D.1
D
The morphology of selected TCO samples
As we have mentioned in Chapter 10, light management is crucial for designing solar
cells. Very often, the TCO layers in thin-film solar cells have nano textured surfaces. The
incident light is scattered at these interfaces such that the average photon path length in the
absorber layer is enhanced. Thus, more light can be absorbed and the photocurrent density
can be increased. However, the texture may also influence the growth of layers that are
deposited onto the TCO and thus alter the electrical properties, which may lead to a
reduction in V oc and the fill factor. Further, the increased interface area due to the texture
may lead to more surface recombination and also reduce the voltage.
Surface parameters
To compare the morphology of different samples, many surface parameters can be used.
Here, we discuss two parameters, the root mean squared (rms) roughness σ r and the
correlation length ℓ c .
The rms roughness in principle is the standard deviation of the height profile. It is
defined as
where N is the number of data points, z i is the height of the i th datapoint and is the
average height. These data can be obtained with atomic force microscopy (AFM). Note
that σ r is insensitive to the lateral feature sizes. Samples with very small or large lateral
features can both have the same rms roughness.
The correlation length gives an indication of the lateral feature sizes. Its derivation is
less straightforward than that of σ r : it has to be extracted from the autocorrelation function
(ACF) and/or the height-height correlation function (HHCF) [194].
For a discrete set of data, the two-dimensional ACF is given by
where δ is the distance between two data points, m = τ x /δ and n = τ y /δ. For AFM scans the
D
The morphology of selected TCO samples
As we have mentioned in Chapter 10, light management is crucial for designing solar
cells. Very often, the TCO layers in thin-film solar cells have nano textured surfaces. The
incident light is scattered at these interfaces such that the average photon path length in the
absorber layer is enhanced. Thus, more light can be absorbed and the photocurrent density
can be increased. However, the texture may also influence the growth of layers that are
deposited onto the TCO and thus alter the electrical properties, which may lead to a
reduction in V oc and the fill factor. Further, the increased interface area due to the texture
may lead to more surface recombination and also reduce the voltage.
Surface parameters
To compare the morphology of different samples, many surface parameters can be used.
Here, we discuss two parameters, the root mean squared (rms) roughness σ r and the
correlation length ℓ c .
The rms roughness in principle is the standard deviation of the height profile. It is
defined as
where N is the number of data points, z i is the height of the i th datapoint and is the
average height. These data can be obtained with atomic force microscopy (AFM). Note
that σ r is insensitive to the lateral feature sizes. Samples with very small or large lateral
features can both have the same rms roughness.
The correlation length gives an indication of the lateral feature sizes. Its derivation is
less straightforward than that of σ r : it has to be extracted from the autocorrelation function
(ACF) and/or the height-height correlation function (HHCF) [194].
For a discrete set of data, the two-dimensional ACF is given by
where δ is the distance between two data points, m = τ x /δ and n = τ y /δ. For AFM scans the