Determination of diffusion coefficients in degenerate electron gas using Monte Carlo simulation

Thobel, Jean-Luc; Sleiman, A.; Fauquembergue, R.

doi:10.1063/1.365892

Cited by 17 publications

(16 citation statements)

References 12 publications

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“…Most published papers assume this relation to hold only for non-degenerate materials. Therefore, at thermal equilibrium, the diffusion coefficient D of charge carriers in a degenerate semiconductor is often related to the mobility µ through the modified relation [2] [3] [5]- [8]:…”

Section: Introductionmentioning

confidence: 99%

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Transport of Electrons in Donor-Doped Silicon at Any Degree of Degeneracy of Electron Gas

Palenskis¹

2014

WJCMP

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The general expressions, based on the Fermi distribution of the free electrons, are applied for calculation of the kinetic coefficients in donor-doped silicon at arbitrary degree of the degeneracy of electron gas under equilibrium conditions. The classical statistics lead to large errors in estimation of the transport parameters for the materials where Fermi level is located high above the conduction band edge unless the effective density of randomly moving electrons is introduced. The obtained results for the diffusion coefficient and drift mobility are discussed together with practical approximations applicable for non-degenerate electron gas and materials with arbitrary degree of degeneracy. In particular, the drift mobility of randomly moving electrons is found to depend on the degree of degeneracy and can exceed the Hall mobility considerably. When the effective density is introduced, the traditional Einstein relation between the diffusion coefficient and the drift mobility of randomly moving electrons is conserved at any level of degeneracy. The main conclusions and formulae can be applicable for holes in acceptor-doped silicon as well.

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Section: Introductionmentioning

confidence: 99%

“…shows, how many times the mean kinetic energy E of randomly moving charge carrier is larger than ( ) 3 2 kT . The average kinetic energy of randomly moving electron E is defined by…”

Section: Introductionmentioning

confidence: 99%

Transport of Electrons in Donor-Doped Silicon at Any Degree of Degeneracy of Electron Gas

Palenskis¹

2014

WJCMP

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“…The above definition of diffusivity is valid only for noninteracting particles, and thus for the case of a nondegenerate electron gas. For degenerate conditions a modified method, assuming the study of two ensembles of background and excess particles, has been proposed . Recently, this method has been successfully applied also to the studies of two‐dimensional graphene .…”

Section: Theoretical Modelmentioning

confidence: 99%

Monte Carlo studies of low‐field electron transport in monolayer silicene and graphene

Borowik

Thobel

Adamowicz

2016

Physica Status Solidi (a)

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Electron mobility and diffusion coefficients in monolayer silicene and graphene are calculated by Monte Carlo simulations using a simplified band structure with linear energy bands. Temperature evolution of the low-field mobility and diffusion coefficients is presented. Calculated characteristics of the low-field mobility in silicene exhibit a 1/T 3 dependence for nondegenerate electron gas conditions, which is attributed to dominant acoustic phonon scattering and to the linear band structure of the material. In degenerate conditions, a 1/T dependence is found in silicene. In graphene, there is no such simple power relation since optical and acoustic phonon scattering have comparable influences on electron transport. It is also found that electron-electron scattering only slightly modifies the low-field electron mobility in a degenerate electron gas.

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“…The average in the above equation must be taken over 'excess' electrons only. Details about the application of this method to MC simulations are given in [14].…”

Section: Diffusion Coefficients In Degenerate Electron Gasmentioning

confidence: 99%

“…Nevertheless, conventional MC simulation cannot yield the diffusion coefficients in a degenerate electron gas, owing to carrier-carrier correlations induced by Pauli exclusion. Recently, a new technique has been proposed in order to overcome this limitation [14]. In this paper we apply this method to the study of diffusion coefficients in degenerate bulk GaAs.…”

Section: Introductionmentioning

confidence: 99%

Oleg Matveevich Nefedov

2006

Russ. Chem. Rev.

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Standard Monte Carlo methods for calculating diffusivity fail when the degeneracy of the electron gas is important. We apply a recently proposed Monte Carlo procedure in order to study diffusion coefficients in degenerate bulk GaAs at 77 K. Two sets of electrons are simulated, the first one representing the uniform 'background' electron density and the second one accounting for additional 'excess' electron concentration. The diffusion coefficients are calculated accounting for 'excess' electrons only. We compare the results obtained using this method with those obtained using the standard technique. We report diffusivity-field characteristics for several electron concentrations. Obtained zero-field values are in good agreement with those predicted by the Einstein relation. We found that, in the low-field region, diffusion coefficients evolve quite slowly with the electric field and the isotropy is conserved.

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Determination of diffusion coefficients in degenerate electron gas using Monte Carlo simulation

Cited by 17 publications

References 12 publications

Transport of Electrons in Donor-Doped Silicon at Any Degree of Degeneracy of Electron Gas

Transport of Electrons in Donor-Doped Silicon at Any Degree of Degeneracy of Electron Gas

Monte Carlo studies of low‐field electron transport in monolayer silicene and graphene

Oleg Matveevich Nefedov

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