**1.2. Application of polymeric dielectric materials.**

Both dielectrics with low and high dielectric constant are essential in electronic industries. Low dielectric constant is required basically as insulators. They are known as passivation materials. Their applications ranged in isolating signal-carrying conductors from each other, fast signal propagation, interlayer dielectric to reduce the resistance-capacitance (RC) time delays, crosstalk and power dissipation in the high density and high speed integration [4]. They are of necessity in very dense multi-layered IC's, wherein coupling between very close metal lines need to be suppressed to prevent degradation in device performance. This role involve packaging and encapsulation. In electronic packaging, they separate interlayers and provide isolated pathways for electronic devices connection in multilayer printed circuit boards. As the trends are towards miniaturization in microprocessor fabrication, any decrease in relative permittivity will reduces the deleterious effect of stray and coupling capacitances. Dielectric naterials are also employed to encapsulate the balls which bridged the die and substrate. This encapsulation is specifically called underfill which helps to protect any circuitary failures as well as reducing thermal mismatch between the bridging layers.(Figure 1) In LED encapsulation low dielectric materials is used for insulation at the lead frame housing.

**Figure 1.** Application of dielectric polymers in IC packaging

As an active components, designing is geared towards high ε value and are used as polarizable media for capacitors, in apparatus used for the propagation or reflection of electromagnetic waves, and for a variety of artifacts, such as rectifiers and semiconductor devices, piezoelectric transducers, dielectric amplifiers, and memory elements. Despite being insulators, hence non-polar, these materials can be made polar by introducing small amount of impurities. In this state, the material is able to store large amount of charges at small applied electrical field. This is the case with polyvinylidene fluoride when introduced with impurities chlorotrifluoroethylene.[5] Indeed several works have been performed on polymers like polyimide with added Al2O3, BaTiO3 and ZrO3 'impurities' [6,7,8] which showed an improved dielectric constant. Once there is large charge storage, it can be readily released on demand. In a rectifier, a capacitor is used to smooth off the pulsating direct current.

### **2. Theory of dielectric properties in polymer**

4 Dielectric Material

lead frame housing.

materials generally have higher dielectric constant compared to polymeric materials. Intrinsically they contains ions and polar groups which contribute to their high dielectric

Materials Dielectric constant, ε Materials Dielectric constant, ε

constant. Air having a dielectric constant of 1.02 is taken as reference dielectric.

TiO2 100 Fluorinated polyimide 2.5 – 2.9 H2O 78 Methylsilsesquioxane 2.6 – 2.8 neoprene 9.8 Polyarelene ether 2.8 – 2.9 PVDF 6.0 Polyethylene 2.3 – 2.7 SiO2 3.9 – 4.5 Polystyrene 2.5 – 2.9 Fluorosilicate glass 3.2 – 4.0 Teflon AF 2.1 Polyimide 2.8 – 3.2 Air 1.02

**Table 1.** Dielectric constant of several polymers and inorganic materials. (Adapted from Ref 3)

Both dielectrics with low and high dielectric constant are essential in electronic industries. Low dielectric constant is required basically as insulators. They are known as passivation materials. Their applications ranged in isolating signal-carrying conductors from each other, fast signal propagation, interlayer dielectric to reduce the resistance-capacitance (RC) time delays, crosstalk and power dissipation in the high density and high speed integration [4]. They are of necessity in very dense multi-layered IC's, wherein coupling between very close metal lines need to be suppressed to prevent degradation in device performance. This role involve packaging and encapsulation. In electronic packaging, they separate interlayers and provide isolated pathways for electronic devices connection in multilayer printed circuit boards. As the trends are towards miniaturization in microprocessor fabrication, any decrease in relative permittivity will reduces the deleterious effect of stray and coupling capacitances. Dielectric naterials are also employed to encapsulate the balls which bridged the die and substrate. This encapsulation is specifically called underfill which helps to protect any circuitary failures as well as reducing thermal mismatch between the bridging layers.(Figure 1) In LED encapsulation low dielectric materials is used for insulation at the

