# Degradation Characteristics and Reliability Assessment of 1310 nm VCSEL for Microwave Photonic Link
## 3 Discussions
### Low-Frequency Noise Characterization  
Measurements of the low-frequency noise (LFN) are vitally sensitive to some of the microscopic processes that could indicate impending failure. The internal defects, surface leakage and bad ohmic contact of the semiconductor laser will increase the LFN, so the noise can be used to reflect the reliability of 1310 nm VCSEL. The 1/F noise power spectral density of the surface non-radiative recombination current can be expressed as:  
\[S_{I_{nr}}=I_{nr}^{2}\bigg{(}\frac{q}{k_{0}T}\times\frac{1}{AN_{ot}}\bigg{)}^{ 2}S_{N_{ot}}(f), \tag{1}\]  
where \(I_{nr}\) is the non-radiative recombination current, \(q\) is the electron charge, \(k_{0}\) is the Boltzmann constant, \(T\) is the degree Kelvin, \(A\) is the cross-sectional area of the PN junction, \(N_{ot}\) is the number of oxide trap charges and \(S_{N_{ot}}(f)\) is the oxide trap charge density. \(S_{N_{ot}}(f)\) can be expressed as:  
\[S_{N_{ot}}(f)=\frac{q^{2}k_{0}TN_{t}\lambda}{f}, \tag{2}\]  
where \(N_{t}\) is the effective body defect density, \(\lambda\) is the attenuation tunneling distance. According to the mobility fluctuation model [23], when the VCSEL is below the threshold current, the 1/F noise caused by the surface non-radiative recombination current can be expressed as:  
\[S_{I_{nr}}(f)=I_{nr}^{2}\frac{q^{4}N_{t}\lambda}{k_{0}TA^{2}N_{ot}^{2}f}. \tag{3}\]  
According to the above 1/F noise model, the 1/F noise of VCSEL with a small injection current is generated by the fluctuation of surface non-radiative recombination current, which depends on the surface oxide trap density and lattice dislocation. At the same time, the defects, impurities, and dislocations of VCSEL form a surface non-radiative recombination current. Therefore, the reliability of VCSEL can be evaluated by measuring the 1/F noise of the device under operating conditions below the threshold current. In order to analyze the dependence of LFN on bias currents below the threshold, a typical sample is selected for analysis under each set of aging stresses. The current noise power spectral density versus frequency at different bias currents are shown in Figure 4. It can be seen from the figure that current noise power spectral density decreases with the increasing frequency, indicating that the current noise of the 1310 nm VCSEL is mainly the 1/F noise in the low-frequency band. Meanwhile, the frequency index factor and noise amplitude gradually increase with the bias current increase from 0.001 mA to 0.5 mA, as shown in Table 2.  
At operation current, the measured low-frequency noise behaviors of the 1310 nm VCSELs before and after aging are graphed in Figure 5. It indicates that the current noise power spectral density increases after the device aging, and the noise increases with the augment of the electrical stress. After 2500 h aging of the device at 10 mA, the noise power spectral density is one order of magnitude higher than the device before aging. The result \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**6 mA**} & \multicolumn{2}{c}{**8 mA**} & \multicolumn{2}{c}{**10 mA**} \\ \hline
**Bias** & **Frequency** & **Noise** & **Frequency** & **Noise** & **Frequency** & **Noise** \\
**Current (mA)** & **Index Factor \(\boldsymbol{\gamma}\)** & **Amplitude at** 1 Hz (A\({}^{2}\)/Hz)** & **Index Factor \(\boldsymbol{\gamma}\)** & **Amplitude at** 1 Hz (A\({}^{2}\)/Hz)** & **Index Factor \(\boldsymbol{\gamma}\)** & **Amplitude at** 1 Hz (A\({}^{2}\)/Hz)** \\ \hline
0.001 & 0.8 & 1.74 \(\times\) 10\({}^{-20}\) & 0.83 & 6.64 \(\times\) 10\({}^{-21}\) & 0.8 & 5.05 \(\times\) 10\({}^{-21}\) \\
0.1 & 0.9 & 1.13 \(\times\) 10\({}^{-17}\) & 1 & 1.16 \(\times\) 10\({}^{-17}\) & 1.08 & 6.51 \(\times\) 10\({}^{-17}\) \\
0.3 & 0.98 & 6.9 \(\times\) 10\({}^{-17}\) & 1.03 & 4.31 \(\times\) 10\({}^{-17}\) & 1.25 & 1.31 \(\times\) 10\({}^{-15}\) \\
0.5 & 1.05 & 6.89 \(\times\) 10\({}^{-17}\) & 1.05 & 2.72 \(\times\) 10\({}^{-16}\) & 1.28 & 4.32 \(\times\) 10\({}^{-15}\) \\ \hline \end{tabular}
\end{table}