Performance comparison of zero-Schottky-barrier and doped contacts carbon nanotube transistors with strain applied

1Department of Electrical and Electronic Engineering, United International University, Dhaka-1209, Bangladesh 2Department of Electrical and Electronic Engineering, East West University, Dhaka-1212, Bangladesh *Corresponding author. Email: awahab@eee.uiu.ac.bd Performance comparison of zero-Schottky-barrier and doped contacts carbon nanotube transistors with strain applied Md. Abdul Wahab1,* and Khairul Alam2

Carbon nanotube (CNT) is a fascinating material that shows metallic or semiconducting behavior depending on its radius and chirality [1][2][3][4][5][6][7]. CNTs can withstand very large mechanical strains [8], and have extremely high Young's modulus [9]. The strain has significant effects on the electronic properties of CNTs [3][4][5][6][7][10][11][12][13][14]. Maiti et al. [14] have shown that strain can change the conductance of a zigzag nanotube by several orders of magnitude. The pioneer experiment by Tombler et al. [15] shows that high strain (~3%) can change the conductance of a metallic single-walled nanotube by two orders of magnitude. In that experiment, strain was applied to a suspended nanotube using atomic force microscope (AFM) tip. Strain can open up a band gap in metallic CNTs, and can modify the band gap of semiconducting CNTs [16]. Small band gap semiconducting or quasi-metallic nanotubes exhibit the largest changes in resistance and piezo-resistive gauge factors, and they can be used as nanoscale pressure sensors [17].
While the study of strain effects on electronic and mechanical properties of CNTs shows significant progress, strain engineering in CNT based devices is still in early stage.
Single-walled carbon nanotube devices have been fabricated on elastomeric polydimethylsiloxane (PDMS) substrates [18]. In those devices, strain has been applied to modulate their electronic properties. The conductance of a suspended multi-walled CNT has been measured by applying strain using AFM tip [19]. The strain effects on the performance of ballistic Schottky-barrier carbon nanotube transistors have been theoretically studied [20].
In this paper, we compare the performance of ballistic zero-Schottky-barrier and doped source-drain contacts carbon
The Poisson's equation, Eq. (1), is discretized using finite difference, and is solved by standard Newton-Raphson method.
The potential is fixed to V GS -Φ G /q at the gate electrode. For Schottky contact, potential is fixed to -Φ S /q at the source electrode and to V DS -Φ D /q at the drain electrode. Here, V GS and V DS are the gate to source and drain to source voltages, and Φ G , Φ S , and Φ D are the work functions of gate, source, and drain metallizations. For doped source-drain contacts, the axial component of electric field is set to zero at the source and drain ends. The radial component of electric field is set to zero along the exposed surface of dielectric.
The CNT is modeled using π-orbital basis of carbon atom.
When strain is applied, we assume that the on-site energy does not change, and the hopping parameter changes following Harrison's formula [23] V ppπ = V 0 ppπ (r 0 /r) 2 . Here, V 0 ppπ and r 0 are the hopping parameter and the carbon-carbon bond length, respectively, of the unstrained CNT, and r is the bond length of strained CNT. With uniaxial strain applied, the axial, r t , and the circumferential, r c , components of a carbon-carbon bond are calculated by the following equations [5] Here, axial strain, ε t and circumferential strain, ε c are related via Poisson's ratio υ=-ε c / ε t , and r 0t and r 0c are the axial and circumferential components, respectively, of the unstrained carbon-carbon bond. A Poisson's ratio value of 0.2 is used in our simulation [7,20]. For torsional strain, the circumferential component of the carbon-carbon bond is modified as r c =r 0c + tan(γ)r 0t where, γ is the shear strain. The Hamiltonian parameter values are taken from Ref. [24].
Here, t's are the coupling matrices, and g 0,0 and g N+1,N+1 are the Here, n is the iteration number. Iterations are repeated until A n and B n are small enough so that the nearest neighbor coupling can be disregarded. Then the surface Green's function can be , the iteration is started with A 0 = t 0,1 and B 0 = t 1,0 . In both cases, the matrix H 0 is the unit cell Hamiltonian of the carbon nanotube, and H s 0 = H 0 . The coherent drain current is calculated from Where, h is Planck's constant, and the transmission is calculated The self-consistent loop is started with an initial guess of the potential profile. We generate the initial profile following Ref. [31]. That is, the initial conduction band edge is a step profile with E C = E CS in the source region, E C = E CS + E g /2 under the gate region, and E C = E CS -eV DS in the drain region. Here, V DS is the drain to source bias, e is the electronic charge, and E CS is the conduction band edge relative to the source Fermi level and is calculated from the charge neutrality condition.
However, for Schottky contact, the potentials are fixed at the gate, source, and drain terminals, and therefore, our initial potential profile is generated from the Laplace equation. The update profile for the next iteration of self-consistent loop is created using Anderson mixing scheme [32].

NUMERICAL RESULTS AND DISCUSSIONS
We simulate coaxially gated zero-Schottky-barrier and The on/off current ratio versus uniaxial and torsional strains with Schottky and doped contacts are shown in Fig. 6.
The on/off current ratio is better in doped contact devices. The change in on/off current ratio with strain is slightly sensitive to the device contact type, especially in case of torsional strain.
This is because the off-state current variation with strain is not sensitive to the contact type, and this sensitivity of on-state current is not significant. For the Schottky contact CNTFETs, the on/off current ratios are 2.
Where, R is the radius of the dielectric covering t ox .