**4.3 Strong confinement regime**

*Quantum Dots - Fundamental and Applications*

One of the most important consequences of the spatial confinement effect is an increase in energy of the band-to-band excitation peaks (blue shift) as the radius R of a microcrystallite semiconductor is reduced in relation with the Bohr radius. However due to significant spatial confinement effect, there is an increase in energy of band-to-band excitation peaks which is called blue shift. The microcrystallite of Radius (R) ranges in semiconductor having less relation with than of the Bohr Radius. Some of minor difference would have happened between the theoretical and experimental of confine effect it is due to electron electron–hole interaction energy, in coulomb term and the confinement energy of the electron and hole in the

To observe this regime, the radius (R) of a crystallite should be greater than the bulk exciton Bohr radius (aB). In this region of weak confinement, the dominant energy is the Coulomb term, and they already occur in size quantization of the exciton motion. The exciton energy states are shifted to higher energies by con-

Δ*E* ≈ ℏ<sup>2</sup>

being the effective masses of the electron and hole, respectively.

Taking another point of view of quantum confinement, especially II–VI semiconductor region, the Bohr radius is equal (a*B*) to the material radius (R) which is called moderate confinement regime, and also the following term conditions should satisfy a*h* < R < a*e* for moderate confinement regime process. A processes were observed in small QDs and a well-restricted motion of a photo-excited hole.

 *π* \_ 2 2 *MR*<sup>2</sup> . The shift "∆E" of the

, with *me* ∗

(2)

<sup>∗</sup> + *mh* ∗

finement, and shifts in energy ∆E are proportional to 1/R<sup>2</sup>

*A schematic diagram of the molecular orbital model for band structure.*

where *M* is the mass of the exciton and it is given by *M* = *me*

exciton ground state is given approximately by

**4.2 Moderate confinement regime**

**18**

and *mh* ∗

kinetic energy.

**Figure 8.**

**4.1 Weak confinement regime**

Finally, the strong confinement regime was confirmed by satisfying the following condition such that R < < aB and R < < a*h.* Due to these conditions, excitations are not formed, and separate size quantization of an electron and hole is the dominant factor. To strong confinement regime, must need two different reasons: the first one is the Coulomb term of electron–hole interaction is small and it's acting as a perturbation, and the second one is independent behavior of electron and holes when the above condition is applied. The optical spectra should then consist of a series of lines due to transition between sub-bands. This factor was confirmed experimentally, and the simple model gives shift in energy as a function of crystallite size as

$$
\Delta E \approx \frac{\hbar^2 \pi^2}{2\mu R^2} \tag{3}
$$

in which the exciton mass M is replaced by reduced exciton mass μ, where

$$\frac{1}{\mu} = \frac{1}{m\_e^\*} + \frac{1}{m\_h^\*} \tag{4}$$

The electrons and holes in QDs are treated as independent particles, and for the excited state, there exists a ladder of discrete energy levels as in molecular systems.

## **5. Summary**

Recently quantum dot-based nanomaterials play a major role in the applications many field such as Q-LEDs, transistors, solar cells, laser diodes for displays, medical imaging, quantum computing, etc. In particular the QDs exhibit significant role in the optoelectronic application, its changes because of precisely controlling the size, shape, emission of color and bandgap tuning. These properties are changing inside the quantum dots, and that leads to different applications from energy harvesting to biomedical application. This entire physical and chemical phenomenon could be explained through theoretical model by using quantum confinement behavior.
