Semiconductor Electronics: Materials, Devices and Simple CircuitsClassification of Metals, Conductors and Semiconductors
On the basis of conductivity. By their electrical conductivity σ, or resistivity ρ = 1/σ, solids fall broadly into three classes:
- Metals have very low resistivity: ρ ~ 10⁻² to 10⁻⁸ Ω m, so σ ~ 10² to 10⁸ S m⁻¹.
- Semiconductors have resistivity between that of metals and insulators: ρ ~ 10⁻⁵ to 10⁶ Ω m, σ ~ 10⁵ to 10⁻⁶ S m⁻¹.
- Insulators have very high resistivity: ρ ~ 10¹¹ to 10¹⁹ Ω m, σ ~ 10⁻¹¹ to 10⁻¹⁹ S m⁻¹.
These values show the orders of magnitude; real materials can fall outside them. The resistivities are so different that they only fit on a scale where each step is a factor of ten. Place six materials on the ladder.
The ladder spans 27 powers of ten. The metals' range and the semiconductors' range even overlap a little, so resistivity alone does not separate the classes; there are other differences, which this chapter brings out.
The semiconductors studied here can be
- elemental: silicon (Si) and germanium (Ge);
- compound: inorganic (CdS, GaAs, CdSe, InP), organic (anthracene, doped phthalocyanines) or organic polymers (polypyrrole, polyaniline, polythiophene).
Most devices today use Si, Ge or inorganic compound semiconductors. Since 1990, devices made from organic semiconductors and semiconducting polymers have begun to appear, the start of polymer electronics and molecular electronics. This chapter sticks to the elemental semiconductors Si and Ge; most of the ideas carry over to compound semiconductors.
On the Basis of Energy Bands
In an isolated atom, the energy of an electron is fixed by the orbit it is in (Bohr's model). In a solid, the atoms are so close that the outer orbits of neighbouring atoms come very near each other, or even overlap. Inside a crystal, no two electrons see exactly the same pattern of surrounding charges, so each has a slightly different energy. These closely spaced levels, with energy varying almost continuously, form energy bands.
Take a crystal of N silicon atoms. Each atom has 4 electrons in its outermost orbit, so the crystal has 4N valence electrons. The outer orbit has room for 8 electrons (2 in an s level and 6 in a p level), so there are 8N energy states for them.
Bring the atoms together and complete the missions. Here a is the spacing in the real crystal.
Distance between neighbouring atoms: r =
At the spacing of the real crystal, the 8N states split into two bands of 4N states each, separated by an energy gap Eg (Fig. 14.1). The lower band, completely filled by the 4N valence electrons at absolute zero, is the valence band. The upper band of 4N states, completely empty at absolute zero, is the conduction band. The lowest level of the conduction band is called EC and the highest level of the valence band EV, so Eg = EC − EV. Above EC and below EV there are very many closely spaced levels.
Note
The bands are not located anywhere in particular inside the solid: EC and EV are overall averages. A straight line drawn for EC just marks the bottom of the conduction band levels.
How Big Is the Gap?
With no external energy, all the valence electrons stay in the valence band. Whether a solid conducts depends on how easily they can get into the conduction band: on the size of the gap Eg, which can be large, small or zero (Fig. 14.2).
Change the gap and complete the missions.
Energy gap: Eg =
The free electrons all sit in the conduction band; the valence band below it is (almost) full.
- Case I, metals. The conduction band is partly filled, or it overlaps the valence band. Electrons move freely into it, so there are plenty of carriers: low resistance, high conductivity.
- Case II, insulators. A large gap, Eg > 3 eV. Thermal energy cannot lift electrons across it, so the conduction band stays empty and there is no conduction.
- Case III, semiconductors. A small gap, Eg < 3 eV. At room temperature some electrons gain enough energy to cross into the conduction band. They are few, so a semiconductor's resistance is lower than an insulator's but far higher than a metal's.
The gaps of diamond (C), silicon and germanium are 5.4 eV, 1.1 eV and 0.7 eV. Tin, also in group IV, has a gap of 0 eV and is a metal.
Speed Round: Classify It
Metals: Eg ≈ 0 and ρ ~ 10⁻⁸ to 10⁻² Ω m. Semiconductors: Eg < 3 eV and ρ ~ 10⁻⁵ to 10⁶ Ω m. Insulators: Eg > 3 eV and ρ ~ 10¹¹ to 10¹⁹ Ω m. Get five right to move on.