Electron’s Energy Level

The NEUTRON is a neutral particle in that it has no electrical charge. The mass of the neutron is approximately equal to that of the proton. An ELECTRON’S ENERGY LEVEL is the amount of energy required by an electron to stay in orbit. Just by the electron’s motion alone, it has kinetic energy.

The electron’s position in reference to the nucleus gives it potential energy. An energy balance keeps he electron in orbit and as it gains or loses energy, it assumes an orbit further from or closer to the center of the atom.

SHELLS and SUBSHELLS are the orbits of the electrons in an atom. Each shell can contain a maximum number of electrons, which can be determined by the formula 2n2.

Shells are lettered K through Q, starting with K, which is the closest to the nucleus. The shell can also be split into four subshells labeled s, p, d, and f, which can contain 2, 6, 10, and 14 electrons, respectively.

VALENCE is the ability of an atom to combine with other atoms. The valence of an atom is determined by the number of electrons in the atom’s outermost shell. This shell is referred to as the VALENCE SHELL. The electrons in the outermost shell are called VALENCE ELECTRONS.

IONIZATION is the process by which an atom loses or gains electrons. An atom that loses some of its electrons in the process becomes positively charged and is called a POSITIVE ION. An atom that has an excess number of electrons is negatively charged and is called a NEGATIVE ION.

ENERGY BANDS are groups of energy levels that result from the close proximity of atoms in a solid. The three most important energy bands are the CONDUCTION BAND, FORBIDDEN BAND, and VALENCE AND.

Electrons and holes in semiconductors

As pointed out before, semiconductors distinguish themselves from metals and insulators by the fact that they contain an “almost-empty” conduction band and an “almost-full” valence band. This also means that we will have to deal with the transport of carriers in both bands.

To facilitate the discussion of the transport in the “almost-full” valence band we will introduce the concept of holes in a semiconductor. It is important for the reader to understand that one could deal with only electrons (since these are the only real particles available in a semiconductor) if one is willing to keep track of all the electrons in the “almost-full” valence band.

The concepts of holes is introduced based on the notion that it is a whole lot easier to keep track of the missing particles in an “almost-full” band, rather than keeping track of the actual electrons in that band. We will now first explain the concept of a hole and then point out how the hole concept simplifies the analysis.

Holes are missing electrons. They behave as particles with the same properties as the electrons would have occupying the same states except that they carry a positive charge. This definition is illustrated further with the figure below which presents the simplified energy band diagram in the presence of an electric field.

A uniform electric field is assumed which causes a constant gradient of the conduction and valence band edges as well as a constant gradient of the vacuum level. The gradient of the vacuum level requires some further explanation since the vacuum level is associated with the potential energy of the electrons outside the semiconductor. However the gradient of the vacuum level represents the electric field within the semiconductor. The electrons in the conduction band are negatively charged particles which therefore move in a direction which opposes the direction of the field. Electrons therefore move down hill in the conduction band. Electrons in the valence band also move in the same direction. The total current due to the electrons in the valence band can therefore be written as where V is the volume of the semiconductor, q is the electronic charge and v is the electron velocity. The sum is taken over all occupied or filled states in the valence band. This expression can be reformulated by first taking the sum over all the states in the valence band and subtracting the current due to the electrons which are actually missing in the valence band. This last term therefore represents the sum taken over all the empty states in the valence band, or:

The sum over all the states in the valence band has to equal zero since electrons in a completely filled band do not contribute to current, while the remaining term can be written as:

This states that the current is due to positively charged particles associated with the empty states in the valence band. We call these particles holes. Keep in mind that there is no real particle associated with a hole, but rather that the combined behavior of all the electrons which occupy states in the valence band is the same as that of positively charge particles associated with the unoccupied states.

The reason the concept of holes simplifies the analysis is that the density of states function of a whole band can be rather complex. However it can be dramatically simplified if only states close to the band edge need to be considered.

As illustrated by the above figure, the holes move in the direction of the field (since they are positively charged particles). They move upward in the energy band diagram similar to air bubbles in a tube filled with water which is closed on each end.