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Resonant Tunneling Diodes
Published in Vinod Kumar Khanna, Introductory Nanoelectronics, 2020
Description of the interaction of the electron with the double barrier structure is formulated in terms of the transmission coefficient T(Ez) representing the probability of tunneling of the electron through the structure: T(Ez)=ProbabilityfluxofthetransmittedwaveProbabilityfluxoftheincidentwave=OutgoingprobabilitycurrentdensityIncomingprobabilitycurrentdensity
Quantum Theory, Energy Bands of Solids, Effective Mass, and Holes
Published in Jyoti Prasad Banerjee, Suranjana Banerjee, Physics of Semiconductors and Nanostructures, 2019
Jyoti Prasad Banerjee, Suranjana Banerjee
The transmitted flux of electrons per unit area per unit time in units of cm−2 s−1 or the probability current is obtained by multiplying the probability density given in Equation (2.126)by the velocity of transmitted electrons in region III. Probability current in the real sense of the term can be obtained by multiplying the flux by electronic charge. If v3 be the velocity of transmitted electrons in region III, then the transmitted flux is |G|2⋅v3. Similarly, the incident flux of electrons in regions is |A|2⋅v1, where v1 is the electron velocity in region I.
Modeling and Analysis of Molecular Electronic Devices
Published in Sergey Edward Lyshevski, Molecular Electronics, Circuits, and Processing Platforms, 2018
The probability current density is J=(iℏ/2m)(Ψn(Ψn+1*−Ψn*/Δh)−Ψn*(Ψn+1−Ψn/Δh)).
The Dirac equation as a model of topological insulators
Published in Philosophical Magazine, 2020
Xiao Yuan, M. Bowen, P. S. Riseborough
The continuity equation for the probability density of the two-dimensional Rashba–Weyl equation is expressed in terms of the density, ρ, and current, densitieswhere the current density ρ and probability current are given byThe thermally averaged current density is given bywhere is the density matrix. The current density, evaluated with the equilibrium density matrix, is zero due to the temporal homogeneity of the equilibrium state. The system is perturbed by the introduction of a static electric field aligned along the x-axis, which is represented by the electrostatic interactionwhich has the effect of perturbing the density matrix by . In the presence of the perturbation remains a good quantum number. To linear-order in the perturbing interaction, the current density is found to bewhere are the Fermi–Dirac distribution for the occupation of the energy eigenstate . The above result corresponds to that found from the linear response theory for the case of a static perturbation.
On the nature of trapped states in an MoS2 two-dimensional semiconductor with sulfur vacancies
Published in Molecular Physics, 2019
Gabriela Ben-Melech Stan, Maytal Caspary Toroker
The time-dependent form of a propagating electron was calculated using the second-order split operator [29,30]. where is the time step of propagation. The exponential terms that contain the potential energy are diagonal in the x-grid basis and therefore are convenient to operate on the wavefunction. In practice, the exponent that contains the kinetic energy operator was transformed into Fourier space according to the Fast Fourier Transform (FFT) algorithm, where in the Fourier basis the kinetic energy term has a diagonal form with corresponding eigenvalues: The probability current is finally calculated according to where is the location of the flux measurement. is located after the vacancy, on the first Mo atom that wasn’t bonded to the absent S atom.
Attoclock revisited on electron tunnelling time
Published in Journal of Modern Optics, 2019
C. Hofmann, A. S. Landsman, U. Keller
For determining the duration of the tunnel ionization process, knowing the moment of when an electron exits from the potential barrier is of course not sufficient. The starting point , when an electron enters the potential barrier (in a pseudo-classical picture) must be defined, too. In strong-field ionization models such as PPT (3, 4), ADK (1, 2, 34), or many others (33, 35, 83, 84, 88) this intuitive definition is typically assigned to the complex transition point , which is a time calculated by the saddle point approximation (34). However, most of these models, with the notable exception of (35), then either define the ionization time to be the real part of , or the calculation automatically yields that relation due to a short-range potential approximation, and neglecting non-adiabatic effects during the tunnelling process (34, 35). This then leads to the interpretation that there is no (real) time passing while the electron tunnels through the potential barrier, since There are several publications suggesting that the starting time should be before the ionizing field reaches its maximum. In (18, 70), the authors monitor the probability current density in a one-dimensional TDSE calculation of strong field ionization. At the classical tunnel entry point , they find that the outflowing current maximizes clearly before the electric field reaches its maximum value. Furthermore, for a large range of intensities tested in (17), the classical backpropagation (after two-dimensional TDSE forward calculation) reaches classical turning points at times . By causality therefore, the starting times also must be . In the Coulomb-corrected non-adiabatic calculation of (35), the complex transition point found has a negative real component. Interestingly, the corresponding ionization time , which is the first time of the trajectory on the real axis, is larger than zero, see Figure 2(d) of (35). In consequence, this particular formalism predicts nonzero real time to pass while the photoelectron tunnels through the potential barrier.