Also, γ 1=−3.2e V and γ 3=−0.3e V refer to the first- and third-nearest neighbor Quisinostat ic50 hopping parameters and Δ γ 1=−0.2 eV is used for the correction to γ 1 due to edge bond relaxation effect. A poisson’s ratio value of 0.165 is used
in this study [31]. The electron effective mass AG-881 supplier of each conduction subband can be calculated by using the formula (4) and at the bottom of the conduction band is given by (5) Figure 2 illustrates the dependence of band gap E G,n of the GNR’s family N=3p+1 on the uniaxial tensile strain ε. As it is seen, in the range of tensile strain 0%≤ε≤15%, E g decreases first and then increases linearly. Therefore, there is a turning point, i.e., as the strain increases, there is an abrupt reversal in the sign of dE g /d ε, making the curves to display a V shape. The turning point moves toward smaller values of strain as the width of the AGNR increases. Moreover, the slope of E g (ε) is almost identical for various N and the peak value decreases see more with increasing N. The above observations are in agrement with the main features revealed by using tight-binding or first-principles numerical calculations [17, 20]. On the other hand, Figure 3 shows the variation of effective mass at the conduction band minimum with strain ε. As it is clearly seen, has similar strain dependence as E g and a linear
relation between and E g is expected which could be correlated to an inverse relationship Amisulpride between mobility and band gap [32]. These effective mass variations is attributed to the change in the conduction band minimum position under various strain values. Figure 2 Band gap variation versus uniaxial tensile strain for different (3 p +1)-GNRs with indices p =3,4,5,6. Figure 3 Effective mass variation versus uniaxial tensile strain for different (3 p +1)-GNRs with indices p =3,4,5,6. Device performance Assuming a ballistic channel, the carriers with +k and −k states are in equilibrium with Fermi energies of the source (E FS) and the drain (E FD), respectively, with E
FS=E F and E FD=E F−qV D. The carrier density inside the channel can be obtained by employing the effective-mass approximation and integrating the density of states over all possible energies [26] (6) where F j is the Fermi-Dirac integral of order j defined as (7) and η n,S =(E FS−E C,n )/k B T, η n,D=(E FD−E C,n )/k B T. Considering the electrostatics describing the structure, the following relation between the gate voltage and Fermi energy E F can be obtained [33] (8) where q is the carrier charge, C ins is the gate-insulator capacitance per unit length of the GNR and V FB denotes the flat-band voltage. The value of V FB depends on the work function difference between the metal-gate electrode and the GNR, and it can be set simply to zero as it is discussed in detail in [34].