Diffusion coefficient of electrons in silicon

Brunetti, Rossella; Jacoboni, Carlo; Nava, F.; Reggiani, L.; Bosman, G.; Zijlstra, R.J.J.

doi:10.1063/1.328622

Cited by 153 publications

(62 citation statements)

References 25 publications

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“…The scattering rate for intervalley scattering is usually calculated using a deformationpotential-type analysis 26 and values of the optical-phonon energies and coupling constants have been inferred from experiment and Monte Carlo simulations. [43][44][45][46] However, the materials we examine in this study are quite different from single-crystal silicon or germanium, and we find that the intervalley parameters inferred for silicon, germanium, or an interpolation of the two, cannot explain the experimental data we analyze in this work. The most likely reasons for this discrepancy are the different phonon spectra between single-crystal silicon or germanium and SiGe alloys, and different coupling constants due to additional scattering mechanisms and high carrier concentrations in the SiGe alloys.…”

Section: B Charge-carrier Relaxation Timescontrasting

confidence: 47%

Modeling study of thermoelectric SiGe nanocomposites

et al. 2009

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Nanocomposite thermoelectric materials have attracted much attention recently due to experimental demonstrations of improved thermoelectric properties over those of the corresponding bulk material. In order to better understand the reported data and to gain insight into transport in nanocomposites, we use the Boltzmann transport equation under the relaxation-time approximation to calculate the thermoelectric properties of n-type and p-type SiGe nanocomposites. We account for the strong grain-boundary scattering mechanism in nanocomposites using phonon and electron grain-boundary scattering models. The results from this analysis are in excellent agreement with recently reported measurements for the n-type nanocomposite but the experimental Seebeck coefficient for the p-type nanocomposite is approximately 25% higher than the model's prediction. The reason for this discrepancy is not clear at the present time and warrants further investigation. Using new mobility measurements and the model, we find that dopant precipitation is an important process in both n-type and p-type nanocomposites, in contrast to bulk SiGe, where dopant precipitation is most significant only in n-type materials. The model also shows that the potential barrier at the grain boundary required to explain the data is several times larger than the value estimated using the Poisson equation, indicating the presence of crystal defects in the material. This suggests that an improvement in mobility is possible by reducing the number of defects or reducing the number of trapping states at the grain boundaries.

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Section: B Charge-carrier Relaxation Timescontrasting

confidence: 47%

Modeling study of thermoelectric SiGe nanocomposites

et al. 2009

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“…1) at 300 K. Here, the longitudinal diffusion coefficient D l in the 100 crystallographic direction is plotted as a function of electric field where the experimental results obtained from ref. [4] are based on the time of flight of technique. From Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Prior work has extracted the diffusion Tarik coefficient for various materials [4][5][6]. Diffusion is related to the spatial spreading of an ensemble of carriers with time as the ensemble responds to both applied drift forces and random forces, such as collision events.…”

Section: Methodology: the Monte Carlomentioning

confidence: 99%

Subthreshold Mobility Extraction for SOI-MESFETs

Khan

Vasileska

Thornton³

2004

J Comput Electron

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Mobility calculation is a difficult task due to the stochastic nature of the particles in a device. This is especially true for a device operated in the sub-threshold region because the transport is a combination of diffusion and drift albeit diffusion dominated. As a result, one can calculate the mobility based on the drift and the diffusion techniques for a device operated in the subthreshold regime. We have developed a transport model, based on the solution of the Boltzmann Transport Equation, for modeling n-channel silicon-on-insulator (SOI) MOSFETs and MESFETs using the Ensemble Monte Carlo technique. All relevant scattering mechanisms for the silicon material system have been included in the model. The model is used to calculate both the diffusion coefficient and the drift based mobility and the results are compared with available experimental values. The mobility of the equivalent SOI MESFET device is a factor of 3-5 times higher than that of the MOSFET in the sub-threshold regime.

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“…In general, the tables are calculated for bulk materials, whence a possible effect of the gradients of the unknowns on the coefficients is lost [20]; in contrast, the surface-scattering effect, which is paramount in MOS devices, has recently been incorporated in the full solution of the BTE based on the spherical-harmonics expansion [21]. In the following, results of relaxation-time calculations are shown, obtained by means of a Monte Carlo simulator for electron transport in Si accounting for the full three-dimensional electron dynamics in the k space for a homogeneous system and including six ellipsoidal, nonparabolic valleys associated to the minima of the conduction band [22,23]. The relaxation times have been determined through the Monte Carlo calculation of the distribution function, the collision integral on the right-hand side of the BTE and the averages in (2.3.5), (2.3.7) and (2.3.9).…”

Section: )mentioning

confidence: 99%

Hydrodynamic simulation of semiconductor devices

Rudan

Lorenzini

Brunetti

1998

Theory of Transport Properties of Semiconductor Nanostructures

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INTRODUCTIONRecently the hydrodynamic model has become popular in the field of analysis and simulation of semiconductor devices*. The model has the merit of providing, along with the concentration and current density of the carriers, also their average energy and average energy flux. At the same time, its equations basically retain the same structure of the simpler drift-diffusion model; because of this, it has been possible to incorporate the hydrodynamic equations into existing deviceanalysis codes, thus exploiting a number of robust solution schemes already available there.The hydrodynamic model is derived by applying the moment technique to the Boltzmann transport equation (BTE) and truncating the series of moments at a suitable order. This yields a number of partial differential equations in the r, t space, specifically, the continuity equations for the carrier number, momentum, average energy and average energy flux. In this procedure, due to the integration over the wave vector space and to the series truncation, some of the information originally carried by the distribution function is lost. However, the information provided by the continuity equations indicated above is in most cases sufficient to describe the electrical behaviour of realistic semiconductor devices.It is worth noting that the term hydrodynamic model is not always given exactly the same meaning in the existing literature. What is meant here by this term is a model derived through the following steps: * Part of this work was carried out within ADEQUAT (JESSI BTl I, ESPRIT 8002) and DESSIS (ESPRIT 6075). E. Schöll (ed.), Theory of Transport Properties of Semiconductor Nanostructures

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Diffusion coefficient of electrons in silicon

Cited by 153 publications

References 25 publications

Modeling study of thermoelectric SiGe nanocomposites

Modeling study of thermoelectric SiGe nanocomposites

Subthreshold Mobility Extraction for SOI-MESFETs

Hydrodynamic simulation of semiconductor devices

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