## 3.1 Crystal structure and structural analysis

The X-ray diffraction was employed to visualize the effect of Dy doping on the crystalline phase of the GaAs lattice. The XRD spectra of the Ga1 − xDyxAs QDs are demonstrated in Fig. 1. These spectra showed peaks corresponding to the patterns arising from the cubic phase of the Ga1 − xDyxAs QDs [10]. The lattice dimension of the cubic crystals was calculated using the following cubic crystal lattice equation [11].

$$a= \frac{d}{\sqrt{{h}^{2}+{k}^{2}+{l}^{2}}} \left(1\right)$$

where d is the interplanar space (d = l/2sinq). The lattice constant increases from 0.563 nm to 0.576 nm as the concentration of Dy doping increases (Fig. 2a). The crystallite size of the prepared quantum dots was also determined using the Scherer formula [12]

$$R= \frac{k\lambda }{\beta cos\theta } \left(2\right)$$

The increase in Dy doping increases the GaAs crystallite size from 3.1 nm to 8.4 nm (Fig. 2b). This increase in the size of the GaAs may back from the introduction of Dy atoms with large ionic radius (0.12 nm) in the position of Ga atoms (0.08 nm) [13]. The strain was calculated by the Willson relation [14] and listed in Table 1.

Table 1. The particle size, lattice strain and volume of the Ga1-xDyxAs QDs

$$\epsilon = \frac{\beta }{4 tan\theta } \left(3\right)$$

The un-doped GaAs exhibit a strain of 2×10− 3, while the Dy-doped GaAs, at x = 0.07, increased the lattice strain to 1×10− 2. Therefore, the difference in ionic radii between Dy and Ga causes an expansion of the volume of the GaAs cubic crystals (V = a3) due to the strain exerted by the Dy atoms on the GaAs crystal lattice as displayed in Table 1.

## 3.2 TEM and SAED analysis

The morphology of the Ga1 − xDyxAs QDs was studied using TEM (Fig. 3). The TEM images inspect a spherical particle-like shape with high mono-dispersion. The mean size of the grown particles increases from 3.2 nm to 8.5 nm with increasing the Dy doping. The SAED pattern of the Ga1 − xDyxAs QDs provided inset of Fig. 3, inspects that the Ga1 − xDyxAs QDs have polycrystalline nature and the diffraction rings correspond to the reflection from (111), (200), and (220) planes of the GaAs cubic crystals [15]. The calculated values of the d-spacing from EDS patterns are listed in Table 1. It is noteworthy that, the Dy doping enlarges the d-spacing of the GaAs cubic crystals, which is a confirmation of the data obtained from XRD spectra.

## 3.3 Optical analysis

The Ga1 − xDyxAs QDs were characterized by UV–vis spectroscopy (Fig. 4a). The spectra showed a variation of the absorbance spectrum against the amount of Dy atoms. The Ga1 − xDyxAs QDs exhibit strong quantum confinement with a peak hump displaced toward the longer wavelength, implying an increase in the particle size and a decrease in the optical band gap. The optical bandgaps were of Ga1 − xDyxAs QDs deduced from Tauc’s equation [16].

$${\left[\alpha h\nu \right]}^{2}=A \left(h\nu - {E}_{g}\right) \left(4\right)$$

The bandgap energy of the Ga1 − xDyxAs QDs increased from 2.31eV to 1.76 eV as the Dy doping increased (Fig. 4b). This may be back to the allocating of Dy levels in the GaAs bandgap [17].

## 3.4 Photoluminescence analysis

The PL emission spectra of the Ga1 − xDyxAs QDs were measured and displayed in Fig. 5. It is noteworthy that the intensity of the emission spectrum increases, the width of spectrum curves decreases, and the spectrum peaks displaced toward the long wavelength in redshift mode as a result of the Dy doping (Fig. 6a). This enhancement of the Pl intensity may back to the reduction of the crystal defects and the monodispersion of the formed nanoparticles due to the doping of GaAs QDs with Dy ions. To confirm this interpretation, the Stokes shift and the quantum yield of the Ga1 − xDyxAs QDs were calculated and plotted as a function of the Dy dopant concentration as shown in Fig. 6b. The Stokes shift decreases and the quantum yield increases as the Dy doping increases. The obtained unique properties may come from the allocation of Dy-levels in the Ga1 − xDyxAs QDs bandgaps. The excited electrons relax to these levels and then move to the ground states and consequently release energetic light photons in a fluorescence process with sharp and intense mode [18].

## 3.5 Electrical analysis

Figure 7 reveals the I-V characteristic curves of the fabricated Ag/Ga1 − xDyxAs QDs/Al diode. The I-V curves show a Schottky diode-like behavior. Furthermore, the increase of the Dy dopant increases the current. The ideality factor and the barrier height of the constructed Ga1 − xDyxAs QDs diode were determined using a thermionic emission model [19]

$$I= {I}_{o}\left\{\text{exp}\left[\frac{e(V-I{R}_{s}}{nkT}\right]-1\right\} \left(5\right)$$

where n is the ideality factor and Io is the saturation current \({I}_{o}=A{A}^{*}{T}^{2}\text{exp}\left(- \frac{e{\phi }_{b}}{kT}\right)\) The ideality factor may be given from the relation [20]

$$n= \frac{e}{kT} \frac{dV}{d\left(lnI\right)} \left(6\right)$$

The barrier height fb may be estimated using the relation [21]

$${\phi }_{b}= \frac{kT}{e} ln\left(\frac{A{A}^{*}{T}^{2}}{{I}_{o}}\right) \left(7\right)$$

The values of the ideality factor and the barrier height are listed in Table 2. The ideality factor decreases to almost unity as the Dy doping increases. The barrier height decreases as the Dy doping increases. The decrease of the barrier height for the developed Dy-doped GaAs diodes may be attributed to the deep LUMO level of Dy dopant compared to GaAs QDs, which decreases the barrier height and increases the current [22, 23].

Table 2. The ideality factor and the barrier height of the Ga1-xDyxAs QDs

## 3.6 Infrared laser diode based on Dy-doped GaAs QDs

Figure 8a displays the I-V curves of the constructed Ga0.93Dy0.07As laser diode at various infrared laser power intensities. It is noted that the increase of the IR-laser intensity increases the photocurrent as shown in Fig. 8b. This behavior follows the power law *I ≈ P**q*, where the fitting exponent q = 0.82. The responsivity of the constructed IR-laser diode was calculated [24] and plotted as a function of wavelength (Fig. 8c).

$$R=\frac{{I}_{ph}-{I}_{D}}{P} \left(8\right)$$

The highest responsivity was achieved at wavelength of 700 nm, implies that this constructed laser diode has a high selectivity at laser wavelength of 700 nm. The reproducibility and repeatability of the constructed laser diode during laser On/Off is displayed in Fig. 8d. The laser photodiode exhibits high stability and fast response (0.5s). Therefore, the Ga1 − xDyxAs QDs showed promising IR-laser photodiode performance for future optical communication application potential.