In-homogeneous luminescent coupling of multi-junction solar cell under non-uniform irradiation and temperature distribution

MULTI-JUNCTION solar cells offer a path to very high conversion efficiency, exceeding 60% in theory [1]. Luminescent coupling between multi-junction solar cell’s subcells is an important phenomenon typical for modern photovoltaic converters with high structural quality of semiconductor layers forming the cell [2]. A part of photo-generated electron-hole pairs in wider band gap material subcell will recombine and emit photons. Some fraction of these photos will be transmitted down into narrower band gap material subcell and be re-absorbed. This phenomenon is known as luminescent coupling. An extreme case of luminescent coupling arises if the reciprocity between absorption and emission is lifted, potentially using magneto-optical materials, which allows the efficiency of an infinite tandem stack to be raised to the Landsberg efficiency of 93.5% [3]. Luminescent coupling can compensate for the mismatch of short-circuit currents among subcells when the tandem’s current is limited by lower junctions. Moreover, it increases limiting subcells’ open circuit voltage and reduces wavelength sensitivity of the tandem [4]. But it can also hinder the precise measurement of tandem cell’s efficiency. Further, non-uniformity of luminescent coupling will reduce conversion efficiency of the limiting subcell in the tandem [5]. Therefore, the knowledge of luminescence coupling is essential for tandem solar cells. It is unavoidable in parameter measurement and optimization design of multi-junction solar cell..

Theoretical techniques to quantify luminescent coupling effect have been released. Detailed balance [6-8] and equivalent circuit [9-14] are the most lightweight method to model this effect. In recent years, Xia, et al [15] presents a comprehensive multi-junction detailed balance model that includes the effects of luminescent coupling, light trapping, and non-radiative recombination. In quasi-3D equivalent circuit modelling of solar cells, Jia, et al [16] firstly incorporates luminescent coupling. Very recently, Jeco-Espaldon, et al [17] proposes a quasi-3D model on account of in-homogeneous luminescent coupling caused by optical losses due to photon escape through the sides of the MJSC and electrical losses due to lateral resistance effects. Moreover, electrical passivation of triple-junction solar cells is done in [17] and both the homogeneity of current and absolute conversion efficiency of cell are improved. Strandberg [18, 19] introduces constants called transfer coefficients which can account for luminescent coupling in series-connected multi-junction solar cells. The use of transfer coefficients and Lambert-W function allow the relation between the voltage and current of the device to be expressed by a convenient closed-form expression. Luminescent coupling is dynamic equilibrium process where radiative recombination current in upper subcell and luminescent current in lower subcell are opposite and inter-conditioned. Thus, Micha, et al [20] proposes a self-consistent interactive model based on detailed balance approach to investigate the impact of luminescent coupling in multijunction solar cells. And Sogabe, et al [21] combines equivalent circuit formula with a self-consistent simulation algorithm to derive the coupling efficiency. On the other hand, techniques associated with Poisson-Diffusion-Drift [22-24] utilizes transfer matrix method to calculate the coupling matrix and the additional photo-generated carrier generation rate at each point due to luminescent coupling, and then incorporates them into PDD based simulation. Compare to detailed balance and equivalent circuit, technique of this type can provide higher accuracy but is much more time-consuming and memory-hogging. 2-D equivalent circuit or detailed balance model cannot deal with distributed parameters. Nonetheless, the practical luminescent coupling is always in-homogeneous, so this paper will employ quasi-3D equivalent circuit model. Furthermore, in order to simulate the solar cell with luminescent coupling under various working conditions, the quasi-3D model and its luminescent coupling mechanism are temperature dependent.

The rest of the paper is organized as follows. In Section 2, the phenomenon of homogeneous luminescent coupling is provided first, together with some discussions on the applying constrains and controlling method of luminescent coupling. The temperature dependent quasi-3D model of a GaInP/GaInAs Ge triple-junction solar cell is prepared in Section 3. And in Section 4, a comprehensive simulation results including in-homogeneous luminescent coupling currents and distribution of other electrical parameters are presented and analyzed. Section 5 concludes the paper.