Quantification of Light Trapping Using a Reciprocity Between Electroluminescent Emission and Photovoltaic Action in a So
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Quantification of Light Trapping Using a Reciprocity Between Electroluminescent Emission and Photovoltaic Action in a Solar Cell Thomas Kirchartz1, Anke Helbig2, and Uwe Rau1 1 IEF5 Photovoltaik, Forschungszentrum Jülich, Leo Brandt Str., Jülich, 52425, Germany 2 Institut für Physikalische Elektronik, Universität Stuttgart, Stuttgart, 70569, Germany
ABSTRACT Spatially and spectrally resolved electroluminescence (EL) measurements are powerful methods to characterize solar cells, if the EL is properly interpreted. The task of interpreting the results and modeling the spectral and absolute EL emission is strongly simplified by considering the link between EL and quantum efficiency. Using this connection, we show how to quantify the influence of light trapping on the solar cell absorptance using EL. INTRODUCTION Luminescence imaging has become a valuable tool for solar cell characterization due to the short measurement time and its sensitivity to various detrimental effects like shunts, increased resistances and recombination. If excess carriers are created optically, i.e. we detect photoluminescence (PL) [1], the measurement is contactless and applicable at all steps in the production process. Electroluminescence (EL) [2], in contrast, needs already completed solar cells, modules or even systems, where a current is applied. The necessary equipment only consists of a Si CCD camera and a current supply, capable of delivering current densities comparable with the short circuit current. The detected luminescence image clearly reveals the regions on the device being most detrimental to the total performance. However, since luminescence imaging contains information about optical, electronic and resistive effects all intermixed, it is rather difficult to undoubtedly find the reasons for the quenched luminescence. Thus, interpretation and modeling of electroluminescence is a crucial prerequisite for the successful application of luminescence imaging. Recently it was both theoretically proven [3] as well as experimentally shown [4,5] that EL measurements are closely related to important solar cell parameters like quantum efficiency and internal voltage. As long as the differential equation for minority carrier transport is linear, the excess photon flux φEL ( E ) emitted by a solar cell with the quantum efficiency Qe(E) under internal voltage bias V follows the reciprocity relation ⎡
⎤ ⎛ qV ⎞ ⎟ − 1⎥ , ⎝ kT ⎠ ⎦
φEL (V , E ) = Qe ( E )φbb ( E ) ⎢exp⎜ ⎣
(1)
where kT / q is the thermal voltage and φ bb ( E ) ≈ 2πE 2 h 3 c 2 exp{− E kT } is the spectral photon density of a black body. Equation (1) explains how recombination, optics and resistive effects affect the EL spectrum as well as the spatially resolved EL image obtained by a CCD camera. The present paper shows how Eq. (1) improves the interpretation of spectral and spatial EL.
Apart from recombinatorial [6] and resistive [7,8] effects on the EL, which are well known in literature, we focus especially on the optics and the detection of the quality of a lig
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