Drift Current in ELECTRICAL CONDUCTION IN SOLIDS
Current is due to the net flow of charge. If we had a collection of positively charged ions with a volume density N (cm-3) and an average drift velocity Vd(cm/s), then the drift current density would be
If, instead of considering the average drift velocity, we considered the individual ion velocities, then we could write the drift current density as
where vi is the velocity of the ith ion. The summation in Equation (3.33) is taken over
a unit volume so that the current density J is still in units of A/cm2 .
Since electrons are charged particles, a net drift of electrons in the conduction
band will give rise to a current. The electron distribution in the conduction band, as
shown in Figure 3.14b. is an even function of k when no external force is applied. Recall
that k for a free electron is related to momentum so that, since there are as many
electrons with a +|k| value as there are with a -|k| value, the net drift current density due to these electrons is zero. This result is certainly expected since there is no
externally applied force.
If a force is applied to a particle and the particle moves, it must gain energy. This
effect is expressed as
where F is the applied force, dx is the differential distance the particle moves, v is the I
velocity, and dE is the increase in energy. If an external force is applied to the electrons
in the conduction band, there are empty energy states into which the electrons
can move: therefore, because of the external force, electrons can gain energy and a net
momentum. The electron distribution in the conduction band may look like that
shown in Figure 3.15, which implies that the electrons have gained a net momentum.
We may write the drift current density due to the motion of electrons as
where e is the magnitude of the electronic charge and n is the number of electrons
per unit volume in the conduction hand. Again, the summation is taken over a unit
volume so the current density is A/cm2 . We may note from Equation (3.35) that the
current is directly related to the electron velocity; that is, the current is related to how
well the electron can move in the crystal.
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If, instead of considering the average drift velocity, we considered the individual ion velocities, then we could write the drift current density as
where vi is the velocity of the ith ion. The summation in Equation (3.33) is taken over
a unit volume so that the current density J is still in units of A/cm2 .
Since electrons are charged particles, a net drift of electrons in the conduction
band will give rise to a current. The electron distribution in the conduction band, as
shown in Figure 3.14b. is an even function of k when no external force is applied. Recall
that k for a free electron is related to momentum so that, since there are as many
electrons with a +|k| value as there are with a -|k| value, the net drift current density due to these electrons is zero. This result is certainly expected since there is no
externally applied force.
If a force is applied to a particle and the particle moves, it must gain energy. This
effect is expressed as
where F is the applied force, dx is the differential distance the particle moves, v is the I
velocity, and dE is the increase in energy. If an external force is applied to the electrons
in the conduction band, there are empty energy states into which the electrons
can move: therefore, because of the external force, electrons can gain energy and a net
momentum. The electron distribution in the conduction band may look like that
shown in Figure 3.15, which implies that the electrons have gained a net momentum.
We may write the drift current density due to the motion of electrons as
where e is the magnitude of the electronic charge and n is the number of electrons
per unit volume in the conduction hand. Again, the summation is taken over a unit
volume so the current density is A/cm2 . We may note from Equation (3.35) that the
current is directly related to the electron velocity; that is, the current is related to how
well the electron can move in the crystal.
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