**2.4 Temperature dependence of dielectric constant, dissipation factor, and breakdown strength**

Polar polymers often exhibit a substantial increase in dielectric constant when the temperature passes through the glass transition temperature (Tg) of

### **Figure 2.**

*Photograph of an unwound metallized film capacitor having poor self-clearing behavior with damage involving adjacent layers.*

### **Figure 3.**

*Schematic of the construction of a metallized polymer film capacitor winding without the end connections.*

### **Figure 4.**

*Typical change in capacitance and dissipation factor (DF) of various polymer film capacitors as a function of temperature at 1 kHz. PET: poly(ethylene terephthalate), PEN: poly(ethylene 2,6-naphthalate), PPS: poly(phenylene sulfide), PC: poly(carbonate), PP: poly(propylene). Data adapted from [42, 43].*

the polymer; however, non-polar polymers, which have only electronic polarization, are less temperature-dependent (**Figure 4**). The temperature dependence of dielectric constant for polar polymers is the result of increased polymer chain mobility as temperature increases through the Tg. This leads to greater freedom in accessible molecular dipole orientations at frequencies below 1012 Hz, while the electronic and atomic contributions tend to occur at around 1012 Hz and above [44]. Furthermore, polymers tend to have a broad distribution of response times as a result of interconnectivity and steric-hindrance imposed by neighboring molecules [45]. Substantial increases in dielectric constant near Tg limit capacitor operation for polar dielectrics to somewhat below Tg for many applications requiring a stable capacitance, including power conditioning/conversion in electronic circuitry, where the operating frequency ranges from tens of kHz for silicon-based switches to a few GHz for gallium nitride transistors [46].

Dissipation factor (DF) of a dielectric is a measure of electrical energy dissipated, usually in the form of heat, when an oscillating electric field is applied.

### *Polyimides as High Temperature Capacitor Dielectrics DOI: http://dx.doi.org/10.5772/intechopen.92643*

Similar to the dielectric constant, the DF is temperature and frequency-dependent and is more pronounced for polar polymers (**Figure 4**). In a capacitor, the total DF is a combination of contributions from the electrode and the polymer. For the electrode, metallization has a characteristic DF of ~0.1%, while the DF of metal foils is negligible. For polymers, DF can range from 0.01% for nonpolar polymers like PP, to as high as 1% for polar polymers such as PET, as shown in **Figure 4**. Depending on the capacitor applications, such as in a snubber or DC link, the requirement for dissipation factor ranges from ~0.01% for the former, to 0.1% for the latter [47–50]. Thus, for a snubber to meet the low DF requirement, metal foil electrodes with a BOPP polymer film is a common capacitor configuration.

The breakdown strength of a dielectric is defined as the maximum electric field that a dielectric can sustain for a given electrode configuration, test area, [51, 52] and voltage waveform (e.g. linear voltage ramp rate for DC breakdown [53]). The breakdown field is a statistical parameter, typically characterized by a Weibull distribution, although sometimes the log-Normal distribution provides a better fit [54]. It is usually determined by extrinsic factors such as weak points or defects such as embedded foreign particles in the dielectric [55]. Therefore, when reporting the breakdown field at the film level (as opposed to a wound capacitor), measurement conditions such as the electrode configuration (ball-plane or parallel plates) and test area should be included. For comparison purposes, all breakdown field data contained in this chapter included a description of the measurement conditions or control measurements with other capacitor-grade polymer films. Presently, BOPP capacitor films have the highest breakdown field of ~700 MV/m (at the 63% Weibull cumulative probability for a test area of ~2 cm<sup>2</sup> and 300 V/s linear ramp voltage) among all commercial polymer capacitor films [56]. The breakdown field of polymers decreases as temperature approaches Tg of amorphous (e.g. poly-ether-imide or PEI) or Tm of semi-crystalline polymers, [such as BOPP and BO poly-phenylene-sulfide

### **Figure 5.**

*Weibull characteristic breakdown field as a function of temperature for various polymers. Electrode area: ~2 cm2 . BOPP: biaxially oriented poly(propylene), PPS: poly(phenylene sulfide), PEI: poly(ether imide). Figure taken from [57].*

**Figure 6.**

*Typical derating of operating voltage for various polymer film capacitors as a function of temperature. PET: poly(ethylene terephthalate), PEN: poly(ethylene 2,6-naphthalate), PPS: poly(phenylene sulfide), PC: poly(carbonate), PP: poly(propylene). Data adapted from [42, 43].*

(PPS)], as shown in **Figure 5** [57]. Hence, the operating voltage of a capacitor is usually derated at elevated temperatures to protect against failure and prolong operational lifetime (**Figure 6**). Although many breakdown mechanisms have been proposed [58–61], extrinsic breakdown in solids is generally driven by power dissipation and eventually "thermal runaway", which leads to breakdown [62, 63].
