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(a) 100 µm - Helmholtz-Zentrum Berlin

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4.2 Temperature profiles 79<br />

R C [% ]<br />

1 0 0<br />

8 0<br />

6 0<br />

4 0<br />

� �<br />

2 0<br />

0<br />

����� �����<br />

H S 2<br />

0 3 0 6 0 9 0 1 2 0 1 5 0<br />

� ������<br />

�<br />

Figure 4.23: Crystallized fraction RC vs. annealing time tA for experiment HS2. The left<br />

and the right curves (dashed lines) are isothermal anneals at 500 °C and 460 °C, respec-<br />

tively. (b) The step temperature TS has been varied from 10 °C, 20 °C, 30 °C to 40 °C at<br />

tS = 60 min.<br />

to be taken into account when calculating the grain size. To determine the nu-<br />

cleation density the number of objects in the micrographs is counted. The largest<br />

number of objects N0 within an image during the entire annealing together with<br />

the image area A0 determines the average final nucleation density NG,F = N0/A0.<br />

The average final grain area AG,F is inversely proportional to the final grain den-<br />

sity NG,F , AG,F = 1/NG,F . The average final estimated grain size dG,F is the square<br />

root of the average final grain area AG,F (dG,F = AG,F 1/2 ). Hence, lower NG,F<br />

is desirable to increase the grain size. The nucleation density NG,S at the step<br />

time tS is calculated similar to NG,F , but using the number of objects N0,S at tS<br />

(NG,S = N0,S/A0). Calculating the average grain area AG,S at the step time tS it<br />

has to be taken into account that not the entire area is covered with silicon but<br />

only the crystallized fraction RC. Thus AG,S is inversely proportional to the nucle-<br />

ation density NG,S multiplied by the crystallized fraction RC,S at the step time tS<br />

(AG,S = RC,S · 1/NG,S). The average estimated grain size dG,S is the square root of<br />

the average grain area AG,S (dG,s = AG,S 1/2 ).

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