The push of conventional electronic amplifier technologies into the deep submillimeter wavelength and THz frequency ranges of the electromagnetic (EM) spectrum has been limited by constraints on their fundamental physics of operation and fabrication limitations. At the same time, optical amplifier technologies can only access this spectral region using inefficient frequency down-conversion. This struggle for practical power amplifiers in the THz band will likely require a new type of amplifier and has led to a desire for a solid-state beam-wave style amplifier using semiconductor fabrication techniques. While there has been considerable progress in creating transistors in the THz region, the small size required to achieve the needed transit times and gate capacitances generally precludes them from producing power above 1 mW. Vacuum electronic devices (VEDs), such as traveling wave amplifiers (TWAs), have also shown great progress into this band. A TWA is an example of a beam-wave style device where gain is achieved by transferring energy from an electron beam to an EM wave at electrically large length scales. However, as traditional TWAs are scaled to higher frequencies, the shrinking wavelength makes fabrication of the corresponding interaction circuit structures and miniscule beam tunnels increasingly difficult through micro-machining or other subtractive metal shaping. Thus, combining the strengths of both these systems into a single device has some merit. Solid-state TWAs have been attempted over many years without success largely due to slow electron drift velocities resulting in beam equivalents that are unsuitable for synchronization with EM slow-wave structures. One possible path towards a beam-wave style THz solid-state amplifier is to couple to a plasma wave characterized by phase propagation much faster than the electron velocity limited by scattering in a material, but this requires a substantial redevelopment of the fundamental beam-wave interaction analysis. Presented here is a novel analysis built upon the prior work on solid-state and VED TWAs with a primary difference in the nature of the charge carrier behavior. In this work the electron beam, which was previously described as bulk carriers in a semiconductor, is now formed with an un-gated 2D electron gas (2DEG). A freely propagating plasma wave is present in the dense 2DEG and takes the place of the typical space charge wave present in VED devices. Example calculations are compared to a generic VED TWA behavior and the basic performance of a realizable device is analyzed through the use of a gallium nitride heterostructure material system and achievable fabrication strategies. It is shown that the concept of a TWA using a 2DEG plasma wave is not practical at best, and fundamentally flawed at worst. However, the understanding gained lays some of the groundwork for other possible beam-wave interaction style amplifiers using a fast 2DEG plasma wave.
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