This page is more technical than those that proceeded it, although the math used is limited to algebra.  If you have never taken a physics course and/or are reading this module just for the concepts, you may skip the next two pages without missing concepts needed on later pages.  If, on the other hand, you are interested in a more exact description of the conductivity of semiconductors (or if your teacher has assigned this reading), continue on with this page.
 
 

Many introductory physics texts discuss the microscopic origins of electric current and what factors determine the amount of current that will flow through a given wire.  The animation below briefly recounts the key points.  The reader is encouraged to grab his or her favorite physics text to obtain more details.

A.  Representative conduction electrons in a wire.  (A real wire contains too many electrons to show; we have included only enough electrons to give a sense of what occurs.)
B.  In the absence of an electric field, electrons move randomly through the wire.
C.  In a sense, applying a potential difference to the wire is like tipping the wire.  The electrons experience a net force toward the higher potential, resulting in a net velocity directed toward that higher potential.  Much random motion, however, remains.  The net velocity is called the drift velocity v_d of the electrons.
D.  All of the charge DQ in the shaded volume DVol of the figure will pass through the highlighted cross section of the wire in a time Dt.  The average current through that cross section of the wire can be found from DQ/Dt.
E.  DQ is found by counting the number of charge carriers (in this case, the number of electrons) and multiplying that number by the charge q of an individual charge carrier (in this case, e, the charge on an electron).  The number of charge carriers, however, is not a property solely of the material but depends on the size DVol.  We therefore separate the number of charge carriers into the charge carrier number density n, which is a property of the material, and the volume DVol.
F.  The amount of time required for the electrons in the shaded volume to pass through the cross-section is related to the drift velocity of the electrons.  On average, electrons in a volume of depth Dx will all pass through the cross-section in a time Dt = Dx/v_d.
G.  Putting the results of the previous two steps together, we arrive at our final expression for the current through this wire.
 
 
 
 

We can now examine the expression for current through a wire

The illustrations above show a material with all atoms in their ground states.  Such ground states exist only when the temperture is at absolute zero.  Most electronics are used and studied at temperatures well above absolute zero.  At these higher temperatures, electrons regularly jump up to higher energy levels by absorbing thermal energy.  Electrons in the conduction band are called conduction electrons.  The more conduction electrons available, the greater the conductivity becomes.  Of course, if one could increase the conductivity of a material just by taking a bigger piece (with its greater number of electrons), conductivity wouldn't be a very good way to characterize a material.  Instead, we divide the total number N_e of conduction electrons in a material by the total volume Vol of the material to get the number density n_e of conduction electrons.  The number density for a given material depends on both the thermal energy available (related to the temperature of the material) and the energy needed to make that band jump (equal to the band gap).  If the bandgap is narrow, enough electrons can make it into the conduction band to allow current to flow at room temperature.  Click on the image to the right to see an animation of this effect.  The amount of current that flows at room temperature through pure these narrow-bandgap insulators is generally pretty low, so they were called semiconductors.  You may have learned in a physics class that resistance increases (and conductivity decreases) as a resistor gets hot.  This is only true of conductors.  Increasing the temperature of pure semiconductors will increase the number of conduction electrons and thus increase the conductivity of the device!
 

What is special about the resistivity of semiconductors? Go to the next page to find out!

Most introductory texts focus on resistance and resistivity rather than on conductivity.  The resistance R of a device is defined as the ratio of the voltage V applied to the device to the current I that flows through the device due to that voltage:

The number of electrons that make it to the conduction band depends on both the thermal energy available (related to the temperature) and the energy needed to make that band jump (equal to the band gap).  Studies of thermodynamics have shown that the thermal energy U available at a specific temperature T is given by

What does all this discussion of bands and band gaps have to do with semiconductors? Go to the next page to find out!