The impact of emerging metal gate work-function fluctuation compare with random dopant fluctuation and process variation effect on device reliability has been discovered and discussed in the previous section. This section then explores the associated device variability in the state-of-art circuits. The dominant fluctuation sources in each circuit characteristics are found and discussed.
5.2.1 CMOS Inverter Circuit
Figures 5.4(a) - 5.4(d) compare the tr, tf, tHLand tLH fluctuations. The tf and tHLare dependent on the Vth fluctuations of NMOS device, and tr and tLH are dependent on the Vth fluctuations of PMOS device. According to the results of Fig. 5.1, the RDF and WKF are the dominating factors in digital timing fluctuations.
5.2 : Circuits Characteristics 85
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Figure 5.4: Comparison of the variations of (a) fall time, (b)
high-to-low delay time, (c) rise time, and (d) low-to-high delay time with respect to RDF, PVE, and WKF.
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Figure 5.5(a) shows the σPdyn of inverter circuits with RDF, PVE, and WKF. The RDF and PVE dominate the dynamic power fluctuation; additionally, the WKF shows less impact due to the smaller gate capacitance fluctuations. Figure 5.5(b) displays σPsc for the studied inverter circuits. Different to the results of σPdyn, the WKF start to play an important role in σPscbecause of the significant σVthinduced by work-function fluctuation.
Figure 5.5(c) summarizes the σPstat. Since the σPstat is related to the device leakage current fluctuation, the RDF and WKF dominant the σPstatdue to the induced larger σVth. The inverter power fluctuations (σPinverter = [(σPP V E)2 + (σPW KF)2 + (σPRDF)2]0.5) are summarized in Fig 5.5(d). The Pstat is one of the major sources of the power fluctuation and the RDF and WKF are the dominating factors in power fluctuation of CMOS inverter.
The inverter power fluctuation is 8.09 nW (5.232 + 3.322 + 5.202), which is about 18%
(σPinverter / Ptotal × 100% = 8.09 / 45 × 100%) of power consumption and may bring significant impacts on the reliability of circuits, such as temperature and timing.
5.2 : Circuits Characteristics 87
Figure 5.5: The (a) dynamic power, (b) short circuit power, (c) static power, and (d) inverter power fluctuations for the explored inverter with RDF, PVE, and WKF.
88 Chapter 5 : The Total Effects of All Fluctuations
5.2.2 6T SRAM Circuit
Figure 5.6 summarizes the SNM fluctuations for 16-nm-gate SRAM, in which the nom-inal SNM is only 86 mV. Since the RDF and WKF induce larger device variability in threshold voltage, the SNM fluctuations of SRAM are thus dominated by RDF and WKF, which are 32% and 29%, respectively. The results are also similar to the results of device σVth, the RDF and WKF are dominating sources.
5.2 : Circuits Characteristics 89
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Figure 5.6: The summarized static noise margin fluctuation induced by RDF, PVE, and WKF.
90 Chapter 5 : The Total Effects of All Fluctuations
5.2.3 Common Source Amplifier Circuit
Figure 5.7(a) shows the circuit gain versus operation frequency, where the solid line shows the nominal device. The circuit gain, 3dB bandwidth, and unity-gain bandwidth fluctuations are explored, as shown in Figs. 5.7(b) -(d), where the insets show the trend of circuit gain, 3dB bandwidth, and unity-gain bandwidth as a function of device characteris-tic and circuit element. The gain of the studied circuit is proportional to gm multiplied by output resistance of circuit. The 3dB bandwidth and the unity-gain bandwidth of the com-mon source amplifier circuit indicate the variations of switching speed. The insets of Figs.
5.7(c) and (d) show the main sources of variations contributed from device characteristics fluctuations, gm, ro, and CG. Similar to the cutoff frequency fluctuation of NMOS device at the same gate bias, the high-frequency characteristic fluctuation of the common source amplifier circuit is dominated by RDF and PVE, and WKF become less important in this analyzing skeleton.
5.2 : Circuits Characteristics 91
Figure 5.7: The (a) frequency response, (b) 3dB bandwidth, (c) high-frequency circuit gain, and (d) unity-gain bandwidth fluctuations induced by RDF, PVE, and WKF.
92 Chapter 5 : The Total Effects of All Fluctuations
5.2.4 Current Mirror Circuit
The mismatch of device influence the reference current and output current value and result in the variations of circuit operation of current mirror circuits. We compare WKF with RDF and PVE induced normalized IOU T fluctuation. The RDF and WKF are the major variation sources of current mismatch, and the results are similar to the results of device σVthdue to the strongly relative between drain current and device threshold voltage.
5.2 : Circuits Characteristics 93
Figure 5.8: The summarized normalized IOU T fluctuations induced by RDF, PVE, and WKF for (a) NMOS and (b) PMOS current mirror circuits.
94 Chapter 5 : The Total Effects of All Fluctuations
5.3 Summary of this Chapter
This chapter has compared the influences of the work-function fluctuation with random dopant fluctuation and process variation effect in 16-nm nanoscale devices and circuits.
The dominating factors of devices and circuits characteristic fluctuations were found and discussed. The WKF induced σVthare competitive with RDF and is one of the dominating factors of the Vth fluctuation; however, the impact of WKF is small, especially at high gate bias. On the other hand, the PVE brings direct impact on gate length and therefore the PVE induced AC characteristic fluctuations are independent of screening effect and should be noticed when the transistor operated in high gate bias. In the timing and power fluctuations of inverter circuit, the SNM of SRAM, and the normalized IOU T fluctuation of current mirror, the WKF is also a dominating factor due to significantly influence of device σVth. For the high frequency characteristics including circuit gain, 3dB bandwidth, and unity-gain bandwidth, the major fluctuation sources are RDF and PVE, and WKF become less important in this analyzing skeleton.
Chapter 6
Conclusions and Future Work
6.1 Conclusion of this Study
The metal gate work-function fluctuation has been highlighted and investigated. The 3D device simulation proposed in this thesis can capture the work-function position effect which can not predict by the previous method. We have successfully examined it by the potential, charge, and band diagram distributions, and then compared with random dopant fluctuation and process variation effect. Our results have shown that the WKF and RDF dominate the device threshold voltage fluctuation; and therefore rule the power and de-lay time of the explored inverter circuit, SNM of SRAM circuit, and current mismatch of NMOS and PMOS current mirror circuits. The delay time, current mismatch, and static noise margin depend on the device Vth; therefore, their fluctuations follow the trend of
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96 Chapter 6 : Conclusions and Future Work
σVth. The total power fluctuation including fluctuation of the dynamic power, the short circuit power, and the static power have been investigated. The RDF and WKF are the dominating factors. For the high-frequency characteristics, the circuit gain, the 3dB band-width, and the unity-gain bandwidth were also explored. Similar to the trend of the device cutoff frequency, the PVE and RDF dominate the device and circuits characteristic fluctu-ations and the WKF shows less impact on high-frequency characteristic owing to the small gate capacitance fluctuation. The sensitivities of circuit performance with respect to device parameter fluctuation have been reported. It is necessary to include both the WKF and RDF effects in studying digital circuit reliability; however, for the high frequency appli-cations, the PVE and RDF effect are dominating factors. Consequently, the links should be established between circuit design and fundamental device technology to allow circuits and systems to accommodate the individual behavior of every transistor on a silicon chip.