International Journal of Photoenergy

Volume 2013 (2013), Article ID 513217, 4 pages

http://dx.doi.org/10.1155/2013/513217

## - Calculations in CdS/CdTe Thin Films Solar Cells with a Interlayer

Escuela Superior de Física y Matemáticas-IPN, Edificio 9 U.P.A.L.M., 07738 México, DF, Mexico

Received 3 June 2013; Accepted 9 August 2013

Academic Editor: Francesco Bonaccorso

Copyright © 2013 A. Gonzalez-Cisneros et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In CdS/CdTe solar cells, chemical interdiffusion at the interface gives rise to the formation of an interlayer of the ternary compound . In this work, we evaluate the effects of this interlayer in CdS/CdTe photovoltaic cells in order to improve theoretical results describing experimental - (capacitance versus voltage) characteristics. We extended our previous theoretical methodology developed on the basis of three cardinal equations (Castillo-Alvarado et al., 2010). The present results provide a better fit to experimental data obtained from CdS/CdTe solar cells grown in our laboratory by the chemical bath deposition (for CdS film) and the close-spaced vapor transport (for CdTe film) techniques.

#### 1. Introduction

Polycrystalline solar cells based on the thin films technology are outstanding candidates for an aggressive expansion of the photovoltaic industry. During the past few years, despite the world economic recession, the photovoltaic market has continued to grow. In Europe and Asia, the market has expanded from the Mega Watt (MW) to the Giga Watt (GW) scale. PV installations grew to 7.3 GW in 2009, which represents 20% from the previous year. The various forecast scenarios predict an increase in the demand from 15.4 to 37 GW in 2014, more than five times the size of the 2009 market [1, 2]. Today, there is much interest and research activity concerning second generation solar cells based on polycrystalline cadmium telluride thin films and cadmium sulfide as “window” layer. Capacitance versus voltage is one of the most important techniques for the device characterization. In this work, we extend the theoretical model used in a previous paper [3] in order to take into account the formation of a layer of the ternary compound (*, *the concentration) at the interface generated by interdiffusion processes [4]. During manufacturing of these solar cells, the interface is subjected to relatively high temperatures giving rise to atomic interdiffusion and the formation of an interfacial region of composition . The understanding of this ternary interlayer will help to conceive improvements in the efficiency of the photovoltaic cell. In this work, we use a theoretical method for the determination of the interface charge density in the heterojunction and the band discontinuity simultaneously. The methodology is based on three cardinal equations as discussed in the theory below. For comparison with our calculations, we used solar cells of maximum efficiency (12.4%) fabricated in our group [5].

#### 2. Theoretical Method

We present the methodology for the simultaneous calculations of the valence band offset and the interface charge density. It is assumed that these two quantities are independent of the bias voltage. This assumption is justified because we are interested in heterojunctions with fixed defect densities.

The clue for obtaining the energy bands at both sides of the interfaces are (a) the two interfacial potentials (, which give the band bending at each side of the interface), (b) the energy increment of the valence band, and (c) the interface charge density. In addition to these, three cardinal equations originating from the displacement of the band line-up equation, charge neutrality, and the total capacitance of the interface are necessary. This method makes no use of any approximations and provides simultaneous determination of the discontinuities of the valence band and the interfacial charge density.

Assuming that the heterojunction is like a parallel plate capacitor, the capacitance-voltage characteristics for low bias voltagesare given by whereis the potential well in the heterojunction,is the bias voltage, is the electron charge,is the acceptor concentration, is the donor concentration, andandare the dielectric constants of n-type and p-type semiconductor [6]. Therefore, in our case, we have a linear dependence of versus close to. We solve numerically the band energy in any site of the heterojunction using the interface according to the experimental data [7]; the spectral response of champion solar cells has an increase in a photon energy close to the band gap . Thus, we have assumed in our equations that the physical properties of the ternary compound are closer to those of for each part of the ternary compound, which are the total bending on each side of the two heterojunction ().

We note that the total band curvature at each side of the interface depends on the bias voltage , that is, and . We assume that the discontinuities of the valence band and the charge density at the interface are independent of the applied voltage, which is a usual assumption for low voltages. Validity of this assumption is validated by a good agreement with experiment.

Because there are a fixed equal number of separated positive and negative charges at the interface between different materials, we consider that the region of spatial charge behaves like a parallel plate capacitor.

##### 2.1. Cardinal Equations for the Interface ( Matching Method)

The band line-up equation in this case is (Figure 1) where “” is the ternary concentration and and are the differences between the quasi-Fermi energy levels with subscripts 1 and 2 corresponding to and , respectively. The valence band offsetand the respective bulk valence band levels are given by The separation between the quasi-Fermi energy levels is determined for the bias voltage: where is the bias voltage in the p-n junction.

The charge neutrality equation under nonequilibrium is given by where the expressions for the semiconductor charge under nonequilibrium, and , are the half semiconductor charges (per unit area) which are given by [8] where Here, and.

The third cardinal equation is obtained from the expression of the half capacitance per unit area of the device: where It is important to note that the energy gap of the ternary is not a simple linear combination but a more complex function of [9]: where is the “optical bowing coefficient” given by 1.69 eV and the valence band offset .

#### 3. Results

We find the ternary concentration value of 0.75 with the best fitting of the curve, which is in good agreement with the results described by Cediel et al. [10]. The various quantities or constants in the cardinal equations were taken from the previous paper [3]. We show the result of the fitting method in Figure 2 for a voltage range from 0 to 0.5 V. A much better fit is obtained by assuming the formation of a ternary compound at the interface.

In addition, we have also obtained the values of the valence band offset and the interface charge density simultaneously, namely, which are in good agreement with the reported values [9, 11, 12].

#### 4. Conclusions

In summary, we have calculated the capacitance versus applied voltage of thin film solar cells considering the formation of a interlayer using the matching method. Our results are in better agreement with experimental data than our previous theoretical results that did not assume the presence of the interlayer. We may also say that the ternary layer acquires the properties of and behaves like the type n semiconductor instead of the itself. This could be taken as evidence of the existence of a ternary compound that plays an important role in solar cell devices. This can be taken as evidence of the existence of the ternary interlayer which plays an important role in the solar cell.

#### Acknowledgments

F. L. Castillo-Alvarado, J. Ortiz-Lopez, and G. Contreras-Puente gratefully acknowledge fellowships granted by COFAA-IPN, EDI-IPN, and EDD-IPN. This work was partially supported by CONACyT (Mexico).

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