Measurement Technique of Ellipsometry

Abstract

Ellipsometry is an optical measurement technique that involves generating a light beam in a known polarization state and reflecting it from a sample having a planar surface. By measuring the polarization state of the specularly reflected beam, the ellipsometry angles (ψ, Δ) can be determined. These angles are specific to the wavelength λ₀ of the light beam and the angle of incidence θ_i of the beam at the sample surface. Upon detailed analysis, the angles (ψ, Δ), along with the associated known values of λ₀ and θ_i, yield information on the sample. Such information for a bulk sample includes the optical properties, i.e. the index of refraction n and the extinction coefficient k, which depend on the wavelength λ₀. Information deduced for samples consisting one or more thin films having plane-parallel surface/interfaces includes the layer thicknesses d and (n, k) of the components. Considering samples that are isotropic, which describe most structures of interest in photovoltaics applications, (ψ, Δ) are defined by tan ψ exp(iΔ) = r_p/r_s, where r_p and r_s are the complex amplitude reflection coefficients for linear p and s-polarization states. For these states, the electric field vibrates parallel (p) and perpendicular (s) to the plane of incidence, defined by the incident and reflected beam propagation directions. Several variations of the ellipsometry experiment have been developed with the goals to obtain a large set of (ψ, Δ) pairs that facilitates data interpretation and to extract as much information as possible on the sample. In spectroscopic ellipsometry , (ψ, Δ) are measured continuously versus the wavelength of the light beam, and in real time ellipsometry , (ψ, Δ) are measured versus time at fixed λ₀. The latter two modes can be integrated to yield real time spectroscopic ellipsometry , utilizing an instrument with a linear detector array for high speed data acquisition in parallel for a continuous distribution of wavelengths. In expanded beam imaging spectroscopic ellipsometry , (ψ, Δ) are measured along a line on the surface of the sample using an instrument with a two-dimensional detector array. One array index is used for the line imaging function and the second array index is used for spectroscopy. Two-dimensional spectroscopic mapping is possible by translating the sample. In general, the most widely used ellipsometers for photovoltaics applications are spectroscopic and span the range from the ultraviolet to the near-infrared (200–2000 nm). Over this spectral range, the (n, k) spectra deduced from spectroscopic ellipsometry provide information on the processes of absorption and dispersion originating from the valence electrons in semiconductors and dielectrics and from the conduction electrons in transparent conducting oxides and metals . Spectroscopic ellipsometry is of great interest in photovoltaics research and development due to its ability to extract {d, (n, k)} information for the multiple layers of the solar cell and (n, k) for the bulk materials, e.g. wafers or substrates. Once this information has been established for the solar cell, it becomes possible to simulate the external quantum efficiency of the device as well as the optical losses due to reflection, absorption in inactive layers, and transmission (if any). Comparisons of simulation and measurements give insights into electronic losses in active layers via recombination.