  In typical thermoelectric energy harvesters and sensors, the Seebeck effect
is caused by diffusion of electrons or holes in a temperature gradient.
However, the Seebeck effect can also have a phonon drag component, due to
momentum exchange between charge carriers and lattice phonons, which is more
difficult to quantify. Here, we present the first study of phonon drag in the
AlGaN/GaN two-dimensional electron gas (2DEG). We find that phonon drag does
not contribute significantly to the thermoelectric behavior of devices with
~100 nm GaN thickness, which suppress the phonon mean free path. However, when
the thickness is increased to ~1.2 $\mu$m, up to 32% (88%) of the Seebeck
coefficient at 300 K (50 K) can be attributed to the drag component. In turn,
the phonon drag enables state-of-the-art thermoelectric power factor in the
thicker GaN film, up to ~40 mW m$^{-1}$ K$^{-2}$ at 50 K. By measuring the
thermal conductivity of these AlGaN/GaN films, we show that the magnitude of
the phonon drag can increase even when the thermal conductivity decreases.
Decoupling of thermal conductivity and Seebeck coefficient could enable
important advancements in thermoelectric power conversion with devices based on
2DEGs.
