Fig. 1. Schematic illustration of the structure used in all simulations. Two crystallographically aligned graphene layers, here of infinite width for the purpose of simulation, are coupled within a region of effective dielectric ε = 2.2 including perhaps partial vacuums in the vicinity (below or above) the condensate region. Quantum Transport Simulations on the Feasibility of the Bilayer PseudoSpin Field Effect Transistor (BiSFET) Xuehao Mou * , Leonard F. Register and Sanjay K. Banerjee Microelectronics Research Center, The University of Texas at Austin 10100 Burnet Road Building 160, Austin, Texas 78758, United States, * Email: xmou@utexas.edu Abstract The feasibility of ultra low-voltage switching in the proposed Bilayer PseudoSpin Field-Effect Transistor (BiSFET) “beyond CMOS” device concept is illustrated using quantum transport simulations. The BiSFET relies on possible room-temperature superfluid condensation in dielectrically separated graphene layers. Simulations illustrate resulting greatly enhanced interlayer tunneling, and critical voltages for switching between ON and OFF interlayer conductance states below the thermal voltage of ~26 mV at 300 K. The BiSFET switching mechanism is also contrasted to the “drag-counterflow” biasing configuration with much higher switching voltages. Introduction The Bilayer PseudoSpin Field Effect Transistor (BiSFET) is a novel “beyond CMOS” device concept based on interlayer- coherent electron-hole exciton condensates in two graphene layers, one n-type and one p-type, separated by a thin dielectric [1]. Such condensates, created by the interlayer exchange interactions, have been predicted to exist possibly above room temperature [2]. In the presence of the condensates, the interlayer tunneling is expected to be greatly enhanced, but only up to a critical current, analogous to the DC Josephson effect and for the similar reasons. Moreover, as a collective effect, in principle the critical voltage associated with the critical current could be smaller compared to the thermal voltage k B T/q, which is ~26 mV at 300 K [1-4]. It has been shown by SPICE-level circuit simulations that the consequent switching power with a 25 mV clocked power voltage could then be on the scale of 10 −20 J (10zJ) per device, lower than the “end-of-roadmap” CMOS by two to three orders of magnitudes [1,5,6]. There are substantial theoretical and experimental challenges to realizing such superfluid condensates and BiSFETs. However, recent theoretical work continued to support the possibility of such a room-temperature condensate, although in very low-k environments [7]. Here, using the quantum transport simulation tool presented in [8], we reexamine the basic transport physics and, in particular, the possibility of sub-k B T/q critical voltages for interlayer transport. For comparison, we also examine transport under the contrasting “current counterflow” biasing condition in which near perfect Coulomb drag is expected between layers [9~11] up to substantially higher voltages. Simulated Device The simulated device structure in this work, detailed further in [8], consists of two graphene layers coupled within channel region of length L through a dielectric layer of thickness d, as shown in Fig. 1. Four semi-infinite leads (BL, BR, TL, TR) are connected to the opposite ends and opposite layers beyond the channel region. This contact scheme differs from that of the proposed BiSFET, which nominally employs only two contacts, one to each layer on the same end of the channel [1]. However this scheme allows us to investigate not only interlayer tunneling as required for the BiSFET scheme, but also more general biasing schemes including the aforementioned current counterflow biasing. The two opposite graphene layers are nominally gated to fixed electrostatic potentials V = ±0.25 V, respectively, corresponding to n = p ≈ 6×10 12 cm -2 . Conceptually, with the tight-binding framework used for quantum transport simulations here, the non-local interlayer Fock exchange interaction V Fock is calculated self-consistently via the tight-binding Schrödinger’s equations as: (1) (2) (3) (4) where H TB,b is the “bare” tight-binding Hamiltonian including intra-layer and interlayer coupling, R T(B) labels a lattice site in the top (bottom) layer, and β labels the injected Bloch states including the lead of injection, band and wave-vector of incidence, transverse wave-vector, and (actual) spin. The applied terminal voltages V i modify the Fermi levels E F,i = −qV i and corresponding Fermi occupation probabilities f β , where i is the lead index. Here, ρ(R B ,R T ) is the density matrix, or more specifically the interlayer density matrix which can be referred to as the collective “pseudospin” which characterizes the coherence between the “which layer” degree of freedom. We emphasize that this simple unscreened model of the ( ) ( ) ( ) ( ) ( ) B T T B Fock B B B b TB, T , R R R R R R R β β β β β ϕ = ϕ + ϕ - ϕ ∑ E V qV H ( ) ) , ( 4 , T B T B 2 T B Fock R R R R R R ρ - πε - = q V ( ) ( ) ( ) ∑ β β β β ϕ ϕ = ρ T * B T B , R R R R f ( ) ( ) ( ) ( ) ( ) T B B T Fock T T T b TB, B , R R R R R R R β β β β β ϕ = ϕ + ϕ - ϕ ∑ E V qV H Channel length L = 15 nm d IEDM13-112 4.7.1 U.S. Government work not protected by U.S. copyright