbara [8], Sony Corporation [1], Xiamen University [9] and Meijo University [10] conducted good work on the designing and manufacturing of blue GaN-based VCSELs. In 2018, Stanley Electric Co., Ltd. demonstrated a GaN-based VCSEL with an output power of 7.6 mW by reducing both the internal loss and the reflectivity of the front cavity mirror [11]. This structure achieved the highest output power of a GaN-based VCSEL ever produced to the best of our knowledge. However, it is still relatively low as a result of ignoring other mechanisms. For example, for InP and other semiconductor-based lasers, lower threshold and higher output power can be achieved by designing the micro-cavities, which may also have good effects in GaN-based VCSELs [12–14].

Beyond designing the micro-cavities, in order to obtain higher output power, methods which maximize the radiative recombination rate have been adopted by minimizing the electron leakage out of the active region. Among those methods, AlxGa1−<sup>x</sup>N electron blocking layer (EBL) is usually placed between the active region and p-GaN layer, since it provides a higher energy barrier in the conduction band between quantum wells (QWs) and the p-layers. The higher energy barrier in the conduction band contributes to the confinement of the electrons in the active region, so stronger output power can be achieved [15]. However, the very commonly used AlxGa1−<sup>x</sup>N EBL sometimes cannot e fficiently reduce electron leakage due to the polarization charge in that layer, which decreases the barrier height for electron transport [16,17]. As such, the blocking e ffects of AlxGa1−<sup>x</sup>N EBL on electron overflow are limited [18]. In addition, there are big di fferences in the polarization value and the energy barrier height in the conduction band between AlxGa1−<sup>x</sup>N EBL and InxGa1−<sup>x</sup>N last quantum barrier (LQB), which results in a large built-in polarization field and significant free electron accumulation at the heterointerface between the two layers. This free electron accumulation outside of the active region severely degrades the internal quantum e fficiency. To solve this problem, Zhang et al. proposed a design which replaces the InxGa1−<sup>x</sup>N LQB with a tapered AlxGa1−<sup>x</sup>N LQB in GaN-based LD [19], and Lin et al. proposed another structure which replaces the AlxGa1−<sup>x</sup>N EBL with a composition-graded AlxGa1−<sup>x</sup>N EBL in the VCSEL [20].

In this work, our concept is to improve the output power by optimizing the carrier transport. We proposed an improved GaN-based VCSEL structure called GVCSEL to reduce the electron leakage. In GVCSEL, the LQB and EBL in the conventional GaN-based VCSEL are replaced with a new layer which consists of a composition-graded p-AlxGa1−<sup>x</sup>N layer and a p-AlxGa1−<sup>x</sup>N layer. The physical and optical properties of the GVCSEL are investigated numerically with the Photonic Integrated Circuit Simulator in 3D (PICS3D) software (Crosslight Corporation, Vancouver, BC, Canada). The results show that the GVCSEL e ffectively confines the electrons in the active region and has a more uniform carrier distribution. This contributes to a better radiative recombination and helps achieve a 70.6% increase of the output power compared with the conventional GaN-based VCSEL.

#### **2. Device Structure and Simulation Parameters**

In this work, the conventional GaN-based VCSEL was used for comparison, as shownin Figure 1a [21], which consists of 11 pairs of Ta2O5/SiO2 as the bottom and top distributed Bragg reflectors (DBRs), respectively. Then, there is a 5.3 μm-thick n-type GaN layer (n-doping = 2.5 × 10<sup>18</sup> cm<sup>−</sup>3) and five periods of In0.1Ga0.9 N/In0.035Ga0.965N multi-quantum wells (MWQs). The thicknesses of the well and the barrier are 4 nm and 8 nm, respectively, the n-doping of the barrier is 1 × 10<sup>18</sup> cm<sup>−</sup>3, whilst the LQB is undoped. Next there is a 20 nm-thick Al0.21Ga0.79N (p-doping = 5 × 10<sup>18</sup> cm<sup>−</sup>3) EBL, followed by a 0.54 μm-thick p-type GaN layer (p-doping = 1 × 10<sup>18</sup> cm<sup>−</sup>3). On the p-type GaN layer, a 20 nm-thick SiO2 is employed as the current-confined layer. Following that, a 20 nm-thick indium-tin-oxide (ITO) layer (p-doping = 1 × 10<sup>19</sup> cm<sup>−</sup>3) is employed as the current spreading layer and the diameter of the current injection aperture is designed to be 10 μm. The top metal ring contact confining the optical mode is 12 μm in diameter. Figure 1b shows the schematic diagram of the GVCSEL in this study, which is formed by replacing the 8 nm-thick In0.035Ga0.965N LQB and 20 nm-thick Al0.21Ga0.79N EBL in the conventional GaN-based VCSEL with a new layer. The new layer consists of a p-Al0→0.21Ga1→0.79 N (p-doping = 5 × 10<sup>18</sup> cm<sup>−</sup>3) layer and a p-Al0.21Ga0.79N (p-doping = 5 × 10<sup>18</sup> cm<sup>−</sup>3) layer, where the thickness of the first layer is L nm and the thickness of the second layer is (28-L) nm. The GaN-based VCSEL samples with L equals 6 nm, 8 nm and 16 nm are named GVCSEL1, GVCSEL2 and GVCSEL3, respectively, and their parameters are given in Table 1. The conventional GaN-based VCSEL is named CVCSEL for comparison.

The physical features and optical properties of the GVCSEL and CVCSEL were investigated numerically with the Simupics3d program of Crosslight software. An important issue in simulation is the selection of proper parameters in the physical models. In this study, we used a Mg activation energy of 170 meV for GaN, which was assumed to increase by 3 meV per Al% for AlGaN [12].

The Shockley-Read-Hall (SRH) lifetime and the Auger recombination coefficient were estimated to be 100 ns and 1 × 10−<sup>34</sup> cm6s−1, respectively [22]. The built-in polarization caused by piezoelectric polarization and spontaneous polarization was represented by fixed interface charges at every heterointerface within the device, which was calculated using the methods developed by Fiorentini et al. [23]. Here we took 50% of the theoretical value by setting the polarization screening to 0.5 [24]. We also considered the energy band offset ratio as 50:50 [25]. Other material parameters in the simulation can be found in [26].

**Figure 1.** Schematic diagrams of the (**a**) conventional gallium nitride (GaN)-based vertical-cavity surface-emitting laser VCSEL (CVCSEL) and (**b**) proposed structure which is formed by replacing the LQB and EBL in the CVCSEL with a new layer (GVCSEL).



#### **3. Results and Discussions**

Since the output power and the threshold current are interlinked, investigating both of them is crucial to understand the performance of GaN-based VCSELs [17], we calculated the two performances of CVCSEL and GVCSEL1-GVCSEL3, as shown in Figure 2. It was found that the output power of CVCSEL was 0.179 mW and was lower than that of the GVCSELs in Figure 2a. In addition, the output power increased from 0.267 mW to 0.306 mW when the thickness of L of the p-Al0→0.21Ga1→0.79N in the GVCSEL was increased from 6 nm to 8 nm, while with further increase of L from 8 nm to 16 nm, the output power decreased from 0.306 mW to 0.303 mW. Thus, the highest output power was obtained in GVCSEL2, which achieved a 70.6% increase of output power compared with the CVCSEL. Figure 2b shows that the current threshold of the four samples first decreased and then went up. The lowest threshold current was also achieved in GVCSEL2.

In order to reveal the origin of the observations in Figure 2, we calculated the distribution of the electrons and the holes and the current density flowing along the vertical direction near the active region of the four samples at an injection current of 6 mA, as shown in Figure 3. We also calculated the distribution of the radiative recombination rate as shown in Figure 4a–d. In Figure 3a, the highest electron concentration in the p-GaN layer was obtained in CVESEL, thus there was the largest electron leakage. For the GVCSELs, the electron concentration in the p-GaN layer decreased when L was increased from 6 nm to 8 nm. However, the electron concentration in the p-GaN layer increased when the thickness of L went up from 8 nm to 16 nm. Therefore, the lowest electron concentration in the p-GaN layer was obtained in GVCSEL2, which means that the largest reduction of the electron leakage was obtained in GVCSEL2. Thus, the reduction of electron leakage is one of the origins of the increase of output power and the reduction of the threshold current for CVCSEL-GVCSEL3. Figure 3b illustrates that the hole concentration in p-GaN layers of the GVCSELs was almost the same with that of the CVCSEL, which means that the hole injection is not changed in GVCSELs compared to CVCSEL. Thus, the hole injection is not the origin of the change of output power and threshold current for the samples. Figure 3c demonstrates that the electron overflow of GVCSEL was e fficiently suppressed and the most e ffective suppression of the electron overflow was obtained in GVCSEL2. There was more uniform carrier distribution with the reduction of electron overflow. As a result, the radiative recombination rate in GVCSEL was improved, as can be seen in Figure 4a–d, and the highest one was obtained in GVCSEL2, as shown in Figure 4c. In summary, Figures 3 and 4a–d show that the increase of the output power and the decrease of the threshold current for samples of GaN-based VCSEL can be attributed to the reduced electron leakage and an increased radiative recombination rate.

**Figure 2.** (**a**) Output power at the injection current of 6 mA and (**b**) threshold current of CVCSEL and GVCSEL.

**Figure 3.** The distribution of (**a**) electron concentration; (**b**) hole concentration; (**c**) vertical electron current density, of GVCSEL1-3 and CVCSEL at an injection current of 6 mA.

Finally, for the purpose of investigating in-depth the origin of the reduced leaking electrons in the GVCSEL, we calculated the distribution of the energy band at an injection current of 6 mA, as plotted in Figure 4e–h. In CVCSEL, the effective barrier height of the EBL for the electrons was 223 meV, which was lower than that of GVCSEL. Therefore, in CVCSEL the electrons were easier to leak into the p-GaN layer. The increase of the electron leakage resulted in a more nonuniform carrier distribution in the active region, thus lowering the radiative recombination rate and the output power. For GVCSELs, when the thickness of L was increased from 6 nm to 8 nm, the effective barrier height increased from 263 meV to 303 meV. But the effective barrier height decreased from 303 meV to 280 meV when the thickness of L further increased from 8 nm to 16 nm. This means that the highest effective barrier height was the origin of the highest output power obtained in GVCSEL2. We can also see that the effective barrier height of EBL for the holes was about 176 meV in CVCSEL and all three GVCSELs. Therefore, the ability inject holes into the active region is almost the same in the CVCSEL and the GVCSELs, as shown in Figure 3b. In summary, the origin of the increased output power for the GVCSEL is not the rate of the injection holes but the suppressed electron leakage.

**Figure 4.** Distribution of (**<sup>a</sup>**–**d**) the radiative recombination rate and (**<sup>e</sup>**–**h**) the energy band of GVCSELs and CVCSEL at the injection current of 6 mA.