**1.2. Application of polymeric dielectric materials.** 

**Figure 1.** Application of dielectric polymers in IC packaging

#### **2.1. Mechanism of interaction with electric field**

Quantitative treatment of a dielectric in an electric field can be summarized using Clausius– Mossotti equation (1).

$$\mathbf{P} = \frac{\varepsilon\_r - 1}{\varepsilon\_r + 2} \cdot \frac{M}{\rho} = \frac{N\_A \alpha}{3\varepsilon\_0} \tag{1}$$

P is the molar polarisability, ߝ is the relative permittivity, ߝ is the permittivity in vacuum, M is molecular weight of a repeat unit, ρ is density, ߙ is polarisability, *N*a is the Avogadro constant. This equation shows that dielectric constant is dependent on polarisability and free volume of the constituents element present in the materials. Polarisability refer to the proportionality constant for the formation of dipole under the influence of electric field. Thus its value is typical for each different type of atom or molecule.[9] The relation between polarizability with the permittivity of the dielectric material can be shown as in Equation (2):

$$
\varepsilon\_r = 1 + \frac{\mathcal{N}\alpha}{\varepsilon\_0} \tag{2}
$$

It shows that relative permittivityߝ is the ratio of total permittivity of one mole of material with that in vacuum. The dependency of free volume of relative permittivity thus originate from the volume involved in one mole of the material. Again the molar volume is characteristic of each different type of atom or molecule. Molar polarization therefore is obtained if the molar volume is introduced into these derivations leading to Clausius– Mossotti equation.

Physically, polarisability is induced when there is electric field applied onto the materials. In the absence of electric field, the electrons are distributed evenly around the nuclei.

#### 6 Dielectric Material

When the electric field is applied the electron cloud is displaced from the nuclei in the direction opposite to the applied field. This result in separation of positive and negative charges and the molecules behave like an electric dipole. There are three mode of polarizations [10]:

Polymeric Dielectric Materials 7

per unit volume. Replacement of hydrogen with fluorine result in lowering of dielectric constant since fluorine occupies higher volume. Thus beside being low polarisability, introduction of fluorine induce a significant decrease of dielectric constant through an

Polymers can be polar or non-polar. This feature affect significantly the dielectric properties. Examples of polar polymers include PMMA, PVC, PA (Nylon), PC while non-polar polymers include PTFE (and many other fluoropolymers), PE, PP and PS. Under alternating electric field, polar polymers require sometime to aligned the dipoles. At very low frequencies the dipoles have sufficient time to align with the field before it changes direction. At very high frequencies the dipoles do not have time to align before the field changes direction. At intermediate frequencies the dipoles move but have not completed their movement before the field changes direction and they must realign with the changed field. The electronic polarization and to some extent atomic polarization, is instantaneous weather at high or low frequency for both polar and non polar polymers. Therefore, polar polymers at low frequencies (eg 60 Hz) generally have dielectric constants of between 3 and 9 and at high frequencies (eg 100 Hz) generally have dielectric constants of between 3 and 5. For non-polar polymer the dielectric constant is independent of the alternating current frequency because the electron polarization is effectively instantaneous hence they always have dielectric constants of less than 3. The chain geometry determines whether a polymer is polar or non-polar. If the polymer is held in a fix confirmation, the resulting dipole will depend whether their dipole moments reinforce or cancell each other. In the case of extended configuration of PTFE, the high dipole moment of –CF2- units at each alternating carbon backbone cancelled each other since their vector are in opposite directions. Its dielectric constant therefore is low (2.1). On the other hand, PVC has its dipole moment directing parallel to each other resulting in reinforcement of dipole. Its dielectric constant is

increase in free volume.

