In an intrinsic semiconductor (pure silicon, pure germanium), at room temperature only a tiny fraction of electrons (about 101210^{-12}) has enough energy to “break free” from the lattice and become mobile. The material conducts, but very little. The carrier density depends exponentially on temperature:

n(T)exp ⁣(Eg/(2kBT))n(T) \propto \exp\!\bigl(-E_g/(2 k_B T)\bigr)

where EgE_g is the band gap energy (1,1\sim 1{,}1 eV for silicon). Just a little heating drastically increases conduction — behaviour opposite to that of metals.

The real technological leap comes from doping: about 1 atom in every 10610^6 of silicon is replaced with atoms of a different element.

  • Type nn (arsenic, phosphorus): 5 valence electrons versus silicon’s 4. The fifth remains free → excess negative carriers.
  • Type pp (boron, aluminium): 3 valence electrons. An electron is missing to complete the bonds → excess positive carriers, the holes.

Pairing an nn region with a pp region forms the pnpn junction: a diode that lets current pass in only one direction (forward bias). Three junctions in succession form a transistor, which allows signals to be amplified or switched with a very small electrical control. All of computing is built on silicon transistors, about 101010^{10} per modern chip (Bloomfield 2016).

Historical context

The point-contact transistor was built at Bell Labs in December 1947 by Bardeen, Brattain and Shockley (Nobel Prize 1956). The first integrated circuit dates back to 1958 (Jack Kilby, Texas Instruments). Since then, according to Moore’s law (1965), the density of transistors on chips has doubled roughly every 2 years: an exponential growth that has lasted, with slowdowns, for over 60 years.

Topics: Electric circuits Concepts: Ohm’s law

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