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А.А. TSELYKOVSKIY, E.V. MELNIK
Scientific adviser – G.I. ZEBREV
Moscow Engineering Physics Institute (State University)
GRAPHENE FIELD EFFECT TRANSISTOR CURRENTVOLTAGE CHARACTERISTICS MODELING TAKING INTO
ACCOUNT VELOCITY SATURATION IN THE CHANNEL
It has been proposed a model of I-V characteristics for bulk graphene based fieldeffect transistors with taking into account the carrier velocity saturation effects due to
high-field driven electric field in the graphene channel.
The fabrication of the first field-effect zero-bandgap graphene-based transistor with pronounced current saturation [1] led to an increase of interest in the
bulk graphene based devices. It was found in [1] that effect of velocity saturation of carriers plays a major role in graphene channel transport. Maximum
drift velocity is of order vSAT ~ 0.06-0.6 v0 (v0  108 cm/s is the universal Fermi
velocity in graphene) due to strong scattering in the channel. Using ideal graphene statistics we have been developed a model of I-V dependencies taking
into account aforementioned effect.
Total channel carrier sheet density (electrons plus holes) can be expressed in
ideal graphene as exact poli-logarithm functions of chemical potential  [2]


2


2  k BT     kBT 
k BT  

.
(1)
eN S  ene  nh    
 Li 2  e
  Li 2   e



   v0 
 



Quantum capacitance through the charge imbalance reads as
  
e d ne  nh  2  e2  k BT 
 .
(2)
CQ 

ln 2  2 cosh




d
   v0  v0 
 k BT  
Current-voltage characteristics of graphene transistor can be described taking into account maximum drift velocity vSAT based on results of [3, 4] by a following expression
CQ
  VD

W 0 e 2 N S2 1   
 ,
(3)
ID 
1  exp  

L
CQ
 
 1   enC 1  0 VDS vSAT L   
where 0 is channel carrier mobility (almost independent on NS),  is the ratio
of the diffusion component of the channel current to the drift one which can be
derived from electroneutralty condition [3]

Cox
C ox  CQ
(4)
For a sufficiently large dimensionless parameter 0 VDS vSAT L we have
saturation current restricted by maximum drift current
(5)
I D  WeN S vSAT
Fig.2. Comparison of simulation results (line)
Fig.1. Simulated drain current dependence as
function of drain voltage VD and gate voltage VGS and experimental data [1] (dots)
All parameters in Eq.3 can be expressed as explicit and exact (for a case of
ideal graphene) function of chemical potential  in graphene. Solving 1D Poisson equation the same procedure can be done for gate voltage VG () that allows to simulate graphene transistor drain current as function of the gate and
drain-source biases (see Figs.1,2). This work is considered as a step to development of comprehensive models for simulation of emerging graphene field
devices.
References
[1] I. Meric, M. Han et al. “Current saturation in zero-bandgap, top-gated graphene field-effect
transistors”, 21 September 2008; doi:10.1038/nnano.2008.268
[2] G.I. Zebrev, “Graphene nanoelectronics: electrostatics and kinetics”, Proceedings of the SPIE,
Volume 7025, p. 70250M-9 (2008).
[3] G.I. Zebrev, “Electrostatics and diffusion-drift transport in graphene field effect transistors”,
MIEL 2008. 26th International Conference on Microelectronics 2008, pp. 159-162.
[4] G.I. Zebrev, “Current-voltage characteristics of a metal-oxide-semiconductor transistor calculated allowing for the dependence of the mobility on a longitudinal electric field”, Soviet physics.
Semiconductors, 1992, vol. 26, no.1, pp. 47-49 , 1992.