## 2 VCSEL Structure and Dynamism Analysis  
Although designs and materials, used for the VCSELs, are not totally the same, these VCSELs have one typical common structure, as shown in Figure 1a. Two multi-layered Bragg reflectors are located at the top of the p-doped region and at the bottom of the n-doped region, with the high-index layer and low-index layer alternating. Constructive interference is caused by the reflections at the interface between the high-index and low-index layers for the reflective wave around the Bragg wavelength, and the multiple layers act as a mirror to improve optical gain [14]. The oxide layer, with a specific aperture size, transversely confines carriers to the active region. The p-doped and n-doped regions provide carrier injection for the active region between them.  
The active region consists of separate confinement heterostructure (SCH) layers, barrier (B) layers, and quantum well (QW) layers, detailed in Figure 1b. The SCH1 layer is adjacent to the n-doped region, while the SCH2 layer is adjacent to the p-doped region. The barrier layers are sandwiched between two adjacent QW layers and have a larger energy bandgap than the QWs. Conventionally, the QWs of 850 nm VCSELs are fabricated using GaAs. However, InGaAs QWs increase the differential gain, which is advantageous to reach higher speeds [15]. In QW layers, carriers have two states: an unconfined state and a confined state. The confined state indicates the carriers are confined at the bottom of the wells and no longer free to move in three dimensions. The carriers in the unconfined state (also referred as the gateway (G) state) are free to move in three dimensions and occupy energy higher than the carriers in the confined state at the bottom of the well [16]. Therefore, the gateway state can be viewed as an intermediate state for carriers originating from either a SCH or barrier layer. The MQW-SCH-G-B  
Figure 1: (**a**) Cross-sectional schematic of a MQW VCSEL. (**b**) The active region of the VCSEL represented by a MQW-SCH-G-B band diagram. The subscript of SCH, QW, G, B represents the position of the corresponding layer. (**c**) The carrier and photon dynamics in the first QW are illustrated. The red and green solid lines represent the conduction and valence band edges, respectively. The black dash line represents the energy state in the quantum well.  
structure is widely adopted for 850 nm VCSEL devices [12; 13]. In [12], the VCSEL performance investigation uses a 7-nm-thick GaAs MQWs separated by 8-nm-thick Al\({}_{0.3}\)Ga\({}_{0.7}\)As barriers.  
The dynamic behavior of the VCSEL is determined by the carrier and photon dynamism illustrated in Figure 1c. The carriers are injected into the active region due to the injection current. Then, carriers drift with applied electric field between the top and bottom contacts (Figure 1a) and diffuse from carrier concentration gradient between the n-doped and p-doped regions. Carrier movements between the two energy bands are labelled _capture_ when the carrier moves to a lower bandgap region, and _escape_ when it jumps to a higher bandgap region. Tunneling is the quantum process, where a carrier penetrates through a barrier region, facilitating a carrier motion between adjacent QW regions. Photons are generated via stimulated emission involving an electron-hole recombination.