Workfunction fluctuation

Fig. 3.5(a). The simulation domain of KMC simulation is flexible. The generated positions of dopants are then mapped in to device channel region for atomistic device simulation, as plotted in Fig. 3.5(b). Figure 3.6(a) shows the distribution of KMC simulated profile.

The simulated distribution can be replaced by measured secondary ion mass spectrometry (SIMS) doping profile. The solid line is the dopant distribution, which can be replaced by SIMS profile. The dash line is the fitted distribution, which is similar to the original dopant distribution. As the distribution of dopants is obtained, we can fit the distribution function of the profile then generate the associated dopant distribution for random dopant simulation, as presented in Fig. 3.6(b). There are 5000 generated dopants, whose distribu-tion along the Si/SiO₂interface is similar to the original profile, the solid line in Fig. 3.6(a).

Consequently, our dopant generation approach is flexible to capture any distribution of dopants with adequate the accuracy.

3.3 Workfunction fluctuation

High-κ/metal-gate technology has been recently recognized as the key to sub-45 nm tran-sistor fabrication due to the small gate leakage current with an increased gate capacitance.

Moreover, the sheet resistance is reduced with the use of metal as gate material. Comparing to the poly-gate technology, the metal-gate material will not react with high-κ material and therefore there existing less interface charge and V_th pinning effect. The gate depletion in

60 Chapter 3 : Simulation of Intrinsic Parameter Fluctuation

Figure 3.7: (a) The SEM pictures and illustration of TiN surface, which containing numbers of grain with various grain orientation.

(b) An illustration of crystal structure of copper with

<200>, and <111> orientation. Each grain orientation has its own strength of dipoles and therefore different

workfunction. Therefore, the combination of device

workfunction will become a probabilistic distribution rather than a deterministic value.

3.3 : Workfunction fluctuation 61

poly-gate material is no longer existed. Additionally, the phono scattering effect is signif-icantly reduced due to the less quantum resonance effect. However, the grain orientation of metal is uncontrollable during growth period. The use of metal as a gate material in-troduces a new source of random variation due to the dependency of workfunction on the orientation of metal grains [121-123]. Figure 3.7(a) shows the SEM pictures of Titanium nitride (TiN) [123]. TiN is a rocksalt-structure (NaCl structure) compound consisting of Ti atoms filled in FCC-based lattice with all octahedral sites filled with nitrogen atoms. As shown in the plot, the surface is composed by numbers of grain and each grain may have different orientation, as illustrated in Fig. 3.7(b). Since the different grain orientation has its own strength of dipoles, the workfunction in each grain orientation is different. The device V_thwill become a probabilistic distribution rather than a deterministic value.

To characterize the metal-gate induced workfunction fluctuation, a statistically sound Monte-Carlo approach is advanced here for examining such distribution. The simulation flow is expressed in Fig. 3.8. At first, the gate area is partitioned into several parts according to the average grain size, as shown in Fig. 3.8(a). Then the grain orientation of each parts and total gate workfunction are randomly generated based on properties of metal as shown in Fig. 3.8(b) [122]. The workfunction of each partitioned area (W K_i) is a random value.

The summation of W K_i is then averaged to obtain the effective workfunction of transistor

62 Chapter 3 : Simulation of Intrinsic Parameter Fluctuation

Figure 3.8: The gate area is partitioned into several pieces according to the average grain size. The workfunction of each

partitioned area (W K_i) is a random value, whose probability follows (b). The obtained probability

distributions of TiN workfunction for devices with (c) 1, (d) 4, and (e) 9, grains on the gate area. (f) Dependence of TiN metal-gate induced σV_{th,W KF} versus the average grain size.

The gate area is 16 × 16 nm²

3.3 : Workfunction fluctuation 63

and then used for WKF-induced threshold voltage fluctaution estimation. Figures 3.8(c)-3.8(e) show the probability distributions of workfunction for devices with one, four, and nine grains on the gate area. The distribution is similar to the normal distribution as the numbers of grain increases. In other words, in nanoscale transistor with scaled gate area, the distribution is not a normal distribution and therefore the WKF-induced σV_thmay not be a normal distribution as the gate area scales. Figure 3.8(f) examines the dependence of WKF-induced σV_th versus the average grain size on a 16 × 16 nm² gate area. The material is TiN. The WKF-induced σV_th increases significantly as the average grain size increases, which imply the importance of controlling metal-gate grain size in reducing WKF effect. The σV_{th,W KF} saturates after 16 nm average grain size because the average grain size becomes larger than gate area. The average grain size of this study is four nm [122]. Notably, the different process of gate formulation, gate first or replacement gate, may change the thermal budget and changes the grain size of metal material.

Notably, the results of statistical generation approach is similar to previous literature [122]. However, the previous literature used a probability density function to estimate the population of workfunction. The estimation approach is fast, but can not consider the residual blocks during the discretization procedure, as illustrated in inset of Fig. 3.9. Thus, we use a monte carlo random generator to estimate the random gate workfunction fluctua-tion. Figure 3.9 presents the MoN induced V_thfluctuation for device with 16-nm-gate area.

64 Chapter 3 : Simulation of Intrinsic Parameter Fluctuation

Figure 3.9: WKF induced V_thfluctuation versus average grain size with and without taking residual gate area into consideration.

The inset illustrates the residual gate area during the

discritization of gate area. The flat area in the solid line may mislead the impact of WKF.

3.3 : Workfunction fluctuation 65

Figure 3.10: WKF induced Vth fluctuation in various technology node with and without taking residual gate area into

consideration. The WKF effect saturates after 32 nm, which is similar to the results of previous literature [122].

However, for the newly developed Monte Carlo simulation approach, the WKF effect saturates after 22 nm. Since the average grain size is 22 nm, having the same Vth

fluctuation after 22 nm is reasonable.

66 Chapter 3 : Simulation of Intrinsic Parameter Fluctuation

The dash and symbol line shows the Monte Carlo results with considering the discreteized residual area. As the average grain size decreases, the gate area contains a large number of grain and therefore the difference of averaged workfunction is averaged. The solid line is the control group without considering residual area. The trend of V_th fluctuation is the same as the other; however, there are several flat area existing in the solid line, which may mislead the impact of WKF. For example, Fig. 3.10 shows the WKF induced Vth fluctua-tion for 90 nm to 16 nm technology node with and without taking residual gate area into consideration. In previous literature, the WKF effect saturates after 32 nm, which is similar to the results without residual gate area. However, for the newly developed Monte Carlo simulation approach, the WKF effect saturates after 22 nm. Since the average grain size is 22 nm, having the same V_th fluctuation after 22 nm is reasonable. The obtained distribu-tion of workfuncdistribu-tion is then mapped to the device gate area for workfuncdistribu-tion fluctuadistribu-tion simulation. We have to notice that though the current computation methodology can pro-vide a fast estimation of WKF-induced fluctuation, the obtained WKF is an averaged result containing no crystallized grain in simulation. Therefore, the impact of WKF may be un-derestimated. More complicated WKF simulation including the nucleation and growth of metal and grain boundary effect has been taken into our future work.