Over 600 semiconducting materials are known. They may be elements or compounds and they have a resistivity somewhere between insulators and conductors. Good conductors have resistivity between 10-7Ωm to 10-8 Ωm at room temperature while the resistivity of insulators is in the range1010 Ωm and 1014 Ωm. Semiconductors fall in between with resistivities between 10-6Ωm to 107Ωm, a range of 14 orders of magnitude.

Pure semiconductors behave like insulators at 0°Kelvin, however at normal temperatures, in contrast to metals, semiconductors have a negative coefficient of resistance due to the increase in the concentration of charge carriers as the temperature rises.

Controlled amounts of other elements, misleadingly called "impurities" (dopant ,doping agent or dope)can be inserted into the crystal lattice of the semiconductor in a process known as "doping" to modify its electrical properties by creating positive or negative charge carriers, selectively increasing its conductivity in the doped region. By doping with precise amounts of different impurities in precise locations very small structures can be built in which the positive and negative charge carriers can interact allowing the creation of a wide range of passive and active electronic devices which in turn can be used as building blocks to create even more complex components.

Some examples of semiconductors frequently used in electronics are given below.

• Lead Sulphide crystals (Galena) were noted for their rectifying properties.
• Selenium was first used in the 1870's to create photo voltaic cells.
• Silicon Carbide crystals (carborundum) were the crystals used with the "cats whisker" to detect the signals in early radio sets.
• Germanium was the material on which early transistors were based. It has a low melting point and is easy to work with and a low resistivity which helps in achieving high frequency response. Unfortunately it also has a low maximum working temperature of 75 °C and suffers from inherent high leakage currents due to its low band gap of only 0.67 eV.
• Silicon is the material used in the vast majority of semiconductor devices today. Manufacturing processes are more difficult but it can work at much higher operating temperatures and suffers less from leakage currents (1.12 eV bangap). Silicon is readily oxidised to form silicon dioxide (SiO2) which is an insulator, essential to the planar manufacturing process. (The oxide of Germanium is water soluble making it unsuitable for this purpose). Silicon dioxide is the compound from which Silicon is derived. It is the most abundant compound in the earth's crust and commonly takes the form of ordinary sand, but also exists as quartz, rock crystal, amethyst, agate, flint, jasper and opal.
• Gallium Arsenide has high electron mobility giving it a much better high speed switching performance than Silicon. It also has better high temperature performance but it is hard to work with and consequently more expensive. Gallium Arsenide is also used in the manufacture of LED's. Gallium by the way is a three valence element while Arsenic is a five valence element. Whereas most semiconductors are four valence elements or compounds, Gallium Arsenide is known as a III-V valence semiconductor. Its crystal structure however permits doping in the same way as an IV valence semiconductor. Gallium Arsenide is considered to be highly toxic and carcinogenic.

Silicon is a crystal material

Diamond lattice: atoms tetrahedrally bonded by sharing valence electrons (covalent bonding)

Each atom shares 8 electrons: low energy and stable situation

Si atomic density: 5 × 10^22 [1/cm^3]

Electrons and Holes

A crystal of pure or intrinsic silicon has a regular lattice structure where the atoms are held in their positions by bonds, called covalent bonds, formed by four valence electrons associated with each silicon atom. Each atom shares each of its four valence electrons with a neighboring atom, with each pair of electrons forming a covalent bond. At sufficiently low temperature, all covalent bonds are intact and no (or very few) free electrons are available to conduct electric current. However at room temperature some of the bonds are broken by thermal ionization and some electrons are freed. When a covalent bond is broken an electron leaves its parent atom; thus a positive charge equal to the magnitude of the electron charge is left with the parent atom. An electron from a neighboring atom may become attracted to this positive charge, leaving its parent atom. This action fills up the hole in the ionized atom but creates a new hole in the other atom. This process may repeat itself with the result that we effectively have a positively charged carrier, or hole, moving through the silicon crystal structure and being available to conduct electric current. The charge of a hole is equal in magnitude to the charge of an electron.

