# Distributed Bragg Reflectors for GaN-Based Vertical-Cavity Surface-Emitting Lasers
## 2 Fabrication Techniques and Design Considerations of Distributed Bragg Reflectors (DBRs)
### Transport Properties: Electrical and Thermal Conductivities  
The choice between non-epitaxial and epitaxial DBRs has a significant implication on the resulting device configuration. In the case of non-epitaxial DBRs, complex processing techniques are required to encase the epitaxial gain/active region with top and bottom dielectric DBRs (Figure 3a). Since non-epitaxial DBRs are typically electrically insulating, one needs to develop schemes for lateral current injection (shown schematically as red arrows in Figure 3a) through intra-cavity current spreading layers. These layers are necessarily thin yet heavily doped, often representing a trade-off between electrical impedance and optical absorptive loss. The issue of joule heating with lateral current injection is exacerbated by the rather poor thermal conductivities of dielectric DBRs (0.1-2 W/m-K). Thermal transport in non-epitaxial DBRs is sometimes improved by lengthening the cavity with additional n-type layers to facilitate lateral heat flow [46; 47], or by incorporating sophisticated CMOS-like 3D heat-sinking schemes through the dielectric DBRs [48]. Epitaxial semiconductor DBR mirrors offer good electrical conductivities and improved thermal conductivities over their dielectric counterpart. In the best case of the mature Al(Ga)As/GaAs system, electrical resistance and thermal conductivity of 10\({}^{-3}\)\(\Omega\)-cm and 300 W/m-K, respectively, can be achieved [49; 50]. Conductive DBRs enable vertical current injection into the gain region of a VCSEL for best current uniformity and device impedance (Figure 3b). This is the configuration nearly all commercial VCSELs employ. However, injecting current though the epitaxial DBR comes with its own challenges. The stacking of alternating layers of different bandgaps, create potential barriers which inhibit carrier flow and increase the overall DBR resistance. Several techniques have been implemented, such as interfacial doping [51] or interfacial alloy grading [52; 53], however, these implementations often come on the expense of the optical reflectivity and thermal properties of the DBRs and a trade-off between the different properties is usually decided. While the epitaxial DBR configuration is a clear preference and the mainstream for the mature infrared and red VCSEL industry, the choice of DBR for AlGaInN-based VCSELs remains a debatable subject and represents a tradeoff among optical properties, transport limitation, and ultimately the manufacturability. In Figure 4 we illustrate these design constraints in a qualitative way. As is described in Section 2.2, semiconductor DBRs sometimes have limited \(\Delta n\) and consequently a narrow width of stopband \(\Delta\lambda_{usable}\). A more pertinent gauge for the manufacturability of VCSELs is not the absolute width of \(\Delta\lambda_{usable}\), as is shown in Figure 4, but a normalized ratio, which we defined as \(\Delta\lambda_{usable}/\lambda_{s}\), that needs to be maintained above a certain margin against the non-uniformities and variations that are often inevitable in epitaxy and fabrication processes. For example, for a blue VCSEL emitting at \(\lambda\) = 450 nm, a \(\Delta\lambda_{usable}\) of 9 nm wide, centered around 450 nm, would require the variation of cavity  
Figure 3: Schematic illustrations of vertical cavity surface-emitting lasers (VCSELs) employing non-epitaxial (**a**) and epitaxial (**b**) DBRs. The pathways for current injection are shown in red and green arrows for the non-epitaxial and epitaxial mirrors, respectively. mode (related to the thickness control) and gain peak (related to indium composition and growth rate) to be with \(\pm\) 1.0% across the wafer to have a sufficient yield of VCSELs. Any deviation across the wafer in thickness or composition that exceeds this 1% margin will substantially change, if not fail, the VCSEL characteristics. \(\Delta\lambda_{usable}\lambda\) therefore can be considered the tolerance in process variations in manufacturing VCSELs.