Study of SRAM Cell for Balancing Read and Write Margins in Sub-100nm Technology using Noise-Curve Method

Study of SRAM Cell for Balancing Read and Write Margins in Sub-100nm Technology using Noise-Curve Method

Malleshaiah G. V

Department of Electronics and Communication Engineering,

Eastpoint College of Engineering for Women (EPCEW), Bangalore, India

1. C. Srinivasaiah

   Department of Telecommunication Engineering, Dayananda Sagar College of Engineering (DSCE), Bangalore, India,

   AbstractIn this paper we perform a study of 3 SRAM cell architectures, namely conventional (single port) 6T (6- transistors), 8T (8-transisitors) and 9T (9-transistors) both with dual ports, to review and evaluate Static Noise Margin (SNM) at low operating voltages. These cells are simulated using SimuCad EDA tool by Silvaco, using generic 90nm process design kit (PDK). It is observed that the 6T SRAM cell suffer from poor writability and severe read disturbance. The write margin of the 8T SRAM cell considered in this paper is comparable with 6T SRAM, having superior read stability. The 9T SRAM cell has superior read and write margins even at extremely scaled supply voltage, VDD. The implication of cell transistor widths on the cell stability and power dissipation are analyzed based on the noise curve technique at VDD=1V. For conventional 6T SRAM, the sensitivity of its static power noise margin (SPNM) to NMOS

   hold state [3, 5]. The SNM has the drawback of disregarding its time dependence during read and write operations [5, 6].

   The read and write margins that are statically determined, cannot predict dynamic read and write margins of the SRAM cell. During the normal cell access, the wordline (WL) is pulsed to VDD for TWL duration. We succeed in cell access, if and only if the cell response time TR<TWL for both read and write operations [3, 5, 7]. The TR is a random variable across the array, which is a function of process variations. So the TWL must have sufficient margin to include the maximum TR i.e. TR+3 , where is its standard deviation [5].

   The dynamic read and write margins of SRAM cell are also

   functions of various other parameters such as CVDD, threshold voltage V of the cell transistors, cell ratio CR= / , and

   pull down transistor width (Wdn) is 1.3W/m and 5.5W/m T

   dn ac

   when Wac=Wpu=0.4m and 2m respectively, where Wac and Wpu are the widths of the NMOS access and the PMOS pull up transistors, respectively. For the same 6T cell, the sensitivity of write trip power (WTP) to Wdn is 3.7W/m and 3W/m when Wac=Wpu=0.4m and 2m, respectively.

   Keywords: Read stability, Write margin, Static voltage noise margin, Static current noise margin, Write trip voltage, and Write trip current.

   1. INTRODUCTION

      Modern microprocessor units (MPUs) have multilevel cache for achieving high throughput of instruction execution for performance critical applications such as digital signal processing, modern Internetworking, etc. The overall integrated circuit (IC) process flow integration for logic and SRAMs have a better compatibility as against the logic versus embedded DRAMs (eDRAMs) [1]. This makes SRAMs a suitable choice for cache, over eDRAMs in the modern MPUs [1, 2]; but the SRAMs are known to be power hungry. To reduce SRAM power consumption, one of the well known approaches is to lower the cell-VDD (CVDD) [3].The reduction in CVDD results in decreased static noise margin (SNM) [3, 4]. The estimation of SRAM cell metrics such as read stability and writability based on cell static noise margin (SNM) is too pessimistic because the SNM approach assumes static noise; in reality the noise will appear at discrete instants, lasting for a short duration when once it appears [5]. The SNM metrics characterize the noise margin of an SRAM cell only during its

      ratio BR=ac/pu, where dn, ac, and pu are the transconductance parameters of the pull down, access, and pull up transistors, respectively [8]. For a reliable read and write operations both the CR and BR should be greater than 1.

      The noise-curve or N-curve (NC) method is one of the practical inline measurement techniques used to determine the cell stability [6]. In this method a set of NC-parameters, namely static voltage noise margin (SVNM), write trip voltage (WTV), static current noise margin (SINM), and

      write trip current (WTI) are derived from the NC. The NC- parameters finds good correlation with the cell SNM. They also provide additional information about cell such as static power noise margin (SPNM) and write trip power (WTP) [5, 6, 9] which are calculated using the NC-parameters. The SPNM and WTP metrics provide deeper insight into the cell power consumption during the read and write operations, respectively. The NC is essentially the cell I-V (current voltage) relation determined by sweeping the voltage at the internal 0 node of the cell, under certain bias conditions, discussed later. The NC enables extraction of all the NC parameters at relevant coordinates of I-V plane.

      This paper is organized as follows: Section-II gives an overview of the conventional single port 6T, 8T and 9T cells both with dual ports. Section III presents the fundamentals of the N-curve methodology used to determine the various NC parameters of the SRAM cell. Section IV discusses on various NC parameters extracted using the methodology of section III. In section V, conclusion is drawn with a discussion on the observations made and its novelty.

   2. AN OVERVIEW OF CONVENTIONAL 6T, DUAL PORT: 8T AND

      9T SRAM CELLS

      Aggressive scaling of device dimensions and voltage gives rise to unacceptable variability in SRAM cell characteristics. The SNM is a function of VDD, threshold voltage VT, CR and BR. The variability in these parameters translates directly to variability in SNM [4, 8]. The increased variability in VT

      due to random dopant fluctuation (RDF) is very severe in sub-

      100nm MOSFETs [4, 6]. Finally, this variability has severe

      M3

      M5 Q=1'

      BL M1

      VDD

      GND

      WL

      M4 QB=0' M2

      M6

      i(V2)

      + V2

      –

      BLB

      implications on yield of SRAM chips [4, 10-13].

