(1) The greater the number of carriers and mobility in the semiconductor surface layer, the greater the surface conductivity. The number of carriers in the surface layer will change with the surface potential Vₛ, thus changing the surface conductivity.
(2) Due to the effect of the surface electric field, additional hole number Δp and electron number Δn are induced in the surface layer per unit area, where μₚₛ and μₙₛ are the effective mobilities of holes and electrons in the surface layer, respectively. The additional conductivity in the surface layer is given by
The total thin-layer surface conductivity is the sum of the thin-layer conductivity when the surface is in a flat band condition and the additional conductivity.
Taking p-type semiconductors as an example, when the surface potential is negative, an accumulation of majority carriers (holes) forms in the surface layer, increasing the surface conductivity, which also increases with |Vₛ|. When Vₛ is positive and sufficiently large to form an inversion layer at the surface, the number of minority carriers (electrons) in the inversion layer increases with the increase of Vₛ, thus increasing the surface conductivity. When Vₛ is positive but small, the surface is in a depletion state, resulting in lower surface conductivity, which has a minimum value.
(3) The electron concentration and mobility at a distance x from the surface are n(x) and μₙ(x), respectively, then the conductivity at that point is given by
The surface conductivity contributed by the electrons in the surface layer is
The effective mobility of electrons is
Qₙ is the charge per unit area formed by electrons in the surface layer.
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