What’s the Cannikin Law and how does it relate to GaN and SiC power converters?

The Cannikin Law, also called Liebig’s Law of the Minimum, states that growing adoption of new technology is not dictated by total resources, but by the scarcest limiting resource. It helps to explain the adoption trajectory and challenges of developing gallium nitride (GaN) and silicon carbide (SiC) wide bandgap (WBG) power semiconductors and expanding their use in power conversion.

Also referred to as the wooden bucket theory, the Cannikin Law states that the capacity of a container (like a wooden bucket), or the performance of a system, is limited by the shortest, least performing plank, not the longest and best performing asset.

For example, perovskite-based thin-film flexible photovoltaic (PV) cells are a promising energy source for a wide range of portable and wearable electronics. The perovskite materials are not necessarily the limiting factor to achieving industrial-scale production.

The hole transport materials (HTM) and electron transport materials (ETM) are less developed than the perovskites themselves. As a result, development efforts should focus more on HTM and ETM to accelerate the commercialization of perovskite photovoltaics. Once all the technology planks have reached similar and acceptable levels of development, commercialization can occur at a rapid pace (Figure 1).

Figure 1. HTM and ETM materials are the short planks that currently limit the commercial development of perovskite-based solar energy. (Image: IOP Materials Science and Engineering)

When displacing traditional silicon with SiC or GaN in power conversion applications, designers face bottlenecks like the commercial development of perovskite-based PV. Like the perovskite materials, SiC and GaN are better developed than some of the support technologies.

The Cannikin Law in GaN/SiC device adoption

Despite the superior performance of GaN and SiC, the corresponding “power conversion barrel” has constrained the adoption of those devices. Price is important, of course, but remaining barriers are primarily due to packaging, thermal limitations, and design complexities. Those issues have been largely addressed, but not eliminated.

Increasingly, the limitations are more related to educating designers rather than improving the devices. The relative lengths of the “limiting planks” vary between SiC and GaN, but there are similar adoption challenges.

Common application development errors that can limit the performance and reliability of SiC and GaN deployments include improper gate drives, inadequate thermal management, and not fully mitigating system-wide implications of increased electromagnetic interference arising from issues related to high-frequency switching, filtering, and circuit layouts.

The Cannikin Law and continuous improvement

Current SiC and GaN power devices provide excellent performance. But, as in all areas of electronics, continuous improvement is an important activity. Some of the factors constraining performance are device structural factors related to materials limitations, interfacial qualities, and thermal management (Figure 2).

Figure 2. Technologies in areas like thermal management and minimization of power losses must evolve to support continuous improvement in WBG device performance. (Image: International Journal of Thermal Sciences)

While the overall considerations are similar, the details differ. For example, GaN has a lower thermal conductivity than SiC. SiC is more brittle and needs a more precise thermal coefficient of expansion (TCE) matching between the device and substrate.

In terms of the Cannikin Law, GaN can be performance-limited by thermal dissipation and substrate defect density issues. SiC can be performance is limited by gate oxide interface quality and lower switching speeds. Both can be limited by package-level inductance.

The Cannikin Law and common sense

The Cannikin Law was developed for high-level analysis to help optimize allocation of resources and speed the proliferation of new technologies. But most designers are focused on today’s challenges, not long-term adoption. GaN and SiC both push performance beyond that possible with Si devices, and each WBG technology is suited for specific applications (Figure 3).

Figure 3. Comparison of typical application spaces for Si, GaN, and SiC power conversion. (Image: Rogers Corp.)

Power converter designers must not only meet primary specification requirements but also must deal with unintended second-order operating realities. The Cannikin Law can provide some common-sense perspective for designers when addressing the unique requirements and challenges of specific design situations.

Summary

The Cannikin Law provides technologists and designers with another perspective for evaluating and prioritizing the development needs of SiC and GaN devices and applications. It can be used for the development of new technologies, the deployment requirements of those technologies, and the identification of the relative importance or urgency of continuous improvement opportunities.

References

FAQs on gallium nitride (GaN) HEMT: Technology and operation, Infineon
Gallium Nitride vs Silicon in Soft Switching LLC Power Supplies Comparative Study, European Passive Component Institute
GaN and SiC: The Power Electronics Revolution Leaving Silicon Behind, Microchip
How does Gallium Nitride fit into the Next Generation of High Performance Electronics, Rogers Corp.
Perovskites for printed flexible electronics, IOP Materials Science and Engineering
Silicon Carbide vs. Silicon: A Comparative Study of Semiconductors in High-Temperature Applications, Stanford Advanced Materials
The cannikin law of the EV battery performance, LinkedIn
Transistor-level thermal management in wide and ultra-wide bandgap power semiconductor transistors: A review, International Journal on Thermal Sciences

What’s the Cannikin Law and how does it relate to GaN and SiC power converters?

The Cannikin Law in GaN/SiC device adoption