In this section, we have present the calculations of energy levels, binding energy ,photoionization cross section of impurity confined in a cone-like QD, under the effects of temperature, polaronic mass, conduction band non-parabolicity and electric field. The parameters for a GaAs are n_r=3.5e=1.6*?10?^(-19)C, and m^*=0.0655m_0 where m_0 is the free electron mass.
We present in figure 1(a, b) the variation of the ground state energy of electron E^1s confined in a GaAs CLQD in the absence of electric field F=0 as a function of the height h for fixed angle (a), and as a function of angle for fixed h (b). It is observed that E^1s present a decreasing character with the parameters geometric, this is due to the increment in the volume of the confinement of an electron, as a result, the wave function reduced since the effect of the confining potential on CLQD.
We report in (c) the variation of E^1s as a function of the electric strength for fixed h and ?, the figure shows clearly that the ground state energy enhanced with the application of F, this behavior can be explain by in the presence of electric field the electronic wave function is more strongly localized inside the QD, therefore the E^1senergy increases.
For figure 1 (d) we traced the dependence of the correlated energy on the h for F=0 and fixed ?. We found a same behavior of E^1s in (a). In addition, we found that the confined energy decreases with introduce the effect of the band non-parabolic and polaronic mass in all inset figures, this effect is more marked for narrow CLQD.
We plotted in figure1 (e) the correlated energy of the electron confined in a GaAs CLQD as a function of the applied electric field for fixed h and ? and at T = 300 K for a parabolic band effect, non-parabolicity effect and nonparabolicity and polaronic mass effects. We show from the figure that the correlated energy increases with applied the electric field. The effects of non-parabolicity and nonparabolicity and polaronic mass is to reduce theE^1s, this reduction become more pronounced if we increase the intensity of electric field.
In figure 2 we present the variation of the binding energy of impurity confined in a GaAS CLQD as a function of the height (a) and angle (b), with take into consideration the effects of parabolic band (solid curve), non-parabolicity (dashed curve) and non-parabolicity and polaronic mass (dotted curve)through the energy dependent effective mass and strengthen the spin-orbit interaction energy. It is clear from figure that the donor binding energy decreases with h and ?. Since the increasing the height of the CLQD, the electronic wave function is less localized inside the QD, thus, the coulomb interaction between the electron and the impurity is diminished and therefore the impurity binding energy reduced. Another finding from the figure is that the impurity binding energy enhances under the effects of nonparabolicity and non-parabolicity and polaronic masse especially for smaller dimension. Indeed the band non-parabolicity has a direct effect on the effective masses of electron, and the numerical calculation shows that the last parameter augmented under the effect of band non-parabolicity, which leads to diminish the separation between the electron and impurity and in turn enhances the binding energy of impurity. For larger values of h and ?, the confinement has a less effect on the impurity, therefore the distance electron-impurity extended and the wave function tend towards the corresponding state of the bulk, so in this region the effect of the band non-parabolicity is not shown
We have plotted in Figure 3 the numerical results of the donor ground state binding energy as a function of the temperature in a CLQD with a parabolic band effect (solid curve), non-parabolicity effect (dashed curve) and non-parabolicity and polaronic mass effects (dotted curve). We have found that the donor binding energy decreases with increasing T(K). Indeed the augmentation of the temperature leads to increase the dielectric constant and the electron effective mass decreases, in addition, the localization of the electrons and the impurity are more separated under the effect of temperature, which results to decrease the binding energy. The figure mentions again that the effect of temperature on the binding energy is more significant for T > 200K thanT ?200K, this behavior is caused by the discontinuous on the coefficients of dielectric constant in the two ranges of temperature that we have considered here (Eq5).
The figure 4 exhibit the variation of binding energy of hydrogenic donor impurity confined in a conical GaAs quantum dot as a function of the intensity of the applied electric field with a parabolic band effect (solid curve), non-parabolicity effect (dashed curve) and non-parabolicity and polaronic mass effects (dotted curve). For three curves the BE augments due to the increase in the electric field. The augment of electric field strength keeps pushing away the probability density towards the cone vertex, thus augmenting the electron–impurity density.
