Near and Far Field Approaches to Light Enhancement in Intermediate  Band Solar Cells using Surface Plasmons and Diffracting Structures Manuel J. Mendes, Alex Mellor, Ignacio Tobías, Antonio Martí, Antonio Luque Instituto de Energía Solar, Universidad Politécnica de Madrid, E28040 Madrid, Spain

Background • The Intermediate Band Solar Cell (IBSC) can convert a greater portion of the solar spectrum into electrical energy than single‐gap cells due to the existence of an electronic band —the intermediate band (IB)— within the semiconductor bandgap. • This concept has a detailed balance efficiency limit of 63.2% compared to 40.7% for single‐gap cells1. • The Intermediate Band can be formed by the confined levels of a quantum dot (QD) array2; however the associated absorption coefficient is weak. • To increase absorption we propose two procedures which employ near and far field structures to amplify infrared light in the QDs array at the particular photon energies of the IBSC absorption bands. InAs dots

E1=1eV E2=0.3eV

GaAs matrix

Plasmonic Light Enhancement in the Near‐field of Metallic Nano‐Spheroids This alternative exploits the high near‐field in the vicinity of metal nanoparticles (MNPs) sustaining surface plasmons. The inclusion of these particles close to the QDs can amplify their absorption. The scattered field is computed using the electrostatic approach (EA) for particles which are small compared to the light’s wavelength3.

(a)

30 nm

(b)

InAs QDs in GaAs host

Left – (a) STEM image of a 10 QD layer stack, with 10nm thick GaAs spacer layers. (b) AFM image of InAs dots grown on the surface of GaAs.

mm

Far‐Field Diffracting Structures The energy density of light within the cell can be increased by illuminating oblique angle rays which have path lengths greater than those of acute rays and can be totally internally confined. This is currently achieved by the randomizing lambertian scheme; however our calculations show that, under common illumination conditions, the lambertian limit can be surpassed appreciably by a diffraction grating on the front or rear surface of the cell (see schematic)5.

Right ‐ Preferential position for inclusion of MNPs in the plane of the QDs (pyramids). MNP sizes in the range of 10‐100nm should behave adequately under EA. The absorption enhancement produced by an MNP is significant up to a distance of about its size.

Left ‐ Average path length of light rays as a function of normalised wavelength for a triangular diffraction grating with unit period (shown in inset). Surrounding phase diagrams show direction cosines of diffraction modes.

/w

Left ‐ Spheroid aspect ratios that maximize scattering for coated and uncoated Ag MNPs in GaAs medium. Metallic particles act as recombination centers causing current degradation, so they should be enclosed in a passivating coating.

Right ‐ Maximum absorption enhancement that can be felt by the QDs4 at the MNP surface, for spheroids shaped for 0.3 and 1eV ‐ the sub‐gap bands in InAs/GaAs QD‐IBSC. The curves for the 0.3eV case are multiplied by 10 for better visualization. The inset is a polar‐plot of the scattered potential at the uncoated MNP surface.

Right ‐ The maximum achievable average path length for an ideal grating as a function of the normalised illumination etendue. The thermodynamic limit and lambertian limit are also shown.

/w

l0[NORM]

uncoated with coating

Acknowledgements References [1] A. Luque and A. Martí, Phys. Rev. Lett. 78, No. 26, 5014–5017 (1997) [2] A. Luque, A. Martí, C. Stanley, N. López, L. Cuadra, D. Zhou and A. Mc-Kee, J. App. Phys. 96, 903–909 (2004) [3] M. J. Mendes, A. Luque, I. Tobías and A. Martí, App. Phys. Lett. 95, 1 (2009) [4] A. Luque, A. Marti, M. J. Mendes and I. Tobias, J. App. Phys. 104, 113118 (2008) [5] I. Tobias, A. Luque and A. Marti, J. of App. Phys. 104 (3), 034502 (2008)

This work was supported by the IBPOWER Grant 211640 of European Commission, the GENESIS FV grant CSD2006‐ 0004 of the Spanish program CONSOLIDER and NUMANCIA grant S‐0505/ENE/0310 of Comunidad de Madrid. M.J.Mendes acknowledges the Portuguese Government fellowship SFRH/BD/21669/2005 of FCT‐MCTES. A. Mellor acknowledges the Spanish studentship of the Personal Investigador de Apoyo (PIA) program of the Consejería de Educación of the Comunidad De Madrid.

For further information Please contact manuel.mendes@ies‐def.upm.es or alex.mellor@ies‐def.upm.es. More information on these and related projects can be obtained at www.ies.upm.es.