The quantum Boltzmann equation in semiconductor physics

Snoke, D. W.

doi:10.1002/andp.201000102

Cited by 27 publications

(22 citation statements)

References 55 publications

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“…4c demonstrates that the phase space for CM and Auger recombination in 2d MDF bands vanishes. We will return to this issue later, in connection with the calculation of the e-e contribution to the collision integral in the SBE 36 .…”

Section: Resultsmentioning

confidence: 99%

“…We use this knowledge of Coulomb-mediated collisions in the framework of the SBE, the standard tool to investigate electron dynamics in metals and semiconductors 36,37 . We consider the equations of motion for the electron [f s,m (k)] and phonon [n ðnÞ q ] distributions, including transverse and longitudinal optical phonons at the C and K points of the Brillouin zone [38][39][40] .…”

Section: Resultsmentioning

confidence: 99%

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Ultrafast collinear scattering and carrier multiplication in graphene

et al. 2013

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Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic and nanophotonic materials. The interaction of light with charge carriers creates an out-ofequilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools emitting phonons. Although the slower relaxation mechanisms have been extensively investigated, the initial stages still pose a challenge. Experimentally, they defy the resolution of most pump-probe setups, due to the extremely fast sub-100 fs carrier dynamics. Theoretically, massless Dirac fermions represent a novel many-body problem, fundamentally different from Schrödinger fermions. Here we combine pump-probe spectroscopy with a microscopic theory to investigate electron-electron interactions during the early stages of relaxation. We identify the mechanisms controlling the ultrafast dynamics, in particular the role of collinear scattering. This gives rise to Auger processes, including charge multiplication, which is key in photovoltage generation and photodetectors.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Ultrafast collinear scattering and carrier multiplication in graphene

et al. 2013

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“…The distribution function f k, ,s,σ represents the probability that a given single-particle state with quantum numbers k, , s, σ is occupied. The equation of motion (EOM) for this distribution function in the presence of e-e interactions is given by [83][84][85] :…”

Section: B Electron-electron Interactionsmentioning

confidence: 99%

Nonequilibrium dynamics of photoexcited electrons in graphene: Collinear scattering, Auger processes, and the impact of screening

et al. 2013

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We present a combined analytical and numerical study of the early stages (sub-100 fs) of the non-equilibrium dynamics of photo-excited electrons in graphene. We employ the semiclassical Boltzmann equation with a collision integral that includes contributions from electron-electron (e-e) and electron-optical phonon interactions. Taking advantage of circular symmetry and employing the massless Dirac Fermion (MDF) Hamiltonian, we are able to perform an essentially analytical study of the e-e contribution to the collision integral. This allows us to take particular care of subtle collinear scattering processes-processes in which incoming and outgoing momenta of the scattering particles lie on the same line-including carrier multiplication (CM) and Auger recombination (AR). These processes have a vanishing phase space for two dimensional MDF bare bands. However, we argue that electron-lifetime effects, seen in experiments based on angle-resolved photoemission spectroscopy, provide a natural pathway to regularize this pathology, yielding a finite contribution due to CM and AR to the Coulomb collision integral. Finally, we discuss in detail the role of physics beyond the Fermi golden rule by including screening in the matrix element of the Coulomb interaction at the level of the Random Phase Approximation (RPA), focusing in particular on the consequences of various approximations including static RPA screening, which maximizes the impact of CM and AR processes, and dynamical RPA screening, which completely suppresses them. arXiv:1305.5943v1 [cond-mat.mes-hall]

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“…The work on bulk semiconductor crystals has been carried out recently [1]. The large amount of work is being done on different semiconductor materials according to their utility towards society [2][3][4][5][6][7][8][9][10][11]. It is known that like X-rays, thermal neutrons have a de Broglie wavelength of the order of the interatomic spacings in crystals so that they can be used in diffraction studies [12].…”

Section: Introductionmentioning

confidence: 99%

Debye-Waller Factor in an Isotopically Disordered Semiconductor Crystal

Gairola

2016

Acta Phys. Pol. A

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The diagonal and non-diagonal parts for the Debye-Waller factor have been established using equation of motion technique of quantum dynamics and the Dyson equation approach. The double time temperature dependent phonon Green function has been taken to find the phonon linewidth and phonon shift. Renormalized mode frequency has been investigated in terms of electron-phonon coupling constant and temperature. The effect of electron-phonon interaction on the Debye-Waller factor has been studied in low temperature limit in low impurity concentration in semiconductor crystals.

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The quantum Boltzmann equation in semiconductor physics

Cited by 27 publications

References 55 publications

Ultrafast collinear scattering and carrier multiplication in graphene

Ultrafast collinear scattering and carrier multiplication in graphene

Nonequilibrium dynamics of photoexcited electrons in graphene: Collinear scattering, Auger processes, and the impact of screening

Debye-Waller Factor in an Isotopically Disordered Semiconductor Crystal

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