Structure of semiconductors

In a semi-conductor, an electron in a solid can only take up energy values within certain intervals known as "bands", more specifically permitted bands, which are separated by other "bands" known as forbidden energy bands or forbidden bands.

When the temperature of the solid tends towards absolute zero, two permitted energy bands play a special role:

  • The last band to be completely filled, called the valence band

  • The next allowed energy band, called the "conduction band".

Fondamental

The structure of silicium and germanium is the same as that of diamond (cubic). Each atom is linked to 4 neighbors placed at the vertices of a tetrahedron by a covalent bond: These elements are “tetravalent”. The figure below corresponds to a representation on a plan of the structure. The lines represent the valence electrons.

Band theory applied to semiconductors leads to consider an entirely full valence band which is separated from a conduction band by a band gap distant from the energy ΔE.

Fondamental

If we provide sufficient thermal or light energy to an electron, it can pass from the valence band to the conduction band with a probability P proportional to:

Ρ ∝ exp(–ΔE / kT)

ΔE is the energy gap separating the two bands.

T the absolute temperature.

k = 1.38.10– 23 JK-1: is Boltzmann's constant.

For T = 300 K, kT = 0.0025 eV

Diamond: ΔE = 7 eV; Silicon ΔE = 1.12 eV; Germanium ΔE = 0.7 eV.

In a semiconductor, ΔE is low enough to allow, at room temperature, the passage of a small number of electrons from the valence band to the conduction band.

DéfinitionConduction by electron and by hole

If a valence bond is broken (thermal agitation, photon, etc.) the electron becomes mobile: it leaves an excess of positive charge in the “hole” (symbolized by a + in a square). This gap will be filled by a neighboring electron released by thermal agitation and which will in turn leave a hole: these seem to move in the network. Electrons (positive mass, negative charge) correspond to holes (negative mass, positive charge). Since the movement of holes is a two-step process, their mobility in the lattice is lower than that of electrons.

µn = 12.10 6 m²v–1s–1 and µp = 5.10 6 m² v–1s–1 .

The intrinsic conductivity of the material σ = e (ni.µn + pi.µp) is very low.