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We present Ag-free low-concentrator bifacial indium-fluorine-oxide (IFO)/(n+pp+)Cz-Si/indium-tin-oxide (ITO) solar cells based on: (i) a shallow phosphorus-doped n+-emitter; (ii) an easy-to-fabricate screen-printed Al-alloyed Al-p+ back-surface-field (BSF); (iii) transparent conductive IFO and ITO layers grown by ultrasonic spray pyrolysis, which act as passivating and antireflection electrode; (iv) Ag-free multi-wire metallization of copper wire attached by the low-temperature lamination method simultaneously to the front IFO layer, rear ITO layer as well as to the interconnecting ribbons arranged outside the structure using transparent conductive polymer films. For the manufacture of solar cells, we used standard commercially available SiNx/(n+pp+)Cz-Si/Al structures. After removal of the residual Al paste, the Al-p+ layer was thinned by one-sided etchback process. A number of solar cells were prepared differing in the sheet resistance of the Al-p+ layer (Rp+), which ranged from 14 Ω/sq (original, non-etched Al-p+ layer) to 123 Ω/sq. It was found that thinning of the Al-p+ layer (increase in Rp+) greatly improved all the parameters of solar cells. The cell with Rp+ = 81 Ω/sq showed the best combination of conversion parameters. Under 1-sun front/rear illumination, the conversion efficiency of this cell is 17.5%/11.2% (against 16.0%/7.5% for the cell with Rp+ = 14 Ω/sq). At 1-sun front illumination and 20/50% albedo of 1-sun illumination, the equivalent efficiency is equal to 19.9%/23.5% (against 17.7%/20.1% for the cell with Rp+ = 14 Ω/sq). At a sunlight concentration ratio (kC) of 2.3–2.7 suns, the cells with Rp+ in the range 45–123 Ω/sq showed approximately similar maximum front-side efficiency, 17.5–17.9%. However, the operating range of sunlight concentration ratio (kC,OR) determined as η(kC,OR) = η(kC = 1) showed a tendency to decrease from 5.8 ± 0.6 suns to 4 ± 0.5 suns with an increase in Rp+ from 14–45 Ω/sq to 63–123 Ω/sq.