Even though a hole is just the absence of an electron, it can act a lot like a particle. Holes are positively charged, and they have an apparent, or "effective," mass--just as electrons do--that reflects their ability to move through a given material. A hole could be effectively "heavy" if collisions with atoms in the material cause it to respond sluggishly to an external electric field. Because holes can act like particles, condensed matter physicists have hypothesized for decades that they might be able to form crystals. The researchers calculated that a hole crystal could form spontaneously in a semi-conductor if three requirements are met: The material has to be cold enough to slow the holes, but not the electrons--perhaps tens of degrees Kelvin--and the holes have to be both numerous and heavy. To help them stay put in a crystal, the team calculates the holes must be at least 80 times heavier than the electrons.

Thermal ionization results in free electrons and holes in equal numbers and hence equal concentrations. These free electrons and holes move randomly through the silicon crystal structure and in process some electrons may fill some of the holes. This process called recombination, results in the disappearance of free electrons and holes. The recombination rate is proportional to the number of electrons and holes, which in turn is determined by the ionization rate. The ionization rate is a strong function of temperature. In thermal equilibrium the recombination rate is equal to the ionization or thermal-generation rate, and one can calculate the concentration of free electrons n, which is equal to the concentration of holes p.
n=p=Ni
where Ni denotes the concentration of free electrons or holes in intrinsic silicon at a given temperature T (in Kelvin), the intrinsic concentration can be found from
Ni^2=BT^3e^(-Eg/KT)
B: material-dependant parameter (5.4*10^31 for silicon)
Eg: band gap energy (1.12[eV] for silicon)
K: Boltzmann’s constant= 8.62*10^-5 [eV/K]
Substitution shows that shows that for intrinsic silicon at room temperature Ni=1.5*10^10 [carriers/cm^3]

Diffusion and Drift

There are two mechanisms by which electrons and holes move through a silicon crystal--diffusion and drift. Diffusion is associated with random motion due to thermal agitation. In a piece of silicon with uniform concentrations of free electrons and holes, this random motion does not result in a net flow of charge. On the other hand if by some mechanism the concentration of, say, free electrons is made higher in one part of the piece of silicon than in another, then electrons will diffuse from the region of high concentration to the region of low concentration. This diffusion process will give rise to a net flow of charge, or diffusion current.
Jp=-QDp(dp/dx)
Jp is the current density [A/cm^2]
Q is the magnitude of electron charge
Dp is a constant called diffusion constant or diffusivity of holes
dp/dx: slope of the concentration curve
In the case of electrons diffusion resulting from an electron concentration gradient, a similar relation applies, giving the electron-current density
Jn=-QDn(dn/dx)
Dn is a constant called diffusion constant or diffusivity of electrons

The other mechanism for carrier motion in semiconductor is drift. Carrier drift occurs when an electric field is applied across a piece of silicon. Free electrons and holes are accelerated by the electric field and acquire a velocity component (superimposed on the velocity of their thermal motion) called drift velocity. The positively charged holes will drift in the direction of E and acquire a velocity given by:
Vdrift=μpE
μp is a constant called the mobility of holes which has the units of [cm^2/V]. For intrinsic siliconμpis typically 480[cm^2/V]. Similarly for intrinsic siliconμnis typically 1350[cm^2/V], about two times greater than the holes mobility(holes are heavier than electrons).
The total drift current is:
Jdrift=q(Pμp+Nμn)E

Simple relationship known as Einstein relationship, exist between the carrier diffusivity and mobility,
Dn/μn=Dp/μp=Vt
Where Vt is the thermal voltage.

ρ =resistivity[Ωcm]
σ =conductivity[Ω^-1cm^-1]
ρ =1/σ = 1/[q(Pμp+Nμn)]
Resistivity commonly used to specify doping level.

Band Theory