Carrier drift-mobilities and solar cell models for amorphous and nanocrystalline silicon
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1153-A15-01
Carrier drift-mobilities and solar cell models for amorphous and nanocrystalline silicon E. A. Schiff Department of Physics, Syracuse University, Syracuse NY 13244-1130, U.S.A. ABSTRACT Hole drift mobilities in hydrogenated amorphous silicon (a-Si:H) and nanocrystalline silicon (nc-Si:H) are in the range of 10-3 to 1 cm2/Vs at room-temperature. These low drift mobilities establish corresponding hole mobility limits to the power generation and useful thicknesses of the solar cells. The properties of as-deposited a-Si:H nip solar cells are quite close to their hole mobility limit, but the corresponding limit has not been examined for nc-Si:H solar cells. We explore the predictions for nc-Si:H solar cells based on parameters and values estimated from hole drift-mobility and related measurements. The indicate that the hole mobility limit for nc-Si:H cells corresponds to an optimum intrinsic-layer thickness of 2-3 µm, whereas the best nc-Si:H solar cells (10% conversion efficiency) have thicknesses around 2 µm. INTRODUCTION The mobility µ of a charge carrier describes its drift-velocity v in the presence of an electric field F: v = µF. Mobilities are significant in solar cells because they affect the useful thickness of the layer of material that absorbs the sunlight. For crystalline solar cells, this thickness is typically that of the “ambipolar diffusion length”: Lamb = 2(kT e )µτ R , (1) where µ is the mobility of the minority carrier (holes in n-type material), and τR is its recombination lifetime [1]. In crystalline silicon, the hole mobility of about 500 cm2/Vs and a recombination lifetime of about 100 microseconds yield a diffusion length of 500 µm. Many materials that are interesting for solar cells have much lower carrier mobilities, and much shorter recombination lifetimes, than are typical for crystalline silicon. Under the conditions present in solar cells, holes in hydrogenated amorphous silicon (a-Si:H) have drift mobilities more than 105 smaller than in c-Si, and recombination lifetimes about 102 smaller. The corresponding ambipolar diffusion lengths are around 0.1 µm. The absorber layers in a-Si:H can be several times thicker than this. The reason that this extra thickness is useful is that, for low-mobility solar cells, the space-charge layer near the junction of the cell also makes a significant contribution. In c-Si the space-charge layer is the depletion region, whose width is determined by the dopant density. In a-Si:H and in other lowmobility, highly insulating materials, the width of the space-charge layer LSC is determined directly by the carrier mobilities and the photocarrier generation rate G [2]. Holes drift so slowly in such materials that the space-charge from slowly drifting holes screens the built-in potential, thus limiting the width of the region from which holes can be collected. Denoting the limiting drift mobility as µp, the expression for the width of this region is [2]: 14
1 2 4 µ εε LSC = (∆V ) p 0 , eG where ∆V is the electrostatic potential dropped acros
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