Figure 5 shows the results that we have obtained for the photoionization cross-section of a hydrogenic donor impurity confined in aGaAsCLQD as a function of the normalized photon energy for different values of the height of the dot (h=30 nm,35 nm,40 nm and 50 nm). As seen from the figure, there are four curves, each of them pertaining to one of the particular geometrical the confinement strength increases as the magnitude of the photoionization cross-section decreases. The maximum photoionization corresponds to the threshold photon energy and it decreases with decreasing the height of the dots. The cross section rises first with increasing the height of the dot and then it decreases at much larger photon energy increases with decreasing height of the dots.
For the figure 6 the effects of nonparabolicity, nonparabolicity, and polaronic mass on the photoionization cross-section of a hydrogenic donor impurity in a conical GaAs quantum dotslocated at(0,0,4h/5)as a function of the incident light are presented in Fig.6, the curves correspond to the value of the electric field20kv/cm. This figure illustrates clearly that introduction the nonparabolicity and nonparabolicity and polaronic mass effects can influence the photoionization cross-section. In which their amplitude increases under the latter effects, also we show that the peak shifts towards smaller frequencies. Also the maximum photoionization achieved by the polaronic mass
In figure 7 we present our results for the donor impurity-related photoionization cross-section as a function of normalized photon energy, for different values of the T = 0, 100, 300, 400K. As the temperature increases, the optical photoionization threshold energy decreases, the probability of finding the electron around the impurity increases, and as a consequence, the magnitude of the cross-section decreases, Because, as the temperature decreases, the geometric confinement of the donor electron increases, and the peak position of the cross-section is shifted towards higher photon energies. and this behavior gives an increment in the donor binding energy. Therefore, it can be concluded that a decrement in the temperature leads to an increment of the binding energy as well as to the optical photoionization threshold energy
The Figure 8 shows the calculated photoionization cross section as a function of the temperature for donor impurity in GaAs quantum dots, the curves is from the intensity 20kv/cm there three graphics in the figure Our calculation for the effect of the Temperature on the PCS for different values of radial-impurity coordinate for perpendicular polarization of the incident radiation is displayed in this figure the PCS decreases with decreasing temperature, we supposed that the energy of the incident photon is great to the impurity binding energy at zero temperature. In all the cases considered, the photoionization cross section decreases with increasing temperature, and this is due to the linear decreasing of the electron effective mass.
In this figure 9, we present our results for the impurity polarization as a function of the
temperature for shallow-donor impurities in GaAs CLQDs. The dimensions of the structure and applied electric field at 20 KV/cm and are taken respectively as: (30nm, 20 degree).. The polarization remains decrease for the parabolic band the conduction and the figure shows that the incorporation of the band non-parabolicity, nonparabolicity and polaronic mass increase the polarizability. The increase of polarizability obtained when the effective mass replaced by the polaronic mass and it further increases when the temperature is applied. This small variation behaviour shows that the small variations in effective mass and dielectric constant with temperature do not appreciably affect the polarizability.
Figure 10 and 11 illustrate the variation of the polarizability of the conical QDs, as a function of the height and angle respectively. The results show that for any curve, the polarizability increases as the dimension of the dot increases for both cases, this increment becomes more pronounced for larger dots. The results show again that the effect of band non-parabolicity and non-parabolicity and polaronic mass effects increase with the increase of the structure dimensions: height and angle. This clearly shows the importance of the electronic confinement on the polarizability. The impurity is less confined in dots of very large size and having more space in and thus, the electronic confinement becomes negligible. This means that when the electric field is applied along one direction (z), the electron accelerates along this direction. As a general feature, the polarizability increases with the size of the structure and on increasing the electric field.
We studied the behavior of the binding energy, photoionization cross section and polarizability of a donor impurity in a conical GaAs quantum dots under the effects of temperature and the variation of the geometric parameters, following a variational method within the effective-mass approximation with taking into consideration the effects of polaronic mass, conduction band non-parabolicity and an electric field. We have shown that the binding energy increases or decreases depending of the combined effects of the applied electric field and the temperature within the nanostructure.
We found that the donor binding energy decreases as temperature increases. In addition, the effect of the temperature on the PCS increases with the inclusion of non-parabolicity and polaronic mass effects and leads to an enhancement of the donor binding energy, on the incidence electric field. We also have shown that the applied electric field enhance the ground state binding energy
We have shown that the polarizability increases with the increases the dimension of the
dots, . The results for the polarizability have a strong dependence on the geometrical form of the dots and for inclusion the effects of polaronic mass, conduction band non-parabolicity and electric field
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