Nonlinear Wave Methods for Charge Transport

Bonilla, Luis L.; Teitsworth, Stephen W.

doi:10.1002/9783527628674

Cited by 47 publications

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“…A simple Boltzmann-Poisson model containing these ingredients evolved from the work of Ktitorov et al [17], Ignatov and Shashkin [18], and later authors. In the limit of strong electric fields for which the Bloch frequency has the same order as collision frequencies, it is possible to derive balance equations for the electron and current densities and the electric field by a systematic Chapman-Enskog perturbation method [14,16,19]. In this situation of a SL very far even from local equilibrium, the performance of a maximum entropy closure can be ascertained by comparison to the perturbation results.…”

Section: Resultsmentioning

confidence: 99%

“…In certain regimes, electronic transport can be described by Boltzmann-type kinetic equations, from which one can derive balance equations for electron density, current density and electric field in a controlled way. In this paper, we derive balance equations using the maximum entropy principle in the hyperbolic limit of large electric field and large collision frequencies, and compare it with existing derivations that use systematic perturbation methods [14,16]. In this limit, transport coefficients appearing in the balance equations depend on the electric field, a feature that is also captured by the maximum entropy closure as we shall see below.…”

Section: Introductionmentioning

confidence: 95%

“…Quasi one dimensional semiconductor superlattices are among the simplest. There is a large literature on nonlinear electronic transport in semiconductor superlattices (SLs); see [14][15][16]. On the one hand, these materials have many interesting properties as they exhibit nonlinear periodic and chaotic time-dependent oscillations, multistability, pinning effects due to the lattice, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Compared to fluids, charges in semiconductors feel the effect of strong external fields, that appear in Boltzmann transport equations and, in the short mean free path and strong field limits, appear in the macroscopic equations and may also affect transport coefficients [14]. To ascertain these effects, it is convenient to study simple systems.…”

Section: Introductionmentioning

confidence: 99%

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Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

Bonilla

Carretero

2016

Entropy

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Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann-Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman-Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

Bonilla

Carretero

2016

Entropy

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“…Следует отметить, что в настоящее время все больше внимания исследователи уделяют рассмотрению транспорта электронов через полупроводниковую сверхрешетку с позиций нелинейной динамики. Это позволяет выявлять и объяснять различные эффекты, наблюдающиеся в исследуемой системе [7][8][9][10][11].…”

Section: поступило в редакцию 1 июня 2017 гunclassified

Исследование Влияния Случайных Флуктуаций Концентрации Легирующей Примеси На Ток В Полупроводниковых Сверхрешетках

Сельский¹,

Короновский²,

Москаленко³

et al. 2017

Письма В Журнал Технической Физики

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Исследуется, как случайные флуктуации концентрации легирующей примеси влияют на вольт-амперные характеристики тока, протекающего через полупроводниковую сверхрешетку. Показано, что в зависимости от амплитуды флуктуаций параметров наноструктуры характеристики тока, протекающего через сверхрешетку, заметно изменяются. По малой выборке удалось найти закон распределения плотности вероятности значений интеграла модуля разности токов при различных значениях амплитуды флуктуаций концентрации легирующей примеси. DOI: 10.21883/PJTF.2017.20.45144.16896

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Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

Alvaro¹,

Carretero²,

Bonilla³

2012

Journal of Computational Physics

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We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is * Corresponding author.Email addresses: mariano.alvaro@uc3m.es (M.Álvaro), manuel.carretero@uc3m.es (M. Carretero), bonilla@ing.uc3m.es (L. L. Bonilla) URL: http://scala.uc3m.es (L. L. Bonilla)Preprint submitted to Elsevier January 1, 2018solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.

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Nonlinear Wave Methods for Charge Transport

Cited by 47 publications

References 0 publications

Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

Исследование Влияния Случайных Флуктуаций Концентрации Легирующей Примеси На Ток В Полупроводниковых Сверхрешетках

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

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