**6. Conclusion**

154 Solar Cells – Thin-Film Technologies

Stationary nucleation together with the growth of supercritical nuclei according to the Jackson-Chalmers equation leads to a continuous increase of the amount of the new phase on account of the parent phase. When one takes account that during the progress of phase transformation more and more parent phase is consumed and less volume is available for actual transformation, one ends up with the Avrami-Mehl equation (Avrami, 1940) for the

4 4 / 1 *<sup>c</sup> t t*

<sup>4</sup> <sup>3</sup> <sup>3</sup> *ct* 

*J* is the stationary nucleation rate of Eq. 4 and *v* is the speed of propagation of a phase front according to Jackson-Chalmers Eq. 1. In deriving Eq. 9 the time lag of nucleation τ has been neglected. To include this effect, one simply replaces *t* by (*t*-τ) in Eq. 9 for *t*>τ. The resulting

> 1.0374 *<sup>v</sup> <sup>D</sup>*

So the grains are the larger the higher the Jackson-Chalmers speed and the lower the nucleation rate is, which sounds reasonable. To get large grains from an undercooled melt one should keep the temperature in a range of not too high undercooling, where nucleation rate is low and growth rate is high (Figs. 6 and 8). Fig. 12 shows the expected final grain size in solid phase crystallization of amorphous silicon. It shows that in the CSG process at about 600°C (see Sect. 3.) grains of several µm are to be expected, which is in accordance with experiments. By increasing the crystallization temperature one cannot change the grain size appreciably. Lowering the temperature would lead to a rather high time needed for crystallization due to higher time lag of nucleation (Fig. 11), lower nucleation rate (Fig. 9),

600 800 1000 1200 1400

Fig. 12. Average grain size after solid phase crystallization of amorphous silicon as

average grain size when the parent phase has been consumed completely is given by

*e* (9)

*Jv* (10)

*<sup>J</sup>* (11)

T/K

Tma

**5.4 Complete kinetics of transformation** 

volumetric amount of the new phase

with the characteristic time

and lower growth rate (Fig. 7).

D/µm

100

1

depending on temperature

10

Multi- and polycrystalline silicon thin film solar cells receive growing interest worldwide. Presently, the maximum efficiency reached by these types of cells is 10.4%. Different cell concepts and preparation methods are under investigation and no clear favourite way is identified up to now. The concepts differ in the resulting grain structure, i.e. size and quality, but also in the preparation technologies used and the processing time needed. Today it is not clear which of the methods will succeed in industrial production. In all the methods, pin holes in the films are an issue since they lead to shunting of the final cells. Another issue is dopand deployment, particularly along grain boundaries. This also may lead to shunting, which today limits the open circuit voltage to slightly above 500 mV. A further point is that TCO cannot easily be used as a front contact in superstrate cells since it hardly withstands the temperatures needed for crystallization. Usually a highly doped silicon layer is used instead, which, however, has somewhat low transparency.

Very important for thin film crystalline solar cell is a perfect light management so that about 2 µm of silicon is enough to absorb the solar spectrum. This can be achieved either by structured substrates or by texturing the surface. In the first case, the irregular substrate surface should not influence the crystallization behaviour. In the second case, the rough surface should not increase surface recombination. Generally, passivation of defects and of the surface is a crucial preparation step.

Concerning the theoretical description of the processes involved in crystallization, the basic equations are well understood. However, there are some issues with the material parameters involved, which, particularly for amorphous silicon, strongly depend on deposition conditions and therefore need to be determined individually. But even if numerical predictions may not completely coincide with experiments due to inadequate numerical values of the materials parameters, general trends can reliably be predicted.

All the mentioned issues need further investigation. Careful study of these topics is expected to lead to full exploitation the potential of the material. Multicrystalline thin film cells with a ratio of grain size over film thickness similar to multicrystalline wafer cells should deliver, if prepared correctly, comparable efficiencies. Therefore we expect the polyand multicrystalline silicon thin film solar cells to gain increasing significance and may replace microcrystalline silicon cells. Multicrystalline silicon also can act as one partner in tandem cells which would further increase the efficiency.
