*IIIrd Generation Solar Cell DOI: http://dx.doi.org/10.5772/intechopen.95289*

*Solar Cells - Theory, Materials and Recent Advances*

quantum dot can be modified as well.

determines several processes in quantum dots.

Being a relativistic effect, the g − factor is strongly related to the spin-orbit coupling and the Zeeman term plays an important role in the physics of the quantum dot. The values of g- factor can vary by two orders of magnitude, e.g. between −0.45 for GaAs and approximately −50 in InSb. The corresponding spin splitting can reach the values of the order of 10 meV at realistic fields of the order of 10 T. We mention here that while the spin-orbit coupling for a given quantum dot is fixed by its material and shape [12], the Zeeman coupling can easily be modified by applying a magnetic field. Thus, the absorption spectra and optics-related properties of the

*spin-orbit coupling: The zeromomentum states have nonzero velocities while finite-momentum states at* <sup>∗</sup>

*Two branches of spectrum of two-dimensional carriers in the presence of the Rashba spin-orbit coupling with* 

 *This shape of the spectrum corresponds to the anomalous velocity in the presence of the* 

The geometry of a quantum dot plays the crucial role for its spectrum and spin-orbit coupling, and, therefore in the light absorption and photovoltaics effects. A qualitative effect of the spin-orbit coupling in quantum dots is the quantum entanglement of particle spin and its position, where the particle wavefunction cannot be presented as a product of the spin and coordinate states. This entanglement

Since in the optical absorption electrons and holes are produced, similar spinorbit coupling and Zeeman Hamiltonians should be defined for the holes as well. The Coulomb interaction between electrons and holes plays the crucial role in the light absorption in quantum dots. The spectrum of holes is described by 4 × 4 matrices due to degeneracy of the spectrum consisting of "light" and "heavy" hole branches. Dependent on the material and shape of the quantum dot, spin-orbit coupling and the Zeeman coupling for holes can be much stronger than that for electrons. In the presence of spin-orbit coupling, spin-defined states are prone to relaxation and loosing well-defined spin values. In bulk systems, where electron momentum is a well-defined quantum number, spins relax mainly due to the celebrated Dyakonov-Perel mechanism [13] with the spin relaxation rate of the

the situation is qualitatively different since the localization suppresses the free motion of carriers. Here the relaxation is mainly due to the so-called" admixture mechanism" caused by the spin-orbit coupling between different orbital states with opposite spins and interaction of these orbital states with lattice vibrations. This mechanism strongly depends on the applied magnetic field. In relatively week magnetic fields, the spin relaxation rate is small, and spin states are conserved for

is the momentum relaxation time. In quantum dots

**348**

order of

**Figure 7.**

<sup>=</sup> *<sup>m</sup> <sup>k</sup>* α

( ) 2 2 <sup>2</sup> <sup>∗</sup> = ± *<sup>k</sup> E k k. <sup>m</sup>*

α

 *have zero velocities.*

2 *<sup>k</sup>* α*k* τ

, where *<sup>k</sup>*

τ

long times of the order of 1 ms or more. If the spin-orbit coupling is sufficient, the resulting spin-position entanglement influences the spin states, and, therefore, the orbital wave functions and the exchange interaction between the injected and original carriers in the quantum dots. In addition, spin states of the injected carriers can be controlled by polarization of the incident light [14]. These interactions should be clearly seen in the absorption spectra and, as a result, influence the photovoltaics and photogalvanic application.

We mention here that a new very large class of very promising for the photovoltaics materials such as perovskites or quantum dots show the spin-orbit coupling in the general form of the Rashba and Dresselhaus terms. Therefore, the spin-orbit coupling-related aspects of their applications can be treated in general terms similarly to semiconductors. This coupling can increase the carrier's lifetime - the quantity important for solar cell applications. However, these rather complex compounds, demonstrating a great variety of different properties, are not yet reliably functionalized in the form of quantum dots. At the same time, whether the combined effects of the spin-orbit coupling lead to an increase or to a decrease in the efficiency of the light-to-voltage conversion in solar cells, is not yet clear even on the qualitative scale.
