Carrier Motion - Electric Fields ECE 2204

Movement of Electrons and Holes Nearly free electrons can easily move in a semiconductor since they are not part of a chemical bond between atoms. Valence electrons are shared between atoms. It turns out that a valence electron can also exchange places with another valence electron that is being shared with a different atom.

Since valence electrons can move, holes can move also.

Carrier Mobility and Velocity Mobility - the ease at which a carrier (electron or hole) moves in a semiconductor ▫Symbol:  n for electrons and  p for holes Drift velocity – the speed at which a carrier moves in a crystal when an electric field is present. The electric field is the force applied to the carrier. ▫For electrons: v d =  n E ▫For holes: v d =  p E

Carrier mobility The ease at which electrons and holes can move depends on the semiconductor material. ▫Nearly free electrons in direct semiconductors are faster than nearly free electrons in indirect semiconductors. Extremely high speed electronic devices are usually made from these materials. Semiconductor  n (cm 2 -V -1 -s -1 )  p (cm 2 -V -1 -s -1 ) Si Ge2000 GaAs

Direction of Carrier Motion Suppose we consider a piece of intrinsic semiconductor to be a resistor (which it is) and attach a dc voltage source to it. ▫Let say that the length of the semiconductor is L, its width is W, and the height is Z. ▫The magnitude of the voltage source is Va.

VaVa Z L W VaVa

Resistance The equation for resistance that we used in ECE 2004 is shown below. R is resistance in .  is resistivity with units of  -cm. L is the distance that the current has to flow as it enters and leaves the resistor. WZ is the cross-sectional area A of the material.

Resistivity and Conductivity Fundamental material properties

Questions Since the resistance of the semiconductor depends on its geometry ▫What do you expect to happen to the resistance of the Si bar if L increases? ▫How about as either W and H increases?

Current Current that is a result of an applied electric field is called a drift current.

Drift Currents

eV a ECEC EVEV EFEF e h h e VaVa IpIp InIn Energy Diagram Slopes on the energy diagram indicate that an electric field is present at that location.

Questions Assume that the electron and hole mobilities are constant. ▫What happens to the resistance of the Si bar as the temperature increases? Suppose there were bars of Si, Ge, and GaAs that had exactly the same dimensions. ▫At a particular temperature (say 300K), which bar has the lowest resistance?