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of each array simply depends on the filling ratio (FR) of the material, i.e.,
FR = πD
2
/3.4A
2
, where D and A are the diameter and the pitch of single-NP array,
respectively. This relates the reflectance of photons to the top surface of NP array
and thus the total reflectance significantly depends on the top surface area fraction
or FR of NP array with similar diameters [13]. As a result, NC array has the lowest
reflectance due to the minimum surface area. Figure 1e shows the optical absorption
of NC array with multiple-NP structure with the same thickness (2000 nm), 1000 nm
pitch size, and different segment (N). The broadband-integrated absorption and the
ideal short-circuit current density (J sc ) of these arrays show that the maximum
absorption and J sc are obtained by increasing the segment number (N). As a result,
NC array shows the highest values for both absorption (95.1%) and J sc (58.4 mA/
cm
2
) as shown in Fig. 1e, due to the lowest surface area and reflection. Figure 1f
illustrates the broadband-integrated absorption of 2000 nm height Ge NC array [2].
In this plot, the y axis is the bottom diameter of NC array and the x axis stands for
the pitch size. It is clear that the reflectance of NC array is marginal regardless of
bottom diameter and pitch size, since the cone tip diameter is assumed to be zero.
Consequently, the largest bottom diameter for each pitch size shows the best optical
absorption [14, 15].
Figure 2a depicts the schematics of NSP array before and after amorphous silicon (a-Si) solar cell fabrication. The angular-view SEM images of NSP substrates
with 1.2  μm pitch size are shown in Fig.  2b1, c1, d1. The substrate is anodized
aluminum oxide (AAO) fabricated through several anodization and etching steps.
Notable, the pitch size can be controlled by applying different voltages. The geometry of nanostructures can be controlled by etching time and the concentration of
solutions. Figure 2b2, c2, d2 illustrate the corresponding a-Si devices fabricated on
NSP substrates with different heights controlled by anodization time (30 min, 3 h,
and 6 h, respectively). As seen, there is structural transportation from nanoconcave
to nanospike by increasing the anodization time. Due to their peak to valley height
differences in Fig. 2b1, c2, d1, they are named as NC 200, NSP 600, and NSP 1200,
respectively [16].
The optical absorption and photo-carrier collection are key factors for improvement of device parameters such as short-circuit current density (J sc ), open circuit
photovoltage, (V oc ), and fill factor (FF), which are coupled strongly. Consequently,
investigation on the coupled optical and electrical properties of solar cell device
based on nanostructures is of critical importance [17, 18]. Figure 2e, f show a systematic study on the geometry optimization of nanostructures and its effect on the
optical and electrical properties of solar cell devices using finite difference time
domain (FDTD).
The integrated optical absorption of a-Si devices versus pitch size and height of
NSP is shown in Fig. 2e. As it can be observed, the optical absorption of solar cell
based on NSP array is much higher than that of the planar device. It is clear that by
increasing the height of NSP array, the optical absorption is monotonically enhanced,
where the highest absorption is 88.8% for 1.2 μm pitch size with 1.2 μm height. This
indicates the higher light trapping effect for the higher aspect ratio. Figure 2f shows
the integrated absorption in a-Si layer calculated by FDTD simulation, represents
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