*3.1.4 Investigations on the ZnS – Cu (In, Ga) Se2 interface: Highlighting of the surface defect layer (SDL)*

Between the ZnS and the absorber, a layer called OVC (Ordered Vacancy Compound) has been identified. Investigations carried out within recent works identify his properties and found that they were similar to that of a Surface Defects Layer (SDL). Ouédraogo et al. [24] and Tchangnwa et al. [25, 26], highlighted the beneficial effect related to the existence of the SDL on cell performance. In fact, the presence of an Indium-enrich micro-layer which exhibits an N-type conductivity (N-SDL), at the top of the P-type conductivity CIGSe material, is responsible of the existence of that defect state layer. That leads to a discontinuity at the band gap level at the interface. It has a positive effect since it enhance the transport of the charge carriers through the junction. Another interpretation is given for the existence of that defect state layer from other authors [27], that is, it results from a copper-poor film at the top of the CIGSe material. Both interpretations complete each other, since the N-SDL is almost located within the CIGSe layer, but exhibits different opto-electrical, electronic and structural properties. As a consequence, at the P-N interface between the N-type ZnS and the P-type CIGSe materials, an homojunction is formed. That is, the N-type SDL is almost fully integrated within the CIGSe structure. That explains why in our structure, we will model our P-N heterojunction (the ZnS-CIGSe junction) as two different interfaces: the ZnS/SDL interface and SDL/CIGSe interface, each of them exhibiting different properties.

## **3.2 General principle**

#### *3.2.1 Mechanism of photovoltaic conversion*

The photovoltaic effect is based on the properties of semiconductor materials. Indeed, the latter are capable of absorbing photons of frequency *ν* whose energy is:

$$\left[E\_{photon} = h\nu - E\_{\text{g}}\right] \ge \left[E\_{\text{g}} = E\_{\text{C}} - E\_{V}\right] \tag{5}$$

The fermi level energy is given by:

*DOI: http://dx.doi.org/10.5772/intechopen.93817*

*EF* <sup>¼</sup> *EC* <sup>þ</sup> *EV*

*<sup>e</sup>* <sup>¼</sup> <sup>0</sup>*:*4*me* and *<sup>m</sup>*<sup>∗</sup>

with: *m*<sup>∗</sup>

conditions [23].

*N*<sup>þ</sup>

*<sup>D</sup>* and *N*�

*3.2.3 Current generation*

2 þ

The Poisson equation for semiconductors is:

*d dx <sup>ε</sup>* *dφ*

The continuity equations for electrons and holes are:

*d*

*d dx Jp*

and generation of electron-hole pairs, respectively.

*J* ¼ *JG*́e*n*́e*ration* � *JRecombinaison* ¼ �*q*

the semiconductor is given by:

in the semiconductor.

**95**

*KT* 2

*<sup>h</sup>* ¼ 1*:*7*me*

ln *NV NC* � �

*Thin-Film Solar Cells Performances Optimization: Case of Cu (In, Ga) Se2-ZnS*

These are the Poisson equation in the presence of an electric potential φ, and the continuity equations of electrons and holes with well-specified boundary

*dx* � � ¼ �*q p* � *<sup>n</sup>* <sup>þ</sup> *<sup>N</sup>*<sup>þ</sup>

*dx Jn* ð Þ¼ *q R*ð Þþ � *<sup>G</sup> <sup>q</sup>*

*p* are respectively the concentration of free carriers for electrons and holes,

The current density in the cell can be written in the following form: (17)

*W* ð þ*L*

�*d*

Where *GL* is the generation function, *Jir* is the recombination current at the interface, R is the recombination function in the volume of the absorbent layer. *d*, *W* and *L* are the widths of the buffer layer, ZCE and ZQN respectively [23].

The rate of generation of electron-hole pairs at one dimension of the surface of

*<sup>α</sup>*<sup>1</sup> (λ) is the number of incident photons per *cm*<sup>2</sup> per *<sup>s</sup>* per unit wavelength. *<sup>R</sup>*ð Þ*<sup>λ</sup>* is the fraction of photons reflected from the surface, *α*1is the absorption coefficient

� � ¼ �*q R*ð Þþ � *<sup>G</sup> <sup>q</sup>*

*ε* is the dielectric constant of the material, *φ* is the electrostatic potential, *n* and

*<sup>A</sup>*- are the densities of ionized donors and acceptors, *Jn* and *Jp* are the current densities due to electrons and holes. *R* and *G* are the rates of recombination

