Device model for graphene bilayer field-effect transistor

Abstract

We present an analytical device model for a graphene bilayer field-effect transistor (GBL-FET) with a graphene bilayer as a channel, and with back and top gates. The model accounts for the dependences of the electron and hole Fermi energies as well as energy gap in different sections of the channel on the bias back-gate and top-gate voltages. Using this model, we calculate the dc and ac source-drain currents and the transconductance of GBL-FETs with both ballistic and collision dominated electron transport as functions of structural parameters, the bias back-gate and top-gate voltages, and the signal frequency. It is shown that there are two threshold voltages, V th,1 and V th,2 , so that the dc current versus the top-gate voltage relation markedly changes depending on whether the section of the channel beneath the top gate (gated section) is filled with electrons, depleted, or filled with holes. The electron scattering leads to a decrease in the dc and ac currents and transconductances, whereas it weakly affects the threshold frequency. As demonstrated, the transient recharging of the gated section by holes can pronouncedly influence the ac transconductance resulting in its nonmonotonic frequency dependence with a maximum at fairly high frequencies.

Analytical device model for graphene bilayer field-effect transistors using weak nonlocality approximation

“…The reinstatement of the energy gap in graphene-based structures like graphene nanoribbons, graphene nanomeshs, and graphene bilayers appears to be unavoidable to fabricate FETs with a sufficiently large on/off ratio. Recently, the device dc and ac characteristics of graphene nanoribbon and graphene bilayer FETs (which are referred to as GNR-FETs and GBL-FETs, respectively) were assessed both numerically and analytically [12][13][14][15][16][17][18][19]. The device characteristics of GNR-FETs operating in near ballistic and drift-diffusion regimes can be calculated analogously with those of nanowire-and carbon nanotube-FETs (see, for instance [20][21][22] and references therein).…”

“…Thus in GBL-FETs, the back gate plays the dual role: it provides the formation of the electron channel and the energy gap. Since the electric field component directed perpendicular to the GBL plane in the channel section below the top gate (gated section) is determined by both V b and V t , the energy gap can be different in different sections of the GBL channel: E g,s (source section), E g (gated section), and E g,d (drain section) [17,18]. At sufficiently strong top-gate voltage (V t < V th < 0, where V th is the threshold voltage), the gated section becomes depleted.…”

“…(2) with the collisional term following the approach applied in Ref. [17]. Considering here the case when the elastic scattering mechanisms under consideration are strong, so that they lead to an effective isotropization of the electron distribution, one can find that the values of the source-drain current and the transconductance obtained in the previous section for the ballistic transport should be multiplied by a collision factor C. This factor is equals to C ∞ = 2π k B T /m/L t ν, where ν = mw/2 is the collision frequency (we put w(q) = w = const.…”

“…The functions f s,p and f d,p are the Fermi distribution functions with the Fermi energies ε F,s and ε F,d , which are determined by the back gate and drain voltages, V b and V d [17,18] (see also the Appendix):…”

“…In this paper, we use a substantially generalized version of the GBL-FET analytical device model [17,18] to calculate the characteristics of GBL-FETs (the threshold voltages, current-voltage characteristics, and transconductance) in different regimes and analyze the possibility of a significant improvement of the ultimate performance of these FETs by shortening of the gate and decreasing of the gate layer thickness. The device model under consideration, which presents the GBL-FET characteristics in closed analytical form, allows a simple and clear evaluation of the ultimate performance of GBL-FETs and their comparison.…”