scholarly journals Size and Grain-Boundary Effects in the Electrical Conductivity of Thin Monocrystalline Films

1978 ◽  
Vol 5 (2) ◽  
pp. 127-131 ◽  
Author(s):  
C. R. Tellier
Keyword(s):  
Electrical Conductivity ◽  
Relaxation Time ◽  
Boltzmann Equation ◽  
Reflection Coefficient ◽  
Grain Boundary ◽  
Boundary Effects ◽  
Boundary Scattering ◽  
Single Relaxation Time ◽  
Monocrystalline Film ◽  
Film Conductivity

By assuming that the scattering processes from other sources than grain-boundaries can be described by a single relaxation timeτ∗and then by solving a Boltzmann equation in which grain-boundary scattering is accounted for, we have obtained an analytical expression for the thin monocrystalline film conductivity in terms of the reduced thicknesskand the grain-boundary reflection coefficientr. Numerical tables are given to show the agreement of the above expression with the Mayadas-Shatzkes expression.

scholarly journals A New Analytical Expression for the T.C.R. of Thin Monocrystalline Metal Films

1979 ◽  
Vol 5 (4) ◽  
pp. 209-213 ◽  
Author(s):  
C. R. Tellier
Keyword(s):  
Electrical Conductivity ◽  
Relaxation Time ◽  
Reflection Coefficient ◽  
Grain Boundary ◽  
Metal Film ◽  
Approximate Equation ◽  
Metal Films ◽  
Exact Equation ◽  
Temperature Coefficient Of Resistivity ◽  
Comparison Of The Results

The analysis of electrical conductivity of continuous thin monocrystalline metal film has been treated by assuming that the scattering from other sources than grain-boundaries can be described by an effective relaxation time. This relaxation time method is applied to the temperature coefficient of resistivity and leads to an analytical approximate equation in terms of the grain-boundary reflection coefficientrand the reduced thicknessk.Comparison of the results with those deduced from the exact equation (derived from the Mayadas and Shatzkes theory) shows that they deviate by less than 5% in largek–,p–, andr– ranges.

Enhancing the average thermoelectric figure of merit of elemental Te by suppressing grain boundary scattering

2020 ◽  
Vol 8 (17) ◽  
pp. 8455-8461 ◽  
Author(s):  
Yehao Wu ◽  
Feng Liu ◽  
Qi Zhang ◽  
Tiejun Zhu ◽  
Kaiyang Xia ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Grain Boundary ◽  
Thermoelectric Materials ◽  
Figure Of Merit ◽  
Thermoelectric Figure Of Merit ◽  
Boundary Scattering ◽  
Thermoelectric Figure ◽  
Grain Boundary Scattering

Suppressed grain boundary scattering contributes to enhanced electrical conductivity and device zT in elemental Te based thermoelectric materials.

scholarly journals On the moment system and a flexible Prandtl number

2014 ◽  
Vol 28 (06) ◽  
pp. 1450048 ◽  
Author(s):  
Raúl Machado
Keyword(s):  
Relaxation Time ◽  
Boltzmann Equation ◽  
Prandtl Number ◽  
Lattice Boltzmann ◽  
Continuous Distribution ◽  
Lattice Boltzmann Equation ◽  
Collision Model ◽  
Single Relaxation Time ◽  
Moment System ◽  
The Moment

The Maxwell–Boltzmann moment system can be seen as a particular case of a mathematically more general moment system proposed by Machado.1 These last moments, of which a suggested continuous distribution and an integral generating form are presented here for some orders, are used in this paper to theoretically show (one of) their usefulness: A flexible Prandtl number can be obtained in both the Boltzmann equation and in the lattice Boltzmann equation with a conventional single relaxation time Bhatnagar–Gross–Krook (BGK) collision model.

scholarly journals Conductivity Size Effect of Square Cross-Section Polycrystalline Nanowires

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2129
Author(s):  
Rui Li ◽  
Lan Mi ◽  
Jian Wang ◽  
Mao Mao ◽  
Wenhua Gu ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Theoretical Model ◽  
Grain Boundary ◽  
Size Effect ◽  
Cross Section ◽  
External Surface ◽  
Surface Scattering ◽  
Boundary Scattering ◽  
Experiment Data ◽  
Carrier Scattering

A theoretical model for the electrical conductivity size effect of square nanowires is proposed in this manuscript, which features combining the three main carrier scattering mechanisms in polycrystalline nanowires together, namely, background scattering, external surface scattering, as well as grain boundary scattering. Comparisons to traditional models and experiment data show that this model achieves a higher correlation with the experiment data.

Effects Of Grain Boundaries on the Resistivity of Cosputtered Wsi2 Films

1981 ◽  
Vol 10 ◽  
Author(s):  
D. R. Campbell ◽  
S. Mader ◽  
W. K. Chu
Keyword(s):  
Thin Films ◽  
Grain Size ◽  
Reflection Coefficient ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Charge Carriers ◽  
Boundary Scattering ◽  
Grain Boundary Scattering

ABSTRACTResistivity and grain size measurements on thin films of co-sputtered WSi2 show that the resistivity in this material is dominated by grain boundary scattering. The reflection coefficient for the transport of charge carriers through the grain boundaries was determined to be approximately 0.9.

The relaxation time of conduction electrons in the noble met

1963 ◽  
Vol 275 (1361) ◽  
pp. 209-217 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Relaxation Time ◽  
Boltzmann Equation ◽  
Fermi Surface ◽  
Low Temperatures ◽  
Lattice Vibrations ◽  
Thermo Electric ◽  
Multiply Connected ◽  
Conduction Electrons ◽  
Experimental Values

The Boltzmann equation for scattering by impurities and lattice vibrations is solved numerically for a metal having a multiply-connected Fermi surface. It is found that the relaxation time for scattering by lattice vibrations at high temperatures or by impurities is approximately constant over the Fermi surface. For scattering by lattice vibrations at low temperatures the relaxation time is highly anisotropic. These results are consistent with the experimental values of the electrical conductivity but cannot predict a positive thermo ­ electric power.

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