*2.3. Quantum Dot Emission*

In this work, we have investigated the effect of various structures of DBR bottom mirrors on the performance of emission at 550 nm wavelength. We have adopted an emission profile based on the published experimental results for ZnTeSe quantum dots for internal emission. The emission peak wavelength of the ZnTeSe alloy QD varied in the range from 530 to 579 nm by controlling the particle size in the range from 3.8 to 6.0 nm [3], the PL emission peak wavelength for of Zn(Te1−xSex) QDs with x = 0.24 ± 0.04 QDs with various diameters of 4.0, 4.2, 4.9 and 6.0 nm are 535, 540, 557 and 576 nm, respectively. The dependence of the emission peaks on the size of the quantum dots is presented in

Figure 4. From these experimental data, an empirical fitting equation has been reproduced to express the relation between the diameter of QD (*d*) and the position of the emission peak wavelength *P*(*d*):

$$P(d) = -3.584d^2 + 56.433d + 366.446\tag{14}$$

**Figure 4.** Emission peak positions against QD size.

The QDs spontaneous emission, *Eint*(*λ*), is reproduced by adopting simulation using Gaussian distribution function, as follows:

$$E\_{int}(\lambda, d) = \exp\left(\frac{-\left(\lambda - P(d)\right)^2}{2v^2}\right) \tag{15}$$

where *P* is the position center of the peak and *v* was given by:

$$v = \frac{\frac{\Delta\lambda}{2}}{\sqrt{2\ln(2)}}\tag{16}$$

where Δ*λ* is the full width at half maximum (FWHM) of *QD* emission. The FWHM of *QD* emission was assumed to be 30 nm [7]. According to Equation (14), the emission at 550 nm wavelength of ZnTeSe alloy *QD* is compatible with quantum dots with a diameter of 4.6 nm.

The refractive index and band gap of *QD* are the main properties that are changed by the size of *QD*. The refractive index of *QD nQD* is calculated as follows [37,38]:

$$m\_{QD} = \sqrt{\frac{1 + \left[ \left( n\_{bulk} \right)^2 - 1 \right]}{\left[ 1 + \left( \frac{0.75}{d} \right)^{1.2} \right]}} \tag{17}$$

where *nbulk* is the refractive index of bulk material, the refractive index of bulk ZnTe and ZnSe at 550 nm are 3.1 and 2.7, respectively [39]. The calculated refractive index of ZnTeSe *QD* with diameter 4.6 nm for the emission at 550 nm is 2.748.

The shift of the optical band gap of *QD* due to quantum confinement has a quantitative form. According to an early effective mass model calculation by Brus, the magnitude of this confinement energy can be modeled as a particle in a box, as seen in Equation (18) [1].

$$E\_{confinement} = \frac{\hbar^2}{2} \frac{\pi^2}{a^2} \left(\frac{1}{m\_\varepsilon} + \frac{1}{m\_h}\right) = \frac{\hbar^2}{2} \frac{\pi^2}{a^2 \ \mu^2} \tag{18}$$

where *me* is the effective mass of the electron, *mh* is the effective mass of the hole, *μ* is the reduced mass of the exciton system, and *a* is the radius of the quantum dot. For Zn (Te0.76Se0.24), *me* is 0.11 *m*<sup>0</sup> and *mh* is 0.64 *m*<sup>0</sup> (where *m*<sup>0</sup> denotes the electron rest mass) [3]. The calculated optical band gap of Zn (Te, Se) alloy *QD* at 550 nm emission is approximately 2.5 eV, and this value is within the origin of the green band.
