# Coupling and Trapping of Light in Thin-Film Solar Cells Using Modulated Interface Textures
## Results
### Light Trapping Model  
In the following we will provide an explanation of these effects based on the anti-reflection effect by the effective medium approximation at the rough front interface, light scattering mainly attributed to reflecting interfaces and simple ray tracing. Figure 6 displays four key surface textures that were previously indicated in Figures 2 and 3 by the letters A through D, to explain the interrelation between surface texture and the optical effects of coupling and trapping in the solar cells. The light-coupling effect is discussed based on the front contact texture only whereas the evaluation of the light-trapping effect also involves the rear surface texture after silicon growth because a significant scattering event occurs here [24]. Thus, the interplay between the two interface textures influences the results. The arrows shown besides the labels \"coupling\" and \"trapping\" within Figure 6 indicate the ability of the respective interface to improve light-coupling and -trapping, respectively. Arrows directed upward, to the right, and downward indicate strong, medium and poor abilities. Surface A (test series 2) shows small features (<250 nm) in diameter with low roughness (<25 nm). This type of surface exhibits features with lateral feature diameters similar to surface B which shows good light coupling properties, however unlike surface B its craters are lacking sufficient depth to generate an antireflective refractive index grading. Additionally, these small features are flattened by the silicon growth [21,59] preventing significant light-scattering at the back surface of the cell. Hence, there is not any noteworthy light-trapping effect. This flattening effect can also be seen by the angular resolved reflection measurement that was performed on the rough ZnO:Al-air interfaces prior to cell deposition and on the silicon-air interface at the cell's rear side. Note that the absolute values cannot be compared easily as the measurements on ZnO:Al and on Si yield different reflectivity values due to different refractive indices at the probe wavelength (ZnO: ca. 1.9, Si: ca. 3.8). The scattered intensity diminishes when comparing the ZnO:Al surface and the evolved silicon surface. The different refractive index of ZnO:Al and silicon would suggest the contrary effect. Hence, the very poor scattering intensity is a result of the smoothing effect. Therefore, surface A does neither support light-coupling nor light-trapping as a result of light scattering at the back reflector. The type B surface (test series 1) on the other hand shows features sizes around 400 nm with a roughness around 90 nm. This surface type facilitates good light-coupling due to an effective refractive index grading. At the same time, the features are not totally smoothed out by silicon growth due to their vertical expansions. Therefore, this surface type also exhibits some light-trapping effects. The strong large angle scattering of the ZnO:Al interface is caused by the significant roughness of the small features, but the scattering angles shift due to the smoothening effect by the silicon growth. The overall scattering intensity, however, remains almost constant. The type C surface (test series 2) shows larger feature sizes around 700 nm-1000 nm in diameter and a roughness value around 70 nm. In this case, the maximum light-trapping in our test series was achieved. The large surface features are passed to the rear side of the solar cell with only minor modifications by the silicon growth. The AID reveals a reduction of the intensity towards large  
Figure 6: Schematic overview of different texture types and their effects on light-trapping and light-coupling. The angular resolved scattering measured at the ZnO:Al/air-interface (red lines) and at the silicon/air- interface (blue lines) is plotted in the graph below each schematic. scattering angles, but it is less pronounced as for previous cases A and B. Therefore, the incident light beam strikes a rough surface on the rear side, which results in good light-trapping.