# Impact of Device Topology on the Performance of High-Speed 1550 nm Wafer-Fused VCSELs
## 3 Results and Discussion
### Small-Signal Modulation
The extracted large damping can be related to a combination of lower mirror loss and higher internal optical loss (to obtain comparable differential efficiency) and/or to higher gain compression in the thin InGaAs QW-based active region as compared to that for the thick InAlGaAs QW-based active region. The simulation of \(S_{11}\)(\(f\)) shows that the main contribution to the parasitic cutoff frequency stems from the parasitic capacitance of the reverse-biased p\({}^{+}\)-n junction region (outside the BTJ region). As the forward voltage increases, the space-charge capacitance decreases, leading to an increase in the parasitic cutoff frequency and saturation at -5 GHz at voltages above 1.6 V (see Figure 5b). In the case of the dominance of only electrical parasitics, the maximum achievable modulation bandwidth is more than 18 GHz (according to the expression \(f_{\mathrm{-3 dB,parasitics}}=(2+\sqrt{3})f_{\mathrm{P}}\)), which significantly exceeds our experimental values of \(f_{\mathrm{-3 dB}}\). In the case of the dominance of thermal effects, the maximum achievable modulation bandwidth depends on the maximum attainable relaxation resonance frequency at drive currents near the thermal rollover, and should lie in the range 15-18 GHz (according to the expression \(f_{\mathrm{-3 dB,thermal}}=\sqrt{(1+\sqrt{2})\,f_{\mathrm{R}}}\)). In the case of the dominance of only damping, the maximum achievable modulation bandwidth is determined by the \(K\)-factor, and also exceeds 18 GHz (according to the expression \(f_{\mathrm{-3 dB,damping}}=2\pi\sqrt{2}/K\)). Thus, we assume that the high-speed performance of the lasers in the \(L\)-type topology is limited by a combination of the first and third mechanism, which leads to a strong decrease in the resonance peak amplitude and overestimation of the intrinsic damping factor. Lasers of \(S\)-type device topology are significantly different in their dynamic characteristics (see Figure 6a,b). Although the dependence of the relaxation resonance frequency \(f_{\mathrm{R}}\) on the square root of the drive current above the threshold shows a behavior similar to the lasers of \(L\)-type topology, an increase in the MCEF-factor up to 4.5 GHz/mA\({}^{0.5}\) is observed (see Figure 6c). The \(D\)-factor is still about 3.3 GHz/mA\({}^{0.5}\), which indicates the same differential gain for both device topologies for a fixed BTJ size. The \(K\)-factor is estimated to be 0.45 ns (see Figure 6d). The estimated \(f_{\mathrm{-3 dB,damping}}\) and \(f_{\mathrm{-3 dB,thermal}}\) values are 20 GHz and 18 GHz, respectively. Modeling the \(S_{11}\)(\(f\)) dependence revealed a strong drop in the parasitic capacitance of the reverse-biased p\({}^{+}\)n-junction region induced by a notable decrease in the second mesa size. As a result, the rise in the \(f_{\mathrm{-3 dB,parasitics}}\) up to 13-15 GHz becomes possible which coincides to results for double-mesa short-cavity VCSELs [28]. As a result, the \(-3\) dB modulation bandwidth \(f_{\mathrm{-3 dB}}\) reaches 13 GHz at drive currents larger than 12 mA (see Figure 6c). This value of the modulation bandwidth is a record for 1550 nm VCSELs fabricated by the WF technology independent of the growth technique, type of active region, and TJ [34; 35; 36]. Our modulation bandwidth differs from the record value of the modulation bandwidth (22-23 GHz) for 1550 nm hybrid short-cavity VCSELs [4; 22; 23; 27] mainly due to a smaller mode volume, higher parasitic frequency, and/or larger differential gain of the highly strained InAlGaAs QW-based active region in Refs. [4; 23]. By carefully optimizing the doping profile of the n-InP overgrowth layer, we managed to find a variant of the intermediate device topology, leading to a parasitic frequency of more than 15 GHz, in which the first mesa does not significantly affect the device static characteristics. It should be noted that the mode volume minimization is associated with a decrease in the output power, so it is necessary to find a balance between high-speed performance and SM output power.