DETERMINATION OF THE EXCITONIC RYDBERG ENERGY , THE EXCITON BOHR RADIUS FOR FREE EXCITON ACCORDING TO THE RATIO Ga Ga + In AND BANDGAP ENERGY IN THE CHALCOPYRITE SOLAR CELL . Soce

Soce Mouhamadou Mamour, Ehemba Alain Kassine, Diallo Demba, Wade Ibrahima and DiengMoustapha. Laboratory of Semiconductors and Solar Energy, Faculty of Science and Technology, Cheikh Anta DIOP University of Dakar, Senegal. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

In the paper, we studied the evolution of the excitonic Rydberg Energy, the exciton Bohr radius of free electron in the Cu(In 1-x Ga x )Se 2 chalcopyrite solar cells for values x= 0; 0. 3

and 1([Ga]/ ([Ga] + [In])).
The study shows that the excitonic Rydberg Energy (R * y ) and Bohr radius (a B ) move inversely. Indeed R * y increase which x while a B decrease which x. Given the approach used, the effective mass of hole and electron of free excitons were also determined as the reduced masse. The evolution of the reduced mass may be related to the performance of the cell. Indeed the greatest reduced mass was obtained for x=0,3 corresponding to the rate where the efficiency is more higher and Cu-poor type. With a theoretical efficiency of over 30%, these types of cells will be in the future leaders of PV technology. Despite the bright future and the many possible combinations and alloys, the major problem of these cell types is the lack of understanding of internal processes that impact on the final efficiency. [1] The study of the quality of these cells can be done with different methods of characterization. Among these methods to characterize the photoluminescence can be identified and its variants, which allow to know the quality of each material in terms of defects. This method shows the different types existing transitions in the material. There are: transitions acceptors or donors (DA) and excitonic transitions (EX) [2]. These excitonic transitionsshows the quality of material and are caused by excitons. The exciton can be defined as an excited state formed an electron-hole pair strongly linked and generated by optical excitation or a double injection of charge carriers. Excitons are often located on a molecule, or part of the chain of a polymer, then it is agreed to consider the exciton as a moving particle, neutral. Therefore, the exciton has a spin following the usual conservation rules.

ISSN: 2320-5407
Int. J. Adv. Res. 4 (9), 1910-1917 1911 The exciton is characterized by its level of electronic energy Eex located in the forbidden band, Bex its binding energy and radius. Bex is inversely proportional to the permittivity of the material and thus the mobility of the charge carriers. There are two types of exciton: that described by Frenkel and described by Wannier. For Frenkel exciton is as strongly related electron-hole pair excitation but can jump from one atom to another. Said Wannier excitons are instead delocalized over several molecules or atoms (free exciton) [3]. Our work aims the determination of the excitonic Rydberg energy, the exciton Bohr radius for free exciton and this evolution according the stoichiometry and bandgap energy.

Model utilisize:-
We use the result of low-field perturbation approach and the hydrogenic model. To be able to determine the characteristics of the exciton, we initially will determine the hole and electron effective mass of the free exciton and then will determine the reduced mass of this one.

Effective mass of electron and hole:-
In solid state Physics, the effective mass is defined by the tensor of order 2 of the derivative second of energy E compared to the vector of wave k: According to the dynamics of Bloch, the effective mass of the electron and hole are given by [4]: * = ħ 2     The results of calculations using the relation is mentioned in table 4. Exciton Bohr radius:-Using the relation from in the paper [7] given the relation of Exciton bohr radius: Where the bohr radius of Hydrogen and ɛ the dielectric constant. The results of are given in the table 5. Energy band:-Referring to the work of Tinoco and al. [10], the energy gap is given by the relation: E g y = 1.620 − 0.840 y + 0.175 y 2 eV ( ) Where y= 1-x. By varying x from 0, 0.3 to 1, we obtained the table 6:

Results and Interpretation:-
The results of all calculations are mentioned in the table 7.

Effective and reduced mass:-
The effective mass of the electron to the free exciton increases a function of x. If x increases, increases like we shown in Figure 1. The effective mass of the electron to the free exciton in CuInSe2 is less than that in CuIn 0.7 Ga 0.3 Se 2 and CuGaSe 2 .
There is another variation curve for the effective mass of the free exciton hole (Figure 2). For this case, the maximum value is obtained for CuIn 0.7 Ga 0.3 Se 2 , and a value for the CuInSe 2 greater than that of CuGaSe 2 .
1914 Figure 2:-Effective mass of holes according x.
The same type of evolution is observed for the reduced mass ( Figure 3). Indeed the mass is again much higher for CuIn 0.7 Ga 0.3 Se 2 . Can bind the evolution of the mass reduced to the performance of these cell types. The best performance is obtained for Cu In 0.7 Ga 0.3 Se 2 and which is a cell with Cu-poor absorber.

Bohr raduis and Exciton Rydberg Energy:-
By varying the value of x from 0,0.3 to 1, we see that the exciton Bohr radius of the exciton free decreases ( Figure  4). The radius of the exciton in CuInSe 2 is much greater than that in the CuIn 0.7 Ga 0.3 Se 2 and CuGaSe 2 . For the exciton Rydberg Energy, we note the oppose effect ( figure 3). Indeed the exciton Rydberg Energy is much higher when x = 1 and corresponding a CuGaSe2. If increase, R* y increase too. X and R* y varies together. The value of x is related to the rate Ga. One can say that the addition of Ga decreases the radius of bohr and increases the excitonic Rydberg Energy of exciton.

Bohr radius a B and Excitonic Rydberg Energy R * y according to Bandgap Eg:-
The addition of Ga on CuInSe2 also affects the energy gap by increasing it. Eg increases with [Ga] / ([Ga] + [In]). The evolution of the parameters of the exciton with x being already studied, and given also that Eg increases with x, the relationship between Eg and the exciton parameters can be established easily. Thus the evolution of Excitonic Rydberg Energy in function of Eg is given by Figure 6, and we note that it evolves with x.
1916 Excitonic Rydberg Energy is related to the bandgap. If the bandgap is high, this energy is high. This trend was deductible because the exciton is a state between the conduction band and valence band (gap of Energy), and these two bands are far more space for the formation of the exciton is great.
We note a Bohr radius of evolution according to Eg contrary to that of excitonic Rydberg Energy (Figure7). Indeed the Bohr radius decreases with increasing Eg.

Conclusion:-
Based on previous results, we can conclude that the performance of these types of cells depends on the reduced mass and the bigger it is the more the performance of the cell are large. The evolution to the performance cannot be directly related to the bohr radius of and exciton Rydberg energy. We found that for the best cell (CuIn 0.7 Ga 0.3 Se 2 ), the characteristics of the exciton (R * y and aB) are free intermediate to the other two respectively corresponding to x = 0 and x = 1. Compared to the gap, the exciton bohr radius a B increases inversely with the energy gap and R* y increases with the energy gap.