# Quick Fabrication VCSELs for Characterisation of Epitaxial Material
## 3 Results and Discussion
### Wavelength Tuning  
We measured the wavelength shift as a function of temperature for standard VCSEL devices to be 0.07 \(\pm\) 0.02 nm/K which is in good agreement with the temperature-induced refractive index shift of the epitaxial material [29] and this is expected for all device types given that the constituent materials of the epi-structures are the same. The uncertainty here  
Figure 7: (**a**) Lasing wavelengths for all devices; (**b**) photovoltage spectra for QF VCSEL samples showing the variation in cavity resonance wavelength. represents the standard deviation as the spread in measured values. Further, we measured the tuning of the fundamental mode wavelength with increasing injection current and a plot comparing these values for each device type is shown in Figure 8a. Comparing a 4 \(\upmu\)m aperture standard VCSEL with a 4 \(\upmu\)m aperture QF device we find the redshift in wavelength is 0.65 \(\pm\) 0.02 and 0.22 \(\pm\) 0.05 nm/mA, respectively. Using the measured wavelength shift with temperature, these values can be converted to a temperature shift per unit current of 9.3 \(\pm\) 0.5 K/mA for the standard VCSEL and 2.7 \(\pm\) 0.7 K/mA for the QF VCSEL. Thus, we find that the standard VCSEL types suffer from greater self-heating which is driven by a combination of an increased electrical and thermal resistance. This uncertainty here derives from the combination of the resolution of the spectrum analyser and that of the current source. In addition, the spread of the measured values of the wavelength shift with temperature combines with that of the wavelength tuning with current to give the uncertainty in the values of temperature shift per unit current. The series resistance of the QF VCSELs is reduced compared to the standard VCSELs due to the leakage path along the bridge, which reduces the degree of Joule heating. Additionally, the thermal resistance of the QF VCSELs is reduced due to the significant difference in cross-sectional areas of the devices. This latter point can be seen in Figure 8b where the wavelength tuning with current is plotted as a function of total device cross-sectional area, including the oxidised regions and the bridge regions. The degree of tuning is seen to be proportional to the inverse of the total cross-sectional area, with a much better fit than when only considering the aperture regions of the QF devices. Furthermore, there is an additional contribution to the reduced thermal resistance from the substrate lapping. For the unoxidised QF devices, the wavelength tuning with current for a 12 \(\upmu\)m mesa is 0.22 \(\pm\) 0.04 nm/mA, and the temperature shift with current is then calculated as 3.5 \(\pm\) 0.7 K/mA--which is similar to the temperature shift of a 4 \(\upmu\)m oxide-aperture QF device and within the margin of uncertainty. Although the Joule heating is much greater for the oxidised devices due to the large electrical resistance, the total device cross-sectional area is much greater and hence the thermal resistance is comparatively smaller. This allows heat to flow away from the active region more easily and facilitates a reduced relative temperature increase for the oxidised device, despite the much smaller active area. Additionally, comparing the wavelength tuning of a 16 \(\upmu\)m unlapped unoxidised QF VCSEL to a 4 \(\upmu\)m aperture standard device (equivalent mesa diameters), we find the redshift of the emission wavelength to be approximately twice as large for the standard VCSEL. Given that the two devices are of equivalent thermal mass, this difference is attributed to the reduced series resistance, and thus Joule heating, in the QF devices. Figure 8: Tuning of the fundamental mode wavelength with injection current as a function of (**a**) device active area; (**b**) total device cross-sectional area, including the oxidised and bridge regions for the QF VCSELs. We also compare the wavelength tuning with current for both the lapped and unlapped QF devices.