## 3 Comparison of Contact and Absorber Textured Solar Cells  
The quantum efficiency of optimized solar cells with textured contact layer and absorber, and a solar cell on a flat substrate are shown in Figure 7. Both textured solar cells exhibit an enhanced quantum efficiency (Figure 7a), and a gain in the short circuit current density compared to a solar cell on a flat substrate (Figure 7b). At short wavelengths (300-380 nm), the solar cells with textured absorber exhibit a higher quantum efficiency compared to solar cells with textured contacts and flat substrate. As a result, a gain in the blue short circuit current density for the nanowires based solar cells is observed. However, for long wavelengths the solar cells with textured contact exhibit a higher  
Figure 6: Quantum efficiency of solar cells with textured contact layers for various edge-length (\(D\)) of the grating. The unit cell period is kept constant at 900 nm. Figure 7: (a) Quantum efficiency of solar cells on flat substrate, textured contact layer (grating edge-length: 640 nm, grating height: 500 nm) and textured absorber layer (nanowire edge-length: 640 nm); (b) Short circuit current density of the solar cell with textured contact layer (grating), textured absorber (nanowire) and flat substrate as a function of the nanowire edge-length (\(D\)). The dashed line represents the short circuit current density of a solar cell on a flat substrate. The unit cell period for all the solar cells is 900 nm. quantum efficiency compared to solar cells with textured (Figure 7a) absorber. Hence, the total circuit current densities of the solar cells with textured contact layers exceed the short circuit current density of the solar cell with flat substrate and textured absorber (Figure 7b). However, due to the increased short circuit to saturation current density ratio, the open circuit voltage of the solar cell using textured absorber might be increased compared to the solar cell with textured contact layers [25; 26]. The open circuit voltage of the solar cell on the flat substrate is given by  
\[V_{OC}^{flat}=\frac{\eta kT}{q}\left[\ln\left(\frac{I_{SC}^{flat}}{I_{S}^{ flat}}\right)+1\right]\approx\frac{\eta kT}{q}\ln\left(\frac{I_{SC}^{flat}}{I_{S}^{ flat}}\right), \tag{7}\]  
where \(\eta\) is the ideality factor, \(k\) is the Boltzmann constant, \(T\) is the absolute temperature, and \(q\) is the elementary charge. \(I_{SC}\) and \(I_{S}\) are the short circuit and saturation current densities, respectively. If we assume equal ideality factors for the solar cell with patterned absorbers and flat substrate, the open circuit voltage of the patterned absorber solar cell can be calculated accordingly. The saturation current density of the nanowire solar cell can be described by \(I_{S}^{NW}=I_{S}^{flat}\times(D/P)^{2}\) leading to a significant drop of the saturation current density as function of the nanowire diameter. The relationship between the short circuit current density of the nanowire solar cell and the flat solar cell can be approximated by \(I_{SC}^{NW}\approx I_{SC}^{flat}\times(D-D_{cut})/(P/2)\), where \(D_{cut}\) is the diameter of the nanowire at which no sun light is able couple in the nanowire anymore. \(D_{cut}\) is calculated to be 30 nm (Figure 4a). This relationship represents an empirical approximation of the short circuit current density, which is valid for \(D_{cut}<D<P/2\). Hence, the following expression for the open circuit voltage of the solar cell with the textured absorber can be calculated:  
\[V_{OC}^{NW}\approx\frac{\eta kT}{q}\ln\left(\frac{I_{SC}^{NW}}{I_{S}^{NW}} \right)\approx V_{OC}^{flat}+\frac{\eta kT}{q}\ln\left(\frac{2(D-D_{cut})P}{D ^{2}}\right)\quad for\,D_{cut}<D<\frac{P}{2} \tag{8}\]  
For a nanowire diameter of 50 nm the gain of the open circuit voltage is larger than 100 mV. For a nanowire diameter of 400 nm the short circuit current density of the textured absorber is equal to the short circuit current density of the flat solar cell and the gain of the open circuit voltage is approximately equal to 60 mV.