Dielectric constant versus Frequency

With an alternating current (AC) field, the dielectric constant is virtually independent of frequency, so long as one of the multiple polarization mechanisms usually present is active (see Section 8.8.1). When the dominating polarization mechanism ceases as the frequency of the applied field increases, there is an abmpt drop in the dielectric constant of the material before another mechanism begins to dominate. This gives rise to a characteristic stepwise appearance in the dielectric constant versus frequency curve. For each of the different polarization mechanisms, some minimum dipole reorientation time is required for reahgnment as the AC held reverses polarity. The reciprocal of this time is referred to as the relaxation frequency. If this frequency is exceeded, that mechanism wUl not contribute to the dielectric constant. This absorption of electrical energy by materials subjected to an AC electric held is called dielectric loss. 

Figure 7 Calculated frequency dependence of the real part of the dielectric constant versus frequency for an array of quantum dots connected by one-dimensional wires (from Ref. 57). The inset presents the measured frequency dependent dielectric constant for four different samples of HCSA doped polyaniline of differing conductivities (from Refs 44...

FIGURE 16.6 Dielectric constant versus frequency of PS and the composites... 

FIGURE 15.11 Dielectric constant versus frequency for neat UPE and its composites reinforced with raw and mercerized Cannabis indica fibers. 

FIGURE 13.2 Dielectric constants versus frequency of various PCB materials. 

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

Fig. 4.2. Imaginary part e" of the complex dielectric constant versus real part with frequency as a parameter (Cole-Cole plot) at different temperatures. Arrows indicate the frequency of 10 Hz in each case. Insert shows thermal activation energy plot. (See Text)...

Aromatic polyimides have found extensive use in electronic packaging due to their high thermal stability, low dielectric constant, and high electrical resistivity. Polyimides have been used as passivation coatings, (1) interlayer dielectrics, (2) die attach adhesives, (3) flexible circuitry substrates, (4) and more recently as the interlevel dielectric in high speed IC interconnections. (5) High speed applications require materials with a combination of low dielectric constant, flat dielectric response versus frequency and low water absorption. 

Measurement of the temperature dependence of the dielectric constant is an important characterization for a ferroelectric material. As mentioned in the introduction section, when a phase transition occurs in a ferroelectric material, the dielectric constant always behaves anomalously. In general, the real part ofthe dielectric constant, e, shows a maximum at the phase transition temperature, where a change from a ferroelectric phase to the paraelectric one (or vice versa) occurs the value of e being higher than that at room temperature usually by 3 orders of magnitude. Figure 22-6 shows how the dielectric constant of barium titanate changes with temperature. At temperatures above the transition temperature, the variation ofthe dielectric constant (at low frequency) as a function of temperature obeys the Curie-Weiss law (see equation (22-2)). Usually, the peak ofthe dielectric constant versus temperature curve determines the Curie point F, and the Curie-Weiss constant C is determined by the slope ofthe curve of(e ) versus T. 

Here e , is the high frequ y limit of s, So is the static dielectric constant (low frequency limit of s ). So - Soo = A is the dielectric increment, fR is the relaxation frequency, a is the Cole-Cole distribution parameter, and P is the asymmetry parameter. The relaxation frequency is related to the relaxation time by fa = (27It) A simple exponential decay of P (oc,P = 0) is characterised by a single relaxation time (Debye-process [1]), P = 0 and 1 < a < 0 describe a Cole-Cole-relaxation [2] with a symmetrical distribution function of t whereas the Havriliak-Negami equation (EQN (4)) is used for an asymmetric distribution of x [3]. The symmetry can be readily seen by plotting s versus s" as the so-called Cole-Cole plot [4-6]. 

High frequency capacitance versus voltage measurements showed that for both oxide thicknesses there was a 10A thickness increase at the highest implantation dose (1016/cm2). Since this can be caused by either a real thickness increase or by a decrease in dielectric constant, the actual thickness was verified using ellipsometry. The result was that there was a real thickness increase. More than a 200mV threshold voltage shift was observed ... 

Figure 1 Dielectric constant and dissipation factor versus temperature at different frequencies in a PbO-MgO-NbaOs composition. (From Ref. 13.)...

The typical three-dimensional plot of the imaginary (e") part of the complex dielectric function, e (co) = e - it", versus frequency and temperature is displayed in Figure 2.17 for the PPX composite film with 8 vol. % of Cu. The complex dielectric behavior of the dielectric losses can be described in terms of several distributed relaxation processes with some common features for all the samples. The e"(/, T) cuts at a constant frequency plane (IkHz) for pure... 

Figure 12.31 Dielectric constant (at a frequency of 8-10 GHz) versus temperature for some ceramics. (From Ref. 42.)...

In addition to an examination of the frequency response of series and parallel components of the circuit impedance/admittance, another approach may be particularly valuable. This analysis method involves plotting the real versus imaginary parts of some such complex quantity as admittance or impedance as parametric functions of frequency. Such Argand or "circle diagrams" have been used for many years in electrical engineering when complex dielectric constant is the quantity considered, they are known as Cole-Cole plots. ... 

Blends of epoxy resins with other types of resins have also been developed. These are used when performance demands exceed the capabilities of even the high-Tg/Td epoxies, but where the costs of the highest performance materials cannot be justified. In many cases, the driving force behind these materials is the need for improved electrical properties versus the standard epoxy offerings. Specifically, improvements in the dielectric constant (permittivity) and dissipation factor (loss tangent) are the properties of interest. Materials with lower values for these properties are needed for circuits that operate at high frequencies. 

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