2-5-4-1 Considering the Variation of Doping Concentration in Semiconductors
In the extraction procedure of the mTLM method, the sheet resistance (Rs) of the diffusion layer is regarded as a critical parameter. Since the Rs is determined by the doping concentration distribution of the diffusion region, if the variation of dosage of implantation is considered, the Rs would not be a constant value for all test structures used during the extraction procedure. The Rf extrapolated from Eq.1-8 may not correct, and then the ρce may deviate from the actual ρc value. Therefore, for the mTLM method, the extraction error stems from the variation of fabrication process would be understandable.
To investigate the influence of variation of doping concentration in diffusion region explicitly, statistic including 100 extraction results is used to depict the reality more closely. First, for the extrapolation of Rf value from the Rtotal-Ld plot, 100 Rtotal values, corresponding respectively to different setting doping concentrations of the top surface of the diffusion region with 1×1020 cm-3 ± 5% in Gaussian distribution for each Ld, are obtained by using test structures with Wc = 1 μm and Lc = 2 μm and the
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actual ρc = 1×10-8 Ω-cm2. Fig.2-15 shows the distribution of the Rtotal for each Ld. Next, randomly choose Rtotal value for each Ld, extrapolate the Rf, and then extract the ρc according to the mTLM procedure. Repeat the above-mentioned process several times, like 100 times in this subsection, to make the results closer to the normal distribution in theory. Fig.2-16(a) illustrates the extrapolation of the Rtotal-Ld plot, and Fig.2-16(b) and (c) show the distribution of the extracted Rs and Rf, respectively.
According to the statistic, the Rs is 218 Ω ± 5.5%, while the Rf is 11.8 Ω ± 370%. It could be observed in Fig.2-16(a) that after the extrapolation, the Rf could vary in a wide range, and in certain cases Rf < 0 may even occur, which is unreasonable in reality. The ρce values, extracted from Rf values, are illustrated in Fig.2-16(d) ignoring the cases of Rf < 0. Comparing to the actual ρc value of 1×10-8 Ω-cm2, a large range varying from 10-10 to 10-7 Ω-cm2 of the ρce is obtained. Inaccurate extrapolation is the major cause. In essence, the extrapolation method tends to contain errors; indeed, changes of the Rtotal value make the extrapolated results more diverse. In conclusion, it is indicated that when the mTLM method is utilized, the variation of doping concentration in diffusion region may lead to the incorrect extrapolation, and consequently deviate the extraction accuracy, which is a crucial difficulty for the mTLM method.
2-5-4-2 Considering the Variation of Tapered Sidewall Angle of the Diffusion Region To define the active region clearly, the STI are chosen in this thesis and the vertical sidewalls of the diffusion region are expected for the mTLM structure.
However, based on the trench etching process and the stress consideration, tapered sidewalls are preferred rather than vertical sidewalls. Compromised between the stress issue and the requirement for precisely defining the gate length, the appropriate angle
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should be larger than 88.2° according to the ITRS [21]. In this subsection, diffusion region with tapered sidewalls is considered and the influence of the tapered sidewall slope on the extraction error of the mTLM method is verified.
Similar to the settings in previous subsection, to investigate the influence of the variation of the tapered sidewall angles of the diffusion region explicitly, statistic including 100 extraction results is used. The same, test structures with Wc = 1 μm and Lc = 2 μm and the actual ρc = 1×10-8 Ω-cm2 are used in this part. The sidewall angles are set 88 ± 2° in the Gaussian distribution for all test structures. The extraction procedure here is identical to that in section 2-5-4-1, and the distribution of the Rtotal for each Ld is shown in Fig.2-17. Comparing with the results in Fig.2-15, the distribution of the Rtotal values for every Ld in Fig.2-17 is more concentrated rather than that in Fig.2-15, indicating that the variation of tapered sidewall angles could be less significant to the extraction accuracy than the doping concentration of the diffusion region. Then, the distributions of the Rs, the Rf, and the ρce are demonstrated in Fig.2-18(a), (b), and (c), respectively. The Rs is 216.7 Ω ± 0.7%, while the Rf is 14.7 Ω ± 30% and the ρce is 1×10-8 Ω-cm2 ± 62%. In contrast with the results in Fig.2-16, the extraction accuracy would be affected slightly by the variation of the tapered sidewall angles indeed. It is noticed that both the doping concentration and the tapered sidewall angle vary the Rs basically. The variation of the doping concentration would change the Rs directly, while the settings of the variation of the tapered sidewall angle would change the Rs in a slighter amount. Accordingly, it is reasonable that in this work the variation of tapered sidewall angles plays a minor role on the error of the ρc extraction rather than the variation of doping concentration of the diffusion region.
