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This paper presents two models for application in multilayer electron sources. In both models the substrate is a semiconductor and the source of the field-emitted electrons generated is in the accumulation layer generated at the silicon-wide band gap material(WBG) interface by the penetration of the intense extraction field. In the "coherent approach", quantum connections between the envelopes of electron wave functions in each region of the structure are taken into account. However, in order to comply with the difference between the probability current in the vacuum and in the substrate, a relaxed connection condition is accepted at the semiconductor-WBG interface. This results in the emission current exhibiting some resonant maxima in the current-electric field plots. In the alternative approach, a sequential tunneling is allowed between the substrate and the vacuum regions, with temporary accumulation of electrons in the conduction band of the WBG material. The increase of space charge in the WBG produces an overall decrease in the internal field in the first barrier and thus reduces the electron injection from the substrate. An optimum height of the vacuum chamber with corresponding maximum field emission current is obtained due to the two concurrent effects of lowering the injection barrier and increasing the amount of space charges.