In this paper, we show how plasma-wave instability in an asymmetrically biased ungated InGaAs high-electron mobility transistor (HEMT) leads to terahertz emissions. Numerical calculations are provided using a new Maxwell-hydrodynamic solver. Using this solver, an accurate plasma-wave model is presented, accounting for nonuniform surroundings and finite dimensions of the 2D electron gas (2DEG) layer within the HEMT. We estimate that hundreds of nanowatts of power can be expected from such devices under ideal boundary conditions and sufficient channel mobility. Effects due to variations of carrier velocity, carrier concentration, and 2DEG confinement on the emitted power levels are also considered to provide design guidelines.