Overview

To calculate the charge density ? inside a semiconductor let us recall some basics of semiconductors. Two types of foreign atoms called impurities are introduced into semiconductors in order to modify the electron and hole carrier densities. This process, called doping, is the most important feature of semiconductors; the fabrication of semiconductor devices is only possible because of it. Donor atoms can donate an electron to the crystal lattice and acceptor atoms can accept an electron from the valence band producing a hole. Donor materials come from group V of the periodic table; the most commonly used materials for n-type silicon are phosphorus and arsenic. Acceptors are elements from group III of the periodic table; the most common acceptor material is boron. Because the dopant atoms are originally neutral, donors become positively ionized when donating an electron while acceptors become negatively ionized when accepting an electron. As a consequence, in the general case, four types of charge are present inside a semiconductor: the fixed positive charge of ionized donors, the fixed negative charge of ionized acceptors, the positive mobile charge of holes, and the negative mobile charge of electrons. We will consider the situations in which all donors and acceptors are ionized, i.e.

where ( ) N _D and ( ) N _A are the (ionized) donor and acceptor atoms per unit volume. On this basis, the net positive charge density is given by

Let us analyze the small deviations from neutrality in the...