SaM - Drift Current • Current Density Equation

Memory Card

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Transport Current = Motion of Electrons: ${\vec{J}}_n={\sigma }_n\vec{E}+q{D}_n(\nabla \cdot n)$ In one dimension:$J_n={\sigma }_{n}E$ Velocity of an electron: $\vec{v}=\frac{q\tau }{m_e^{\ast }}\vec{E}$ Relation between the avereage time between collisions ($\tau$) and the average free path ($\lambda$):$\tau =\frac{\lambda }{V_{TH}}$Where $v_{TH}$ is called the “mean thermal velocity”, and it is defined as:$V_{TH}=4\sqrt{\frac{kT}{2\pi m_e^{\ast }}}$The transport current, supposing an symmetrical distribution of carriers (so: $\nabla \cdot n=0$), will be equal to:\begin{align} \vec J_n & = n q \vec v \\[3px] & = \frac{n q^2 \tau}{m_e^*}\vec E \\[3px] & = \sigma_n \vec E \\[3px] & = n q \mu_n E \end{align}

• ==The time between collision ($\tau$), at $300$ Kelvin, is about $\frac{1}{10}$ of a picosecond==.
• ==While the free path ($\lambda$) is about $10$ nanometer==, this represents the length in average, that the electrons travels without colliding with another atom.