**2.2. Effect of chain polarity** 

4.5. This is illustrated as in Figure 2.

**Figure 2.** PTFE (a) and PVC (b) with arrow showing the net dipole moment.

The designing of dielectric material so as to achived the desired dielectric properties should take careful consideration of net polarity of the structure. This has been exemplified by the opposite effect in indiscriminately subsitituting fluorine atom into a polyimide chain resulting in an increase in otherwise low dielectric constant material.[11] There is no dipole polarization contribution for non-polar polymers as found in polar polymers. This different


When a static electric field is applied on to these materials the dipoles become permanently polarized giving a dielectric constant as εstatic. However if the field changes as when alternating electric current is applied, polarization will also oscillate with the changing electric field. All three modes of polarization contributing to the overall dielectric constant will be dependent on the frequency of the oscillating electric field. Obviously the electronic polarization is instantaneous as it is able to follow in phase with the changing electric field compared to atomic polarization which in turn better able to follow the oscillating electric field compared to the orientational polarization. Certain structures and elements display a higher polarisibility than the others. Aromatic rings, sulphur, iodine and bromine are considered as highly polarisable. The present of these groups induced an increase in dielectric constant. The π bond in the aromatic rings is loosely attached compared to the sigma bond. Therefore it is easily polarized. For large size atoms like bromine and iodine, the electron cloud is so large and further apart from the influence of electrostatic attraction of the positive nucleus. It is expected to display a high polarisibility. This is as oppose to fluorine which has small atomic radius and concentrated negative charge. It is able to hold the electron cloud much tightly resulted in a low polarisability. This will induce a lower dielectric constant.

Free volume is also an important factor in determining the dielectric constant. Free volume is defined as the volume which is not occupied by the polymeric material. The free volume associated with one mole of repeat units of the polymer may be estimated by subtracting the occupied molar volume of a repeat unit, *V*o, from the total molar volume, M/ρ, where M is the molar mass of the repeat unit. [10] The fractional free volume *V*n is given by Equation (3):

$$V\_n = \frac{M \mid \rho - V\_0}{M \mid \rho} \tag{3}$$

The addition of pendant groups, flexible bridging units, and bulky groups which limit chain packing density have been utilised to enhance free volume. [21] The presence of free volume in the form of pores will similarly result in a decrease in dielectric constant as it being occupied by air whose relative permittivity is about one. A higher fractional free volume means that the density of the material will be lower resulting in a lower polarisible group

per unit volume. Replacement of hydrogen with fluorine result in lowering of dielectric constant since fluorine occupies higher volume. Thus beside being low polarisability, introduction of fluorine induce a significant decrease of dielectric constant through an increase in free volume.

## **2.2. Effect of chain polarity**

6 Dielectric Material

polarizations [10]:

dielectric constant.

given by Equation (3):

When the electric field is applied the electron cloud is displaced from the nuclei in the direction opposite to the applied field. This result in separation of positive and negative charges and the molecules behave like an electric dipole. There are three mode of

i. Electronic polarization – slight displacement of electrons with respect to the nucleus.

dipole to align by the electric field to give a net polarization in that direction

iii. Orientational polarization – For polar molecules, there is a tendency for permanent

When a static electric field is applied on to these materials the dipoles become permanently polarized giving a dielectric constant as εstatic. However if the field changes as when alternating electric current is applied, polarization will also oscillate with the changing electric field. All three modes of polarization contributing to the overall dielectric constant will be dependent on the frequency of the oscillating electric field. Obviously the electronic polarization is instantaneous as it is able to follow in phase with the changing electric field compared to atomic polarization which in turn better able to follow the oscillating electric field compared to the orientational polarization. Certain structures and elements display a higher polarisibility than the others. Aromatic rings, sulphur, iodine and bromine are considered as highly polarisable. The present of these groups induced an increase in dielectric constant. The π bond in the aromatic rings is loosely attached compared to the sigma bond. Therefore it is easily polarized. For large size atoms like bromine and iodine, the electron cloud is so large and further apart from the influence of electrostatic attraction of the positive nucleus. It is expected to display a high polarisibility. This is as oppose to fluorine which has small atomic radius and concentrated negative charge. It is able to hold the electron cloud much tightly resulted in a low polarisability. This will induce a lower

