SaM - Ohm's Law

Remeber:

• Conductivity and resisitivty are reciprocal:$\rho =\frac{1}{\sigma }$
• We have defined the transport current (assuming $\nabla \cdot n=0$) as:${\vec{J}}_n={\sigma }_n\vec{E}$==This is also the definiton of the Ohm’s Law== (more commonly defined as $V=R\cdot I$).
  However, we need to make a distintion:

1. ==For metals==, we only care about electrons, so we can approximate this formula as we just saw:${\vec{J}}_n={\sigma }_n\vec{E}$

2. ==For semiconductors== instead, we also need to account for the holes:${\vec{J}}_n={\sigma }_n\vec{E}+{\sigma }_p\vec{E}$

• ==So $\sigma$ is conductivity==.
  ==And $\mu$ and is the mobility==.
• The relationship between conductivity and mobility is: ${\sigma }_n=nq{\mu }_n$Where:
  • $n$ is the charge carrier density.
  • $q$ is the charge of the electron, $q\simeq -1.6\cdot 10^{-19}\text{ C}$
• Also the mobility is defined as: ${\mu }_n=\frac{q\tau }{m_e^{\ast }}$

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Memory Card

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==So $\sigma$ is conductivity==.
==And $\mu$ and is the mobility==.

The conductivity is defined as: ${\sigma }_n=\frac{n{q}^2\tau }{m_e^{\ast }}$ The mobility is defined as: ${\mu }_n=\frac{q\tau }{m_e^{\ast }}$ The relationship between conductivity and mobility is: ${\sigma }_n=nq{\mu }_n$ Also the unit of measure of the two are:

• Conductivity: $[{\sigma }_n]=\frac{\mho }{\text{m}}$
• Mobility: $[{\mu }_n]=\frac{{\text{m}}^2}{\text{V}\cdot \text{s}}$

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Conductivity and Resisitivty are reciprocal:$\rho =\frac{1}{\sigma }$

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We have defined the transport current (assuming $\nabla \cdot n=0$) as ${\vec{J}}_n={\sigma }_n\vec{E}$This is also the definiton of the Ohm’s Law.

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We need to make a distintion:

1. For metals, we only care about electrons, so we can approximate this formula as we just saw:${\vec{J}}_n={\sigma }_n\vec{E}$
2. For semiconductors instead, we also need to account for the holes:${\vec{J}}_n={\sigma }_n\vec{E}+{\sigma }_p\vec{E}$

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