Self-consistent study of the resonant-tunneling diode

Kluksdahl, N.C.; Kriman, A. M.; Ferry, D. K.; Ringhofer, Christian

doi:10.1103/physrevb.39.7720

Cited by 436 publications

(235 citation statements)

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“…21,22) Kluksdahl et al incorporated dissipative and self-consistent effects by employing the Poisson-Boltzmann equation by adopting a relaxation time approximation and succeeded in modeling the experimentally observed hysteresis behavior of the I-V curve. 23) Jensen and Buot developed a numerical scheme to treat systems of the same kind and reported that current oscillation and plateau-like behavior arise from intrinsic bistability. 24,25) In the previous studies, dissipative effects of electron transport have been taken into account by using the Boltzmann equation.…”

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confidence: 99%

“…We set the parameters used in the HEOM as ¼ 12:1 THz ( À1 ¼ 8:27 fs), ¼ 72:5 GHz ( À1 ¼ 13:8 ps), and T ¼ 300 K to create conditions close to those used in previous theoretical studies. [21][22][23][24][25] The depth of the hierarchy and the number of Matsubara frequencies were chosen as N 2 f2; 3; 4; 5; 6g and K 2 f1; 2; 3g, respectively. The third-order up-wind and down-wind difference schemes respectively were used in the positive and negative p regions to approximate the spatial derivative of the kinetic term, Àðp=mÞ@=@q, in order to facilitate implementation of the inflow and outflow boundary conditions.…”

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An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

Sakurai

Tanimura

2013

J. Phys. Soc. Jpn.

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The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of a rigorous treatment for the first time. We employ a Caldeira-Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study the effects of non-Markovian thermal fluctuations and dissipation at finite temperature in a rigorous manner. Hysteresis, double plateau-like behavior, and self-excited current oscillation are observed in a negative differential resistance (NDR) region of the current-voltage curve. We find that while most of the current oscillations decay in time in the NDR region, there is a steady oscillation characterized by a tornado-like rotation in the Wigner space in the upper plateau of the NDR region.KEYWORDS: quantum transport, Caldeira-Leggett, dissipative dynamics, resonant tunneling, non-MarkovianThe Caldeira-Leggett (or Brownian) Hamiltonian has been applied to the investigation of quantum dissipative dynamics in several fundamental contexts, including quantum tunneling, 1-3) chemical reactions, 4) SQUID rings, 5) nonlinear optical response, 6) and quantum ratchets. 7) Because a complete model of quantum dissipative dynamics must treat phenomena that can only be described in real time, a great deal of effort has been dedicated to the problem of numerically integrating equations of motion derived from the Hamiltonian that describe real-time behavior. [8][9][10] Although such equations are analogous to the classical kinetic equations, which have proved to be useful in the study of classical transport phenomena, they are difficult to derive in a quantum mechanical framework without approximations and/or assumptions.In this paper, we demonstrate that the reduced hierarchy equations of motion (HEOM) in the Wigner space representation provide a powerful method to study quantum dissipative dynamics in systems subject to non-Markovian and non-perturbative thermal fluctuations and dissipation at finite temperature. [11][12][13][14][15] As an example, we employ a model describing the thermal effects in resonant tunneling diodes (RTDs). 16,17) Although the validity of the Caldeira-Leggett Hamiltonian for describing electron transport phenomena has not yet been investigated thoroughly, because it has a firm quantum mechanical foundation, and because we feel that it is necessary to investigate the validity of the previous theoretical results in a fully quantum mechanical treatment, we believe that the present study will be helpful in constructing a general understanding of electron transport phenomena.Due to quantum effects, an RTD system exhibits novel negative differential resistance (NDR) in its current-voltage (I-V ) relation. 18) Moreover, current oscillations, 19) plateaulike behavior and hysteresis of the I-V curve have been observed in the NDR region. 20) Theoretically, Frensley found NDR in the I-V curve in...

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An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

Sakurai

Tanimura

2013

J. Phys. Soc. Jpn.

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“…The topic of quantum plasmas has received considerable attention in the recent literature [1]- [8]. The main reason for this is the increasing importance of quantum effects in the manufacturing process and performance of today's micro-electronic devices.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a three-stream quantum-plasma equilibrium

Haas¹,

Manfredi²,

Goedert³

2003

Braz. J. Phys.

