Drift Current

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 v_d (cm/s) , then the drift current density would be

(1)

If, instead of considering the average drift velocity, we considered the individual ion velocities, then we could write the drift current density as

(2)

where v_i is the velocity of the ith ion. The summation in Equation (2) 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 1.1b. 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.

Figure 1.1 The E versus k diagram ut the conduction and valence bands of a semiconductor at (a) T = 0 K and (b) T > 0 K.

If a force is applied to a particle and the particle moves, it must gain energy. This effect is expressed as

(3)

where F is the applied force, dx is the differential distance the particle moves, v is the velocity, and d E 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 1.2, which implies that the electrons have gained a net momentum.

We may write the drift current density due to the motion of electons as

(4)

where e is the magnitude of the electronic charge and n is the number of electrons per unit volume in the conduction band. Again, the summation is taken over a unit

Figure 1.2 The asymmetric distribution of electrons in the E versus k diagram when an external force is applied.

volume so the current density is A/cm². We may note from Equation (4) 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.