3.1. Effect of cooling rate on the interstitial iron concentration
Figure 1. shows the distribution mapping and average concentration of Fei in original wafer and its sister wafers after 1000 ℃ heating for 30 min, and cooling at 0.05 ℃/s, and 30℃/s respectively.
The Fei concentration of the original wafer, the “slow cooling” (0.05 ℃/s) wafer and the “fast cooling” (30 ℃/s) wafer are 4.97×1011 cm-3, 1.05×1012 cm-3and 1.60×1012 cm-3, respectively. Compared with the original wafer, the increase percentage of iron concentration is 112% for the “slow cooling” wafer and 223% for the “fast cooling” wafer, respectively. Each mc-Si wafer is cooling from the melt point temperature to room temperature at an extremely slow cooling rate during directional solidification process. So the original wafer could be considered as a sample with a slower cooling rate than those of the other two processed wafers. The results in Fig. 1 suggested that the Fei concentration increases as the cooling rate increases.
During high temperature heating, iron precipitates and complexes of all or part in silicon will be dissolved. According to the formula of solid solubility of iron in silicon[14]: 5×1022exp (8.2-2.94eV/k) (900℃ < T < 1200℃), the solid solubility of iron in silicon at 1000℃ is 4.1×1014cm-3. The total iron content of the cast mc-Si wafer used is 3.9×1014 cm-3, indicating that all of iron precipitates and complexes in silicon will be dissolved during 1000℃ heating. These iron atoms are released and distribute uniformly in silicon lattice. During the subsequent cooling, most of the iron atoms precipitate again, while the others do not and became Fei atoms [8]. The faster the cooling rate, the shorter the time for diffusion and precipitation of iron atoms, and thus the fewer iron precipitates and the higher Fei concentration.
It is also found that the distribution mapping of Fei concentration in original wafer is about the same as that of the “slow cooling” wafer: iron concentration varies from grain to grain, and is uniform within each grain. Since each two-dimensional grain in Fig. 1 represents a specific crystal orientation, the above situation means that the iron atoms prefer to precipitate on some specific crystal planes when slowly cooled after heating. So far, no conclusion has been reached on which crystal planes iron atoms tend to gather in. In contrast, the distribution of Fei in the “fast cooling” wafer is not restricted by grain boundaries and tends to be uniform in silicon, which should be the reason that the fast cooling does not provide enough time for iron atoms to diffuse to the specific crystal planes.
3.2. Effect of cooling rate on the recombination activity of structural defects
Figure 2 shows the PL image of original wafer and its sister wafers after 1000℃ heating for 30min, with 0.05 ℃/s slow cooling and 30 ℃/s fast cooling, respectively.
The color of purple and green are automatically painted by the equipment. The purple areas represent recombination active dislocations area which lifetime differ from the surrounding area by at least the lifetime value specified as “defect area limit” (0.35µs). It is the same with the green areas, representing recombination active grain boundaries area [15]. In the original wafer, as shown in Fig. 2 (a), the percentage of recombination active dislocations(the purple areas)and recombination active grain boundaries༈the green areas༉ are both relatively low, 2.61% and 1.75% respectively, which indicated a good electrical activity of defects. In the “slow cooling” wafer, as shown in Fig. 2(b), the purple and green areas increase significantly, and the percentages of recombination active dislocations and recombination active grain boundaries are 7.03% and 3.10%, respectively. Compared to the original wafer, they increase by 169% and 77%. It indicates that the recombination active dislocations and grain boundaries of the mc-Si wafers increase significantly after high temperature heating, even when the cooling is as slow as 0.05 ℃/s.
Dislocations without metal decoration and grain boundaries without metal aggregation have no electrical activity, or very weak electrical activity. As thus they are not the recombination centers of charge carriers and do not affect the electrical properties of cast mc-Si [16–18]. If metals and other impurities gather and precipitate on dislocations or grain boundaries, new deep level centers will be formed on them, and their electrical activity and hence the electrical properties of silicon are related to the state of aggregation of metal impurities. Fine and dispersive precipitates/atomic aggregates reduce the diffusion length of minority carriers significantly [5, 6], and corresponding dislocations and the grain boundaries have a strong electrical activity.
When cast mc-Si is heated at high-temperature, metal precipitates are dissolved to an extent and metalic atoms are released and distribute in silicon crystal lattice uniformly. During cooling, according to the theory of solid solution, metal atoms would gather again and their state are associated with the undercooling of cooling process. Lower cooling rate means smaller undercooling, and metal atoms tend to gather in the grain boundaries and dislocations. In this case, nucleation rate is low and small number of nucleates grow into large size precipitates. Density of precipitates is low and exhibit low electrical activity, which is usually the case with the original wafer, where extremely slow cooling from high temperature to room temperature is involved after directional solidification. The PL image of original wafer is shown in Fig. 2 (a).
