Comparison of methods to determine bandgaps of ultrathin HfO2 films using spectroscopic ellipsometry

Abstract

With the replacement of SiO2 by high-k Hf-based dielectrics in complementary metal–oxide–semiconductor technology, the measurement of the high-k oxide bandgap is a high priority. Spectroscopic ellipsometry (SE) is one of the methods to measure the bandgap, but it is prone to ambiguity because there are several methods that can be used to extract a bandgap value. This paper describes seven methods of determining the bandgap of HfO2 using SE. Five of these methods are based on direct data inversion (point-by-point fitting) combined with a linear extrapolation, while two of the methods involve a dispersion model-based bandgap extraction. The authors performed all of these methods on a single set of data from a 40 Å HfO2 film, as well as on data from 20 and 30 Å HfO2 films. It was observed that the bandgap values for the 40 Å film vary by 0.69 eV. In comparing these methods, the reasons for this variation are discussed. The authors also observed that, for each of these methods, there was a trend of increasing bandgap with decreasing film thickness, which is attributed to quantum confinement. Finally, the authors observed a greater variation in bandgap values among the methods for the 40 Å films than among the methods for the 30 and 20 Å films. This is attributed to the larger tail in the extinction coefficient k curve for the 40 Å film.

Plasma-Assisted Atomic Layer Deposition of SrTiO3: Stoichiometry and Crystallinity Studied by Spectroscopic Ellipsometry

“…The bandgap value corresponds to the intercept value of this line with the horizontal axis. 37,38 This procedure for the determination of E g is illustrated in the inset of Figure 5b ) ratio for samples which were analyzed by RBS. The figure clearly shows that the film composition can also be estimated by probing the refractive index and/or the bandgap of the deposited film.…”

Oxide or carbide nanoparticles synthesized by laser ablation of a bulk Hf target in liquids and their structural, optical, and dielectric properties

“…The higher value for the band gap which is obtained for the nanoparticles synthesized using a lower energy as compared to the value for the band gap for the nanoparticles synthesized using a higher energy might be due to the quantum confinement effect because of the smaller median diameter of the nanoparticles (4.6 as compared to 5.3 nm, Fig. 1(e) and (f)), similarly to the case of hafnia thin films (2, 3 or 4 nm thickness) to which the increase of the band gap was attributed to the quantum confinement effect along the vertical direction [43] in analogy with quantum well heterostructures.…”

Perspective: Optical measurement of feature dimensions and shapes by scatterometry

“…Information such as the band gap predicted by each of these approaches will differ as discussed in Ref. 3. The formula for the imaginary part of the dielectric function for the Tauc-Lorentz model is presented in Eq.…”

“…The complex refractive index of hafnium dioxide changes with the crystalline form. 3 Other important examples are the complex refractive index of silicon and germanium and their alloys. 4 The complex refractive index of pseudomorphic Si x Ge 1x on Si is shown as a function of composition x in Fig.…”

“…There are now a number of examples of the impact of the film thickness on the dielectric function for materials that are used in integrated circuits. Examples include metal films, 3 semiconductor layers such as silicon 4 or germanium, and dielectric films. 5 Furthermore, the optical properties of materials such as the gate dielectric layer are a function of process conditions which alter the crystal phase and grain size.…”