Vertical field-effect transistor based on wave-function extension

We demonstrate a mechanism for a dual layer, vertical field-effect transistor, in which nearly depleting one layer will extend its wave function to overlap the other layer and increase tunnel current. We characterize this effect in a specially designed GaAs/AlGaAs device, observing a tunnel current increase of two orders of magnitude at cryogenic temperatures, and we suggest extrapolations of the design to other material systems such as graphene.

Figure 1

(a) Potential profile of a shallow barrier next to a rectangular well that is raised so the energy $E_0$ of its bound subband edge goes from $-9$ to $-1$ meV. (b) Simulated wave functions corresponding to the two subband energies, with the raised subband having a greatly extended wave function. (c) WET composition, consisting of a GaAs/AlGaAs heterostructure with gates and dielectric on either side. A self-consistent simulation of the conduction band edge for the structure is shown below,[10] with the source gate varying the subband edge of the source quantum well from $-9$ to $-1$ meV and extending its associated wave function.

Figure 2

(a) Schematic of WET device (not to scale), with depletion gates (DG) limiting access of the contacts to the tunneling region. (b) Photograph of the finished sample with the GaAs mesa, outlined in purple, supported by epoxy. Hook-shaped protrusions in the mesa are visible where gates overlap, included to ensure continuity during gate deposition over the mesa step.

Figure 3

(a) Tunneling conductance as a function of source and drain gate voltages in the main heterostructure H1. Density-matched bilayer resonances (around gray line) are absent, but barrier-modulated tunnel increases along dotted lines are strong. (b) A different heterostructure (H2) with resonant tunneling is shown for comparison. The axes of (a) and (b) are chosen so that both layers are depleted at the lower left corner, with a star added for reference where each layer has a carrier density of $2\times {10}^{11}$ cm${}^{-2}$. (c) Cuts along dotted lines in (a) reveal the large tunnel increases. All data were taken at 4.2 K.

Figure 4

(Current modulation by the drain gate as a function of (a) positive and (b) negative source-drain bias. The insets depict a possible explanation for the difference in modulation for large positive and negative biases.

Figure 5

(a) Schematic of a graphene WET (two graphene layers marked by dotted red lines) and (b) plot of the conduction band with simultaneously varied subband wave functions (shaded). (c) Quantum capacitance, due to a discrete density of states, weakens the effect of the gate, but the device still is able to match 60 mV/decade over several decades (d).