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We apply the Nyquist method to analyze the stability of small amplitude electrostatic waves in quantum plasmas described by the Wigner-Poisson system. The technique is presented in detail to assess the stability of a threestream equilibrium distribution function. The topology of the Nyquist diagrams is substantially changed with increasing quantum diffraction effects. I IntroductionThe topic of quantum plasmas has received considerable attention in the recent literature [1]- [8]. The main reason for this is the increasing importance of quantum effects in the manufacturing process and performance of today's micro-electronic devices. For instance, no classical transport model can adequately incorporate quantum effects such as resonant tunnelling, which is the basis for the operation of devices like the resonant tunnelling diode. Accordingly, there has been much work dedicated to the development of quantum transport models. One of such models is provided by the Wigner-Poisson system [9,10], which is the main concern of the present paper. We address the question of the stability of small amplitude electrostatic waves described by the Wigner-Poisson system. In the formal classical limit, the Wigner-Poisson system goes into the Vlasov-Poisson system, with linear stability properties much better understood than those of the corresponding quantum model. One natural question in this regard is: how do quantum effects modify the linear stability properties of typical classical plasma equilibria? Here we address this question in detail for the case of a three-stream plasma equilibrium.The subject of quantum plasma stability is a subtle one. In [11] it was shown that two counter-streaming beams generate a linearly unstable mode that is not present in the corresponding classical situation. In the opposite direction, for large wave-numbers quantum effects are responsible for the suppression of all unstable modes. The extra details appearing in the quantum context can be traced back to the subtle nature of quantum wave-particle interactions in a plasma. In [12], the quantum plasma instability question is addressed by means of the Nyquist method. Let ´ µ Ö´ µ · ´ µ ¼ be the dispersion relation for the quantum plasma, where and are the frequency and wave-number of linear waves, and where the dispersion function is decomposed into its real and imaginary parts. In the Nyquist method, the stability of a mode of fixed wave-number is checked by varying (taken as a real variable) from minus to plus infinity. Drawing the corresponding curve in the Ö ¢ plane, we obtain the socalled Nyquist diagrams. The number of unstable modes is equal to the number of times the Nyquist diagram encircles the origin. For Vlasov-Poisson plasmas, the Nyquist method shows that monotonically decreasing equilibrium functions of the energy are stable against small amplitude perturbations. Also, in this classical case the sign of the associated Penrose functional [13,14] determines the linear stability of symmetric equilibria with at most two maxima. For Wigner...

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“…In real systems, even onedimensional problems can be quite difficult to solve analytically and often approximative, such as in perturbation theory, and/or numerical methods are required [1][2][3][4][5][6]. Semiconductor heterostructures are good examples of one-dimensional systems of technological interest where numerical solutions of the Schrödinger equation (SE) are often employed for self-consistent studies of electronic devices [7][8][9][10][11]. Studies of vibrational bound states of molecules in physical chemistry, as well as of other oscillatory systems in atomic and nuclear physics are treated as one-dimensional problems when summarized in the radial SE; they consist another class of important examples in which numerical methods are also often employed [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

General recursive solution for one-dimensional quantum potentials: a simple tool for applied physics

Morelhão¹,

Perrotta²

2007

Rev. Bras. Ens. Fis.

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A revision of the recursive method proposed by S.A. Shakir [Am. J. Phys. 52, 845 (1984)] to solve bound eigenvalues of the Schrödinger equation is presented. Equations are further simplified and generalized for computing wave functions of any given one-dimensional potential, providing accurate solutions not only for bound states but also for scattering and resonant states, as demonstrated here for a few examples. Keywords: one-dimensional quantum potentials, numerical solutions, computational methods, Schrödinger equation.Uma revisão do método recursivo proposto por S.A. Shakir [Am. J. Phys. 52, 845 (1984)] para solucionar autovalores de estados ligados da equação de Schrödingeré apresentado. As equações são ainda mais simplificadas e generalizadas para computar funções de onda em qualquer potencial unidimensional, fornecendo soluções acuradas não somente para estados ligados mas também para problemas de espalhamento e ressonância, como demonstrado aqui em alguns exemplos. Palavras-chave: potenciais quânticos unidimensionais, soluções numéricas, métodos computacionais, equação de Schrödinger.

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Self-consistent study of the resonant-tunneling diode

Cited by 436 publications

References 57 publications

An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

Stability analysis of a three-stream quantum-plasma equilibrium

General recursive solution for one-dimensional quantum potentials: a simple tool for applied physics

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