###### Abstract  
This theoretical study is devoted to the effects of pressure and temperature on the optoelectronic properties assigned to the first lowest transition of the \((D^{+},X)\) excitonic complex (exciton-ionized donor) inside a single \(AlAs/GaAs/AlAs\) spherical quantum dot. Calculations are performed within the effective mass approximation theory using the variational method. Optical absorption and refractive index as function of the degree of confinement, pressure, and temperature are investigated. Numerical calculation shows that the pressure favors the electron-hole and electron-ionized donor attractions which leads to an enhancement of the binding energy, while an increasing of the temperature tends to reduce it. Our investigations show also that the resonant peaks of the absorption coefficient and the refractive index are located in the terahertz region and they undergo a shift to higher (lower) therahertz frequencies when the pressure (temperature) increases. The opposite effects caused by temperature and pressure have great practical importance because they offer an alternative approach for the adjustment and the control of the optical frequencies resulting from the transition between the fundamental and the first excited state of exciton bound to an ionized dopant. The comparison of the optical properties of exciton, impurity and \((D^{+},X)\) facilitates the experimental identification of these transitions which are often close. Our investigation shows that the optical responses of \((D^{+},X)\) are located between the exciton (high energy region) and donor impurity (low energy region) peaks. The whole of  
medium, numerous experimental and theoretical research have studied and identified the spectral lines attributed to these transitions [5; 6; 7; 8; 9; 10]. One of the most interesting and fascinating complexes is \((D^{+},X)\), which is formed by the Coulomb interactions between an ionized donor, one hole, and one electron \((D^{+},e,h)\). Thus, it admits two possible paths for its formation or even for its dissociation \((D^{+},X)\to D^{+}+X\) or \((D^{+},X)\to D^{0}+h\). [PERSON] et al. [11] have discussed its stability in spherical quantum dots and demonstrated that the first process is more stable. In the last few years, we have developed many theoretical studies concerning the identification of the spectral lines of this complex using an electric field and comparing the Stark shift [12]. More recently, the effects of the magnetic field and host dielectric environment on the \((D^{+},X)\) binding energy has been analysed [13]. The comparison between the two protocols of dissociation has been studied and analysed deeply by considering the binding energy and optical absorption [14]. We have found considerable investigations on optical properties in literature, for more detail we refer the reader to some interesting manuscripts [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Recently we have studied the non-linear optical properties of an exciton confined in different QD shapes taking into account the pressure \((P)\) and temperature \((T)\) effects. We have shown that all these properties are deeply dependent on these external perturbations [26; 27; 28]. Related to our current work, there is a few studies which have treated the optical properties of the \((D^{+},X)\) complex. The most important of them concerns the oscillator strength related to the intersubband transition in a disc-like parabolic QD as function of the frequency of the parabolic confining potential [29]. [PERSON] et al. [30] also analysed the effects of \(T\) and \(P\) on the absorption properties of an exciton-donor complex in a disc-shaped quantum dot with Gaussian potential. Other interesting studies are those done by [PERSON] et al. [31] who calculated the optical properties of \((D^{+},X)\) confined in strained wurtzite ZnO/Mg\({}_{0.25}\)Zn\({}_{0.75}\)O quantum dots. They have found that the absorption coefficient peak presents a blueshift for strong confinement. At last, an investigation was done by [PERSON] et al.