Boundary instability of a two-dimensional electron fluid
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OW-DIMENSIONAL SYSTEMS
Boundary Instability of a Two-Dimensional Electron Fluid1 M. I. Dyakonov Laboratoire de Physique Théorique et Astroparticules, Université Montpellier 2, CNRS, France Received February 6, 2008; accepted for publication February 11, 2008
Abstract—It was shown previously that the current-carrying state of a Field Effect Transistor with asymmetric source and drain boundary conditions may become unstable against spontaneous generation of plasma waves [1]. By extending the analysis to the two-dimensional case we find that the dominant instability modes correspond to waves propagating in the direction perpendicular to the current and localized near the boundaries. This new type of instability should result in plasma turbulence with a broad frequency spectrum. More generally, it is shown that a similar instability might exist, when a strong enough current goes through a single boundary between the gated and ungated regions. PACS numbers: 85.30.Tv, 72.15.Nj DOI: 10.1134/S1063782608080186
It was shown previously [1] that the current-carrying state of a Field Effect Transistor may become unstable against spontaneous generation of plasma waves in the transistor channel, provided there is an asymmetry in the boundary conditions at the source and at the drain. An extreme case of such asymmetry is the ac short-circuit condition at the source and the ac open circuit at the drain. For submicron gate lengths, the frequencies of the plasma oscillations are in the terahertz range; thus the FET can, in principle, serve as a generator of terahertz radiation. The nonlinear properties of the electron fluid in the transistor channel can also be used for detection and frequency mixing in the terahertz domain [2]. Experimentally, both terahertz emission [3–5] and detection [6] in nanometric transistors were demonstrated. Figure 1 presents experimental data [7] for a GaAlN/GaN HEMT at 4 K clearly showing the emission threshold at a certain source-drain voltage (or current) and a typical broad emission spectrum in the terahertz domain. Contrary to the prediction of [1], the spectrum depends neither on the gate length nor on the gate voltage. Similar results for terahertz emission were obtained at room temperature [5]. It is not firmly established that the observed emission is indeed related to the instability predicted in [1] (see [5]). However, one cannot directly compare the theory with the experiments, because the experimental geometry is very different from the one-dimensional model adopted in [1]. In the standard experimental situation, the width of the gate W is much larger than the gate length L; typically W/L ~ 100 (see Fig. 2, left). Under such conditions, the one-dimensional model, 1 The
text was submitted by the authors in English.
where the plasma density and velocity depend on the coordinate x only, is not appropriate, since obviously oblique plasma waves with a non-zero component of the wave vector in the y direction can propagate. In such a geometry, the gated region is not a resonator, but rather a wav
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