Plasma waves in two-dimensional electron channels: Propagation and trapped modes

Plasma waves in two-dimensional electron channels with nontrivial geometry and governing electrodes are described by the hydrodynamical equations combined with the Poisson equation for the self-consistent electric potential. If the amplitudes of the oscillations of the velocity, the concentration, and the potential are much smaller than the stationary values of these variables, then the hydrodynamical equation for oscillations can be linearized and transformed to the wave equation on a two-dimensional network. We consider the scattering problem for the wave equation and develop a semi-analytic method to calculate the transmission coefficients through the junction. The formulas for the transmission coefficients have resonance character and can be used in design of manipulated 2D-networks of plasma channels.

[1]  I. Gohberg,et al.  AN OPERATOR GENERALIZATION OF THE LOGARITHMIC RESIDUE THEOREM AND THE THEOREM OF ROUCHÉ , 1971 .

[2]  A. Chaplik.  Possible Crystallization of Charge Carriers in Low-density Inversion Layers , 1972 .

[3]  N. G. Galkin,et al.  Quantum splitter controlled by Rasha spin-orbit coupling , 2005 .

[4]  Alston S. Householder,et al.  Handbook for Automatic Computation , 1960, Comput. J..

[5]  S. Datta,et al.  Electronic analog of the electro‐optic modulator , 1990 .

[6]  Hilbert,et al.  Methods of Mathematical Physics, vol. II. Partial Differential Equations , 1963 .

[7]  M. Shur,et al.  Plasma mechanism of terahertz photomixing in high-electron mobility transistor under interband photoexcitation , 2002 .

[8]  Dirichlet-to-Neumann Techniques for the Plasma-waves in a Slot-diod , 2007 .

[9]  L. Guillopé.  Théorie spectrale de quelques variétés à bouts , 1989 .

[10]  B. Pavlov,et al.  Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction , 2009 .

[11]  L. Schwartz.  Théorie des distributions , 1966 .

[12]  Raj Mittra,et al.  Analytical techniques in the theory of guided waves , 1971 .

[13]  B. Pavlov,et al.  Standing waves and resonance transport mechanism in quantum networks , 2007 .

[14]  Michael S. Shur,et al.  Plasma wave detection of sub-terahertz and terahertz radiation by silicon field-effect transistors , 2004 .

[15]  B. Pavlov,et al.  Parameter regime of a resonance quantum switch , 2005 .

[16]  Shur,et al.  Shallow water analogy for a ballistic field effect transistor: New mechanism of plasma wave generation by dc current. , 1993, Physical review letters.

[17]  John Sylvester,et al.  The Dirichlet to Neumann map and applications , 1989 .

[18]  Modelling of Quantum Networks , 2003, math-ph/0312038.

[19]  Michele Governale,et al.  Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling , 2003 .

[20]  A star-graph model via operator extension , 2007, Mathematical Proceedings of the Cambridge Philosophical Society.

[21]  B. Pavlov,et al.  Intermediate Hamiltonian via Glazman's splitting and analytic perturbation for meromorphic matrix‐functions , 2007 .

[22]  Boris Pavlov,et al.  Scattering on a Compact Domain with Few Semi-Infinite Wires Attached: Resonance Case , 2002 .

[23]  H. Langer,et al.  Spectral Components of Selfadjoint Block Operator Matrices with Unbounded Entries , 1996 .

[24]  J. H. Wilkinson,et al.  Handbook for Automatic Computation. Vol II, Linear Algebra , 1973 .

[25]  D. Pierotti.  Uniqueness and trapped modes in the linear problem of the steady flow over a submerged hollow , 2006 .

[26]  M. Harmer,et al.  Boundary condition at the junction , 2004, math-ph/0404059.

[27]  M. Marletta,et al.  A simple method of calculating eigenvalues and resonances in domains with infinite regular ends , 2006, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[28]  W. Müller.  Manifolds with cusps of rank one , 1987 .

[29]  R. Newton.  Scattering theory of waves and particles , 1966 .

[30]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[31]  Admittance of a slot diode with a two-dimensional electron channel , 2003 .

[32]  B. Pavlov.  S-Matrix and Dirichlet-to-Neumann Operators , 2002 .

[33]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .