Resilience and yield of flip-flops in future CMOS technologies under process variations and aging

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1 Published in IET Circuits, Devices & Systems Received on 24th November 2012 Revised on 4th July 2013 Accepted on 4th July 2013 Resilience and yield of flip-flops in future CMOS technologies under process variations and aging Christoph Werner, Benedikt Backs, Martin Wirnshofer, Doris Schmitt-Landsiedel Lehrstuhl Technische Elektronik, Technical University Munich, Theresienstr.90, Muenchen 80290, Germany ISSN X Abstract: In this study, the failure rate of flip-flops in future 16 nm complementary metal-oxide-semiconductor (CMOS) technologies is investigated. Using transistor level Monte Carlo simulations, the authors studied the influence of process variations and long term aging on the yield. The statistical distribution of the switching time (clock-to-q delay) is shown to be highly asymmetric compared to a Gaussian distribution leading to a drastically enhanced fraction of very slow or metastable samples. Moreover, the failure rates will rise additionally during the device lifetime because of aging effects. To improve the yield the authors investigated several possible countermeasures including enhanced supply voltage or ensuring larger data-to-clock times as well as process and circuit optimisation. 1 Introduction The influence of the ever increasing process variations in future CMOS technologies on the performance and the yield of digital CMOS circuits have received increasing attention in recent publications [1 3]. Whereas the impacts on static random access memory (SRAM) reliability as well as on timing of digital circuits have been studied in broad scope in a large number of papers [4 8]. However, the consequences of increased process variations on the switching behaviour of flip-flops or clocked storage elements in digital circuits have been investigated only by a small number of publications, which so far have led to quite contradictory results. Most authors [9, 10] use rather optimistic predictions (e.g. a 3σ value of 18% for the threshold voltage variations) from older International Technology Roadmap for Semiconductors (ITRS) roadmaps from 2007 [11] for the future process stability, which lead them to results, that seem quite manageable in future CMOS generations. In [9] the influence of process variations on the delay of five different flip-flop architectures was studied for a predictive 32 nm CMOS technology. From the ITRS prediction on the V th variation they deduce mean delay variations of 15 56%. On the other side, in [12], much higher process variations were found by atomistic device simulations, which were significantly higher than assumed in In accordance to that, the newer ITRS roadmaps publish an allowable threshold voltage variation (ATVV) of 42%, which would result in a 1σ value of 37 mv for the high performance 16 nm CMOS technology, investigated in this paper. In [13], it is shown that these process variations lead to a highly asymmetric distribution of delay variations in a CMOS D-flip-flop leading to a 3 higher failure rate for slowly switching elements than a symmetric Gaussian distribution would predict. In [14], the impact of process variations in an industrial 65 nm CMOS process on delay and energy of five different flip-flop architectures is investigated which results in 3σ values of 15 25%. In [15] four designs of D-flip-flops are studied experimentally in a 65 nm process technology. The authors found a very asymmetric distribution leading to an enhanced number of very slowly switching elements. In this paper, we will follow the newer assumptions and investigate in more detail the influence of process variations on the performance of two typical flip-flop architectures. Investigations on long-term aging for six different types of flip-flops have been published in [16] for a 32 nm technology. It is predicted that the mean values for setup-, hold- and switching times are delayed by less than 1 ps in nearly all cases after an aging period of 5 years, which seems small enough for all applications. However, the authors of [16] did not consider the effect of process variations, which will lead to enhanced failure rates in the aged samples as we will show in Section 3 of this paper. The rest of this paper is organised as follows: In the next section two typical flip-flop architectures are investigated, a transmission-gate master-slave flip-flop (TGMS) as it is used in PowerPC CPU and also in many application specific integrated circuit (ASIC) and system-on-chip (SOC) technologies and even in the newest 22 nm Intel processors [17] and the semi-dynamic flip-flop (SDFF), which is much faster but more power consuming, a variation of which is used in the ultra scalable processor architecture (USPARC) processor. Extensive Monte Carlo simulations are presented using predictive technology models (PTM) for a future 16 nm CMOS technology [18] and process variations as predicted by the ITRS roadmap Section 3 gives results on degraded devices after long term aging by biastemperature-instability effects (NBTI and PBTI). In Section 19

2 4 we present possible countermeasures to reduce the failure rates, which include increased supply voltage, ensuring larger data-to-clock times, reduction of process variations and design improvements. Section 5 concludes the paper and gives an outlook to further work. 2 Influence of process variations Fig. 1 shows the two flip-flop architectures studied in this work, a TGMS and a SDFF. These two architectures have been chosen since they represent two opposite corners in the energy-delay space as shown in [19 23]. In Fig. 1a, we see the TGMS flip-flop [10], which has a classical master-slave structure with two statically back-coupled inverter stages. This leads to a rather slow but stable switching behaviour at low power consumption. The transistor dimensions were adapted to the used 16 nm technology according to an established design in 65 nm. The detailed values are given in Table 1. An additional optimisation step for our predictive 16 nm technology will be described in Section 4. More detailed optimisation procedures for various flip-flop architectures have been published in [9, 21, 22]. In Fig. 1b, the SDFF is shown [10]. It has a dynamic precharge phase for the internal node X during the clock signal low phase. During the clock high phase X is discharged if the data input D is high. This leads to a very fast switching of the output Q, but also to enhanced power consumption because of the permanent charge discharge cycles even if the input remains constantly high. As a consequence the SDFF has a stable setup time near zero and its switching behaviour is more critical for rising than for falling data edges. However, the hold time required for the SDFF is somewhat larger than for the TGMS [24]. The flip-flop design was adopted from [10] resulting in the Fig. 1 Circuit diagram of the two flip-flops investigated a TGMS b Semi-dynamic flip-flop (SDFF) [10] For the TGMS the most degradation-sensitive PMOSFET at the data input is indicated, which will be optimised for higher yield in Section 4 20

3 Table 1 Values for the transistor widths used in our simulations of the SDFF and TGMS flip-flops SDFF TGMS Width, nm Width, nm Width, nm Width, nm M1 96 MN1 72 MP17 87 MN15 64 M2 432 MP1 139 MP19 65 MN16 48 M3 588 MN2 48 MP22 85 MN17 61 M4 660 MP2 96 MP25 87 MN22 64 M5 660 MN3 48 MP18 67 MN23 48 M6 204 MP3 48 MP15 80 MN24 56 M7 204 MN4 144 MP33 48 MN25 48 MPA 60 MP4 48 MP13 67 MN28 48 MPB 228 MN5 372 MP23 48 MN36 48 MNA 60 MP5 648 MP32 48 MN37 48 MNB 72 MN6 48 MP31 48 MN38 48 MP6 72 MP43 67 MN49 48 The length is taken as 16 nm for all MOSFETs transistor dimensions given in Table 1. For the simulation BSIM4 parameters have been used for high performance planar 16 nm CMOS from the PTM in [18]. The Monte Carlo simulations have been done with the circuit simulator HSPICE [25]. The scatter plots of Fig. 2 shows our results for both types of flip-flops. We plot the clock-to-q switching delay (c2q) for the rising against the falling edge for a number of 3000 samples. In most of the cases we see a good correlation between falling and rising edge especially for small values. However, in all cases there are a number of samples, where either the falling or the rising data edge has an extremely slow switching time (metastability). This is due to a metastable behaviour of the circuit [10], which can lead to an unpredictable switching because of small noise sources (or numerical uncertainties in the simulation). For the TGMS the plots contain also a number of samples with c2q = 0 for the falling edge and one for the rising edge. This is displayed for failing samples, which remained at their old value and did not switch within 3 ns. In Fig. 3, we compare the distribution function for different values of the threshold variations in a TGMS. We consider both the local variations of the threshold voltage within the circuit and the global variations between different circuit samples. The local variation, which is mainly because of the intrinsic random dopant variations (RDF), cannot be reduced by process optimisation. It is described by Pelgrom s law σ = A/(WL) 0.5 with a Pelgrom parameter of