Device Model for Graphene Bilayer Field-Effect Transistor

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 ‘Reprinted with permission from V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, and N. Kirova (2009). Device model for graphene bilayer field-effect transistor, J. Appl. Phys., 10S, 104510. Copyright © 2009 American Institute of Physics.

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ISBN 978-981-4800-75-4 (Hardcover), 978-0-429-32839-8 (eBook) 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, Кл>1 and ^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.


The features of the electron and hole energy spectra in graphene provide the exceptional properties of graphene-based heterostructures and devices [1-6]. However, due to the gapless energy spectrum, the interband tunneling [7] can substantially deteriorate the performance of graphene field-effect transistors (G-FETs) with realistic device structures [8-11]. To avoid drawbacks of the characteristics of G-FETs based on graphene monolayer with zero energy gap, the patterned graphene (with an array of graphene nanoribbons) and the graphene bilayers can be used in graphene nanoribbon FETs (GNR-FETs) and in graphene bilayer FETs (GBL- FETs), respectively. The source-drain current in GNR-FETs and GBL- FETs, as in the standard FETs, depends on the gate voltages. The positively biased back gate provides the formation of the electron channels, whereas the negative bias voltage between the top gate and the channels results in forming a potential barrier for electrons which controls the current. By properly choosing the width of the nanoribbons, one can fabricate graphene structures with a relatively wide band gap [12] (see also Refs. [13-16]). Recently, the device dc and ac characteristics of GNR-FETs were assessed using both numerical [14] and analytical [17-19] models. The effect of the transverse electric field (to the GBL plane) on the energy spectrum of GBLs [20-22] can also be used to manipulate and optimize the GBLFET characteristics. A significant feature of GBL-FETs is that under the effect of the transverse electric field not only the density of the two-dimensional electron gas in the GBL varies, but the energy gap between the GBL valence and conduction bands appears. This effect can markedly influence the GBL-FET characteristics. The structure of a GBL-FET is shown in Fig. 2.1. In this chapter, we present a simple analytical device model for a GBL-FET, obtain the device dc and ac characteristics, and compare these characteristics with those of GNR-FETs.

The chapter organized as follows. In Section 2.2, we consider the GBL-FET band diagrams at different bias voltages and estimate the energy gaps and the Fermi energy in different sections of the device. Section 2.3 deals with the Boltzmann kinetic equation, which governs the electron transport at dc and ac voltages and the solutions of this equation. The cases of the ballistic and collision dominated electron transport are considered. In Sections 2.4 and 2.5, the dc transconductance and the ac frequency-dependent transconductance are calculated using the results of Section 2.3. Section 2.6 deals with the demonstration and analysis of the main obtained results, numerical estimates, and comparison of the GBL- FET properties with those of GNR-FETs. In Section 2.7, we draw the main conclusions. In Appendix, some intermediate calculations related to the dynamic recharging of the gated section by holes due to the interband tunneling are singled out.

Schematic view of the GBL-FET structure

Figure 2.1 Schematic view of the GBL-FET structure.

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