Conductivity Conductivity s is the ability to conduct

Conductivity • Conductivity s is the ability to conduct electric current. s=1/r, where r is the resistivity. • Both electrons and holes contributes to the conductivity in SM. • The higher the concentration of carriers, the higher the conductivity; • The more scattering the carriers experience, the lower the conductivity;

Mobility of the carriers in EM fields • Movements of carriers in EM fields: Random+drift

• In the following discussions, we take electrons as example. • Let field strength=E, and the effective mass of electron is m*, then the accelerator of the electron is • Suppose random scattering, i. e. , v=0 after each scattering, then we have average speed of carriers • where t is the average free time between two consecutive scatterings.

Definition of the mobility • Mobility m: average speed of carrier under unit field, which is a quantity reflects the easiness of carrier movements in SM. • Or

Mobility of common SM（cm 2/VSec） SM mn mp Silicon 1350 480 Germanium 3900 500 Gallium Arsenide 8000 100 -3000 It can be seen that the mobility of electrons are higher than that of holes, that why that electronic devices that based on N-type SM runs faster that devices based on p-type SM.

Dependence of m on doping level Why?

Dependence of m on T

Relation between Current density and mobility • Current density: charges pass through a unit area in unit time • Density of carriers: n, p; • Carriers in above column can pass through the unit area in unit time, so

Relation between Conductivity and mobility • Total conductivity of SM

Hot electrons—mobility under high field • When E>103 V/cm or so, • Since electric field will not affect carrier concentration until E~105 V/cm, when E~103 V/cm is mainly caused by the change of mobility, i. e. , m is not a constant when E> E~103 V/cm.

Dependence of the average drift speed of carriers on E for some SM

Reasons for the change of mobility • E=0, carrier and lattice are at thermal equilibrium; • When E is not too strong, carriers absorb energy from external field, and the speed of the carriers increase. At the same time, part of the absorbed energy give to lattice by scattering process which cause the SM become warm or even hot. • When E is very high, the speed of carriers is very fast, so scattering happens so frequently that all the absorbed energy from the external field gives to the lattice. The speed of the carrier no longer increase, which result the decrease of mobility. • Classical analogy: A ball free falls from the space: At the begin, when the speed is low, air friction is small, so the speed of the ball increases, but as the speed of the ball reaches a certain value, the kinetic energy gained from gravitational field are transferred to the air, and the speed of the ball no longer increase.

Some Phenomena of SM • • • Gunn’s effect Hall effect Magneto-resistance Thermoelectric Phonon-electron effect Ultrasonic amplification Mechanical pressure-resistance Mageneto-optical effect Quantum Hall effect

Gunn’s effect • In 1963, Gunn found that when the bias voltage reaches a certain value, , there are oscillations in the circuit at frequency of GHz. This phenomenon is called Gunn’s oscillation.

Gunn’s Diode

Physics of the Gunn’s effect • Characteristic of the band structure of Ga. As: 1, Direct band, a valley at k=0; 2, In [111] direction, there is another valley at L, which is 0. 29 e. V higher than the valley at k=0; • The effective mass at these two valleys are quite different, at L, m* is 0. 55, while at k=0, m*=0. 067.

Negative differential conductivity • When E is not too big, electrons in CB are near the valley at k=0, so m is big since the effective mass at k=0 is smaller; • When E is big enough, electrons can transfer from the valley at k=0 to the valley at L. Because the electrons at L is heavier, the speed of the electrons at L is also smaller, i. e. , m is smaller; • When such transition is severe, the conductivity decreases, and a I-V curve with negative differential appears; • Because of the negative resistance, the circuit is not stable, so oscillation ocuurs.

Relation between conductivity and carrier concentration • Not linear, there are some transitions. The reason for this is that the dominate scattering mechanism of the carrier changes. • In addition, when heavily doped, impurities are not fully ionized, which reduces carrier concentration, which results in nonlinear relation between doping level and conductivity. • For electrons and holes, because of the difference in effective mass, conductivities are different even when the carrier concentrations are the same.