Impact of the Aggressive Scaling on the Performance of FinFETs: the Role of a Single Dopant in the Channel
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Green’s function. Equation (2) is equivalent to the Schrödinger equation, while the equation (3) is a quantum generalization of the semi-classical Boltzmann equation. The simulations are carried out in the mode space approach [4,5], which decomposes the problem into the transversal and longitudinal spaces. The Schrödinger equation is solved in every cross-section (with nt mesh points) of the device (transversal space) to obtain the wavefunctions and subband energies (each corresponding to one mode). The transport is then solved in the product space of the longitudinal space with the mode space, which has a dimension (nlxM), where nl is the number of mesh points in the longitudinal dimension and M the number of modes. The advantage of this methodology is that (nlxM) is much smaller than (nlxnt), thus allowing for more efficient calculations than a solution of the problem directly in the real 3D space discretization [5]. The effects of electron-phonon scattering have been included via the self- consistent Born approximation and using local self-energies. Acoustic and optical phonon scattering are considered in the whole device. Non-equivalent and equivalent inter-valley, as well as intravalley, transitions have been considered in our simulations. The parameters are the same used in [2,6], which are those extracted for bulk MOSFET structures, which provide a good agreement with more sophisticated transport models in the calculation of mobility and ballisticity of Si nanowire transistors [6].
RESULTS AND DISCUSSION We consider two different devices with channel lengths of 11.8 and 6.6 nm and body thicknesses of 5.8 and 4.2 nm, respectively. For both devices we considered a ratio between fin height and thickness of 2:1. All simulations were carried out at a drain bias of VD=0.2 V and gate biases of VG=VT-0.2V, VT and VT+0.2V. Despite the thinner body of the smaller device, the increased tunneling due to the reduced gate length leads to a worse subthreshold slope of 87.5 mV/dec compared to the slope of 75.7 mV/dec of the bigger device. Figure 1 shows the ID-VG characteristics for both devices as well as the devices with the dopant in the centre of the channel. For the bigger device the donor in the middle of the channel enhances the current by 242, 44 and 11%, respectively, for the three different biases. An increase of the current due to the donor impurity in the middle of the channel is expected due to two factors. Firstly, it reduces the barrier height. Secondly, it introduces states in the middle of the channel which lead to an increase of the tunneling current. This last effect is also reflected in the degradation of the subthreshold slope. The acceptor impurity in the middle of the channel produces a reduction of the current of 61, 35 and 14%, respectively, for the simulated bias points. Even though the change is more moderate in the subthreshold region, the impact above the threshold voltage is even higher than that of the donor impurity. Figure 2 represents the first subband at VG=VT-0.2 V for the three simu
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