Dielectric function and spectrophotometry: from bulk to nanostructures

The world of group IV nanomaterials for applications in photovoltaics is vast and heterogeneous. It includes silicon and germanium quantum dots and nanowires and their combination; quantum wells, graphene, and carbon nanotubes. Silicon and germanium nanoparticles are candidates in tunable bandgap absorbers in third generation multijunction solar cells [1]; nanowires exhibit remarkable scattering, and are used to enhance the absorption well beyond the value of the corresponding bulk materials [2]; if fabricated in quantum dimensions, they combine tunable bandgap with electrical transport properties [3]; graphene sheets have been proposed as transparent-conducting material in organic photovoltaic devices [4]; Ge nanoparticles are used to enhance photocurrent in dye-sensitized solar cells [5]. The different materials cover different roles, have different experimental characteristics, and are treated in different ways. For materials of optical quality, spectroscopic ellipsometry (SE) and reflectance function (DF), detect features such as the crystallized fraction, or investigate the surface quality. SE can be applied to non-depolarizing materials, whereas R&T spectroscopy is the only option for depolarizing, highly scattering materials, such as nanowires or structured surfaces. In photovoltaics, the relevant spectral range is determined by the range of highest intensity of the solar spectrum; that is, photon energies from 0.8 to less that 4 eV, as can be seen in Fig.2.1 (yellow pattern), that is described in section 2.3.1. For bulk silicon, most of this region corresponds to the range of medium-low absorption (Fig.2.1). This region is best analyzed by R&T rather that SE, that is only moderately sensitive to low absorption. In contrast, in the opaque range where T=0 and R&T bears limited information, SE performs at best. SE detects the spectral shape of the DF around the crytical points, and gives a fundamental insight into the material. R&T spectroscopy is the best choice to determine the absorption edge of materials, the optical gap, and its direct or indirect character. R, T are parameters of direct interest for those devices whose performance is related to absorption or transparency. SE and R&T do not detect the sub-band gap absorption related to defect states. Knowledge of such parameter allows to gain an insight into material quality rather than being of interest in photovoltaic conversion, and will not be discussed in this text. This chapter is mainly focussed on R&T spectroscopy. Reviews on the state of the art of SE and polarimetry applied to the nanoscale can be found in [6], [7]. When speaking of nanoparticles applied to photovoltaics, an emerging topic is the application of metal nanoparticles for plasmon induced light trapping. This exciting topic is however out of the scope of this review.