Multi-band Wigner function formulation of quantum transport

Ünlü, Mehmet; Rosen, Bernard; Cui, Hong‐Liang; Zhao, Pei‐Ji

doi:10.1016/j.physleta.2004.05.022

Cited by 13 publications

(8 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution f (0) = ϕ given by (51)-(54) is essentially the local equilibrium Ω given by (26)-(28) modified by the field-dependent terms Θ i that appear in the Wigner equations (13) and (14). This solution yields convective terms in the balance equations which contain first order differences.…”

Section: The Chapman-enskog Methods and Balance Equationsmentioning

confidence: 99%

“…For the same system, multiband Wigner function approaches have also been considered [14][15][16][17] . Unlu et al 14 use a nonequilibrium Green function formulation that includes scattering due to weak coupling to a phonon bath to derive equations for the multiband Wigner functions. A treatment of space-dependent but time-independent NGF and Wigner functions in MOSFET can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Two miniband model for self-sustained oscillations of the current through resonant-tunneling semiconductor superlattices

Alvaro

Bonilla

2010

Phys. Rev. B

View full text Add to dashboard Cite

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 ChapmanEnskog 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.

show abstract

Section: The Chapman-enskog Methods and Balance Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two miniband model for self-sustained oscillations of the current through resonant-tunneling semiconductor superlattices

Alvaro

Bonilla

2010

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…After taking the transient portion of the WTE into account, the discretized WTE finally results in To summarize, by comparing (25) to this results, the proper numerical approximation of the corresponding differential operators can be determined resulting in…”

Section: Derivation Of the Phase Space Exponential Operatormentioning

confidence: 99%

“…Here, the proper numerical treatment of second-order derivatives within the Wigner formalism is discussed. Indeed, when multi-band Hamiltonians are considered, a numerical approximation of second-order derivatives is mandatory [25]. The formalism is utilized to include the spatially varying effective mass, which represents by far the simplest system, in which the Wigner formalism considers a second-order derivative.…”

Section: Introductionmentioning

confidence: 99%

Formulation of a phase space exponential operator for the Wigner transport equation accounting for the spatial variation of the effective mass

Schulz

2020

J Comput Electron

View full text Add to dashboard Cite

A novel numerical approximation technique for the Wigner transport equation including the spatial variation of the effective mass based on the formulation of an exponential operator within the phase space is derived. In addition, a different perspective for the discretization of the phase space is provided, which finally allows flexible discretization patterns. The formalism is presented by means of a simply structured resonant tunneling diode in the stationary and transient regime utilizing a conduction band Hamilton operator. In order to account for quantum effects within heterostructure devices adequately, the corresponding spatial variation of the effective mass is considered explicitly, which is mostly disregarded in conventional methods. The results are validated by a comparison with the results obtained from the nonequilibrium Green's function approach within the stationary regime assuming the flatband case. Additionally, the proposed approach is utilized to perform a transient analysis of the resonant tunneling diode including the self-consistent Hartree-Fock potential.

show abstract

“…[18]. This approach to the exclusion principle is not general and is valid in situations that are not too far from semi-classical transport, meaning that the Green's function G < (x,k;E) has non zero values only around…”

Section: ∑ ∫ ∫mentioning

confidence: 99%

Wigner ensemble Monte‐Carlo simulation of nano‐MOSFETs in degenerate conditions

Querlioz

Saint-Martin

et al. 2008

Phys. Status Solidi (c)

View full text Add to dashboard Cite

Wigner quasi‐distribution function is an appropriate quantum mechanics formulation to study the transition from semi‐classical to quantum transport in nano‐devices since it can accurately describe quantum transport including the decoherence due to scatterings. We have recently developed an efficient approach to solving the Wigner transport equation using a Monte Carlo (MC) algorithm that has been applied to Resonant Tunnelling Diodes and nano‐MOSFET simulation. The approach is here extended to incorporate degeneracy effects that are important in highly doped MOSFETs. The calculation is compared with Non Equilibrium Green's Function and the semi‐classical Boltzmann equation. Relative importance of quantum transport and decoherent scattering is discussed at low and room temperatures. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

show abstract

Multi-band Wigner function formulation of quantum transport

Cited by 13 publications

References 22 publications

Two miniband model for self-sustained oscillations of the current through resonant-tunneling semiconductor superlattices

Two miniband model for self-sustained oscillations of the current through resonant-tunneling semiconductor superlattices

Formulation of a phase space exponential operator for the Wigner transport equation accounting for the spatial variation of the effective mass

Wigner ensemble Monte‐Carlo simulation of nano‐MOSFETs in degenerate conditions

Contact Info

Product

Resources

About