1. When defects are present in a semiconductor, intermediate energy levels are formed allowing carriers to “step” down to lower energy levels and recombine by releasing heat. This energy is lost so defect related recombination reduces the efficiency of photovoltaic cells. In the complex model we allow for differing defect and band occupation densities and calculate the recombination as Where: A τ = 1 / defect capture time (1/τ ) B = radiative constant dN = number of electrons in the conduction band dP = number of holes in the valence band dDn = number of trapped electrons dDp= number of trapped holes Occupation densities and recombination rates depend on the defect-related density of states function, which is generated using Adam Topaz’s fitter program.* This recombination model does a much better job of modeling the experimental data as shown left. * A. Topaz (Davidson '08), B.A. West (Davidson '08), T.H. Gfroerer, and M.W. Wanlass, Applied Physics Letters 90, 092110 (2007). In the simple model we assume that all defect states are located near the middle of the bandgap so we can neglect thermal excitation of carriers into bands. In this case: Where: dN = number of electrons in the conduction band dP = number of holes in the valence band n = total number of excited electrons or holes We calculated the recombination rate as follows Where: A = defect-related constant B = radiative constant This model does not seem to produce very good results with constant A values (which must be the case in a real physical system). Defect-related recombination and free-carrier diffusion near an isolated defect in GaAs Mark Crowley and Tim Gfroerer, Davidson College, Davidson, NC Mark Wanlass, National Renewable Energy Lab, Golden, CO Conduction Band Valence Band ENERGY Defect Level HEAT + - Conduction Band Valence Band LIGHT + - Defect-related Recombination Radiative Recombination Motivation Diffusion D - x y D - - + d + - - - + D d Low-excitation DefectElectronHole High-excitation + + + y x Electrons and holes (carriers) can diffuse before recombining. At lower excitation, fewer carriers are present and therefore it takes longer for them to pair up and recombine. This extended lifetime allows more time for a carrier to encounter a defect. At higher excitation, more carriers are present and individual carriers are more likely to find a partner for radiative recombination before reaching the defect. Abstract We model the defect as an isolated central pixel with a greater defect-related recombination rate. In each time step, we compute the change in the carrier density in each pixel in the following way: Time Evolution Algorithm Where: We use Laplacian diffusion to determine the flux between adjacent pixel. We end the simulation when a steady-state carrier distribution is obtained. (Depend on the model) Simple Recombination Model Conclusions Even in high quality solar cells, defects produce “dead spots” where defect-related recombination is high. These defects act as sinks, drawing in nearby charge carriers by diffusion. Due to the low population and long lifetime of carriers at lower laser intensities, more distant carriers diffuse to the defect, producing a larger dead volume relative to higher laser intensities. When modeling these defects, if we use a simple model that does not account for the occupation of defect and band states separately, we are unable to reproduce the experimental images. When state occupations are computed independently, the model produces much better images. Depletion in Solar Cells When defects are present in semiconductors, localized energy levels appear within the bandgap. These new electronic states accommodate heat-generating recombination – a problematic energy loss mechanism in many semiconductor devices. But at high excitation, the density of electrons and holes is higher, so they encounter each other more frequently. Early encounters augment light-emitting recombination, reducing the average lifetime and diffusion distance so the carriers are less likely to reach defects. In images of the light emitted by GaAs, we observe isolated dark regions (defects) where the darkened area decreases substantially with increasing excitation. When we model the behavior with a simulation that allows for lifetime- limited diffusion and defect-related recombination only through mid-bandgap energy levels, we do not obtain good agreement between the experimental and simulated images. A more sophisticated model which allows for an arbitrary distribution of defect levels within the bandgap produces results that are more consistent with experimental images. New Images To Reduce Error In order to try to reduce error further, we have obtained new, more carefully taken images of a defect in the same material. Although the modeling process has not been completed, the figures below show how the complex recombination model fits the radiative efficiency measurements better than the simple model. Complex Recombination Model Defect-related dead volume Absorption Layer ~ 2  m Carrier diffusion creates depleted (or dead) regions near defects in solar cells. At high excitation (above), the depletion region is small and many carriers can be extracted for electricity. At lower excitation (below) the depletion region of the defect grows and carriers close to the defect will be lost to defect-related recombination. ~ 2 nm Absorption Layer ~ 2  m Defect Pixel Non-Defect Pixels 1.0.66.9.6.3.2.75.5.001W T =296K.01W T =296K 1W T =296K.1W T =296K 1.0.66.75.5.9.6.3.2 1W T =296K.1W T =296K.01W T =296K.001W T =296K 100 μm Complex Model Images Experimental ImagesSimple Model Images Acknowledgement: We thank Jeff Carapella for growing the test structures and the Donors of the American Chemical Society – Petroleum Research Fund for supporting this work.