Bipolar Quantum Research Articles

Semiclassical limit for bipolar quantum drift-diffusion model

Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.

The logic of YinYang and the science of TCM: An eastern road to the unification of nature, agents and medicine

Many wonder whether Traditional Chinese Medicine (TCM) is science; many TCM practitioners are eager to fit TCM into western medicine for acceptance; some TCM scholars suggested to abandon YinYang in favour of western tradition; some researchers suggested to avoid relativistic and quantum theories in TCM research in favour of established scientific theories. Faced with these tough choices, this paper unveils the salient nature of YinYang related to Greek philosophy and identifies its critical role in logic, TCM, and modern science. Surprisingly, it is shown that YinYang bipolar relativity has opened an eastern road toward quantum gravity – Einstein's unfinished scientific unification of general relativity and quantum mechanics. Furthermore, it is shown that not only does YinYang bipolar quantum gravity constitute a physical theory but also a mental, logical, social, and biological quantum theory.

The Multidimensional Bipolar Quantum Drift-diffusion Model

Abstract We investigate the bipolar quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions. First, we establish the global weak solution with large initial value and periodic boundary conditions. Then we show the semiclassical limit by using new methods based on delicate interpolation estimates and compactness argument. Furthermore, when the doping profile is a constant, we find that the weak solution approaches its mean value exponentially as time increases to infinity.

Reconciling semiclassical and Bohmian mechanics. VI. Multidimensional dynamics

In previous articles [J. Chem. Phys. 121, 4501 (2004); J. Chem. Phys. 124, 034115 (2006); J. Chem. Phys. 124, 034116 (2006); J. Phys. Chem. A 111, 10400 (2007); J. Chem. Phys. 128, 164115 (2008)] an exact quantum, bipolar wave decomposition, psi=psi(+)+psi(-), was presented for one-dimensional stationary state and time-dependent wavepacket dynamics calculations, such that the components psi(+/-) approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well behaved, even when psi has many nodes or is wildly oscillatory. In this paper, both the stationary state and wavepacket dynamics theories are generalized for multidimensional systems and applied to several benchmark problems, including collinear H+H(2).

Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors

The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R 3 . We prove that the unique strong solution exists and converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and that of the classical drift–diffusion system under the combined relaxation and semiclassical limits.

Long-time self-similar asymptotic of the macroscopic quantum models

The unipolar and bipolar macroscopic quantum models derived recently, for instance, in the area of charge transport are considered in spatial one-dimensional whole space in the present paper. These models consist of nonlinear fourth-order parabolic equation for unipolar case or coupled nonlinear fourth-order parabolic system for bipolar case. We show for the first time the self-similarity property of the macroscopic quantum models in large time. Namely, we show that there exists a unique global strong solution with strictly positive density to the initial value problem of the macroscopic quantum models which tends to a self-similar wave (which is not the exact solution of the models) in large time at an algebraic time-decay rate.

ALGEBRAIC TIME DECAY FOR THE BIPOLAR QUANTUM HYDRODYNAMIC MODEL

The initial value problem is considered in the present paper for the bipolar quantum hydrodynamic (QHD) model for semiconductors in ℝ3. The unique strong solution exists globally in time and tends to the asymptotical state with an algebraic decay rate as time goes to infinity is proved. And, the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above and below is shown. This means that in general we cannot get an exponential time-decay rate for bipolar QHD system, which is different from the case of unipolar QHD model (where global solutions tend to the equilibrium state at an exponential time-decay rate) and is mainly caused by the nonlinear coupling and cancelation between two carriers. Moreover, it is also shown that the nonlinear dispersion does not affect the long time asymptotic behavior, which by product gives rise to the algebraic time-decay rate of the solution of the bipolar hydrodynamical model in the semiclassical limit.

Focus on lasers and optics

Focus on lasers and optics

Reconciling semiclassical and Bohmian mechanics. V. Wavepacket dynamics

In previous articles [B. Poirier J. Chem. Phys. 121, 4501 (2004); C. Trahan and B. Poirier, ibid. 124, 034115 (2006); 124, 034116 (2006); B. Poirier and G. Parlant, J. Phys. Chem. A 111, 10400 (2007)] a bipolar counterpropagating wave decomposition, psi = psi(+) + psi(-), was presented for stationary states psi of the one-dimensional Schrodinger equation, such that the components psi(+/-) approach their semiclassical Wentzel-Kramers-Brillouin analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well behaved, even when psi has many nodes, or is wildly oscillatory. In this paper, the method is generalized for time-dependent wavepacket dynamics applications and applied to several benchmark problems, including multisurface systems with nonadiabatic coupling.

Microscopic nonequilibrium theory of quantum well solar cells

We present a microscopic theory of bipolar quantum well structures in the photovoltaic regime, based on the non-equilibrium Green's function formalism for a multi band tight binding Hamiltonian. The quantum kinetic equations for the single particle Green's functions of electrons and holes are self-consistently coupled to Poisson's equation, including inter-carrier scattering on the Hartree level. Relaxation and broadening mechanisms are considered by the inclusion of acoustic and optical electron-phonon interaction in a self consistent Born approximation of the scattering self energies. Photogeneration of carriers is described on the same level in terms of a self energy derived from the standard dipole approximation of the electron-photon interaction. Results from a simple two band model are shown for the local density of states, spectral response, current spectrum, and current-voltage characteristics for generic single quantum well systems.

