Analysis of the contact-barrier height taking into account the distribution of surface states along coordinate x perpendicular to the insulator–semiconductor interface is performed for metal–semiconductor contacts with a dielectric gap. It is shown that taking into account the spatial dependence of the density of surface states at rather high semiconductor doping levels leads to a substantial decrease in the barrier height, which promotes the realization of ohmic contacts. It is established that the smaller the metal–semiconductor contact potential difference ϕ_ ms is, the stronger the effect of barrier-height lowering. If ϕ_ ms is negative, this effect can lead to potential sign reversal, i.e., to the realization of an enrichment layer in the space-charge region of the semiconductor even at a high density of surface states. This in turn promotes the manifestation of an anomalous dependence of the contact resistivity on temperature; the resistivity increases with an increase in temperature.