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High-k Dielectric Materials: Structural Properties and Selection
Published in Niladri Pratap Maity, Reshmi Maity, Srimanta Baishya, High-K Gate Dielectric Materials, 2020
P. Sri Harsha, K. Venkata Saravanan, V. Madhurima
High-k dielectrics are materials in which no steady current can flow through (Landau et al., 2013) as a result of which the static electric field in not zero as is the case in conductors. Dielectrics can be summarized as insulators that can be polarized by the application of electric field. The relationship between relative permittivity εr (generally k) and electric polarizability, P, is expressed by Clausius–Mossotti relation (eq 3.1): ε−1ε+2=13ε0ΣNjαj where Nj is the concentration and αj is the polarizability of the atom j, which is the sum of electronic, vibrational, and orientation polarization (Kittel, 2005). Ionic and inter-facial polarization are not accounted by Clausius–Mossotti relation, so in a sense it is important to understand polarization so as to understand dielectric constant since polarization is more universal in nature (Zhu, 2014).
Absorption and Scattering by Particles and Agglomerates
Published in John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel, Thermal Radiation Heat Transfer, 2020
John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel
DDA algorithms consist of expressing the external field around an agglomerate or irregularly shaped object in terms of an integral equation. The equation contains an internal field term that is unknown, which is represented at each point as a sum of the incident field and the field induced by all other interior points. Once the internal field is obtained, the external field is calculated with the help of the integral equation. In the model, the response of each dipole to the incoming electromagnetic field is represented by its complex polarizability α, which is given by the Clausius–Mossotti relation (Bohren and Huffman 1983, Jackson 1989, Draine 1998): αCM=3Nε¯(ri)−1ε¯(ri)+2
Coating of Glass Microspheres
Published in Giancarlo C. Righini, Glass Micro- and Nanospheres, 2019
Davor Ristić, Mile Ivanda, Maurizio Ferrari, Andrea Chiappini, Giancarlo C. Righini
where α is the linear thermal expansion coefficient, N is the refractive index of the material, and ρ is the density of the material. The first summand in Eq. (4.6) describes the change in the refractive index of a given material caused by its thermal expansion, whereas the second one is the temperature-induced change in the refractive index under constant density. Usually, the second part of the equation is much smaller than the first one, the bulk of the change of the refractive index being caused by the thermal expansion [38, 39]. The effect of the thermal expansion on the thermo-optic coefficient is usually determined by two different physical mechanisms. First, since the dielectric constant of a given material is proportional to the material density, the decrease in material density due to the thermal expansion causes the refractive index to decrease. Second, the thermal expansion causes change in the lattice parameter of the material, which in turn affects the position of the molecular and/or collective resonances. A general description of the thermooptic coefficient can be derived if we describe the refractive index behavior by the Sellmeier equation and the Clausius–Mossotti relation: () N2−1N2+2=ρCE02−E2
Vacancy Tuning in Li,V-Substituted Lyonsites
Published in Solvent Extraction and Ion Exchange, 2020
Joseph N. Tang, Dillon M. Crook, Geneva Laurita, M. A. Subramanian
Dielectric constants were measured for the x = 0 and x = 2 members, as they have not been reported. The relative permittivity for the x = 0 compound exhibits both temperature and frequency dependence, increasing with both parameters as expected (Figure 14). This compound is also very lossy, with high loss tangent values. At room temperature, κ is frequency-independent, and the experimental data correlate well to the polarizability values obtained from the Clausius-Mossotti relation,[73,74] with κth = 9.47 at 1 MHz, and κexp = 10.04. It must be noted that there is no established literature value for the atomic polarizability of Mo, and as such, it had to be approximated as 4.00, neighboring the Nb value of 3.97. The x = 2 compound exhibited little temperature and frequency dependence, and displayed high loss values, which hints at a conduction mechanism (Figure 15). This sample also corresponds to a Li-rich compound, and the high loss could be due to ionic conduction along the A3 site as mentioned.[31,55–57] However, the lack of vacancies would prevent this pathway; it is more likely that the conduction pathway is three-dimensional, reversibly changing the entire host structure as the Li ions move through interstitial spaces. The room temperature experimental permittivity (6.24 at 1 MHz) also agrees well with the polarizability obtained from the Clausius-Mossotti relation (9.25 at 1 MHz).
Multipole resonances-mediated dual-band tunable circular dichroism via vanadium dioxide chiral metamaterials
Published in Waves in Random and Complex Media, 2023
Shi Li, Tian Sang, Chaoyu Yang, Chui Pian, Yueke Wang, Bolun Hu, Cheng Liu
By using the Clausius-Mossotti relation, we can replace the polarizability by the dielectric constant to achieve the permittivity εi of VO2 for different f: where εm is the permittivity of the metallic state of VO2, and εd is the permittivity of the dielectric state of VO2.
Investigations on structure, dielectric and ferroelectric properties of SrBi2Ta2O9 ceramic via A-site defect engineering
Published in Phase Transitions, 2022
G. K. Sahu, S. Behera, S. R. Mishra
The dielectric permittivity (ϵr) of these materials varies with temperature (Figure 3(a–f)) at selected frequencies in a similar behavior of other Bismuth layered structure ferroelectrics [17–20] The reduction in both dielectric constant and ferroelectric phase transition with the increase of concentration of dopant cations is an indication of the development of ionic bond (Y–O) from covalent bond (Bi–O) in the Bi2O2 layer [21] Additionally, the lowering of both the dielectric parameters (ϵr and Tc) is explained in terms of reduction of TaO6 octahedron distortion of SBT ceramics. The unit cell dimension and lattice deviation of the parent SBT ceramic increase because of the incorporation of the cation Y3+ having a larger covalent radius as compared to Bi3+. The lone pair of 6s2 electrons present in Bi3+ ion actively participate in the induction of dipole moment (polarization) in the perovskite layers of SBT structure as compared to bonded electron pairs. Consequently, the absence of lone pair of electrons in the lanthanide cation (Y3+) reduces the net induced polarization and B site octahedral distortion. Again, according to Shannon [22], the room temperature polarizability for Bi3+ is more than Y3+. From Clausius–Mossotti relation, the lower polarizability will shift the Tm and Tc lower temperature site. Again, it is also stated that doping with a small cationic radius in A site of SBT ceramics creates more rattling space resulting in more dielectric constant with high transition temperature while the incorporation of large ionic radius results in a reverse effect [23,24] So, both the maximum dielectric constant (ϵm) and transition temperatures (Tc) fall down with increasing doping concentration. Lowering of maximum dielectric constant values with doping concentration has a significant effect on the improvement of remnant polarization in SBT-based ceramics useful for memory applications.