A =10 9 Vm, as reported from measurements in a recent technology [1]. Please note that in contrast to the local variations, which are quite consistent in literature, the global variations to be expected in future technologies are widely different between various publications. As described in [1], global variations result from non-ideal manufacturing processes including patterning proximity effects and variations in the gate dielectric and in the metal gate. The 2007 ITRS roadmap [11] demanded a 3σ value of 18% for the global V th variations which would be a 1σ of 15 mv in our predictive technology, whereas in the 2009 edition a total ATVV of 42% is reported, which in our technology would result in a σ of 37 mv and recent atomistic simulations predict 40 mv or even more [6]. In our work we only considered variations in the MOSFET threshold voltage V th, both local and global variations. In a real 16 nm technology Fig. 2 Correlations of c2q delay times for rising and for falling data edges of the two flip-flops investigated a TGMS flip-flop where the data edge comes 50 ps before the clock edge b SDFF with a data-to-clock delay of 0 ps Zero delay times are displayed for failing samples which do not switch at all (HSPICE Monte Carlo simulations with 3000 samples) 21

4 Fig. 3 Probability distribution functions (giving the percentage of occurrences in each bin of 16ps) for three different values of the global threshold variation (52, 37 and 22 mv) in a TGMS, for rising and falling transitions with a fixed data-to-clock delay of 100 ps It is seen that the smallest variation has no fails and no metastabilities (at least for the MC samples investigated), whereas the highest variation leads to fails and metastabilities in the percentage range we expect also variations on other parameters either correlated or uncorrelated to the V th variations. Nevertheless, the threshold variations are considered to have the highest impact and thus, as a first step, the other variations are neglected in our investigations. In our work we assumed a Gaussian distribution of V th using a local variation given by Pelgrom s law and global variations with a number of different σ values. Future technology nodes will presumably use undoped FinFETs, which will result in significant reduction of the doping induced local variations. However, because of line edge roughness (LER) of the fins and because of metal gate granularity (MGG), comparable values of σ th are predicted by atomistic device simulations [26] (e.g. σ th = 31.5 mv for L =20nm, σ th = 41.5 mv for L = 14 nm, and σ th = 51.6 mv for L = 10 nm), though these are considered as local variations, whereas in our study we focus more on the global variations. In Fig. 3, we see a failure rate of 0.01% for the σ th (global) = 37 mv variation whereas a value of 52 mv leads to fails in the percentage range. No fails or metastabilities were found at σ th (global) = 22 mv for the MC samples. A linear extrapolation of the distribution function to c2q = 100 ps, where the other curves show the first metastabilities, would predict fails below In Fig. 3, we see that the width of the c2q delay distribution is a strong function of the threshold voltage variation and also the number of metastable or non-switching states increases for larger variations. Beyond a certain c2q (about ps) we consider the flip-flops to be in their metastable state. Moreover, for σ(global) = 52 mv we even found some percent of totally failing flip-flops, which do not propagate at all the data input D to the output Q within 3 ns. In Fig. 4, we show the distribution function for the c2q delay for a typical data-to-clock time (0 ps for SDFF, 100 ps for TGMS) as a result of MC samples. We see a Fig. 4 Comparison of distribution functions for TGMS flip-flop and SDFF ( Monte Carlo samples (V dd = 0.7 V, data-to-clock delay = 0 and 100 ps, resp., virgin circuits, σ(global) = 37 mv) Both PDFs are strongly asymmetric leading to a higher fraction of slow samples. Both distributions are very similar showing a small number of metastable samples at a rather low level (a factor of 1E 4 below the maximum). The values are the percentage of occurrences in each bin of 4 ps 22