Free volume is also an important factor in determining the dielectric constant. Free volume is defined as the volume which is not occupied by the polymeric material. The free volume associated with one mole of repeat units of the polymer may be estimated by subtracting the occupied molar volume of a repeat unit, *V*o, from the total molar volume, M/ρ, where M is the molar mass of the repeat unit. [10] The fractional free volume *V*n is

<sup>0</sup> /

(3)

/ *<sup>n</sup> M V*

*M* 

The addition of pendant groups, flexible bridging units, and bulky groups which limit chain packing density have been utilised to enhance free volume. [21] The presence of free volume in the form of pores will similarly result in a decrease in dielectric constant as it being occupied by air whose relative permittivity is about one. A higher fractional free volume means that the density of the material will be lower resulting in a lower polarisible group

*V*

ii. Atomic polarization – distortion of atomic position in a molecule or lattice

Polymers can be polar or non-polar. This feature affect significantly the dielectric properties. Examples of polar polymers include PMMA, PVC, PA (Nylon), PC while non-polar polymers include PTFE (and many other fluoropolymers), PE, PP and PS. Under alternating electric field, polar polymers require sometime to aligned the dipoles. At very low frequencies the dipoles have sufficient time to align with the field before it changes direction. At very high frequencies the dipoles do not have time to align before the field changes direction. At intermediate frequencies the dipoles move but have not completed their movement before the field changes direction and they must realign with the changed field. The electronic polarization and to some extent atomic polarization, is instantaneous weather at high or low frequency for both polar and non polar polymers. Therefore, polar polymers at low frequencies (eg 60 Hz) generally have dielectric constants of between 3 and 9 and at high frequencies (eg 100 Hz) generally have dielectric constants of between 3 and 5. For non-polar polymer the dielectric constant is independent of the alternating current frequency because the electron polarization is effectively instantaneous hence they always have dielectric constants of less than 3. The chain geometry determines whether a polymer is polar or non-polar. If the polymer is held in a fix confirmation, the resulting dipole will depend whether their dipole moments reinforce or cancell each other. In the case of extended configuration of PTFE, the high dipole moment of –CF2- units at each alternating carbon backbone cancelled each other since their vector are in opposite directions. Its dielectric constant therefore is low (2.1). On the other hand, PVC has its dipole moment directing parallel to each other resulting in reinforcement of dipole. Its dielectric constant is 4.5. This is illustrated as in Figure 2.

**Figure 2.** PTFE (a) and PVC (b) with arrow showing the net dipole moment.

The designing of dielectric material so as to achived the desired dielectric properties should take careful consideration of net polarity of the structure. This has been exemplified by the opposite effect in indiscriminately subsitituting fluorine atom into a polyimide chain resulting in an increase in otherwise low dielectric constant material.[11] There is no dipole polarization contribution for non-polar polymers as found in polar polymers. This different

#### 8 Dielectric Material

mode of mechanism lead to the resonance spectra in the case of electronic polarization which occur at frequency beyond 1012 Hz. At below this frequency, the relaxation spectra prevail relating to the behavior of dipole polarization. This observation can best be summarized as in the following Figure 3:

**Figure 3.** Dielectric constant and loss dispersion of dielectric materials against frequency (adapted from Wikipedia)

#### **2.3. Relaxation and dielectric loss**

Relative permittivity can be express in complex form as in Equation (4) below:

$$\begin{array}{c} \text{e}^\* = \text{e}^\* - \text{j}\text{e}^\* \end{array} \tag{4}$$

Polymeric Dielectric Materials 9

where αd is the dipole polarisability and αo is the low frequency (static) polarisability. It normally occur in the microwave region. Figure 3 above shows the variation in real dielectric constant with the imaginary dielectric loss. There is a sudden drop in dipole polarization region (< 1012 Hz) for dielectric constant ε accompanied with the maximum dielectric loss ε". This maximum represent the complete failure for the dipole to follow the oscillating electric field beyond which the dipole remain freeze with no effective contribution to the dielectric constant. The mechanism for electronic and atomic polarization occur at higher frequency (shorter wavelength eg. infra-red region). This region involved excitation of electrons which is characterized by the quantized energy level hence is known as resonance behaviour. The dielectric constant display a maximum before a symmetrical drop about a certain frequency. These maximum and minimum represent the optimum polarization in phase with the oscillating frequency. The frequency at which the turning point occur is term the natural frequency ωo. At this point the frequency of applied electric field is at resonant with the natural frequency hence there is a maximum absorption. Consequently this lead to maximum dielectric

Temperature affect dielectric properties. As the temperature is increased the intermolecular forces between polymer chains is broken which enhances thermal agitation. The polar group will be more free to orient allowing it to keep up with the changing electric field. At lower temperature, the segmental motion of the chain is practically freezed and this will reduce the dielectric constant. At sufficiently higher temperature, the dielectric constant is again reduced due to strong thermal motion which disturb the orientation of the dipoles. At this latter stage the polarization effectively contribute minimal dielectric constant. Beside the kinetic energy acquired, free space in the polymer matrix is of necessity so as to induce segmental movement. Throughout the measured frequency and temperature, electronic and atomic polarization are spontaneous. The dipole polarization, on the other hand, would significantly be affected during heat treatment by effectively reducing the relaxation time (τ) since the polymer chain τ would reduced as the temperature is increased hence the polymer segment would be better able to follow in phase with the oscillating electric field. Significant chain and segmental motions occur in polymers and they are identified as

i. α relaxation: Micro-Brownian motion of the whole chain. Formally this motion is

ii. β relaxation: Rotation of polar groups about C-C bond eg. CH2Cl and –COOC2H5,

iii. γ relaxation: libration of phenyl ring and limited C-H segmental chain movement.

loss ε'.

follows [39]:

designated as glass transition.

conformational flip of cyclic unit.

**2.4. Effect of temperature** 

It consist of the real part which is dielectric constant and the imaginary part which is the dielectric loss. The ratio between the dielectric loss with the dielectric constant is quantified as tan *δ* ie:

$$
\tan \delta \text{ : } = \frac{\varepsilon''}{\varepsilon'}
$$

Dielectric loss result from the inability of polarization process in a molecules to follow the rate of change of the oscillating applied electric field. This arise from the relaxation time (τ) in a polymer which is the time taken for the dipoles to return to its original random orientation. It does not occur instatntaneously but the polarization diminished exponentially. If the relaxation time is smaller or comparable to the rate of oscillating electric field, then there would be no or minimum loss. However when the rate of electric field oscillate well faster than the relaxation time, the polarization cannot follow the oscillating frequency resulting in the energy absorption and dissipated as heat. Dipole polarisability is frequency dependent and can be shown as in Equation (5)

$$\alpha\_{\rm d} = \frac{\alpha\_o}{1 + jot} \tag{5}$$

where αd is the dipole polarisability and αo is the low frequency (static) polarisability. It normally occur in the microwave region. Figure 3 above shows the variation in real dielectric constant with the imaginary dielectric loss. There is a sudden drop in dipole polarization region (< 1012 Hz) for dielectric constant ε accompanied with the maximum dielectric loss ε". This maximum represent the complete failure for the dipole to follow the oscillating electric field beyond which the dipole remain freeze with no effective contribution to the dielectric constant. The mechanism for electronic and atomic polarization occur at higher frequency (shorter wavelength eg. infra-red region). This region involved excitation of electrons which is characterized by the quantized energy level hence is known as resonance behaviour. The dielectric constant display a maximum before a symmetrical drop about a certain frequency. These maximum and minimum represent the optimum polarization in phase with the oscillating frequency. The frequency at which the turning point occur is term the natural frequency ωo. At this point the frequency of applied electric field is at resonant with the natural frequency hence there is a maximum absorption. Consequently this lead to maximum dielectric loss ε'.