<sup>¼</sup> *EC* <sup>þ</sup> *EV* 2 þ *KT* 2

*<sup>D</sup>* � *N*� *A* � � (12)

> *∂n ∂t*

> > *∂p*

*Jn* ¼ *qμen*∇*φ* þ *qDe*∇*n*; (15) *Jp* ¼ *qμpp*∇*φ* þ *qDp*∇*p* (16)

> *W* ð þ*L*

> > 0

*R x*ð Þ*dx* (17)

*GL*ð Þ *λ*, *x dx* � *Jir* þ *q*

*GL*ð Þ¼ *λ*, *x α*1ð Þ*λ F*ð Þ*λ* ð Þ 1 � *R*ð Þ*λ* exp ð Þ �*α*1*x* (18)

ln *<sup>m</sup>*<sup>∗</sup> *h m*<sup>∗</sup> *e* � �<sup>3</sup> 2

; (13)

*<sup>∂</sup><sup>t</sup>* (14)

(11)

Where *Eg* is the value of the forbidden band, *EC*and *EV* are respectively the energy values of the conduction band and the valence band of the illuminated material.

A semiconductor material alone cannot generate electric current. In order to generate the electric current, one must assemble two semiconductors of different types, thus creating a P-N junction [21]. In this chapter, let consider the denomination heterojunction because the constituent materials of our two semiconductors are different. The P-doped zone is that containing the CIGSe, and the N-doped zone groups together the buffer layer (ZnS) and the window layers (i-ZnO, ZnO: B). During contact between the P and N zones, the majority carriers of each diffuse through the contact surface, at this time a depletion zone is created, positively charged on the side of the N-type semiconductor and a negatively charged zone on the P-type semiconductor side. This transition zone is called the Space Charge Zone (ZCE). The Fermi levels of the two zones equalize, causing the band diagram to bend, introducing a potential barrier *Ve* at the interface.

The concentration gradient of the majority carriers induces the presence of a permanent electric field in this ZCE at equilibrium. The electric field thus created leads each type of carrier towards the zone where it is the majority carrier (the electrons towards the N zone and the holes towards the P zone). It follows the mechanism of the collection of each majority carrier.

#### *3.2.2 Densities of states and concentrations of charge carriers*

Electrons and holes obey the Fermi-Dirac statistic, the probability that an energy level E is occupied by a charge carrier is given by:

$$f\_{FD}(E) = \frac{1}{1 + \exp\left(\frac{E - E\_f}{K\_b T}\right)}\tag{6}$$

Assuming we are in non-degenerate states of energies we have *E* � *Ef* � �*=KbT* ≫ 1 and *<sup>f</sup> FD*ð Þ! *<sup>E</sup>* exp � *<sup>E</sup>*�*<sup>E</sup> <sup>f</sup> KbT* � �.

The densities of electrons and holes in the conduction and valence band respectively are given by the following integrals [28].

$$m = \int\_{E\_c}^{\infty} N(E)f(E)dE = f\_{FD}(E\_c) = \text{Nc } \exp \quad -\left(\frac{E\_c - E\_f}{K\_b T}\right) \tag{7}$$

$$p = \int\_{-\infty}^{E\_V} N(E) \left( \mathbf{1} - f(E) dE = f\_{FD}(E\_V) = \mathbf{N} \mathbf{v} \cdot \exp\left(\frac{E\_V - E\_f}{K\_b T}\right) \right) \tag{8}$$

With:

$$N\_C = \frac{2\left(2\pi m\_e^\* \, KT\right)^{3/2}}{\hbar^3} \tag{9}$$

and

$$N\_V = \frac{2\left(2\pi m\_h^\* \, KT\right)^{3/2}}{\text{ft}^{3.}}\tag{10}$$

*Thin-Film Solar Cells Performances Optimization: Case of Cu (In, Ga) Se2-ZnS DOI: http://dx.doi.org/10.5772/intechopen.93817*

The fermi level energy is given by:

$$E\_F = \frac{E\_C + E\_V}{2} + \frac{KT}{2} \ln\left(\frac{N\_V}{N\_C}\right) = \frac{E\_C + E\_V}{2} + \frac{KT}{2} \ln\left(\frac{m\_h^\*}{m\_e^\*}\right)^{\frac{1}{2}}\tag{11}$$

with: *m*<sup>∗</sup> *<sup>e</sup>* <sup>¼</sup> <sup>0</sup>*:*4*me* and *<sup>m</sup>*<sup>∗</sup> *<sup>h</sup>* ¼ 1*:*7*me*
