Description of Movement of Carriers in Semiconductors
Electrons and holes in the respective in the conduction band and valence band are said to be free carriers based on that their free movement across the whole semiconductor lattice that forms the material’s crystal structure. The carrier movement can be described simply –yet adequately- as the movement of each carrier in a random direction at a specific velocity.
The scattering length is the distance the carrier moves in the random direction before colliding with a lattice atom. After the collision happens, the carrier then moves away in a changed random direction.
The carriers’ velocity is based on the temperature of the lattice. The average velocity of the carrier is the thermal velocity. The carrier’s thermal velocity is normally distributed around the carriers average thermal velocity. Hence, some carriers have a lower velocity while others have higher.
Excluding specific conditions there is no net outcome for movement of carriers in a certain direction. Every direction for movement of carrier is equally possible. As a result, the carrier’s motion in a single direction will ultimately be negated by the carrier’s movement in an opposite direction.
Therefore, despite a semiconductor’s carriers being in continuous random motion, there can’t be a net motion of all carriers except if there exists an electric field, or a concentration gradient.
What causes Movement of Carriers in Semiconductors
All movements of free carriers in the semiconductor produces a current. This movement can be triggered by some electric field due to a voltage which is applied externally, because of the carriers being charged particles. This transport mechanism will be referred to as carrier drift. Also, carriers move away from areas of high carrier density is high to areas of lower carrier density. Thermal energy and the random motion of carriers associated with it causes this carrier transport. This transport mechanism is referred to as carrier diffusion. The semiconductor’s total current is equal to the sum of the two currents: the drift current and the diffusion current.
When an electric field is applied to a semiconductor, the electrostatic force at first makes the carriers accelerate and after that reach v (the constant average velocity) because of lattice vibrations and collisions with impurities. Mobility is defined as a ratio of the velocity to the applied field. At high electric fields the velocity saturates where it reaches the saturation velocity. When carriers flow at the semiconductor’s surface some extra scattering happens. And it leads to a lower mobility because of the interface or surface scattering mechanisms.
Carriers diffusion is achieved by the creation of a carrier density gradient. This gradient can be achieved by changing the doping density in the semiconductor or by the application of a thermal gradient. The two carrier transport mechanisms are linked because of the involvement of the similar particles and scattering mechanisms. This creates the Einstein relation which is the relationship between the mobility and the diffusion constant.