The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model*

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model, a fourth order parabolic system. Using semi-discretization in time and entropy estimate, the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann (or periodic) boundary conditions. Furthermore, by a logarithmic Sobolev inequality, it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.

Reconciling Semiclassical and Bohmian Mechanics: IV. Multisurface Dynamics

In previous articles (J. Chem. Phys. 2004, 121, 4501; 2006, 124, 034115; 2006, 124, 034116) a bipolar counter-propagating wave decomposition, Psi = Psi+ + Psi-, was presented for stationary states Psi of the one-dimensional Schrödinger equation, such that the components Psi+/- approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes or is wildly oscillatory. In this paper, the method is generalized for multisurface scattering applications and applied to several benchmark problems. A natural connection is established between intersurface transitions and (+ <--> -) transitions.

DEVELOPMENT AND NUMERICAL ANALYSIS OF "BLACK-BOX" COUNTERPROPAGATING WAVE ALGORITHM FOR EXACT QUANTUM SCATTERING CALCULATIONS

In a recent series of papers,1-3 a bipolar counter-propagating wave decomposition, Ψ = Ψ+ + Ψ-, was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ± approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Ψ has many nodes, or is wildly oscillatory. In this paper, the earlier results are used to construct an universal "black-box" algorithm, numerically robust, stable and efficient, for computing accurate scattering quantities of any quantum dynamical system in one degree of freedom.

Exponential decay to a quantum hydrodynamic model for semiconductors

This paper deals with large-time behavior of solutions for a viscous bipolar quantum hydrodynamic model with third-order terms. By applying the entropy method, we prove exponential decays of solutions towards constant steady states for the one-dimensional and the multi-dimensional cases. The argument is based on a series of a priori estimates. As a byproduct, the decay of solutions for the viscous hydrodynamic model is obtained as well.

LWIR/SWIR switchable two color device based on InP/InGaAs integrated HBT/QWIP

A novel two color infrared (IR) device that allows fast electrical switching between the short wavelength IR (SWIR) band (0.9–1.6μm) and the long wavelength IR (LWIR) band (8–12μm) is presented. The integrated sensor is based on MOCVD grown, lattice matched (to InP substrate) epilayers of InGaAs/InP and consists of two, monolithically integrated sections of heterojunction bipolar transistor (HBT) and quantum well infrared photodetector (QWIP).

On the bipolar multidimensional quantum Euler–Poisson system: The thermal equilibrium solution and semiclassical limit

In this paper we establish the existence of a unique thermal equilibrium solution of the bipolar multidimensional quantum Euler–Poisson system over the whole space R 3 and obtain the relevant semiclassical limit and a combined Planck–Debye length limit through using energy estimating methods and a fixed point theory.

Characterization of photonic devices by secondary electron potential contrast

Secondary Electron Potential Contrast has been shown recently to be a very effective method for two-dimensional mapping the dopant distribution in Silicon Carbide devices. This work extends the range of applications of the technique to the characterization of photonic devices. Special attention is paid here to the analysis of unipolar and bipolar junctions, heterostructures, and quantum wells.

Reconciling semiclassical and Bohmian mechanics. II. Scattering states for discontinuous potentials

In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition, psi = psi1 + psi2, was presented for stationary bound states Psi of the one-dimensional Schrodinger equation, such that the components psi1 and psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well behaved, even when psi has many nodes or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step potential, and square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a companion paper [C. Trahan and B. Poirier, J. Chem. Phys. 124, 034116 (2006), following paper].

Reconciling semiclassical and Bohmian mechanics. III. Scattering states for continuous potentials

In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition psi = psi1 + psi2 was presented for stationary bound states Psi of the one-dimensional Schrodinger equation, such that the components psi1 and psi2 approach their semiclassical WKB analogs in the large-action limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classical-like and well behaved, even when Psi has many nodes or is wildly oscillatory. A modification for discontinuous potential stationary scattering states was presented in a second, companion paper [C. Trahan and B. Poirier, J. Chem. Phys.124, 034115 (2006), previous paper], whose generalization for continuous potentials is given here. The result is an exact quantum scattering methodology using classical trajectories. For additional convenience in handling the tunneling case, a constant-velocity-trajectory version is also developed.

Bipolar quantum corrections in resolving individual dopants in ‘atomistic’ device simulation

In ‘atomistic’ device simulation the resolving of discrete charges onto a fine-grained simulation mesh can lead to problems. The sharply resolved Coloumb potential can cause simulation artefacts to appear in classical simulation environments using Boltzmann or Fermi–Dirac statistics. Various methods have been proposed in an effort to reduce or eliminate such artefacts as the localisation of mobile carriers by sharply resolved Coulomb wells, however they have met with limited success. In this paper we present an alternative approach for handling discrete charges in drift diffusion ‘atomistic’ simulations by properly introducing the related quantum mechanical effects using the density gradient formalism for both electrons and holes. This eliminates the trapping of mobile charge in heavily doped regions of the device and the related artefacts in the simulated device characteristics.