Frequently Asked Questions

Carrier Concentrations

• When is it correct to use the simplified equations for n and p?
• What is meant by total ionization of dopant atoms?
• What does the graph in Figure 2.22(a) on page 66 represent?

• When is it correct to use the simplified equations for n and p?

The equations for n and p are:

These can be used all the time; it happens to be that if one of the doping concentrations is much greater than the other, , they will be simplified to equations 2.30 and 2.31 on page 60 of your textbook. On the other hand, if the doping concentrations are comparable to n_i, you should not use the simplified equations, both terms should be kept.

See also:
Carriers - Equilibrium Carrier Concentrations
Problems & Problem Solving - Concentration Problems (Sorry! Still under construction!)

• What is meant by total ionization of dopant atoms?

Atoms used as donors have one more valence electron than silicon. When the atom loses the electron, a negative charge, the atom is ionized and is positively charged.

Acceptors have one fewer valence electron than silicon, so they do not bond completely with the rest of the silicon atoms. When it takes an electron from a neighboring silicon atom to complete a bond it becomes ionized and negatively charged with the extra electron, and a hole is created.

At room temperature, dopants are assumed to be fully ionized. At 0 K, no dopants are ionized.

• What does the graph in Figure 2.22(a) on page 66 represent?

It is many things.  It is a plot of carrier concentration versus temperature.  The graph illustrates how dopants are ionized as a function of temperature.

It depicts how the ratio of the majority carrier concentration (n) to the doping concentration (N_D) changes with temperature T(K). In the freeze out region, below 100K, the ratio is less than 1, meaning few dopants are ionized and the majority carrier is mostly due to electrons from ionized donors. In the extrinsic T region, the ratio is approximately 1, meaning that the majority carrier is made mostly of donor electrons and all of them are ionized. Increasing the tempreature no longer increases the electron concentration because there are no unionized donors to ionize.  Above 500K the ratio is greater than 1 so the carrier concentration is greater than the doping concentration. At this point, electrons coming from the valence band begin to outnumber the electrons coming from donor sites.

This graph can be applied for holes also, substituting N_A for N_D and holes for electrons. Can you plot the minority carrier concentration that would correspond to this plot?

See also:
Carriers - Temperature Dependence
Problems & Problem Solving - Energy Band Problems