  Low-dimensional systems with sharp features in the density of states have
been proposed as a means to improving the efficiency of thermoelectric devices.
Quantum dot systems, which offer the sharpest density of states achievable,
however, suffer from low power outputs while bulk (3-D) thermoelectrics, while
displaying high power outputs, offer very low efficiencies. Here, we analyze
the use of a resonant tunneling diode structure that combines the best of both
aspects, that is, density of states distortion with a finite bandwidth due to
confinement that aids the efficiency and a large number of current carrying
transverse modes that enhances the total power output. We show that this device
can achieve a high power output ($\sim 0.3$ MW$/m^2$) at efficiencies of $\sim
40\%$ of the Carnot efficiency due to the contribution from these transverse
momentum states at a finite bandwidth of $kT/2$. We then provide a detailed
analysis of the physics of charge and heat transport with insights on parasitic
currents that reduce the efficiency. Finally, a comparison between the resonant
tunneling diode and a quantum dot device with comparable bandwidth reveals that
a similar performance requires ultra-dense areal quantum dot densities of $\sim
10^{12}/cm^2$.
