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Chapter 7
7.4.2 Diffusion of sodium
In order to study whether the sodium diffusion as described before would actually
be possible, both in elevated and room temperatures, indicative theoretical diffusion
lengths have been calculated based on a model proposed by Lämmle et al. [10]. In this
reference, it was shown that sodium can migrate, which largely happens via the grain
boundaries, thereby influencing the properties of the solar cell.
Reference [10] studied the diffusion behaviour of sodium applied via Post Deposition
o
o
Treatment (PDT) NaF within CIGS cells at increased temperatures (157-400 C): at 157 C,
the diffusion coefficient for sodium within a grain was around 4x10 cm /s, while it
2
-13
o
was 2x10 cm /s in a grain boundary. At 157C or lower diffusion temperatures, the
-11
2
diffusion along the grain boundaries is therefore the dominant mechanism. The grain
o
o
boundary diffusivities determined between 157 C and 226 C are about 20 – 50 times
higher than the corresponding diffusivities in the CIGS bulk.
The sodium diffusion coefficient for sodium in the grain boundaries was fitted by an
Arrhenius equation as a function of temperature:
D Na = . 6510exp − 021eV. cm s -1 (7.1)
x
9
GB
2
k T
B
o
By extrapolating to 107 C according to this equation, the diffusion coefficient should
-11
2
be around 1.1x10 cm /s. It should be noted that the fit of the diffusion coefficients
at high temperatures are empirical, so extrapolating to lower temperatures does not
necessary yield correct values.
In order to estimate how far sodium can diffuse at different temperatures, the
expected diffusion length for sodium in grain boundaries has been calculated for 10
o
and 100 hours (Figure 7.18). When 107 C is considered, the expected diffusion lengths
are approximately 9 and 28 micrometres for 10 and 100 hours respectively. This would
100 hours exposure
Expected diffusion length (µm) 60
10 hours exposure
40
20
0
0 50 100 150 200 250
o
Figure 7.18 Temperature ( C)
Figure 4.17: Expected diffusion length in micron after 10 and 100 hours
Expected diffusion length in micron after 10 and 100 hours for sodium present in the grain boundaries based on the extrapo-
for sodium present in the grain boundaries based on the extrapolation
of the diffusion coefficients as presented in reference [11].
lation of the diffusion coefficients as presented in reference [10].
234
7.4.2 Diffusion of sodium
In order to study whether the sodium diffusion as described before would actually
be possible, both in elevated and room temperatures, indicative theoretical diffusion
lengths have been calculated based on a model proposed by Lämmle et al. [10]. In this
reference, it was shown that sodium can migrate, which largely happens via the grain
boundaries, thereby influencing the properties of the solar cell.
Reference [10] studied the diffusion behaviour of sodium applied via Post Deposition
o
o
Treatment (PDT) NaF within CIGS cells at increased temperatures (157-400 C): at 157 C,
the diffusion coefficient for sodium within a grain was around 4x10 cm /s, while it
2
-13
o
was 2x10 cm /s in a grain boundary. At 157C or lower diffusion temperatures, the
-11
2
diffusion along the grain boundaries is therefore the dominant mechanism. The grain
o
o
boundary diffusivities determined between 157 C and 226 C are about 20 – 50 times
higher than the corresponding diffusivities in the CIGS bulk.
The sodium diffusion coefficient for sodium in the grain boundaries was fitted by an
Arrhenius equation as a function of temperature:
D Na = . 6510exp − 021eV. cm s -1 (7.1)
x
9
GB
2
k T
B
o
By extrapolating to 107 C according to this equation, the diffusion coefficient should
-11
2
be around 1.1x10 cm /s. It should be noted that the fit of the diffusion coefficients
at high temperatures are empirical, so extrapolating to lower temperatures does not
necessary yield correct values.
In order to estimate how far sodium can diffuse at different temperatures, the
expected diffusion length for sodium in grain boundaries has been calculated for 10
o
and 100 hours (Figure 7.18). When 107 C is considered, the expected diffusion lengths
are approximately 9 and 28 micrometres for 10 and 100 hours respectively. This would
100 hours exposure
Expected diffusion length (µm) 60
10 hours exposure
40
20
0
0 50 100 150 200 250
o
Figure 7.18 Temperature ( C)
Figure 4.17: Expected diffusion length in micron after 10 and 100 hours
Expected diffusion length in micron after 10 and 100 hours for sodium present in the grain boundaries based on the extrapo-
for sodium present in the grain boundaries based on the extrapolation
of the diffusion coefficients as presented in reference [11].
lation of the diffusion coefficients as presented in reference [10].
234
