## 3 Results and Discussions  
Before presenting the behaviour of optical properties, we will focus on the influence of size, pressure, and temperature on the binding energy of the \((D^{+},X)\) complex confined in a \(GaAs\)\(SSQD\). All parameters used in our calculation are given in Table 1.  
In our previous work [14] we have demonstrated that the most probable dissociation process of the \((D^{+},X)\) complex is : \((D^{+},X)\to D^{+}+X\). This is why it is more convenient to analyse this stability by defining the binding energy \(E^{b}_{(D^{+},X)}(P,T)\) as the difference of the correlated and non-correlated charge carriers: \(E^{b}_{(D^{+},X)}(P,T)=E_{e}(P,T)+E_{h}(P,T)-E_{(D^{+},X)}(P,T)\), where \(E_{h}\) and \(E_{e}\) are the confined energies of single hole and electron respectively. \(E_{(D^{+},X)}(P,T)\) is the total energy of \((D^{+},X)\) complex obtained by minimization. According to this definition, we present in Figure 1a,b the contour plot of the \((D^{+},X)\) complex binding energy as function of pressure and temperature for two confinement regimes, \(R=2\,a_{D}\) and \(3\,a_{D}\) respectively. As a first remark, when the pressure is applied, we observe an increase in binding energy for both types of confinements. This growth is slightly sensitive to pressure for \(R=2\,a_{D}\) due to the fact that the strong confinement is predominant and the \((D^{+},X)\) complex is not influenced by this external perturbation. For \(R=3\,a_{D}\) the effect becomes significant. This is because in the case of weak confinement, the wave function is more extensive, and the charge carriers become more sensitive to the effect of pressure. Indeed, when the pressure increases, the dot size reduces which leads to a strong localization of the electronic density around the ionized donor, and therefore the pressure effect becomes more remarkable. To confirm this interpretation, the fit of our numerical results concerning the variation of \(E^{b}_{(D^{+},X)}\) as function of pressure leads to an interesting law:  
\[E^{b}_{(D^{+},X)}(P)=E^{b}_{(D^{+},X)}(0)+0.00239P.\]  
From these curves we can see also, that \(E^{b}_{(D^{+},X)}\) decreases when temperature (\(T\)) increases, because the \(T\) tends to reduces the Coulomb interaction between the opposite charges in \((D^{+},X)\) what leads to loss of the stability of complex i.e. an increase of the temperature leads to significant decrements of the geometrical confinement contribution in the \((D^{+},X)\) binding energy. The variation of \(E^{b}_{(D^{+},X)}\) according to the temperature follows \begin{table}
\begin{tabular}{c c} \hline \(m_{e}^{*}=0.067\,\,m_{0}\) & \(m_{h}^{*}=0.079\,\,m_{0}\) \\ \(E_{g}=1.607\,\mathrm{eV}\) & \(\varepsilon=13.18\) \\ \(\sigma=3\times 10^{22}\,\,\mathrm{m}^{-3}\) & \(\Delta_{0}=0.341\,\mathrm{eV}\) \\ \(n=3.2\) & \(\Gamma_{fi}=0.2\,\,\mathrm{ps}^{-1}\) \\ \(S_{11}=1.16\times 10^{-2}\,\mathrm{GPa}^{-1}\) & \(a_{D}=10.41\,\,\mathrm{nm}\) \\ \(S_{12}=-3.7\times 10^{-3}\,\,\mathrm{GPa}^{-1}\) & \(R_{D}=10.5\,\,\mathrm{meV}\) \\ \(I=200\,\,\mathrm{MW/m}^{2}\) & \\ \hline \end{tabular}
\end{table} 
Table 1: Physical parameters of \(GaAs\) and light properties [50]. Figure 1: Binding energy variation of an exciton bound to an ionized donor as a function of pressure and temperature for the radius \(R=2\,a_{D}\) (**a**) and \(R=3\,a_{D}\) (**b**). the law: \(E^{b}_{(D^{+},X)}(T)=E^{b}_{(D^{+},X)}(0)-0.00178~{}T\). Furthermore, looking at these behaviours, we see clearly that pressure and temperature generate two antagonistic effects which allow the control of transition energies without modify the sizes. Now let us turn to the optical responses including the linear, non-linear and total AC and RI related to the \(1s-1p\) transition of \((D^{+},X)\) complex. Figure 2a shows the behaviours of the three components of AC versus the incident photon energy \(\hbar\omega\) taking into account just the confinement effect.