## 4 All-dielectric-DBR GaN-based VCSELs  
In addition to nitride semiconductors, it may be possible to fabricate DBR mirrors having wide stopbands with dielectric materials, due to the wide range of refractive indices of these substances. As an example, the two dielectric materials SiO\({}_{2}\) and Ta\({}_{2}\)O\({}_{5}\) exhibit a large refractive index difference. Assuming refractive index values of 1.5 and 2.0 for the two dielectric materials and a reflectance peak wavelength of 450 nm, the associated stopband width would be more than 80 nm, which is much wider than the values reported for nitride semiconductor DBRs. Thus, GaN-based VCSELs with dielectric DBRs could avoid some of the issues associated with nitride semiconductor DBRs. In a pragmatic approach reported by [PERSON] et al., both DBRs were made of dielectric materials [8], adopting a p-side structure similar to that of [PERSON] et al. [4; 5]. The p-side was bonded to a silicon wafer while the n-side was polished to generate a thin nitride plate so as to obtain p-type, active and n-type layers on the silicon wafer. Subsequently, a dielectric DBR acting as the n-side mirrors and other metallic electrodes were deposited. In this process, both mirrors were composed of crack-free dielectric materials possessing wide stopbands. To date, there have been numerous reports of work with this type of GaN-based VCSEL [8; 9; 10; 11; 12; 13]. These GaN-VCSEL devices still have associated difficulties regarding control of the cavity length. Typically, the cavity must simultaneously meet two conditions to allow laser operation. The first condition concerns the optical mode loss and Figure 1a,b plot the roughly estimated coupling (diffraction) loss and mode spacing as functions of cavity length [16]. Figure 1a demonstrates that a shorter cavity is preferable because it leads to a smaller coupling (diffraction) loss after a round trip. Accounting for an estimated gain of up to 2000 cm\({}^{-1}\)[23], the amplification resulting from the active layer in the VCSEL is estimated to be approximately 1% for a typical total thickness on the order of 10 nm. Thus, the cavity should preferably be shorter than several microns to limit the diffraction loss to less than 1%. The second condition concerns the longitudinal modes. The wavelength of each longitudinal mode is determined from the cavity length, which must be controlled so that one of the modes overlaps with the gain spectrum of the active region used in the device. As an example, even though the loss in such devices appears to be sufficiently low, in the case of a 5-\(\upmu\)m-long cavity, the mode spacing is approximately 7 nm (Figure 1b). Consequently, the modes can easily miss the gain spectrum and lasing will not occur unless the cavity length is precisely controlled such that one of the longitudinal modes is located near the top of the gain spectrum of the InGaN quantum wells. It is evident that highly sophisticated technology would be required to control the cavity length to below several microns by polishing. Longer cavities can provide narrower longitudinal mode spacing to ensure that one of the modes appears near the top of the gain spectrum without precise control of the cavity length. For example, a cavity longer than 20 \(\upmu\)m gives rise to a longitudinal mode spacing narrower than 2 nm, which is sufficiently narrow to overlap the gain spectrum of typical InGaN quantum wells. However, a cavity of this length often results in a diffraction loss of greater than 1%, which is sufficient to prevent the device from lasing. These requirements for precise control over the cavity length have thus far prevented the mass production of GaN-VCSELs. It is apparent that precise control over the cavity length (to below 5 \(\upmu\)m) or reduction of the optical diffraction associated with longer cavities, is required for the robust production of GaN-based VCSELs with all-dielectric DBR configurations.