When the cooling rate after high temperature heating is faster, i.e., undercooling is larger, the metal atoms tend to gather uniformly within grains in addition to those on grain boundaries and dislocations, and nucleate with homogeneous nucleation method subsequently. Nucleation rate is high and large number of nucleates appear in the system. Since the period for nucleates to grow is much limited, the resulting precipitates are small in size and high in density (number of precipitates per unit volume), which leads to a higher electrical activity. For “slow cooling”wafer, the cooling rate of 0.05 ℃/s is still much higher than that after directional solidification, so the precipitates and atomic aggregations of metallic impurities are smaller and more dispersed than those in the original wafer, which shows a higher electrical activity of grain boundaries and dislocations. The PL image is shown in Fig. 2 (b).
Figure 2 (c) is the PL image of the cast mc-Si wafer after 1000℃ heating with 30℃/s rate fast cooling. It can be seen that the purple and the green areas disappear, the whole silicon wafer, including grains, grain boundaries and dislocations, are all dark,the“dark area percent” defined as area of the wafer that has lower lifetime than the absolute limit specified as “dark limit”(1µs) [15] is 100% (that of the original wafer and the “slow cooling ” wafer are 0.23% and 1.48% respectively), indicating that the whole “fast cooling” wafer is contaminated by metallic impurities, and the whole crystalline silicon wafer has a high recombination activity. This is due to the 30℃/s rapid cooling after high temperature heating. In this case, vast majority of metal atoms in crystal nucleate in homogeneous way, and the nucleation rate is very high, more than 99% of the metal impurity distribute in grains, grain boundaries and dislocations in extremely small dispersion state of precipitations, less than 1% of the metal impurities are "frozen" down in the atomic state[19], and also distribute in grains, grain boundaries and dislocations scatterly, the results make whole crystal recombination active area greatly increase. The lifetime difference between the structure defects of dislocations or grain boundaries and the surrounding area is less than “defect area limit”, so the purple and the green areas disappear and the PL image of the whole wafer are dark, and the“dark area percent” is 100%.
The cooling process may cause the dislocation multiplication and increase the recombination active dislocation. In order to discriminate the main reason of the increase of recombination active dislocation, the microstructure of the original wafer and the “slow cooling” wafer were observed and the average dislocation density of the 9 pairs corresponding positions in the same area on the original and “slow cooling” wafer were measured. Figure 3 shows the 6 position dislocation outcrops. Table 1 shows the contrast of dislocation density between the original wafer and its slow cooled sister wafer.
Table 1 and Fig. 3 show that there is a slight increase in dislocation density of the cast mc-Si wafer after 1000 ℃ heating for 30 min and then cooling down at 0.05 ℃/s rate (average increase of + 3.5%), which is far smaller than the increase of active dislocation area (169%). This further indicates that the increase of the recombination active dislocations is not mainly caused by the increase of dislocation density but by the contamination of metallic impurities.
3.3. Effect of cooling rate on the minority carrier lifetime
Figure 4 shows the minority carrier lifetime mapping of original wafer and its sister wafers after 1000 ℃ heating for 30 min, with 0.05 ℃/s slow cooling and 30 ℃/s fast cooling, respectively. The minority carrier lifetime of the original wafer, the “slow cooling” wafer and the “fast cooling” wafer are 46.3µs, 11.2µs, and 1.3µs, respectively. The result shows that the minority carrier lifetime decreases with increase of the cooling rate.
According to the experimental results, the reasons for the TID of minority carrier lifetime is explained as follows:(1)After high temperature heating, the iron precipitates in the cast mc-Si decompose and the Fei concentration are increased. Although the iron precipitation and Fei atoms are both deep level centers, the distribution of Fei atoms in the crystal is more dispersive, and this actually increases the spatial density of the deep level center in the silicon crystal; (2) Compared with the cooling process after directional solidification of the original cast mc-Si, the undercooling and the nucleation rate during the cooling after high temperature heating in this study is larger and the re-formed iron precipitate is finer and more dispersive. The result is that the spatial density of the deep level center in the silicon crystal is increased. Both the above two points can enhance recombination activity of the cast mc-Si, and eminimize the diffusion length of the minority carriers. (3) The high temperature heating increases the recombination active grain boundaries and dislocations, which also reduces the diffusion length of minority carriers.