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The charge carrier distribution in dual-gate field-effect transistors is investigated as a function of semiconductor thickness. A good agreement with 2-dimensional numerically calculated transfer curves is obtained. For semiconductor thicknesses larger than the accumulation width, two spatially separated channels are formed. The cross-over from accumulation into depletion of the two channels in combination with a carrier density dependent mobility causes a shoulder in the transfer characteristics. A semiconducting monolayer has only a single channel. The charge carrier density, and consequently the mobility, are virtually constant and change monotonically with applied gate biases, leading to transfer curves without a shoulder.