Calculation of the position-dependent inner collection efficiency in PIN solar cells using an electrical–optical model U. Dutta a , P. Chatterjee a, * , P. Roca i Cabarrocas b , P. Chaudhuri a , R. Vanderhaghen b a Energy Research Unit, Indian Association for the Cultivation of Science, Kolkata 700 032, India b Laboratoire de Physique des Interfaces et des Couches Minces (UMR 7647 CNRS), Ecole Polytechnique, 91128 Palaiseau cedex, France Available online 9 April 2004 Abstract The position-dependent inner collection efficiency (PDICE) is defined as the probability for an electron–hole pair generated at a certain depth inside a solar cell to be collected. The quantum efficiency (QE) of a PIN solar cell yields the I-layer carrier collection probability as a function of the wavelength, whence only a crude idea of its position dependence can be obtained. Hence for optimizing carrier collection within the intrinsic layer, knowledge of its PDICE is also important. So far PDICE has been calculated by matrix inversion from external QE measurements, a procedure that leads to non-physical oscillations. In this report we determine PDICE in thin film solar cells using our electrical–optical model, which solves the Poisson’s equation and the continuity equations. Our method requires the simulation of a large number of experimental results, from which the parameters reproducing the char- acteristics of a given device are extracted. These parameters are then used to calculate PDICE. To the best of our knowledge this is the first time that such a model has been used to calculate PDICE. We next apply the method to calculate PDICE in PIN solar cells prepared under various conditions. Ó 2004 Elsevier B.V. All rights reserved. PACS: 85.30.De; 72.40.+w 1. Introduction The position-dependent inner carrier collection effi- ciency (PDICE – also designated as the dynamic inner collection efficiency or DICE), under given bias voltage and illumination conditions, is an important quantity to calculate. This is because it indicates at which positions inside the device carrier collection is weak, so that the problem maybe rectified. PDICE cannot be obtained directly from experiments and has to be extracted from measurable quantities. Takahama et al. [1] and Fischer [2] have calculated PDICE for amorphous silicon (a- Si:H) PIN solar cells using QE experiments. Electron beam-induced current (EBIC) technique at variable electron beam energy has also been used to calculate PDICE [3]. In these methods PDICE at ‘m’ grid points in the device, must be calculated using the measured QE’s at ‘n’ photon wavelengths or electron beam ener- gies, using matrix inversion. The problem is that gen- erally m  n, since in typical solar cells, under operating illumination conditions, the electric field is strongly position dependent. On the other hand, appreciable re- sponse from a-Si:H cells is obtained only over a rela- tively small wavelength range. We are thus led to oscillatory solutions [2,4]. In the present formalism, we simulate a large number of experimental characteristics of a given device, e.g. the J –V and QE data under various conditions of a solar cell, using our electrical–optical model (ASDMP) based on the solution of the Poisson’s and the continuity equations. The simulations are used to extract the parameters characterizing the cell (e.g. as given in Table 1), which are then used via the procedure described in Section 3, to calculate the PDICE profile under given bias illumination and voltage conditions. 2. Simulation model The one-dimensional electrical–optical model AS- DMP [5] (Amorphous Semiconductor Device Modeling * Corresponding author. Fax: +91-33 473 6612. E-mail address: parsathi_chatterjee@yahoo.co.in (P. Chatterjee). 0022-3093/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.03.066 Journal of Non-Crystalline Solids 338–340 (2004) 677–681 www.elsevier.com/locate/jnoncrysol