It seems that everybody knows that power density keeps increasing, inexorably. How are we going to manage that? In my discussions with otherwise knowledgeable folks, however, it becomes immediately apparent that there’s a huge disconnect in what we mean by power. Case in point: someone mentioned to me last week a “1 cm cell phone.” Now to be perfectly honest, I’m not really even sure what a “1 cm cell phone” would be, but it sounds to me an awful lot like one of those wearable Star Trek NG communicators.
So what, exactly, is power? If power is functionality, then a 1 cm cell phone epitomizes increasing power density. You’ve got a tiny device with sophisticated signal processing capability, incredible RF sensitivity, interplanetary range, probably a voice-activated and voice-recognizing operating system with multi-lingual automatic translation, and almost certainly a body-energy-harvesting power supply. (And for all we know, it’s got super-HD video recording capability that they never bothered to disclose on the TV series, along with exabyte onboard memory.) Somehow you manage to cram all that functionality into a fabric-thickness, 1-cm square, lapel pin. Compare that with today’s cell phones, which are 100 times thicker, 100 times the surface area (that’s 10,000 times the volume) and there’s no argument that the functional power density of the 1-cm phone is spectacularly higher than today’s device. Unfortunately, this definition of “power” is pretty much irrelevant when it comes to thermal management.
Similarly, the actual device guys (I’m thinking the electrical engineers I work with) tend to think in terms of current density. To accomplish the functions of this 1-cm cell phone, they may need the same number of amperes as they need today (say to pump the transmit power out the antenna), but it has to originate in a comparatively microscopic silicon area – hence the amps/cm^2 density may be similarly orders of magnitude higher than today’s technology – and as I say, when the device guys say “power” density, they’re typically thinking of current. But if R-ds-on resistance also drops by orders of magnitude with improved technology, perhaps the true power density (to use the formal physics definition) hasn’t increased at all.
Which brings me to my final point – and a third meaning of power density. What limits the amount of power (physics definition) in a semiconductor device is actually how well you can remove it, not how much it can intrinsically generate. Today’s cell phone is mainly convectively cooled from outside the case by the air, and to a similar extent, possibly, by your hand when you’re holding it. (Your circulatory system provides the cooling fluid – your blood flow – through the external heatsink, which is your hand.) It’s the total external surface area of the phone, then, that dictates, ultimately, how much power you can get out of the phone, hence how much power the devices inside it can generate. If you reduce the external surface area by two orders of magnitude, you have to reduce the total power dissipation by two orders of magnitude, or you can’t keep it running at the same temperature. True power density, therefore, is roughly constant, and it’s constrained by everything that’s external to the device. Sure, you can reduce the circuit size by 100x, and you can increase the amps/cm^2 by 100x, but if you don’t hold the watts/cm^2 roughly constant, you can’t build that 1-cm cell phone – not, at least, if you’re going to continue to cool it with the human operator.
So, until you start wearing your first 1-cm cell phone, be cool!