Silicon Photonics: Fundamentals and Devices

2.4 Impurities

It is well known that the introduction of impurities drastically changes the properties of semiconductors, especially the electrical conductivity of the materials. Impurities can also affect the optical properties in semiconductors. In this section, we shall consider mainly the energy levels of the impurity ions in a semiconductor. The effect of impurities in optoelectronic processes will be presented in a later section.

2.4.1 Donors and Acceptors

Consider first that a pentavalent impurity, such as P, is introduced into a semiconductor crystal having tetravalent Si atoms. Si is bonded with its four nearest neighbors by sharing its four valence electrons. When a P atom replaces a Si atom, four of the outermost electrons of the P atom participate in the bonding process. The fifth electron is loosely bound to its parent nucleus, which possesses a charge of +e. The combination of a positively charged P nucleus and an electron revolving around it is equivalent to the hydrogen atom picture. Bohr's theory of the H-atom may readily be applied, taking into account the fact that the electron, revolving in a material of relative permittivity ε_r, possesses an effective mass, m*, characteristic in a crystal. The ionization energy is written simply as

(2.18)

where a_B is the effective Bohr radius of the impurity atom.

Example 2.4

Let us assume ε_r = 12 and m* = 0.26 m₀, which correspond ...