Microscopic approach to reciprocity and photon recycling in ultrathin solar cells

The most promising and commercially viable route to solar cell efficiencies beyond the Shockley-Queisser limit is offered by tandem architectures featuring a combination of a high-efficiency silicon bottom and thin film top cells. Suitable candidate materials for the thin film components, such as III-V semiconductors [1], but also the more recent metal-halide perovskites [2], exhibit strong light absorption, with steep absorption edges, and have been shown to operate close to the radiative limit [3]. Together, these properties promote the appearance of photon recycling (PR) effects [4], like the enhancement of the open circuit voltage (V_OC) [5]. While for tandem applications, the subcell thickness can be kept in the sub-micron range, even thinner architectures have been proposed for light-weight, flexible and low-cost single junction applications, in conjunction with intricate lighttrapping schemes [6]. In these ultra-thin solar cells, absorption and emission of light depend on the applied bias voltage via the built-in field, as was predicted theoretically [7], and recently confirmed experimentally [8]. This dependence has important implications for the proper application of the reciprocity relations [9] as frequently used for the analysis of solar cells by means of luminescence experiments. Furthermore, wave optical simulations indicate maximum V_OC enhancement due to PR at absorber thicknesses below 100 nm [4].

A rigorous theoretical assessment of the optoelectronic reciprocity relations between absorption and emission in ultra-thin absorber solar cells can be obtained from simulations based on the non-equilibrium Green’s function (NEGF) framework [7]. The formalism considers electronic and optical modes in open systems under electronic and optical excitation (bias voltage and illumination) and provides electronic (scattering) rates and currents as well as optical rates (absorption, emission) and photon fluxes, which are evaluated consistently and on equal footing as derived directly from the NEGF. The approach lends itself to the consideration of photon-recycling effects since they arise naturally in such a coupled description. In contrast to predictions of V_OC enhancement from detailed balance [10] and optical modelling [11], we obtain dV_OC directly from the renormalized current-voltage characteristics, i.e., under consideration of both, optical cavity effects and the full transport problem including contact layers.

More details will be given at the NUSOD-20 conference.

Fig. 1. (a) Absorptance and front-side emission of a 100 nm GaAs p-i-n solar cell with a gold rear reflector, displaying the impacts of built-in field variation with applied voltage and of reabsorption [7]. (b) Current-voltage characteristics of a 50 nm GaAs p-i-n solar cell,with photon recycling (full symbols) and without PR (empty symbols). The additional generation from reabsorption results in a V_OC enhancement of about 10 mV. The peculiar shape of the curve around MPP is due to the bias dependence of the photocurrent. Inset: Schematic representation of the self-consistent opto-electronic NEGF formalism used to assess reciprocity and photon recycling. The coupling between electronic and optical degrees of freedom proceeds via the electron-hole polarization function and the electron-photon self-energy.

[1] S. Essig, C. Allebé, T. Remo, J. F. Geisz, M. A. Steiner, K. Horowitz, L. Barraud, J. S. Ward, M. Schnabel, A. Descoeudres, D. Young, M. Woodhouse, M. Despeisse, C. Ballif, and A. Tamboli, “Raising the one-sun conversion efficiency of III-V/Si solar cells to 32.8% for two junctions and 35.9% for three junctions,” Nat. Energy 2, 17144 (2017).

[2] Helmholtz Zentrum Berlin (HZB), press release, Jan. 2020.

[3] I. L. Braly, D. W. deQuilettes, L. M. Pazos-Outón, S. Burke, M. E. Ziffer, D. S. Ginger, and H. W. Hillhouse, “Hybrid perovskite films approaching the radiative limit with over 90% photoluminescence quantum efficiency“, Nat. Photonics 12, 355–361 (2018).

[4] T. Kirchartz, F. Staub, and U. Rau, “Impact of photon recycling on the open-circuit voltage of metal halide perovskite solar cells,” ACS Energy Lett. 1, 731–739, (2016).

[5] R. Brenes, M. Laitz, J. Jean, D. W. deQuilettes, and V. Bulović, “Benefit from photon recycling at the maximum-power point of state-of-the-art perovskite solar cells,” Phys. Rev. Applied, 12, 014017 (2019).

[6] H.-L. Chen, A. Cattoni, R. De L´epinau, A. W. Walker, O. Höhn, D. Lackner, G. Siefer, M. Faustini, N. Vandamme, J. Goffard, B. Behaghel, C. Dupuis, N. Bardou, F. Dimroth, and S. Collin, “A 19.9%-efficient ultrathin solar cell based on a 205-nm-thick GaAs absorber and a silver nanostructured back mirror,” Nat. Energy 4, 761–767 (2019).

[7] U. Aeberhard and U. Rau, “Microscopic perspective on photovoltaic reciprocity in ultrathin solar cells,” Phys. Rev. Lett. 118, 247702 (2017).

[8] M. van Eerden, J. van Gastel, G. Bauhuis, P. Mulder, E. Vlieg, and J.J. Schermer, ”Observation and Implications of the Franz-Keldysh Effect in Ultra-Thin GaAs Solar Cells”, Prog. Photovolt: Res. Appl. (2020) (published online).

[9] U. Rau, “Reciprocity relation between photovoltaic quantum efficiency and electroluminescent emission of solar cells,” Phys. Rev. B, 76, 085303 (2007).

[10] U. Rau, U. W. Paetzold, and T. Kirchartz, “Thermodynamics of light management in photovoltaic devices,” Phys. Rev. B 90, 035211 (2014).

[11] S. Nanz, R. Schmager, M. G. Abebe, C. Willig, A. Wickberg, A. Abass, G. Gomard, M. Wegener, U. W. Paetzold, and C. Rockstuhl, “Photon recycling in nanopatterned perovskite thin-films for photovoltaic applications,” APL Photonics 4, 076104 (2019).