Sure. You could use an SOT23 or a QFN like this: http://www.digikey.com/product-detail/en/texas-instruments/T...

That's 4 mm x 4 mm (more with passives, but not too bad), and hits a solid 95% efficiency at the normal load of an iphone, and is above 90% all peak loads. Heat dissipation will be fine, all parts cost about $1.20. Low EMI.

However, its still a dozen new components. It's a ~10% tradeoff somewhere and while that may be totally worth it, its not simple. Phones do not have square millimeters to spare.

>Phones do not have square millimeters to spare.

Actually, they do, when you're replacing the battery with one with 3 times the energy density. Use some of the saved space for your DC-DC converter.

Its like... adding a turbocharger to a car. Yes, it is possible. There are even kits, after a fashion. But it is still not simple.

Also, its not even at the stage of a hypothetical question yet. This battery would last about two weeks in an iphone under these load conditions. The only reason it "looks" possible is if you're considering a battery that is not this one.

If it's a true boost converter, it's also going to need an inductor somewhere. If it's really just driving an LED, it could be a charge pump, which uses capacitors instead. But charge pumps probably can't handle the current level that a phone requires.

"If it's a true boost converter, it's also going to need an inductor somewhere."

We use resistors as inductors. Plenty of wound resistors in teeny-tiny packages exist, that's how we have metal detectors with credit card-sized boards, the literal bulk of the unit is the frame and coil assembly and board housing + adjustment controls.

Older gas charge pumps can handle it, but they're bulky and they are lossy and generate a lot of heat.

what's the efficiency of that boost converter? how much energy gets dissipated as heat in that setup, and is that likely to cause a fire?

Modern boost converters have efficiency from 80% to 95%. They also operate at high frequencies – 1MHz or even 3MHz, which allows to make inductors incredibly small. Boost converters aren't a problem for a long time now.