## Materials and Methods  
Amorphous silicon solar cells were deposited onto various nanostructured substrates at the National Renewable Energy Laboratory (NREL). Although a variety of nanostructured substrates were considered, one in particular had a spatial gradient of areal density of higher aspect ratio nanostructures, which allowed for the convenient study of the effect of the morphology of the nanostructured substrate on the a-Si solar cell device performance (and thus on the material quality). Zinc oxide nanostructures were deposited onto indium tin oxide (ITO)-coated glass substrates using an electrochemical deposition method that is similar to the method described in a patent [3] and a patent application [4] of nLiten Energy Corporation, but with the application of an electrical bias. A brief description of the method is provided here. All chemicals used in the zinc oxide nanostructure growth process were obtained from Sigma Aldrich. The growth solution was prepared by dissolving zinc nitrate (0.001 M), hexamethylene tetramine (0.001 M), and polyethyleneimine (0.03 M) in deionized water. The pH of the solution was adjusted to 10.5, and then the solution was heated to 80 \({}^{\circ}\)C. For each sample, a piece of ITO-coated glass (2\({}^{\prime\prime}\)\(\times\) 2\({}^{\prime\prime}\)) was used as the working electrode (upon which the zinc oxide nanostructures were deposited), a zinc foil (2\({}^{\prime\prime}\)\(\times\) 2\({}^{\prime\prime}\)) was used as the counter electrode, and a Saturated Calomel Electrode (SCE) was used as the reference electrode. The distance between the working electrode and the counter electrode was 2 cm. The electrochemical deposition was performed at \(-\)1.0 V for different times, depending on the average size of the nanostructures desired. For the substrate with graded areal density of larger nanostructures described below, the deposition time was 10 min. Our hypothesis is that the short deposition time and the resistance of the ITO (reduced applied voltage further from the wire contact to the ITO substrate) resulted in a gradient in the areal density of larger nanostructures, i.e., for the short deposition time, incomplete growth resulted in a gradient in the number of high aspect ratio nanostructures on a substrate, with a lower number of larger nanostructures further away from the edge of the substrate where the voltage is applied. Finally, the coated substrate was withdrawn from the solution and then rinsed, first with deionized water, and then with methanol. Prior to deposition of amorphous silicon thin-film solar cells, a 250 nm layer of ITO was deposited on top of the nanostructured substrate to ensure the conductivity of the nanostructured layer is high enough for efficient carrier extraction. Note that this layer is not thick enough to passivate all \"structural defects\", as will be discussed below [2]. The a-Si:H solar cells with p-i-n structure (superstrate configuration) produced at NREL were deposited on ITO coated glass by plasma-enhanced chemical vapor deposition (PECVD) using a RF power of 13.56 MHz in a multi-chamber cluster tool (MVSystems, Inc., Arvada, CO, USA) at a substrate temperature of approximately 200 \({}^{\circ}\)C. The p-layer (\(\sim\)8 nm) with E\({}_{\rm{Tauc}}\) of 2.1 eV and dark conductivity of 5 \(\times\) 10\({}^{-4}\) S/cm was grown using SiH\({}_{4}\), BF\({}_{3}\), and H\({}_{2}\) in the PECVD chamber. The i-layer (\(\sim\)500 nm) with E\({}_{\rm{Tauc}}\) of 1.78 eV and dark conductivity of 2 \(\times\) 10\({}^{-10}\) S/cm was grown using SiH\({}_{4}\) without hydrogen dilution in the PECVD chamber. The n-layer (\(\sim\)20 nm) with E\({}_{\rm{Tauc}}\) of 1.75 eV and dark conductivity of 2 \(\times\) 10\({}^{-2}\) S/cm was grown using a SiH\({}_{4}\) and PH\({}_{3}\)/H\({}_{2}\) mixture in the PECVD chamber.