Self-consistent three-dimensional models for quantum ballistic transport in open systems

A quasi-three-dimensional model for quantum ballistic transport in nanostructures is proposed. The model goes beyond the Thomas-Fermi approximation and is numerically more tractable than the full three-dimensional Schr\"odinger-Poisson model. Its derivation relies on the strong confinement of electrons at the heterojunction which allows us to split the three-dimensional Schr\"odinger equation into a one-dimensional Schr\"odinger equation for the confined direction and a two-dimensional Schr\"odinger equation in the transport direction. The space charge effects are taken into account in a three-dimensional framework. Numerical simulations of quantum waveguide devices such as T stubs and directional couplers are used to illustrate the accuracy of the quasi-3D model versus the fully 3D model and to show the importance of quantum effects.

[1]  W. Porod,et al.  Coupled finite element/boundary element method for semiconductor quantum devices with exposed surfaces , 1994 .

[2]  F. Stern,et al.  Electronic properties of two-dimensional systems , 1982 .

[3]  Didier Lippens,et al.  Space lateral transfer and negative differential conductance regimes in quantum waveguide junctions , 2000 .

[4]  R. Landauer,et al.  Generalized many-channel conductance formula with application to small rings. , 1985, Physical review. B, Condensed matter.

[5]  T. Palm.  Self‐consistent calculations of an electron‐wave Y‐branch switch , 1993 .

[6]  Jan-Olof J. Wesström,et al.  SELF-GATING EFFECT IN THE ELECTRON Y-BRANCH SWITCH , 1999 .

[7]  Tekman,et al.  Novel features of quantum conduction in a constriction. , 1989, Physical review. B, Condensed matter.

[8]  H. Tsuchiya,et al.  Nonequilibrium Green’s function approach to high-temperature quantum transport in nanostructure devices , 1998 .

[9]  K. West,et al.  Electron mobilities exceeding 107 cm2/V s in modulation‐doped GaAs , 1989 .

[10]  K. H. Ploog,et al.  Proposal of novel electron wave coupled devices , 1990 .

[11]  Roland W. Freund,et al.  Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices , 1992, SIAM J. Sci. Comput..

[12]  C. J. Lambert,et al.  General Green’s-function formalism for transport calculations with spd Hamiltonians and giant magnetoresistance in Co- and Ni-based magnetic multilayers , 1999 .

[13]  Craig S. Lent,et al.  The quantum transmitting boundary method , 1990 .

[14]  Macucci,et al.  Quasi-three-dimensional Green's-function simulation of coupled electron waveguides. , 1995, Physical review. B, Condensed matter.

[15]  P. Ruden,et al.  Self-consistent calculation of the electronic structure of semiconductor quantum wires: Semiclassical and quantum mechanical approaches , 1993 .

[16]  Simulation of a quantum-dot flash memory , 1998 .

[17]  S. Datta,et al.  Quantum transport in ultrasmall electronic devices , 1990 .

[18]  Jian Wang,et al.  Electron waveguide coupler: A four‐terminal device , 1991 .

[19]  M. Anantram,et al.  Two-dimensional quantum mechanical modeling of nanotransistors , 2001, cond-mat/0111290.

[20]  Jian Wang,et al.  Ab initio modeling of quantum transport properties of molecular electronic devices , 2001 .

[21]  Karl Hess,et al.  Theory for a quantum modulated transistor , 1989 .

[22]  A. Szafer,et al.  Theory of quantum conduction through a constriction. , 1989, Physical review letters.

[23]  John H. Davies,et al.  Electronic states in narrow semiconducting wires near threshold , 1988 .

[24]  Davies,et al.  Breakdown of quantized conductance in point contacts calculated using realistic potentials. , 1991, Physical review. B, Condensed matter.

[25]  Massimo V. Fischetti,et al.  Master-equation approach to the study of electronic transport in small semiconductor devices , 1999 .

[26]  S. Datta,et al.  Proposed structure for large quantum interference effects , 1986 .

[27]  Naoki Chinone,et al.  Ultrahigh relaxation oscillation frequency (up to 30 GHz) of highly p-doped GaAs/GaAlAs multiple quantum well lasers , 1987 .

[28]  H. Gummel.  A self-consistent iterative scheme for one-dimensional steady state transistor calculations , 1964 .

[29]  Ballistic electron transport in stubbed quantum waveguides: experiment and theory , 2000, cond-mat/0002284.

[30]  J. Harris,et al.  Two‐dimensional electron gas structures with mobilities in excess of 3×106 cm2 V−1 s−1 , 1987 .

[31]  A. Weisshaar,et al.  Analysis and modeling of quantum waveguide structures and devices , 1991 .

[32]  Roland W. Freund,et al.  A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems , 1993, SIAM J. Sci. Comput..

[33]  P. Jiang,et al.  A theoretical investigation on the quantum field effect directional coupler , 1993 .