**4. Conclusions**

In our work, in order to improve the output power of GaN-based VCSEL, we proposed a structure called GVCSEL, based on the concept of modulating the carrier distribution. A new layer was used by combining the LQB and EBL in the conventional GaN-based VCSEL, which was made up of a L nm-thick composition-graded p-AlxGa1−<sup>x</sup>N layer and a (28-L) nm-thick p-Al0.21Ga0.79N layer and the Al component in the graded AlxGa1−<sup>x</sup>N changed from 0 to 0.21. The thickness of L for the three GVCSEL samples was selected to be 6 nm, 8 nm and 16 nm. The numerical simulation results showed that all the GVCSELs had improved output power. The higher output power in the GVCSELs is an attribute of the decrease of the large built-in polarization field and the reduction of the free electron accumulation at the heterointerface between the LQB and the AlxGa1−<sup>x</sup>N EBL. This further helped the suppression of the electron leakage and contributed to a more uniform carrier distribution in the active region, resulting in a higher radiative recombination rate in the quantum wells. What is more, this proposed layer also introduced a stronger quantum barrier which can confine the carriers in the quantum wells. In the GVCSELs, the one with a thickness of L of 8 nm obtained the highest output power, which was 70.6% stronger over that of the CVCSEL, since it had higher e ffective barrier height in the conduction band for electrons. Therefore, the GVCSEL output power can be accurately designed by selecting the thickness of L.

**Author Contributions:** Conceptualization, H.L. and J.L.; data curation, H.L.; methodology, H.L.; project administration, J.L. and M.L.; supervision, M.L.; validation, M.L.; writing original draft, H.L.

**Funding:** This work was supported by the Science Challenge Project (No. TZ2016003-2), National Key R&D Program of China (No. 2017YFB0403103), and National Natural Science Foundation of China (No. 61804140).

**Conflicts of Interest:** The authors declare no conflict of interest.
