12 Apr 2021

What properties of functional materials can we learn in the IR

Introduction to FTIR spectroscopy: what properties of functional materials can we learn in the IR

The interaction of light with matter is macroscopically described by a dielectric function according to Maxwell's equations. Analysis of the dispersion of the dielectric function constant enables the study of phenomena such as absorption by free charge carriers (1), excitation of lattice oscillations (2), polarization of atoms by displacement of the valence electrons (3), absorption by localized defect states (4), and interband transitions of the electrons (5) as shown in Fig. 1.

Fig.1. Schematic presentation of the dispersion of the real and imaginary parts of the dielectric function.

The dispersion of the dielectric constant is obtained by modelling experimental data recorded in reflection, transmission, or attenuated total reflectance (ATR). Spectra at various temperatures, for example, could be recorded using Specac’s High Temperature High Pressure cell.

Below we discuss some theoretical aspects of the optical properties which may be studied in this way.
In an ideal semiconductor there are no free charge carriers. They can be introduced by including defects and/or impurities in the crystal lattice. Phosphorus or boron can be introduced into silicon to achieve this effect. In the case of phosphorus, one excess electron per atom results in a band of donor levels that are located just below the edge of the conduction band and may have sufficient charge carriers to populate the conduction band with much lower thermal energies. With the introduction of boron impurities having one valence electron, there is also the appearance of a band of empty acceptor states slightly above the valence band. The population of these acceptor states is due to valence electrons. This makes electronic transitions possible between the valence band and the donor levels, between the acceptor and donor levels, and between the acceptor levels and the conduction band. The latter causes a strong absorption, forming a corresponding peak in the dispersion of the imaginary part of the dielectric constant in spectral regions remote from the band gap. This follows from the local shielding field that occurs when electrons are dense in n, and they are stimulated to move coherently, thus forming a plasma against the background of positive ions (or a hole plasma against the background of negative ions).
Free charge carriers react to incident electromagnetic fields with coherent oscillations, reflecting incident radiation. This phenomenon is defined by Drude's formalism in the form of:

where wp - plasma frequency, which is defined as w2p = ne2/ e0me (n - concentration of carriers, me - electron mass, e - electron charge), e - high-frequency dielectric constant, g is the attenuation coefficient of oscillations of free charge carriers.

The plasma frequency determines the upper limit of the incident radiation frequencies to which free carriers can respond, i.e. effectively shield it. At lower frequencies wp the real part of the permeability is negative, which indicates that the electromagnetic wave does not penetrate into the material. The attenuation coefficient g is determined by the scattering of free charge carriers by other electrons, defects, or phonons with the scattering time t = 1/g.
Under the action of an external electric field, the outer electrons of an atom or molecule are displaced against a positively charged nucleus, forming a dipole moment P, which is related to the field strength. The electron shell formed by valence electrons is displaced against the nucleus in time with the electromagnetic wave, but its energy is insufficient to release electrons into the conduction band. This contribution to the dielectric function is described by the high-frequency dielectric constant.
Increasing the energy of the quanta of electromagnetic radiation to a level sufficient for the transition of electrons to the excited state, leads to an increase in the absorption of electromagnetic radiation by matter. High absorption area (a > 104 cm−1) includes optical transitions between states in the valence band and the conduction band. Energy which corresponds to an absorption of 104 cm−1 determines the width of the optical band gap.
Application of FTIR spectroscopy in study of the properties of materials for energy saving windows

Zinc oxide (ZnO) has been attracting scientific interest for the last few decades. It is used in the fabrication of transparent electrodes for thin film solar cells, as well as touchscreens and liquid-crystal displays. The zinc oxide films used in industry are commonly doped with aluminum or nitrogen and belong to the family of transparent conducting oxides (TCO). This doping helps to obtain electrical conductivity, which is required in practical applications. The perfect combination of properties would include high transparency in the visible range with good electrical conductivity. Environmental protection and energy efficiency open another market for zinc oxide thin film, which can also be utilized in the fabrication of low-emissivity architectural glazing. The functionality of these energy saving windows arises from a combination of the high reflectivity in the IR region with transparency in the visible range.
Optical spectroscopy may be used to study the properties of heavily doped zinc oxide films at different temperatures. This is especially interesting from the practical point of view, as energy saving windows are supposed to work at temperature difference inside and outside the buildings.

Fig.2. Reflectance spectra of ZnO thin film as a function of temperature.

Reflectance spectra of a heavily doped 700 nm thick ZnO film, which was deposited onto a glass substrate, have been measured in the mid IR range at temperatures from 50K to 300K. In contrast to single crystals, the thin film is polycrystalline, so polarized radiation is not required in the experiments. As shown in Fig. 2, the plasma edge of the ZnO thin film is located above 5000 cm-1. This means that below this wavenumber the studied thin film is not transparent and reflects almost all IR radiation in this range. In addition, using the high-frequency dielectric constant of ZnO, e = 3.62, and the parameters of the contribution of free charge carriers to the dielectric constant, we can estimate the electrical conductivity of ZnO film at different temperatures. Due to the mobility of free charge carriers, doped ZnO thin film has high conductivity. At the same time, the charge carrier density is small enough that the material is largely transparent in the visible spectral range. The temperature dependence of the electrical conductivity is shown in Fig. 3, and is typical for doped semiconductors and metals.

Fig.3. Evolution of the electric conductivity of ZnO thin film at low temperatures.
Thus, the analysis of reflectance spectra based on the Drude model can be used for studying and evaluating both optical and electrical properties of functional materials.

Guest Article by Konstantin Shportko, Senior Research fellow at the V.E. Lashkaryov Institute for Semiconductor Physics of NAS of Ukraine