5 very asymmetric distribution yielding a reduction of the PDF of 1E4 below the maximum level at μ +9σ at the slow side and at μ 2σ at the fast side for the SDFF. The distributions are quite similar for rising and falling data edges and show a 2 3 faster switching time for SDFF compared to TGMS. In Section 4 we will use a definition for the total failure rate as the sum of total fails, which do not switch at all either at a rising or at a falling edge, plus the sum of metastabilities with a c2q delay above μ +9σ. This is rather similar to [3] where a failure is assumed for a 10 enhanced switching time of the latch. In most publications [19 23], which compare different FF architectures, the sum of an optimum setup time plus the resultant c2q delay (D-to-Q delay) is considered as the key figure. As we will show in Section 4 by adapting the data-to-clock delay the number of fails can be significantly reduced. Nevertheless, since we want to estimate the percentage of very slow or failing flip-flops in one chip because of process variations, we have to use a fixed data-to-clock delay for all our samples with a sufficient margin to the nominal setup time (50 or 100 ps for TGMS and 0 ps for SDFF). So we plot our yield as a function of c2q delay and not of D-to-Q delay as in [19 23]. For the TGMS, we show in Fig. 5 the individual correlations between the threshold variation of the single MOSFETs and the flip-flop failure rate as defined above. We selected all the Monte Carlo samples with metastable or failing behaviour in a TGMS. Now we looked how much the mean V th values of each individual transistor in this failing subset deviated from the mean V th of this MOSFET in the whole MC distribution. From this we could identify those MOSFETs whose deviations would mostly influence the FF fails. We found that the strongest correlation occurs for high absolute values of PMOS threshold in the global variation and also for the transistors MP43 and MN24, which have to Fig. 5 Sensitivity of the failure rate of a TGMS flip-flop on the single threshold voltage variations The graph shows the mean deviations of the threshold voltages from the nominal value (in number of sigmas) of the 14 most sensitive MOSFETs in all samples that were found metastable or failing in a 100 sample Monte Carlo simulation. Since the PMOS threshold voltages have a negative value, the negative values for the PMOSFETs mean that an enhanced absolute value of PMOS V th leads to a higher failure rate charge the master node at a falling data signal. As we will see in Section 4 an increased width of MP43 can help to reduce the failure rate. For the SDFF we found the sensitivities of the c2q delay on the threshold voltages to have rather similar values for all NMOSFETs, whereas for the PMOSFET threshold voltages there was a somewhat lower correlation. 3 Long term aging In today s CMOS technologies the threshold shift induced by long term aging is an increasing problem. To investigate this, we assume V th shifts in those transistors that are permanently under NBTI or PBTI stress as long as a constant input signal is applied. In our estimations we assumed that 50% of V th shift for those transistors that see a toggling clocking signal permanently switching between 0 and V dd, since the BTI aging under AC conditions is about that factor lower than for DC [27]. For a worst-case consideration with minimum recovery we assume that the aged flip-flops see a constant input signal for a long time which is changed for just one clock cycle and then written back again. Moreover, hot carrier instability will also occur at the NMOSFETs that see a switching input signal, but this effect can be considered to have a smaller impact. Usually circuits have to be designed to allow a maximum voltage shift of about 30 mv in the MOSFETS that experience the highest stress conditions without leading to circuit failures. Because of lacking experimental data for our predictive 16 nm high-k technology we assumed the same mean value of 30 mv for NBTI effects on PMOS and PBTI on NMOS transistors, which might be quite a good guess from today s experimental results [28, 29]. Moreover, future CMOS devices will experience a strong variability in the V th shifts induced by long term aging. We used the statistical model for the bias temperature instability effect in aged MOSFETs published in [30] which is based on the most advanced physical models, and implemented it into SPICE to allow Monte Carlo simulations considering the variability of the virgin devices as well as the variations in the aging effects themselves. Our model can well describe the non-gaussian distribution, which can be described by a Gamma function as shown in Fig. 6 and leads to an increased fraction of samples with large threshold voltage shift. It can accurately describe the stress/recovery behaviour of V th in MOSFETs in a 65 nm CMOS technology and will allow also predictions of aging induced failure rates in our 16 nm CMOS circuits. Details were given in [31]. In Fig. 7, we see the influence of long term degradation on the distribution