# Parasitic Parameters Extraction of High-Speed Vertical-Cavity Surface-Emitting Lasers
## 3 Results and Discussion
### Bandwidth Improvement Suggestions  
Since the 3 \(\upmu\)m device has the highest bandwidth, we only analyse the effect of the parasitic value of the device on the bandwidth with a 3 \(\upmu\)m oxide aperture size. Table 1  
Figure 6: (**a–f**) show the extracted values and 95% fit confidence bounds of \(R_{p}\), \(C_{p}\), \(C_{a}\), \(R_{a}\), \(R_{m}\), and \(L\), respectively, as a function of different bias currents for the 3, 5, 7, and 9 \(\upmu\)m 850 nm oxide aperture diameter VCSELs at 25 \({}^{\circ}\)C. In the legend, I is the polynomial fitting curve, II is the 95% fit confidence bounds.  
lists the \(f_{-3\,\mathrm{dB}}\) at different currents with a 30% reduction of \(L\), \(C_{a}\), \(R_{m}\), \(R_{p}\), and \(C_{p}\) and compares the results with the original values.  
Figure 7 shows the improvement of \(-3\) dB bandwidth for a 30% decrease of single parasitic parameters, including \(L\), \(C_{a}\), \(R_{m}\), \(R_{p}\), and \(C_{p}\) at 5 mA, 8 mA, and 12 mA, respectively. As seen in the figure, the reduction in \(C_{p}\) led to a maximum improvement of \(f_{-3\,\mathrm{dB}}\), and a 30% reduction in \(C_{p}\) led to an improvement of 20.02% at 5 mA, 18.46% at 8 mA, and 18.15% at 12 mA. At the same time, we noticed that the effect of \(R_{a}\), \(C_{a}\), \(R_{m}\), and \(R_{p}\) on the bandwidth was weak as the injection current increased. For instance, a 30% reduction of \(C_{a}\) led to an improvement of only 0.59%, 0.67%, and 0.60% at 5 mA, 8 mA, and 12 mA, respectively, for \(f_{-3\,\mathrm{dB}}\), and a 30% reduction in \(R_{a}\) had barely any improvement, probably due to the extremely low value of \(R_{a}\). A 30% reduction in \(R_{p}\) and \(R_{m}\) led to an increase of approximately 0.41% and 0.27% at 5 mA, 2.87% and 0.14% at 8 mA, and 2.49% and 0.13% at 12 mA for \(f_{-3\,\mathrm{dB}}\). It is also observed that as the current increased, the effect of inductance \(L\) decreased; at 5 mA, the inductance is reduced by 30%, and \(f_{-3\,\mathrm{dB}}\) is improved by 12.54%, and when the current reached 12 mA,\(f_{-3\,\mathrm{dB}}\) improved by 17.21%.  
It should be noted that our results are different from those of previous works [11; 14; 26]. This shows that \(C_{a}\) is not the most important factor affecting the \(-3\) dB bandwidth because the conventional method of determining the most significant effect on the bandwidth of an element is by reducing the corresponding value by 30% and then calculating the value of the change in the \(f_{-3\,dB}\) bandwidth. However, for the same component, the larger the parasitic value is the larger the 30% change in bandwidth. Our value of \(C_{a}\) is small enough relative to the value in [11; 14; 26].  
Consequently, the values of \(R_{a}\), \(C_{a}\), \(R_{m}\), and \(R_{p}\) based on our six-layer oxide structure are already low enough; therefore, further enhancement of the bandwidth should focus on  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(f_{-3\,\mathrm{dB}}\) (GHz)} \\ \hline
**Current** & **Original Value** & **L \(\downarrow\)** & **C\({}_{a}\)\(\downarrow\)** & **R\({}_{a}\)\(\downarrow\)** & **R\({}_{m}\)\(\downarrow\)** & **R\({}_{p}\)\(\downarrow\)** & **C\({}_{p}\)\(\downarrow\)** \\
**(mA)** & **off\(f_{-3\,\mathrm{dB}}\)** & **30\%** & **30\%** & **30\%** & **30\%** & **30\%** & **30\%** \\ \hline
5 & 18.63 & 21.3 & 18.74 & 18.63 & 18.68 & 19.39 & 22.20 \\ \hline
8 & 21.23 & 24.74 & 21.37 & 21.23 & 21.26 & 21.84 & 25.15 \\ \hline
12 & 23.3 & 27.31 & 23.44 & 23.3 & 23.33 & 23.88 & 27.53 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dependence of the parasitic \(-3\) dB frequency on 30% reductions of various circuit elements.  
Figure 7: Improvement of \(-3\) dB bandwidth for a 30% decrease of single parasitic parameters, including \(L\), \(C_{a}\), \(R_{m}\), \(R_{p}\), and \(C_{p}\) at 5 mA, 8 mA, and 12 mA, respectively.  
minimizing \(C_{p}\) and \(L\), for example, adjusting the BCB flattening height and area, replacing other flattened materials, and optimizing the pad size.