Semiconductor

A semiconductor is a substance with electrical conductivity intermediate between metals and insulators. Most commonly these materials are solids.

Density of states

(CC) Image: John R. Brews
Calculated density of states for crystalline silicon.

In liquid and solid materials where atoms are in close proximity to one another, the energy levels available to electrons fall into bands separated by energy gaps. The density of energy levels per unit energy as a function of energy might look as in the figure. This density of states relate to the semiconducting behavior of this material as follows:

1. Bands of allowed energy are separated by an energy gap. Those above the gap are called conduction band energy levels, and those below are valence band energy levels.
2. At low temperatures, electrons occupy all the energy levels below the gap, and none above the gap.
3. The energy gap is small enough that at normal temperatures some electrons can acquire thermal energy sufficient to occupy a few conduction band energy levels above the gap, leaving vacant levels (holes) in the valence band energy levels below the gap.
4. The conduction band energy levels, and possibly the higher-energy hole energy levels too, correspond to states spatially extended through large regions of the material and are not localized. That spatial extension means that conduction-band electrons (and possibly valence-band holes too) can travel easily (conduct) by moving between adjacent levels in response to an applied field.

It may be noted that the number of electrons and holes present in a semiconductor is often adjusted by introducing impurities into the semiconductor that alter the balance, allowing the hole and electrons densities to differ.

Electric field penetration

(CC) Image: John R. Brews
Top panel: Applied voltage bends bands, depleting holes from surface (left). The charge inducing the bending is balanced by a layer of negative acceptor-ion charge, as shown on the upper right. Bottom panel: Larger applied voltage further depletes holes but conduction band becomes low enough in energy to populate an inversion layer.

In a metal the electron density that responds to applied fields is so large that an external electric field can penetrate only a very short distance into the material. However, in a semiconductor the lower density of electrons (and possibly holes) that can respond to an applied field is sufficiently small that the field can penetrate quite far into the material. A consequence is that the energy levels available to electrons are altered by the applied field to considerable depths from the surface, and that in turn changes the occupancy of the energy levels in the surface region. A typical treatment of such effects is based upon a band bending diagram showing the positions in energy of the band edges as a function of depth into the material.

An example band-bending diagram is shown in the figure for a two-layer structure consisting of an insulator as left-hand layer and a semiconductor as right-hand layer. An example of such a structure is the MOS capacitor, a two terminal structure made up of a metal gate contact, a semiconductor body (such as silicon) with a body contact, and an intervening insulating layer (such as silicon dioxide, hence the designation O). The left panels show the lowest energy level of the conduction band and the highest energy level of the valence band. These levels are "bent" by the application of a positive voltage V. By convention, the energy of electrons is shown, so a positive voltage penetrating the surface lowers the conduction edge. A dashed line depicts the occupancy situation: below this Fermi level the states are occupied and above it they are empty, assuming zero temperature. At operating temperatures, however, some electrons populate the conduction band, and some vacancies (holes) populate the valence band.

The example in the figure shows the Fermi occupancy level in the bulk material beyond the range of the applied field as lying close to the valence band edge. This position for the occupancy level is arranged by introducing impurities into the semiconductor. In this case the impurities are so-called acceptors which soak up electrons from the valence band becoming negatively charged, immobile ions embedded in the semiconductor material. The removed electrons are drawn from the valence band levels, leaving vacancies or holes in the valence band. Charge neutrality prevails because the negative acceptor ion has created a positive deficiency in the host material: a hole is the absence of an electron, it behaves like a positive charge. When no field is present, neutrality is achieved because the negative acceptor ions exactly balance the positive holes.

Next the band bending is described. A positive charge is placed on the left face of the insulator (for example using a metal "gate" electrode). In the insulator there are no charges so the electric field is constant, leading to a linear change of voltage in this material. As a result, the insulator conduction and valence bands are therefore straight lines in the figure, separated by the large insulator energy gap.

In the semiconductor at the smaller voltage shown in the top panel, the positive charge placed on the left face of the insulator lowers the energy of the valence band edge. Consequently, these states are fully occupied out to a so-called depletion depth where the bulk occupancy reestablishes itself because the field cannot penetrate further. Because the valence band levels near the surface are fully occupied due to the lowering of these levels, only the immobile negative acceptor-ion charges are present near the surface, which becomes a region without holes (the depletion layer). Thus, field penetration is arrested when the exposed negative acceptor ion charge balances the positive charge placed on the insulator surface: the depletion layer adjusts its depth enough to make the net negative acceptor ion charge balance the positive charge on the gate.

The conduction band edge also is lowered, increasing electron occupancy of these states, but at low voltages this increase is not significant. At larger applied voltages, however, as in the bottom panel, the conduction band edge is lowered sufficiently to cause significant population of these levels in a narrow surface layer, called an inversion layer because the electrons are opposite in polarity to the holes originally populating the semiconductor. This onset of electron charge in the inversion layer becomes very significant at an applied threshold voltage, and once the applied voltage exceeds this value charge neutrality is achieved almost entirely by addition of electrons to the inversion layer rather than by an increase in acceptor ion charge by expansion of the depletion layer. Further field penetration into the semiconductor is arrested at this point, as the electron density increases exponentially with band-bending beyond the threshold voltage, effectively pinning the depletion layer depth at its value at threshold voltage.

The added impurities that control the Fermi level marking the occupancy are called dopants. In some materials, such as silicon, besides acceptor dopants, different impurities can be found that act as donors, moving the Fermi occupancy level close to the conduction band edge. Thus, materials can then be prepared to have holes as the zero-field mobile charge (p-type materials), or to have electrons as the zero-field mobile charge (n-type materials).