# Distributed Bragg Reflectors for GaN-Based Vertical-Cavity Surface-Emitting Lasers
## 3 Epitaxial DBRs for GaN Vertical Cavity Surface-Emitting Lasers (VCSELs)  
### Al(Ga)N/GaN DBRs  
A lattice mismatching of 2.4% between AlN and GaN introduces excessive tensile or compressive strain and stress (\(\sim\)7 kPa) in AlN/GaN heteroepitaxial layers [55]. Instead of using the two binary ends (AlN and GaN) as the DBR materials, adjusting the AlN or GaN mole fraction in a ternary AlGaN compound can help to reduce the strain accumulation during DBR growth and minimize the possibility of crack formation. However, the index contrast between AlN and GaN is only \(\sim\)0.34 [56; 57]. Using a ternary layer as one of the DBR layers will significantly reduce the index contrast, which then necessitates a large number of AlGaN/GaN pairs (\(>\)50 pairs) to achieve a high reflectance.  
While the index contrast between AlN and GaN is 0.34, the large lattice mismatch (2.4%) between the two compounds would introduce excessive tensile or compressive strain and stress (\(\sim\)7 kPa) within the AlN/GaN heteroepitaxial layers, extremely deteriorating the DBRs properties. Therefore, it is common adjust the AlN and GaN mole fraction in a ternary AlGaN compound to reduce strain accumulation and minimize the possibility of crack formation. However, due to the lowered refractive index contrast, in an AlGaN/GaN DBR, a large number of pairs (\(>\)50) is required to achieve high reflectance, which is indeed not an easy growth task.  
In 1991, [PERSON] et al. [58] reported the first Al\({}_{0.2}\)Ga\({}_{0.8}\)N/GaN DBRs in the blue (442 nm) and violet (375 nm) wavelengths. A small amount of Al was used in ternary AlGaN for the ease of growth but compromised the reflectance (80-95%). In 1996, [PERSON] et al. [59] reported the first optically pumped GaN-based VCSEL with a 10-\(\upmu\)m GaN active region sandwiched between 30 pairs of Al\({}_{0.40}\)Ga\({}_{0.60}\)N/Al\({}_{0.12}\)Ga\({}_{0.88}\)N top and bottom DBRs with reflectances of 93% and 84%, respectively. The low-reflectivity mirrors and a long cavity lead to a very high threshold pumping power (2.0 MW/cm\({}^{2}\)). To overcome the stress generation and enable growth of a larger number of DBR pairs with good epitaxial quality, several proposals were made using either short-period superlattices (SLs) [60] or thin low-temperature AlN interlayers [61] below or inside the DBRs to release the strain. Between 1999 and 2000, several groups reported optically pumped VCSEL operation using AlGaN/GaN epitaxial DBRs [17; 18; 62]. The research on AlGaN DBRs continued in subsequent years [60; 63; 64; 65; 66; 67]. Electrical injection with AlGaN/GaN DBR microcavity began with a resonant cavity light-emitting diode (LED) in 2001 [68]. The continual pursuit of Al(Ga)N epitaxial DBR-based VCSEL culminated in 2008 when National Chiao Tung University (NCTU) reported the continuous-wave operation at room temperature of an electrically injected GaN VCSEL, using a strain-engineered AlN/GaN DBR in combination with a top dielectric Ta\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) DBR [19]. An AlN/GaN superlattice AlN/GaN insertion layer was employed to ease the mismatch. In Figure 6 the TEM micrographs and the corresponding reflectance spectrums are shown to demonstrate the benefit [69].  
Figure 6: _Cont._Usually before reaching the required number of pairs for high reflectance, the growth of the AlGaN/GaN DBRs already encounters significant cracking, morphological degradation, or generation of dislocations. As VCSEL devices require exceptionally accurate control in longitudinal and lateral modes, any strain or wafer bowing would have serious consequences in production. After the demonstration by NCTU, the effort in making VCSELs using Al(Ga)N/GaN DBRs has somewhat subsided, likely because of the almost insurmountable problem in epitaxial strain management, especially in a manufacturing environment.