Collection length

Faughnan and Crandall (1984) have developed a simple model that calculates the fill factor of p-i-n cells by using Eq. (4). They found that the collection length (at short circuit) must be 2. 5 times greater than the thickness of the i layer to obtain a fill factor of 0.72. Figure 12 shows how the fill... 

Fig. 12. Fill factor as a function of collection length for a-Si H p-i-n cells. [From B. W. Faughnan and R. S. Crandall (1984).]...

By referring back to the I- V relationship in Eqs. (6) and (17) and Rs expressed in terms offix in Eq. (14), the fill factor and normalized efficiency, as shown in Fig. 11, are determined as a function of the electron /it product. These relationships shown in Fig. 11 could be tested by utilizing recent work by Faughnan, Moore, and Crandall in which the electron collection length in the cell s i layer at JT = Jx are determined from quantum efficiency measurements at various bias potentials applied to the cell (Faughnan et al., 1984). The collection length at V= 0 is a product of fix times the internal electric field and the internal field may be determined by the theory from the potential drop across Rs at JT = JK. Fill factor and efficiency data as a function of the fix product extracted from the electron collection length before and after extended cell illumination can be used to test this proposed model. 

It is apparent that the key to an efficient p-i-n sensor is a low defect density in the i layer, so that the collection length is as large as possible. For this reason the creation of metastable defects by illumination is a significant problem for solar cells and a-Si Ge H alloys, which are desirable from the point of view of collecting more of the solar spectrum, have been difficult to develop because they have a higher defect density. 

Fig. 10.19 shows the relation between the collection length measured under short circuit conditions and the fill factor for many different solar cells (Faughnan and Crandall 1984). The data are described... 

Fig. 10.19. The dependence of the solar cell fill factor on the carrier collection length (Faughan and Crandall 1984).

The vector C can be any parameter that is appropriate to model through D. Examples of C include species concentration, time of data collection, length of hydrocarbon chain or other performance parameters. The estimated relation between C and T is called the regression vector, B. Using a calibration set of data where, for each NMR spectrum, the concentration is known, B is estimated using the T matrix estimated from the PCA step. 

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