# Study of the Photo-Response of Doped GaAs with Aging
## 3 Results and Discussion
In addition, it can be seen that at temperatures below 40 K, the defect peaks have a structure made up of two peaks and a shoulder, separated by 0.030 eV corresponding to the LO phonon of GaAs [15]. PR is a surface-modulated optical technique that has been mostly used to measure the critical points of the solid, in particular the energy gap. In this technique, the change in reflectance over reflectance at a specific wavelength is measured. As it is a superficial technique, these changes are proportional to the ability of the electric field of light to affect the surface charges of the material. Figure 4 shows the PR spectra taken in 1995, 2001 and 2021 for a GaAs:Sn \(1\times 10^{17}\) atoms cm\({}^{-3}\) sample The spectra were fitted using a line composed of the combination of a first derivative Lorentzian function (FDLF) (for the  
Figure 3: Photoluminescence spectra of the defect zone for the sample GaAs:Sn \(1\times 10^{17}\) cm\({}^{-3}\) taken in 2001 and 2021 at different temperatures. exciton) and a third derivative Lorentzian function (TDFL) (for the band-to-band transition), which is known as the Aspnes equation [20]:  
\[\frac{\Delta R}{R}=Re(\sum_{j=1}^{n}C_{j}e^{i\theta_{j}}\big{(}\hbar\omega-E_{j}+ i\Gamma_{j}\big{)}^{-m}) \tag{1}\]  
In Equation (1), the parameter m takes the value of 2.5 for the band-to-band transition and 2 for the excitonic transition. Four fitting parameters are used in the line shape analysis: \(Cj\), \(\theta\), \(Ej\) and \(\Gamma\). \(Cj\) is the amplitude of the shape of the j line, \(\theta j\) the phase angle, \(\Gamma j\) the phenomenological broadening parameter and \(Ej\) the energy of the jth transition. The letter j runs for 2 values of transitions, the excitonic and the band-to-band. The results of these fittings are listed in Table 1 for the results of 2001 and 2021. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**2021**} & \multicolumn{3}{c}{**2001**} \\ \hline \(N\) (atoms cm\({}^{-3}\)) & \(1\times 10^{16}\) & \(1\times 10^{17}\) & \(2\times 10^{18}\) & \(1\times 10^{19}\) & \(1\times 10^{16}\) & \(1\times 10^{17}\) & \(2\times 10^{18}\) & \(1\times 10^{19}\) \\ \hline \(C_{1}\) & 3.16 & 5.44 & 1.41 & 3.22 & 2.18 & 4.31 & 16.11 & 4.20 \\ \hline \(Eg\) (eV) & 1.4164 & 1.4142 & 1.4055 & 1.4031 & 1.4196 & 1.4174 & 1.4070 & 1.4050 \\ \hline \(\Gamma_{1}\) (eV) & 0.025 & 0.049 & 0.420 & 0.512 & 0.014 & 0.024 & 0.100 & 0.250 \\ \hline \(\theta_{1}\) & \(-2.760\) & 0.584 & 0.965 & 0.788 & \(-2.156\) & 0.088 & 3.124 & \(-0.005\) \\ \hline \(C_{2}\) & 9.15 & 8.32 & 4.39 & 7.16 & 8.16 & 10.12 & 32.11 & 15.92 \\ \hline \(Ex\) (eV) & 1.4096 & 1.4068 & 1.3988 & 1.3961 & 1.4123 & 1.4107 & 1.3997 & 1.3977 \\ \hline \(\Gamma_{2}\) (eV) & 0.049 & 0.032 & 0.081 & 0.193 & 0.005 & 0.019 & 0.074 & 0.120 \\ \hline \(\theta_{2}\) & \(-12.570\) & \(-1.483\) & \(-1.506\) & \(-6.209\) & 0.052 & 0.092 & 0.433 & \(-0.051\) \\ \hline \end{tabular}
\end{table} 
Table 1: Results of fitting to the PR spectra with Equation (1). Figure 4: PR spectrum taken for the GaAs:Sn \(1\times 10^{17}\) cm\({}^{-3}\) sample at 300 K on different dates. The undoped GaAs sample did not give an observable PR signal in 2001 and 2021. For this sample, no change in reflectance could be measured, possibly because the electric field of the exciting light turned out to be very small in the face of the high surface electric field of the charged vacancies. The impossibility of obtaining a PR spectrum in the undoped sample shows the low crystalline quality of the aged undoped GaAs sample, as mentioned above. With this analysis, it was found that the exciton energy, \(\mathrm{Eex}=\mathrm{Ex}-\mathrm{Eg}\), gave an average of 7.3 meV in correspondence with the reported value of 7.2 meV [15]. The linewidth of both the exciton and the band-to-band transition increased considerably with aging. Table 1 shows the values of Eg obtained from fitting Equation (1) to the PR spectra for the different concentrations of impurities in the GaAs samples.