2.2.4 Summary to: Conductors - Definitions and General Properties
- Page ID
- 2762
What counts are the specific quantities:
|
\[[\rho]=\Omega\text{m}\\ [\sigma]=(\Omega\text{m})^{-1}=\mathbf{S/m} \text{; S = "Siemens"}\] |
The basic equation for σ is: n = concentration of carriers, µ = mobility of carriers. |
\[\sigma=|q|\cdot n\cdot \mu\] |
Ohm's law states: It is valid for metals, but not for all materials. |
\[\underline{j}=\sigma\cdot\color{purple}{\underline{E}}\] |
σ (of conductors / metals) obeys (more or less) several rules; all understandable by looking at n and particularly µ.
Matthiesen rule: |
\[\rho=\rho_\text{Lattice}(T)+\rho_\text{defect}(N)\] |
"ρ(T) rule": |
\[\Delta\rho=\alpha_\rho\cdot\rho\cdot\Delta T\approx\frac{0.4\%}{^\circ C}\] |
Nordheim's rule: Reason: Scattering of electrons at B atoms decreases µ. |
\[\rho\approx\rho_\text{A}+\text{const.}\cdot [B]\] |
Major consequence: You can't beat the conductivity of pure Agby "tricks" like alloying or by using other materials
(Not considering superconductors).
Non-metallic conductors are extremely important.
Transparent conductors (TCO's) ("ITO", typically oxides). |
No flat panels displays = no notebooks etc. without ITO! |
Ionic conductors (liquid and solid). | Batteries, fuel cells, sensors, ... |
Conductors for high temperature applications; corrosive environments, .. (Graphite, Silicides, Nitrides, ...). |
Example: MoSi2 for heating elements in corrosive environments (dishwasher!). |
Organic conductors (and semiconductors). | The future High-Tech key materials? |
Numbers to know (order of magnitude accuracy sufficient)
- ρ(decent metals) about 2 μΩcm.
- ρ(technical semiconductors) around 1 Ωcm.
- ρ(insulators) > 1 GΩcm.