Light trapping with particle plasmons Kylie Catchpole 1,2, Fiona Beck 2 and Albert Polman 1 1 Center for Nanophotonics, FOM Institute AMOLF Amsterdam, The Netherlands 2 Australian National University Canberra, Australia

Poor absorption below the bandgap solar spectrum Si solar cell EgEg Indirect bandgap Semiconductor (Si): poor absorption just below the bandgap  thick cell required

Solution: light trapping Goal: Increased efficiency (IR response) and/or Reduced thickness (=cost) f subs f f air

Plasmon-enhanced photocurrent: 5 examples Nakayama et al., APL 93, (2008) GaAs Stuart and Hall, APL 69, 2327 (1996) SOI Derkacs et al., APL 89, (2006) a-Si Si SOI Pillai et al., JAP 101, (2007) Schaadt et al., APL 86, (2005) Si

Plasmon-enhanced photocurrent: 5 examples Nakayama et al., APL 93, (2008) GaAs Stuart and Hall, APL 69, 2327 (1996) SOI Derkacs et al., APL 89, (2006) a-Si Si SOI Pillai et al., JAP 101, (2007) Schaadt et al., APL 86, (2005) Si What are the physical principles and limitations

Light scattering E p  p p Rayleigh scattering from point dipole Scattering from point dipole above a substrate Preferential scattering into high-index substrate See, e.g.: J. Mertz, JOSA-B 17, 1906 (2000) 4 % 96 %

(a) (b) Absorption ~ r 3 Scattering ~ r 6 Metal nanoparticle scattering Scattering vs Ohmic losses Albedo  1 for D > 100 nm Ag Resonant scattering Plasmon resonance:  = -2 m () Albedo

Metal nanoparticle scattering Cross section > 1 All light captured and scattered into substrate (=AR coating)

Resonance tunable by dielectric environment Ag, D=100 nm Si 3 N 4 (n=2.00) Si (n=3.5) D Q D Q O H Optics Express (2008), in press

From point dipole to particle plasmon Fraction scattered into substrate highest for cylinder & hemisphere: Strongest near-field coupling Tradeoff: larger size  larger albedo but lower coupling 96 % 0 FDTD calculations Appl. Phys. Lett. 93, (2008)

Maximum path length enhancement Highest path length enhancement for cylinder and hemisphere Geometric series f subs f f air Appl. Phys. Lett. 93, (2008) Fraction scattered into substrate Path length enhancement 30 x (A=0.95) (A=0.90)

Scattering cross-section with dielectric spacer σ scat normalized to particle area Larger spacing: Interference in driving field But: lower coupling fraction (+ local density of states variation modifies albedo) 30 nm 10 nm D Q Appl. Phys. Lett. 93, (2008) tot sub

Thermal SiO 2 d ave = 135 nm f = 26% n=1.46 Ag nanoparticle formation on SiO 2 /Si 3 N 4 /TiO 2 on Si LPCVD Si 3 N 4 d ave = 220 nm f = 28% n=2.00 APCVD TiO 2 d ave = 215 nm f = 30% n=2.50 Thermal evaporation of 14 nm Ag °C anneal

c-Si 100 μm Integrating sphere 30 nm SiO 2 Si 3 N 4 TiO 2 Optical absorption (1-R-T) in Si wafers Si 3 N 4 TiO 2 SiO 2 Si 3 N 4 TiO 2 SiO 2 Ref. Strongly enhanced near-IR absorption egineered by dielectric spacer AR effect, interference for shorter wavelength + redshift

Photocurrent, external quantum efficiency Red-shifted EQE enhancement with refractive index of underlying dielectric Decrease at short wavelength due to phase shift Small increase at long wavelength for TiO 2 Si 3 N 4 TiO 2 SiO 2 front back

Relative photocurrent, EQE enhancement Si 3 N 4 TiO 2 SiO 2 Si 3 N 4 TiO 2 SiO 2 front back TiO 2 coated Si: EQE enhancement 2.7 fold at λ = 1050 nm Note: particle size and distribution are not optimized

Design principles for plasmon-enhanced solar cells 1) Metal nanoparticles  scat > 1 2) Coverage ~ % required 3) D>100 nm  albedo > 0.95 i.e. Ohmic losses < 5% 4) Angular distribution (=path length) increased 5) Coupling fraction f = 0.96 for point dipole 6) f reduces for larger particle size 7)  scat increases with spacer thickness 8) f decreases with spacer thickness Design parameter optimization Include: inter-particle coupling

Appl. Phys. Lett. 93, (2008) For details/references visit: VACANCIES in nano-photovoltaics see:

Flexible rubber on thin glass Conform to substrate bow and roughness No stamp damage due to particles PDMS Stamp Thin glass PDMS stamp (6”) on 200 µm AF- 45 glass 1  m Full-wafer soft nano-imprint Marc Verschuuren, Hans van Sprang Spring MRS 2007, 1002-N03-05 Substrate Conformal Imprint Lithography

Angular dependence of scattered light Increased power around critical angle for dipole compared to isotropic Lambertian less oblique path f air W d av Dipole d av ~1.5 Lambertian d av =2 K.R Catchpole and A. Polman, APL (2008)

Tadeoff between cross section and incoupling Optics Express (2008), in press Point dipole