function of the c2q delay for a TGMS with a data-to-clock time in the critical range of 50 ps. It is not clear today how large the degradation effects in future technologies will be, but it can be assumed that a maximum drift of 30 mv at the permanently stressed transistors as used in our MC simulations must still be allowed before circuit failures occur. The results show that the mean switching speed of the flip-flop is degraded by less than 10 ps and the 3σ value by 20 ps, which should not give rise to problems in the circuit behaviour, but the number of slowly switching samples with c2q delays of more than 100 ps is increased by a factor of 2 10 in the aged samples compared to the virgin circuit. Moreover the number of failing samples, which do not switch at all, is increased by more than a factor of 10. As we will see in Section 4 these fails can be 23

6 Fig. 6 Probability distribution function for the threshold voltage shift from a Monte Carlo simulation of 3000 samples after s stress at V GS = 1.5 V followed by recovery at V GS = 0 V for 10, 1000 and s Each value gives the number of samples in a bin of ΔV th = 12.8 mv. NBTI model from [31], parameters adapted for a 65 nm CMOS technology. The results can quite well be fitted by Gamma functions Fig. 7 Probability distribution functions for virgin and aged distributions of the switching delay in a TGMS with σ(global) = 37 mv (data-to-clock = 50 ps, V dd = 0.70 V) The y-axis give the percentage of samples falling into a bin of 5 ps. The number of slowly switching samples increased by a factor of 2 5, whereas the number of fails increased by more than a factor of 10 Fig. 8 Probability distribution functions for virgin and aged distributions of SDFF (T d2c = 0 ps, hold time = 150 ps, V dd = 0.70 V, rising edge, σ(global) = 37 mv) The y-axis give the percentage of samples falling into a bin of 5 ps. The mean value of c2q is enhanced by 10 ps by the aging, whereas 0.1% of metastables occurs after aging will study the possibility to additionally reduce the failures and metastabilities in the flip-flops by reducing frequency and increasing the supply voltage. We will estimate how much yield can be regained, when limited constraints in power and delay are accepted, that is, with somewhat enhanced supply voltage or ensuring longer data-to-clock time or by process or design optimisation. In Fig. 9, we show the failure rates of our two flip-flop architectures as defined in Section 2 as a function of data-to-clock time. It can be seen that an increase from 50 to 100 ps for the TGMS can reduce the failure rate for the aged circuit by a factor of 30, whereas for SDFF a low value is already achieved for the nominal setup time of 0 ps, and for longer data-to-clock times only marginal improvements are seen. This is true both for virgin and aged circuits. In Figs. 10 and 11, the influence of supply voltage can be seen. An increase of V dd from 0.70 to 0.75 V will result in a decrease of fails by a factor of 10 or more. avoided by guaranteeing a higher data-to-clock time or by increasing the supply voltage by 50 mv. A similar behaviour is seen for the SDFF in Fig. 8. Here we have an AC stress for most of the internal MOSFETs because of the dynamic charge/discharge architecture, only the input and output stages see a permanent stress. Again we used our statistical NBTI model from [31] with a mean threshold shift of 30 mv for all NMOS and PMOS transistors which are permanently under PBTI or NBTI stress and 15 mv for the MOSFETs under AC stress. We see only a small shift in the mean switching time, but a drastic increase in metastable samples. Here we also see a fraction of 0.1% of the samples that completely fail. 4 Countermeasures Clustered voltage scaling (CVS) and adaptive voltage and frequency scaling (AVFS) have been discussed extensively as an approach to reduce leakage power as well as timing errors in combinational logic paths [8]. In this section we Fig. 9 Percentage of failures for both flip-flop types as a function of data-to-clock times for virgin and aged circuits For the TGMS the failure rates can be drastically reduced for enhanced data-to-clock times, whereas for SDFF only a small improvement is seen 24

