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MobilityElectrons in doped semiconductor that is thermalised at room temperature have a thermal energy which allows

them to wander in any direction. Under thermal equilibrium, elementary statistical mechanics tells us that the

average kinetic energy associated with each electron, is 1/2 kB

T , per degree of freedom, and since the electron is

free to wander in 3 dimensions the total kinetic energy is given by

(1)

The electron travels in a straight line until it path is influenced by another atom in the lattice, impurity atom or other

scattering mechanism. The average distance which the electron travels before being scattered is known as the

mean-free path and the average time between collisions is imaginatively called the mean-free time t c . As you might

expect, it depends on the material but typical magnitudes are 10 -5 cm and a few picoseconds, respectively.

If an electric field E is applied across the semiconductor, the free electrons will experience a force F =- qE . In the

opposite direction of the field (since the electron has negative charge). Now the additional component of the electric

field is imposed on the random motion of the electron causing an overall drift in the opposite direction to the electric

field.

By equating the momentum gained by the electron during its mean free flight to the momentum lost in a collision we

can obtain the drift velocity.

(2)

(3)

We call the ratio of the drift velocity to the applied electric field the mobility and it has the units (cm 2 V -1 s -1 ). A

similar argument applies to holes in the valence band, with the result that the mobility is given by (5) where we have

used m h* as the effective mass of the hole.

(4)

(5)

Coming soon

Table 1. Electron and Hole mobilities for various semiconductor materials

Looking at equations (4) and (5) we can see that mobility is directly effected by the mean free time for electrons andholes which is determined by the various scattering mechanisms. The most important are lattice scattering and

impurity scattering.

Lattice scattering results from the thermal motion of the lattice atoms at temperatures above T= 0 K. The agitation of

ier Mobility in Semiconductors http://britneyspears.ac/physics/mobility/mobility.htm

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the atoms cause variations in the potential resulting in the emission of phonons which transfer energy between the

lattice and the free carriers. Lattice scattering becomes dominant at higher temperatures because lattice vibrations

increase with increasing temperature. A full theoretical analysis is shows that the mobility due to lattice scattering

varies as T -3/2 .

Impurity scattering results from the ionised donor and acceptor impurities. A passing charge carrier will be deflected

due to the Coulomb force between it and the ion. The probability of impurity scattering depends on the doping

density and the proportion of those atoms that are ionised. Impurity scatting become less significant with

temperature since above a certain temperature, the impurity atoms will have ionised and also the charge carriers

are moving faster and interact with the impurity for a shorter time. The variation mobility due to impurity scattering

decreases as T 3/2 / N T , where N T is the total impurity concentration.

In summary, the total scattering time is the sum of two scatting times, the lattice scatting time t L and the impurity

scattering time t I . Using (4) we can simply obtain (7),

(6)

(7)

References[1] Ilegems, M., Montgomery, H.C., J. Phys. Chem. Solids 34 (1972) 885.

[2] Ilegems, M., Dingle, R., J. Appl. Phys. 44 (1973) 4234.

[3] Crouch, R.K., Debnam, W.J., Fripp, A.L., J. Mater. Sci. 13 (1978) 2358.

[4] S. M. Sze, Semiconductor Devices Physics and Technology.

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