K. Kotsovos

Institute of Microelectronics, NCSR Demokritos, 153 10, Athens, Greece V. Perraki

Department of Electrical and Computer Engineering, University of Patras, GR 26110 Patras, Greece, email:perraki@ee. upatras. gr

ABSTRACT

This paper presents a three-dimensional (3D) theoretical model of n+pp+ type epitaxial solar cells, illuminated on the n+side. The solution, by the Green’s Function method, is 3D analytical expressions in form of convergent series. The final aim is determination of the best device parameters through a computer program, in order to obtain cell performance as close to the optimum as possible. A number of cells made from upgraded metallurgical grade polycrystalline substrates, boron doped and free from transition metal impurities have been studied and their spectral response is interpreted in terms of this model. To optimize such polycrystalline Si solar cells the influence of certain parameters such as the thickness of the diffusion region and the variation of grain size and grain boundary recombination velocity on spectral response and white light photocurrent are crucial. A comparison, among one­dimensional and three-dimensional results is shown. Further elaboration is needed in order to investigate other characteristic parameters such as the open — circuit voltage and the fill factor.

1. INTRODUCTION

Efforts made for increasing the conversion efficiency and reducing the fabrication cost of solar cells have necessitated the study of the influence of certain parameters on the performance of solar cells.

We have already [1] introduced a simplified three-dimensional (3D) analytical model in order to simulate the effect of grain size, grain boundary recombination velocity and epilayer thickness on spectral response and photocurrent of epitaxial solar cells.

The cells have been fabricated by CVD (Chemical Vapour Deposition) [2] on wafers from impure polycrystalline silicon with columnar grains. The generated strong BSF by the low/high junction is taken into account and expressions for the photocurrent densities are obtained, resulting from solutions of the diffusion equation solved in 3D. The model is based on the superposition principle and the variables’ separation technique applied on the minority carrier transport equations. Taking into account the action of the grain boundaries, the back contact recombination velocity, bulk recombination, grain size and the illumination level we optimize cell thickness. A computer program has been developed in order to perform optimization of cell parameters during a procedure in which the parameters considered are adjusted through a systematic method, respecting their interaction.

Finally a comparison, among 1D [3], 3D and previous extracted experimental results [2] of photocurrent, is performed.

2. MODEL

The epitaxial n+pp+ type solar cell (figure 1) is divided in four main regions (front layer, SCR, epilayer, and substrate). According to this model the thicknesses of these regions are d1-wn, wn+wp, d2-wp, d3, respectively.

The following considerations have been introduced, in the framework of a realistic approach, in order to simplify our model:

i) The polycrystalline silicon grains are assumed as columnar and perpendicular to the n+/p junction (as a result of the ingot preparing technique). They have homogeneous physical and electrical properties (doping, mobility and diffusion length of minority carriers) along the three dimensions, for each region and the grain boundaries are considered as surfaces of a very small width compared to the grain size, characterized by a distribution of interface states.

ii) The effects of other imperfections of the crystal structure are ignored.

iii) The absorption coefficient a(A) is given by Runyan [4] for this type of material, while the reflection coefficient R(A) is calculated [5] for a single layer TiO2 anti reflective coating of optimal thickness 77 nm. There is a metal coverage coefficient of 13.1%, corresponding to the front metal grid.

iv) The p/p+ junction is considered a low/high junction, incorporating a strong BSF, assuming that the p+ region’s contribution to the total photocurrent is negligible [6].

v) The front and the back surface recombination velocity SF and SB respectively and the series resistance Rs, are the same as in [1]. The effective grain boundary recombination velocity is assumed constant all over the surface of the grain and has been estimated to vary from 102 to 106 cm/sec [7] depending on the interface states density at the grain boundary and the doping concentration of the semiconductor material.

The excess minority carrier density is obtained by solving the three-dimensional diffusion equation in each region. The steady state continuity equation for the front layer is expressed by

where pn-pn0 is the hole concentration, Lp is the minority carrier diffusion length, Dp is the corresponding diffusion coefficient and F is the light generation rate. The previous equation is subjected to the following boundary conditions

where Sng is the grain boundary recombination velocity in this layer and Seff is the effective back surface recombination velocity due to the low high junction as described previously. Since the substrate is considered heavily doped, the following relation gives the expression for Seff

where Nr is the substrate doping, Dn* and its minority carrier diffusion coefficient and diffusion length respectively.

In order to simplify the calculations the grain boundary recombination velocity in the front and active layer is considered the same and symbolized as Sgb.

Using the mathematical treatment previously described in [8], the analytical expressions of Jp, Jn representing the photocurrent density of the front and the active layer are calculated in the model, while the contribution from the Space Charge Region is calculated from the 1D model [3].