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2-5-4-3 Considering the Recessed Contact
Similarly to the CBKR method mentioned in section 2-5-2-2, as the recessed contact is considered, an additional contact surface arises at the side of the recessed contact and the current distribution of the mTLM structure would be changed. As the recession happens, the Rf becomes to be determined by the parallel connection of the current path at the side contact and at the planar contact. Also, the extraction results would be affected by different ρc values as well. In Fig.2-19(a), the relative error as a function of the recession depth with various ρc values is shown. In Fig.2-19(b), the difference between the ρce and the ρc is also presented, which would help the following argument understandable. First of all, for higher ρc, the ρce increases with the recession depth. In this case, the current tends to flow into the planar contact instead of the side contact which has a relative larger resistance with smaller cross-section and/or higher ρc. As the recession depth increases, the depth of the diffusion region decreases, raising the Rs under the contact and the ρce consequently.
On the contrary, for lower ρc, the side contact with a lower ρc value would be a preferable path for the current flowing into the contact, though the Rf is larger than that without the recessed contact due to the smaller cross-sectional area of the side contact. Then, as the recession depth increases, i.e., the side contact becomes dominant, the deeper the recession depth is, the more the current flows into silicide through the side contact with gradually larger cross-section, inferring that the ρce
would decrease with the deeper recession of the contact. Therefore, it could be concluded that all the ρce values increase for shallow recession of the contact, 10 nm in this simulation for example; as the contact recesses deeper enough, the ρce values increase more for higher ρc, while reduce for lower ρc.
Moreover, the above results are compared to those of the CBKR method in Fig.2-10, concluding that as the recession depth increases, the extraction results would
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reduce gradually for the CBKR method, while increase at first and then reduce for the mTLM method.
Briefly, the CBKR structure provides an easier extraction method, and could obtain better extraction accuracy by reducing the Ac and choosing an appropriate δ.
However, limitations caused by fabrication process would degrade its accuracy.
Smaller Ac would suffer from the corner rounding more seriously and consequently would arise the extraction error. The recessed contact resulting from silicidation process would underestimate the ρc and result in a more complex situation. Because these errors originate from some unavoidable parameters, they would be unfortunately inevitable and therefore limit the accuracy.
As for the mTLM structure, it is easier to be fabricated, and it shows a better accuracy at low ρc regime according to the simulation results in this thesis. It is free from the δ owning to its self-aligned feature. The most difficult for the ρc extraction is the sensitivity to the process variation. The recessed contact changes the current distribution and has a more complicated influence for the mTLM method. The dopant concentration and the tapered sidewall angle of the active region would vary with the process and hence vary the ρce. Fortunately, errors originating from the process variation could be eliminated by averaging lots of data. According to the law of large numbers in probability theory, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed [69]. Therefore, the average of a large amount of the extracted results could avoid the dependence of the process variation and enhance the ρc
extraction validity. This would enhance the applicability of the mTLM method. It is noticed that the extraction procedure is complicated by nature for the mTLM method, and if the large number of data is needed, it would be more complicated and time-consuming. Finally, in this simulation, it is observed that even though both
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methods could improve their accuracy by some means, there are still error sources affecting the extracted results.
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Fig. 2-1 The general 3-D simulated structures of the CBKR method.
(a)
(b)
Fig. 2-2 Definition of parameters for CBKR method (a) with a square contact, and (b) with a circular contact. The metal layer is not drawn here.