8.1. INTRODUCTION In previous chapters, standard and improved technologies for producing silicon solar cells have been described. In the present chapter, considerations relevant to the detailed design of silicon cells will be discussed. Answers will be found to questions such as: What is the optimum level of dopants on either side of the junction? Where is the best location for the junction? What is the best shape for the top contact to the cell? How can optical losses from the cell be minimized? Although answers to these questions will be provided specifically for silicon cells, parallel considerations will apply to cells made from other materials discussed in Chapter 10. 8.2 MAJOR CONSIDERATIONS 8.2.1 Collection Probability of Generated Carriers A spatially dependent parameter, the collection probability, can be defined as the probability a light-generated minority carrier 138

Sect. 8.2 Major Considerations 139 has of contributing to the short-circuit current of a solar cell. This is a function of the position the carrier is generated within the cell. This parameter will be seen to be critical in determining the physical design of solar cells. To find the collection probability, the artificial situation shown in Fig. 8.1(a) will be analyzed. Generation of electron-hole pairs by light will be assumed to occur only at points lying on a single plane throughout the cell. For the case where symmetry allows a one-dimensional analysis, the generation rate as a function of distance through the cell will be an impulse function, as indicated in Fig. 8.1(b).

The aim of the analysis will be to find the proportion of electrons generated at the point x, which contribute to the corresponding current flowing in the cell under short-circuit. During the analysis, it will be seen that no nonlinearities are involved and, by the superposition principle, the results can be applied to cases where the form of the generation rate corresponds more closely to practical situations. The analysis closely parallels that of Section 4.6. In region 1 of Fig. 8.1(b), the generation rate is zero everywhere except at the single point x, right at the edge of the region. The differential equation that the excess minority carriers, An, must satisfy is therefore similar to Eq. (4.25): d?An_ An aT (8.1) Generation n | Pp rate Depletion region 4-7 Generation only at this plane fe x ie x

Distance from surface (a) (b) Figure 8.1. Idealized carrier-generation conditions used to calculate collection probabilities. An expression for the fraction cf carriers generated at point x; which contribute to the cell short-circuit current is found in the text. Region 2 140 Design of Silicon Solar Cells Chap. & where L, is the diffusion length. The general solution is, as before,