Figure 3. (a) Evolution of the contact resistance with respect to the doping concentration for four different n-Si(100)|aTiSi interface models. The gray triangle and red stars correspond to the values computed for the energetically most stable interface models and to the experimental values reported by Yu et al. 15 for the same system, respectively. (b) Evolution of the associated energy barrier height (b) and width (c) to be crossed for an electron injection for the four different interface models. The evolution of the barrier height induced by image force lowering 16 is added a visual guideline for two Schottky Barrier heights values 0.5 eV and 0.75 eV. 

The disordered nature of amorphous metals such as TiSi makes the simulation of their interfaces with silicon complex. Indeed, the degrees of freedom at the interface in terms of local bond lengths, coordination number and composition make the development of an interface model challenging. In an attempt to capture these effects, we investigated the contact resistance of four different Si(100)-aTiSi interface models, in which the Ti and Si concentrations set in contact with the silicon substrate, their local coordination and bond lengths were varied. An atomistic model corresponding to the most stable energetic configuration is illustrated in Figure 1. All models lead to a current versus voltage (I.V.) characteristic curves similar to the one reported in Figure 2a, where a linear evolution of the current versus the applied voltage is obtained up to a bias of ∼0.1 V, after which the systems display a non-ideal linear behavior. The linear regime evolution was then used to extract the intrinsic contact resistance of the modeled interface. For instance, the intrinsic contact resistance of Figure 1 corresponds to 9.5 × 10 −8 .cm 2 for a doping concentration of 1 × 10 20 |e|/cm 3 and reflects the needs for the injected electrons to cross the interface potential set by the tail states 19 present at the metal-semiconductor interface (Figure 2b). Interestingly, this model leads to contact resistances values relatively close to what has been recently measured experimentally by Hao et al., 15 as illustrated in Figure 3a. As expected, the contact resistance evolves linearly with the doping concentration to reach values as low as 1.8 × 10 −10 .cm 2 for an active doping concentration of 1 × 10 22 |e|/cm 3 . These findings are consistent with the recent demonstration of a sub 10 −9 .cm 2 con- tact resistance for PMOS devices. 20 Remarkably, the first-principles simulations also suggest that beyond this value the contact resistance should saturate, even for a completely unrealistic active dopant con- centration of 1 × 10 23 |e|/cm 3 .

Further, the evolution of the contact resistance computed for dif- ferent interface models underlines that the impact of the interface morphology/composition on the intrinsic contact resistance is strongly reduced upon large doping. While at 1 × 10 20 |e|/cm 3 fluctuations of the intrinsic contact resistance vary up to 2 decades, they i) linearly decrease to reach a modulation factor 2 at 1 × 10 21 |e|/cm 3 , ii) be- come almost undistinguishable as from 3 × 10 21 |e|/cm 3 to iii) finally saturate. Our simulations suggest that at high doping concentrations, the impact of the interface composition is strongly reduced and be- comes less prominent. Consequently, the intrinsic contact resistance starts being dominated by the intrinsic properties of the metal and of the semiconductor. This is further confirmed by the evolution of the potential energy barrier height (Figure 3b) and its width (Figure 3c) to be crossed during the electron injection. Interestingly, the intrinsic Schottky barrier heights, 0.5 eV (for model 1) and 0.75 eV (for models 2 to 4) lie close to the experimental values reported for Si|Ti (0.6 eV) and Si|TiSi2 (0.5 eV) 29 H. R. Liauh et al. 30 (Figure 3b).

Further, the evolution of the contact resistance computed for dif- ferent interface models underlines that the impact of the interface morphology/composition on the intrinsic contact resistance is strongly reduced upon large doping. While at 1 × 10 20 |e|/cm 3 fluctuations of the intrinsic contact resistance vary up to 2 decades, they i) linearly decrease to reach a modulation factor 2 at 1 × 10 21 |e|/cm 3 , ii) be- come almost undistinguishable as from 3 × 10 21 |e|/cm 3 to iii) finally saturate. Our simulations suggest that at high doping concentrations, the impact of the interface composition is strongly reduced and be- comes less prominent. Consequently, the intrinsic contact resistance starts being dominated by the intrinsic properties of the metal and of the semiconductor. This is further confirmed by the evolution of the potential energy barrier height (Figure 3b) and its width (Figure 3c) to be crossed during the electron injection. Interestingly, the intrinsic Schottky barrier heights, 0.5 eV (for model 1) and 0.75 eV (for models 2 to 4) lie close to the experimental values reported for Si|Ti (0.6 eV) and Si|TiSi2 (0.5 eV) 29 H. R. Liauh et al. 30 (Figure 3b).

Further, the evolution of the contact resistance computed for dif- ferent interface models underlines that the impact of the interface morphology/composition on the intrinsic contact resistance is strongly reduced upon large doping. While at 1 × 10 20 |e|/cm 3 fluctuations of the intrinsic contact resistance vary up to 2 decades, they i) linearly decrease to reach a modulation factor 2 at 1 × 10 21 |e|/cm 3 , ii) be- come almost undistinguishable as from 3 × 10 21 |e|/cm 3 to iii) finally saturate. Our simulations suggest that at high doping concentrations, the impact of the interface composition is strongly reduced and be- comes less prominent. Consequently, the intrinsic contact resistance starts being dominated by the intrinsic properties of the metal and of the semiconductor. This is further confirmed by the evolution of the potential energy barrier height (Figure 3b) and its width (Figure 3c) to be crossed during the electron injection. Interestingly, the intrinsic Schottky barrier heights, 0.5 eV (for model 1) and 0.75 eV (for models 2 to 4) lie close to the experimental values reported for Si|Ti (0.6 eV) and Si|TiSi2 (0.5 eV) 29 H. R. Liauh et al. 30 (Figure 3b).

A closer analysis reveals that, while at low doping concentration, they both are strongly modulated by the image force potential gen- erated at the metal-semiconductor interface 16 (Figures 3b and 3c), an increase in the doping concentration leads to a transition of the dom- inant electron injection mechanism from a thermionic regime to an electron tunneling one. As from ∼3 × 10 21 |e|/cm 3 on, the height of the barrier and its width are so significantly reduced that an electron tunneling starts dominating the injection. As from mid-10 21 |e|/cm 3 on, there is no barrier anymore. The electron injection process then becomes dominated by the intrinsic interface transmission probabil- ity (T p ), which reflects the electron injection from the semiconductor into the metal and saturates. As analytically formulated by Baraskar et al., 3 the latter depends on bulk intrinsic material parameters such as the effective masses of the semiconductor (m s ) and of the metal (m m ), and their k vectors (k MZ and k SZ for the metal and semiconductor, respectively):