7 Fig. 10 Probability distribution functions for virgin and aged samples of SDFF (t d2c = 0 ps) An enhancement of V dd from 0.70 to 0.75 V can reduce the failure rate back to the values of the virgin samples at 0.70 V Fig. 12 Percentage of failures for TGMS flip-flop with two different designs as a function of data-to-clock times for virgin and aged circuits Whereas the failure rates are not changed for long d2c times in the virgin circuit, it can be reduced significantly for the aged circuit and for very short d2c times in the virgin circuit Fig. 11 Percentage of failures for a TGMS flip-flop as a function of data-to-clock times for virgin and aged circuits An enhancement of V dd from 0.70 to 0.75 V can reduce the failure rate by a factor of 10 back to the values of the virgin circuit Of course an increased V dd will result in slightly higher power consumption as well as in somewhat increased long term aging. Nevertheless, we think that the advantage of higher yield will be worth the cost, especially when V dd is increased only if necessary by use of adaptive voltage scaling (AVS) [8] and/or only in the blocks where fails might occur (CVS). In today s CMOS technology flip-flops are optimised with regard to power consumption and timing delay, but without too much attention to reliability [9]. Therefore for the TGMS we also tried a simple design improvement of the circuit. In Fig. 12, we compare the failure rates for two modifications, where the width of the most critical PMOSFET (MP43 in Fig. 1a) of the input stage was enhanced by 50% (from 4 L min to 6 L min ), whereas all other components remain unchanged. We found that the stronger pullup PMOSFET helps to reduce the failure rate for the case of a rising data signal in the aged circuit by factors of 3 10, without any drawback for the falling data signal. Whereas the TGMS failure rate can be significantly reduced by guaranteeing a higher setup time, the SDFF does not benefit from a data-to-clock time increased above 0 ps neither for the virgin nor for the aged device. Since the SDFF is known to be sensitive to the hold time [24], we looked at this influence in Fig. 13. It is seen that the failure rate for the virgin circuit increases significantly for hold times below 30 ps. However, additional failures that occur after aging cannot really be avoided by increasing the hold time. Thus for the SDFF only an enhanced supply voltage can avoid failures in the aged device, as can be seen from Fig. 10. Finally, we also consider the influence of improved process technology, which could reduce the global variation of the threshold voltage. This has already been shown in Fig. 3 of Section 2. There it can be seen that our failure rate could be very low, if it would be possible to reduce the global threshold voltage variation down to a σ value of 22 mv. An extrapolation of the curves in Fig. 3 would suggest a value of 10 8 for metastable and failing flip-flops. Therefore if it really would be possible to achieve the ambitious goals of the 2007 ITRS roadmap, we will obtain Fig. 13 Percentage of failures for SDFF flip-flop as a function of hold times for virgin and aged circuits The failure rates can be significantly reduced for longer hold times in the virgin circuit, but the additional number of failures that occur in the aged circuit remain the same for all hold times 25

8 Table 2 Relative number of fails for virgin and aged flip-flops with different working conditions V dd, V Data-to-clock, ps sufficient yield at least for the virgin circuits. However, may be the other options presented before will be achievable with less effort. In Table 2, we summarise the effects of our different countermeasures on the yield of the two flip-flop architectures. We do that both for the unstressed circuits and for aged circuits, where the threshold voltage of those MOSFETs that experience the highest stress conditions has shifted by 30 mv. The results show that we can reduce the failure rate by factors of 5 10, which is about the same factor which we loose because of the long term aging. 5 Conclusion Monte Carlo transistor level simulations of typical flip-flops in a future 16 nm CMOS technology have shown that a considerable number of metastable or failing samples must be expected. For typical process variations we found that up to of the flip-flops will fail because of metastable or completely non-switching behaviour. This is primarily because of a strongly asymmetric distribution function with a long tail of slow switching flip-flops. In addition, already a 30 mv shift of threshold voltage because of long term aging of the circuit (BTI) will lead to an increased number of fails by a factor of In our study, we have also investigated a number of countermeasures in order to reduce the number of failures. These include an increased data-to-clock time or an enhanced hold time, which leads to a reduction of the failure rate by a factor of 5 10, as well as increasing the supply voltage by 50 mv, which leads to a 10 reduction of failures. 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