472 research outputs found
Self-sustained current oscillations in the kinetic theory of semiconductor superlattices
We present the first numerical solutions of a kinetic theory description of
self-sustained current oscillations in n-doped semiconductor superlattices. The
governing equation is a single-miniband Boltzmann-Poisson transport equation
with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary
conditions for the distribution function describe electron injection in the
contact regions. These conditions seamlessly become Ohm's law at the injecting
contact and the zero charge boundary condition at the receiving contact when
integrated over the wave vector. The time-dependent model is numerically solved
for the distribution function by using the deterministic Weighted Particle
Method. Numerical simulations are used to ascertain the convergence of the
method. The numerical results confirm the validity of the Chapman-Enskog
perturbation method used previously to derive generalized drift-diffusion
equations for high electric fields because they agree very well with numerical
solutions thereof.Comment: 26 pages, 16 figures, to appear in J. Comput. Phy
Nonequilibrium free energy, H theorem and self-sustained oscillations for Boltzmann-BGK descriptions of semiconductor superlattices
Semiconductor superlattices (SL) may be described by a Boltzmann-Poisson
kinetic equation with a Bhatnagar-Gross-Krook (BGK) collision term which
preserves charge, but not momentum or energy. Under appropriate boundary and
voltage bias conditions, these equations exhibit time-periodic oscillations of
the current caused by repeated nucleation and motion of charge dipole waves.
Despite this clear nonequilibrium behavior, if we `close' the system by
attaching insulated contacts to the superlattice and keeping its voltage bias
to zero volts, we can prove the H theorem, namely that a free energy
of the kinetic equations is a Lyapunov functional (, ). Numerical simulations confirm that the free energy decays to its
equilibrium value for a closed SL, whereas for an `open' SL under appropriate
dc voltage bias and contact conductivity oscillates in time with the
same frequency as the current self-sustained oscillations.Comment: 15 pages, 3 figures, minor revision of latex fil
Wigner-Poisson and nonlocal drift-diffusion model equations for semiconductor superlattices
A Wigner-Poisson kinetic equation describing charge transport in doped
semiconductor superlattices is proposed. Electrons are supposed to occupy the
lowest miniband, exchange of lateral momentum is ignored and the
electron-electron interaction is treated in the Hartree approximation. There
are elastic collisions with impurities and inelastic collisions with phonons,
imperfections, etc. The latter are described by a modified BGK
(Bhatnagar-Gross-Krook) collision model that allows for energy dissipation
while yielding charge continuity. In the hyperbolic limit, nonlocal
drift-diffusion equations are derived systematically from the kinetic
Wigner-Poisson-BGK system by means of the Chapman-Enskog method. The
nonlocality of the original quantum kinetic model equations implies that the
derived drift-diffusion equations contain spatial averages over one or more
superlattice periods. Numerical solutions of the latter equations show
self-sustained oscillations of the current through a voltage biased
superlattice, in agreement with known experiments.Comment: 20 pages, 1 figure, published as M3AS 15, 1253 (2005) with
correction
Theory of charge fluctuations and domain relocation times in semiconductor superlattices
Shot noise affects differently the nonlinear electron transport in
semiconductor superlattices depending on the strength of the coupling among the
superlattice quantum wells. Strongly coupled superlattices can be described by
a miniband Boltzmann-Langevin equation from which a stochastic drift-diffusion
equation is derived by means of a consistent Chapman-Enskog method. Similarly,
shot noise in weakly coupled, highly doped semiconductor superlattices is
described by a stochastic discrete drift-diffusion model. The current-voltage
characteristics of the corresponding deterministic model consist of a number of
stable branches corresponding to electric field profiles displaying two domains
separated by a domain wall. If the initial state corresponds to a voltage on
the middle of a stable branch and is suddenly switched to a final voltage
corresponding to the next branch, the domains relocate after a certain delay
time, called relocation time. The possible scalings of this mean relocation
time are discussed using bifurcation theory and the classical results for
escape of a Brownian particle from a potential well.Comment: 14 pages, 2 figure
Two mini-band model for self-sustained oscillations of the current through resonant tunneling semiconductor superlattices
A two miniband model for electron transport in semiconductor superlattices
that includes scattering and interminiband tunnelling is proposed. The model is
formulated in terms of Wigner functions in a basis spanned by Pauli matrices,
includes electron-electron scattering in the Hartree approximation and modified
Bhatnagar-Gross-Krook collision tems. For strong applied fields, balance
equations for the electric field and the miniband populations are derived using
a Chapman-Enskog perturbation technique. These equations are then solved
numerically for a dc voltage biased superlattice. Results include
self-sustained current oscillations due to repeated nucleation of electric
field pulses at the injecting contact region and their motion towards the
collector. Numerical reconstruction of the Wigner functions shows that the
miniband with higher energy is empty during most of the oscillation period: it
becomes populated only when the local electric field (corresponding to the
passing pulse) is sufficiently large to trigger resonant tunneling.Comment: 26 pages, 3 figures, to appear in Phys. Rev.
Generalized drift-diffusion model for miniband superlattices
A drift-diffusion model of miniband transport in strongly coupled
superlattices is derived from the single-miniband Boltzmann-Poisson transport
equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent
Chapman-Enskog method to analyze the hyperbolic limit, at which collision and
electric field terms dominate the other terms in the Boltzmann equation. The
reduced equation is of the drift-diffusion type, but it includes additional
terms, and diffusion and drift do not obey the Einstein relation except in the
limit of high temperatures.Comment: 4 pages, 3 figures, double-column revtex. To appear as RC in PR
Semiconductor Superlattices: A model system for nonlinear transport
Electric transport in semiconductor superlattices is dominated by pronounced
negative differential conductivity. In this report the standard transport
theories for superlattices, i.e. miniband conduction, Wannier-Stark-hopping,
and sequential tunneling, are reviewed in detail. Their relation to each other
is clarified by a comparison with a quantum transport model based on
nonequilibrium Green functions. It is demonstrated how the occurrence of
negative differential conductivity causes inhomogeneous electric field
distributions, yielding either a characteristic sawtooth shape of the
current-voltage characteristic or self-sustained current oscillations. An
additional ac-voltage in the THz range is included in the theory as well. The
results display absolute negative conductance, photon-assisted tunneling, the
possibility of gain, and a negative tunneling capacitance.Comment: 121 pages, figures included, to appear in Physics Reports (2001
Uncovering spatio-temporal patterns in semiconductor superlattices by efficient data processing tools
Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatiotemporal transport mechanisms are uncovered by applying (to the computed data) two recent data processing tools, known as the higher order dynamic mode decomposition and the spatiotemporal Koopman decomposition. Outcomes include a clear identification of the asymptotic self-sustained oscillations of the current density (isolated from the transient dynamics) and an accurate description of the electric field traveling pulse in terms of its dispersion diagram. In addition, a preliminary version of a data-driven reduced order model is constructed, which allows for extremely fast online simulations of the system response over a range of different configurations.The authors are indebted to two anonymous referees for some useful comments and suggestions on an earlier version of the paper. This work has been supported by the Fondo Europeo de Desarrollo Regional Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación, under Grants No. TRA2016-75075-R, No. MTM2017-84446-C2-2-R, and No. PID2020-112796RB-C22, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23) and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)
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