**4. Designing of polymer dielectric materials**

Based on the preceding discussions, designing of polymer dielectric materials can be made using several approaches. The following examples review two approaches undertaken of late namely free volume and copolymerization.

#### **4.1. Free volume**

16 Dielectric Material

groups per unit volume.

structure for polynorbonene (b).

**3.3. Dielectric breakdown** 

Sample F1s/C1s(%) Dielectric constant,<sup>ε</sup>

**Table 3.** The effect of Fluorine content on the dielectric constant of a polyimide

F0 0 2.93 2.90 F2 57.8 2.64 2.60 F3 67.7 2.42 2.41 F4 78.6 2.28 2.27 F5 87.4 2.37 2.26

Similar result was obtained in a series of polyimides synthesised from starting monomers bearing varying percentage of fluorine content. [21] The decreased in dielectric constant as the fluorine content is increased can be explained as due to the low polarizability of fluorine. The electrons of fluorine being very tightly held and close to the nucleus. The polarizability of the fluorinated polyimides is decreased as the number of fluorine atoms is increased, due to the lower electronic polarizability of a C–F bond relative to that of a C–H bond that has been displaced. [22,23] The free volume concomitantly increases due to the relatively large volume of fluorine compared with hydrogen, which reduces the number of polarizable

The effect of free volume can be seen when introducing adamantane into a polyimide chain. [24] Adamantane is a bulky group which induce an increase in the free volume. The dielectric constant achieved was 2.7 at 1 KHz. This value is well below the commercial Kapton H film (25.4 *μ*m) with a dielectric constant of approximately 3.5 at 1 kHz and 3.3 at 10 MHz. Besides, hydrophobicity was reduced thus preventing absorption of moisture. Low dielectric loss is important for a good capacitors and insulation. The strategy of introducing bulky substituents is further exemplified in a commercial Avatrel™ dielectric polymer made up of polynorbonene for passivation applications. It has a dielectric constant of 2.55, a loss tangent less than 0.002. These electrical properties held constant up to above 1 GHz. The

bulky structures in these polymers are illustrated in the following Figure 10:

**Figure 10.** Adamantane structure incorporated into polyimide chain (a, from Ref 12) and the generic

(a) (b)

Electrical breakdown occurs when the dielectric strength which is the maximum electric field applicable on dielectric material is exceeded. It underwent catastrophic failure leading

102(Hz) 106 (Hz)

Based on Maxwell-Garnet theory, the presence of second phase of lower dielectric constant in a composite will affect a significant decrease in dielectric constant.[25] This concept was applied in generating foam structure with the introduction of air-filled pores. At least two methods were utilised. One is to synthesised block copolymer of different thermal lability [26] and the other is performing solution etching of soluble component in a composite matrix. [27] The former method involved the use of block copolymer composed of high temperature and high Tg polymer and a second component of lower thermal property which can preferentially undergoes thermal decomposition. One of such a triblock polymer is shown below:

**Scheme 3.** Triblock polyimide structure illustrating the thermally labile and stable segments.

This triblock composed of thermally stable polyimide and thermally labile phosphate ester block. This copolymer is subjected to thermal treatment such that the temperature is sufficient to degrade the thermally labile block and leaving the thermally stable block intact. A small size scale of microphase saparation is then generated with spherical pore morphology, monodispersed in size and discontinuous. These nanopores are filled with air (ε = 1.0) which is responsible for the reduction in dielectric constant. Thermally labile oligomers include polymethylstyrene, polypropylene oxide and polymethylmethacrylate.

#### 18 Dielectric Material

Nanofoam with dielectric constant of 2.3 was achievable with system made-up from PMDA/4BDAF/PPO triblock of void volume 16%. Figure 11 illustrate the relationship between the void content with the dielectric constant for PMDA/3FDA/PPO triblock system.[28]

**Figure 11.** Relation between the dielectric constant with the void fractional volume in PMDA/3FDA/PPO triblock system.

