Dave Posluszny designed and built a net-zero house in Massachusetts from an existing foundation. No fossil fuels are used to power the house: HVAC and electric all come from solar panels on site. Posluszny aimed to make the house inexpensive (not commonly associated with net zero, at least up front) and easy to build, which led to some unusual details. Green Building Advisor shares this article he wrote about the design, and it’s worth a read to understand his decision-making process.

Vapor barrier, WRB, and thermal break at the top of the leveled foundation wall.
One detail actually generated a disclaimer on the article and much discussion in the comments. For his the water-resistant barrier (WRB) on the wall sheathing, Posluszny used Ice & Water Shield, which is also impermeable to vapor. This detail results in what some builders call a wrong-side vapor barrier, located outside the insulation instead of inside, which threatens to trap condensation in the walls and cause mold. Posluszny claims there won’t be any vapor to trap because the house is airtight and properly flashed, but a lot of builders feel uneasy.

The entire house is wrapped in Ice & Water Shield.
Posluszny describes several other unusual but logical decisions he made. Instead of making the insulation better (at a cost of square footage and budget), Posluszny opts to just install more solar panels instead. A roof vent above the scissor truss was accomplished with two layers of sheathing in order to place the WRB on the underside. The house has few windows, which is very smart from an insulation perspective; a semi-gloss white paint on ultra-smooth plaster ceilings brightens the interior.
I applied this thinking to all my decisions, and found that the least expensive way to be net-zero is not always the most energy-efficient way.
–Dave Posluszny

Open floor plan, showing one of the two lofts.
BONUS! Here is a glossary of the four barriers a house requires to maintain the temperature and humidity inside – in other words, to keep you comfortable.
Air barrier: The layer that prevents ambient air from entering the building, or conditioned air from leaving it. The sheathing usually serves as the air barrier, but builders need to be religious about filling in accidental holes (with spray foam, perhaps) in order to make a house completely airtight.
Thermal barrier, aka insulation: The layer that prevents heat from moving in or out of the building. The thermal barrier defines the building envelope. A conducting material that passes through the thermal barrier is called a thermal bridge, which wastes energy and should be avoided.
Vapor barrier: The layer that prevents water vapor in the air from entering the building. Exterior-grade plywood, plastic or aluminum sheeting, or Ice & Water Shield may be used as a vapor barrier. (If the house has a perfect air barrier with no holes, then the air barrier also serves as a vapor barrier.) Installed incorrectly, a “wrong way” vapor barrier may trap water vapor in the walls, leading to mold.
Water-resistant barrier (WRB), aka drainage plane: The layer that keeps rain and other liquid water from entering the building. Most houses use felt paper, also known as housewrap, but this house uses peel-and-stick Ice & Water Shield, which doubles as a vapor barrier as described above.