**5. Polyimide aging**

Polyimide lifetime is studied through high voltage endurance test. Any insulator, given sufficient time and voltage, will break down. An example setup is shown in **Figure 8**. Multiple parts are connected electrically in parallel, and multiple groups of parts are stressed in different high voltages from high voltage power supplies, and a switch/measurement unit such as Agilent 34,980 together with a PC can be used to monitor the time the number of units have broken down. This can be a timeconsuming process where it can take days to months for the units to break down.

The distributions for the time to failure can be analyzed through Weibull plots as shown in **Figure 9**. Groups of 16 parts were stressed at six different voltages, where each group forms a fairly decent Weibull distribution. Through Weibull plots, mean time to failure (MTTF) or time to failure at certain failure rates such as 1 ppm can be estimated. Obviously, time to failure at high voltages takes much less time compared to that at low voltages. Per VDE0884-11, the smallest to the largest MTTFs need to span at least two orders of magnitude and at the lowest test voltage, the 63% time to failure needs to be longer than 107 s or about 116 days. As it can be seen from **Figure 9**, the data sets generated at these six voltages meet these requirements.

To extrapolate working voltage, time to failure is plotted against stress voltages. For basic insulation, working voltage is determined from the voltage with 20% derating where time to failure or lifetime at 1000 ppm is greater than 24 years. Similarly for reinforced insulation, working voltage is determined from the voltage with 20% derating where lifetime at 1 ppm is greater than 30 years.

The dominant breakdown mechanism is through charge injections as a result of the direct electron impact from the electrodes to the polyimide surface regions. The breakdown process begins as charges are injected into polyimide surface under

**Figure 8.** *Experimental setup for high voltage endurance test.*

**Figure 9.** *Weibull distribution for isolators with 20-μm thick polyimide.*

HVac conditions. The charges can become trapped in some local trapping sites at the surface. Once trapped, energy will be released, which will cause local mechanical tension because of stored electrostatic energy. Through quantum activation process, this tension will eventually cause local free volumes, voids or micro-cracks, which act as more local trapping sites. If the HVac remains long enough, this process will lead to the continued degradation of insulation and eventually electrical punch-through.

Through thermodynamic analysis, the lifetime, *L* [4], can be expressed as Eq. (1),

$$L \sim \frac{e^{-(E-E\_t)^n}}{\left(E-E\_t\right)^m} \tag{1}$$

where *Et* is the threshold field where no charge injection will happen, and *m, n* are scaling constants.

The HVac endurance data of *i*Coupler devices were analyzed according to the procedure specified by ANSI/IEEE Std 930-1987, the "IEEE Guide for the Statistical Analysis of Electrical Insulation Voltage Endurance Data," and they are observed to follow:

$$L \sim e^{V^{-\*}} \tag{2}$$

This phenomenological fit as shown in Eq. (2) was used to get worst-case lifetime because it assumes no threshold field as specified by the thermodynamic model. The duration of the HV test becomes prohibitively long if we try to measure the threshold field. Eq. (2) was used to model the time to failure for **Figure 10**. As you can see, the model fits the data rather well.

We also observed that the lifetime of *i*Coupler devices under DC or unipolar AC is much longer compared to that under bipolar AC; it is at least two orders of magnitude higher. For unipolar waveforms, the trapped charges tend to form an

**Figure 10.** *Time-to-failure plot for isolators with 20-μm thick polyimide.*

**Figure 11.**

*Field barrier region with zero net e-field formed by the trapped charges.*

internal field barrier region (i.e., homocharge) around the electrodes that prevents further injection of charge into the polyimide as shown in **Figure 11**. With a bipolar AC waveform, the reverse of field will prevent formation of this steady field barrier, and the trapped regions will keep progressing into the polyimide and eventually lead to the electrical breakdown. SiO2, on the other hand, tends to give worse lifetime for DC or unipolar AC, especially for thick films [5].

The lifetime as shown in **Figure 10** is based on worst-case bipolar AC waveforms. HV lifetime is even greater for unipolar AC or DC waveforms. It should be noted that the models described in this chapter relate to polyimide insulation and have no bearing on isolators that use SiO2 insulators as the primary means for isolation. Likewise, models that predict the HV lifetime of SiO2-based digital isolators have no bearing on polyimide-based isolation systems.

**Figure 12** shows how lifetime for unipolar is compared to that of bipolar for polyimide films. As it can be seen, the peak stress voltage for unipolar is about twice that of the peak stress voltage for AC bipolar for the same time to failure. In essence, the lifetime is dependent on peak to peak rather than the peak stress voltage for the polyimide films.

**Figure 12.** *Time-to-failure comparisons for AC bipolar versus unipolar.*