In solution etching method, porosity were achieved by solution etching of soluble component in a nanocomposites leaving the chemically stable matrix intact. This was attempted using polyamic acid, a polyimide prepolymer, as the matrix while inorganic TEOS was incorporated through sol-gel method. Once the inorganic phase was homogeneously distributed in the polymer matrix, the composite was thermally cured followed by hydrofluoride etching. This will dissolved away the acid labile inorganic phase with the generation of nanosize closed cell pore of uniform density. The steps involved during its fabrication is illustrated as in the following Scheme (4):

**Scheme 4.** Preparation of porous Polyimide using sol-gel method

The level of porosity is dependent on the TEOS content incorporated into the polymer matrix. Table 4 shows the dependence in dielectric constant on fluorine content and level of porosity based on TEOS content added during the materials fabrication

Polymeric Dielectric Materials 19

F (Wt %) 0% TEO 10% TEOS % TEOS

0 2.71 2.84 3.41

15 2.45 2.71 3.25

17 2.61 2.69 3.18

33 2.50 2.62 2.98

**Table 4.** Dielectric constant of a series of polyimides at varying TEOS content

The results above display a general trend of decreasing dielectric constant as the TEOS concentration used during sol gel technique were increased. This was ascribed to an increased in void structures which reduced the dielectric property as the result of the presence of air. There was a linear decreased in dielectric constant as the weight percent of fluorine content in the structures were increased. Further the rate of decrease is almost constant between different TEOS content. Of the four synthesized polyimides, BAPP-BPDA showed the highest dielectric constant since this sample contains no fluorine. The SEM

picture for the fracture surface morphology is shown in the following Figure 12.

**Figure 12.** SEM scan of fracture surface of pure (a) PI/SiO2 10% (b) and PI/SiO2 20 % porosity (c)

on whether the substitution of the atoms are symmetric or asymmetric.

Simpsons *et al* [21] concluded that the presence of fluorine increases the free volume, lower electronic polarization and can either increase or decrease the dielectric constant depending

(a) (b) (c)

**Table 4.** Dielectric constant of a series of polyimides at varying TEOS content

18 Dielectric Material

system.[28]

PMDA/3FDA/PPO triblock system.

Nanofoam with dielectric constant of 2.3 was achievable with system made-up from PMDA/4BDAF/PPO triblock of void volume 16%. Figure 11 illustrate the relationship between the void content with the dielectric constant for PMDA/3FDA/PPO triblock

**Figure 11.** Relation between the dielectric constant with the void fractional volume in

during its fabrication is illustrated as in the following Scheme (4):

**Scheme 4.** Preparation of porous Polyimide using sol-gel method

porosity based on TEOS content added during the materials fabrication

In solution etching method, porosity were achieved by solution etching of soluble component in a nanocomposites leaving the chemically stable matrix intact. This was attempted using polyamic acid, a polyimide prepolymer, as the matrix while inorganic TEOS was incorporated through sol-gel method. Once the inorganic phase was homogeneously distributed in the polymer matrix, the composite was thermally cured followed by hydrofluoride etching. This will dissolved away the acid labile inorganic phase with the generation of nanosize closed cell pore of uniform density. The steps involved

The level of porosity is dependent on the TEOS content incorporated into the polymer matrix. Table 4 shows the dependence in dielectric constant on fluorine content and level of

The results above display a general trend of decreasing dielectric constant as the TEOS concentration used during sol gel technique were increased. This was ascribed to an increased in void structures which reduced the dielectric property as the result of the presence of air. There was a linear decreased in dielectric constant as the weight percent of fluorine content in the structures were increased. Further the rate of decrease is almost constant between different TEOS content. Of the four synthesized polyimides, BAPP-BPDA showed the highest dielectric constant since this sample contains no fluorine. The SEM picture for the fracture surface morphology is shown in the following Figure 12.

**Figure 12.** SEM scan of fracture surface of pure (a) PI/SiO2 10% (b) and PI/SiO2 20 % porosity (c)

Simpsons *et al* [21] concluded that the presence of fluorine increases the free volume, lower electronic polarization and can either increase or decrease the dielectric constant depending on whether the substitution of the atoms are symmetric or asymmetric.