      While going beyond sub-100nm technology node, dual port 8T and 9T cell architectures will be of choice to achieve the required read stability and writability [3]. In this paper the

      WBL

      WWL VDD

      M3

      (a)

      M4

      WBLB

      discussion and analysis of dual port 8T and 9T SRAMs

      M5 M6

      follows the earlier reports from [3, 7].

      Fig. 1(a) shows the conventional 6T SRAM cell, connected to bitlines BL, BLB and the wordline WL. The storage action is

      Q=1' M1

      QB=0' M2

      RBL

      M8

      M7

      accomplished by two inverters on left and right sides, built using a pair of transistors M1-M3, and M2-M4, respectively. The BL and BLB contents will be written to Q and QB nodes via. the access transistors M5 and M6 when their gates connected to WL, is pulsed. The reading of the cell content (from Q and QB nodes) is done by precharging both the BL and BLB bitlines to VDD normally, followed by pulsing of the wordline, WL. The complementary bits stored in the Q and QB nodes develop a differential voltage V across BL and BLB through charge sharing effect. The voltage V is amplified by a sense amplifier to interpret the bits stored in the cell.

      The read stability and writability are very important metrics

      WBL

      M5

      GND

      WWL VDD

      M7

      =1'

      M3 Q

      SL

      M1

      GND

      (b)

      (c)

      M8

      QB'

      M4 QB=0'

      SR

      M2

      RWL

      WBLB

      6

      M9

      RBL RWL

      that characterize SRAM cells. During the read operation, the cell bits are flipped due to read disturbance mainly at the internal 0 node (i.e. the node holding 0 bit). At this node the precharged BL and BLB lines develop a voltage above VTRIP also called inverter threshold voltage. When this condition is met, the back to back connected left and right side inverters will enter into a regenerative feedback action, eventually flipping the cell bits. For the SRAM cell to flip, the feedback has to be maintained for a minimum duration of cell response time TR. The condition of TWL >TR must be satisfied for a successful read and write operations [5]. The VTRIP, voltage defined earlier related to VDD and transconductance parameters of M1-M3 or M2-M4 (Fig. 1) is given as:

      + | |

      Fig. 1: Various SRAM cell topologies (a) Conventional 6T, (b) Dual port 8T, and (c) Dual port 9T. Note: GND is the ground terminal.

      The cell ratio CR and beta () ratio BR defined earlier will characterize read stability and writability of the SRAM. Balancing the dynamic read stability and dynamic writability requirements in 6T SRAMs considering the critical timing of various signals such as WL, BL, BLB, etc., is very challenging. In view of addressing the read stability and writability issues, the SRAM cell architecture has evolved to advanced dual port 8T and 9T architectures. These cell architectures overcome the challenges that arise in sub-100nm conventional 6T SRAM cells using write-assist and read-decouple techniques. These techniques are explained for 8T and 9T cells shown in Fig. 1(b) and Fig. 1(c), respectively.

      =

      1+

      (1)

      Fig. 1(b) and Fig. 1(c) presented in this paper are dual port 8T and 9T SRAM cells developed for low power applications, as reported in [3]. Fig. 1(b) shows an 8T cell with independent

      where dn and pu are the transcoductance parameters of pull

      down (M1 or M2) and pull-up (M3 or M4) transistors, respectively in the SRAM cell of Fig. 1(a). VTn and VTp are the threshold voltage of the M1 (or M2), and M3 (or M4)

      2

      transistors, respectively. From Equation (1) = , when

      |VTn|=|VTp| and dn=pu. When the access transistors M5 and M6 are turned ON by pulsing the WL, the internal 0 node will try to rise above ground potential. If this rise reaches VTRIP level given by Equation 1, it leads to read disturbance, eventually flipping storage node (Q and QB) bits, which has its implications over Wdn.

      read and write ports which is a modification of the conventional 6T SRAM cell of Fig. 1(a) by the addition of transistors M7 and M8. The read and write operations are performed through two mutually exclusive datapaths (ports), one for writing into cell similar to BL/BLB bitlines of conventional 6T SRAM cell, while the other datapath is a single ended read port RBL, decoupled from the internal storage nodes (Q/QB). When the write wordline WWL is pulsed, the write bitline WBL/WBLB voltages will be written into the Q/QB storage nodes of the cell. This write operation is similar to writing in the conventional 6T SRAM of Fig. 1(a).

      The 8T cell decouples the storage nodes while reading, using M7 and M8 transistors. When the gate of M8 transistor RWL is pulsed, the internal storage node voltage causes the voltage on the precharged RBL bitline to change (by V), which is sensed and amplified to logic levels corresponding to 0V or VDD. The gate of M7 transistor provides the necessary read decouple of RBL from Q/QB storage nodes. However, this 8T cell does not increase the write margin significantly. This cell is reported to work till a minimum range of VDD=260-450mV [3].

      The Fig. 1(c) shows a 9T SRAM cell with exclusive read and write datapaths (ports) which works till a minimum VDD=130mV [3] corresponding to deep subthreshold operation, and is found functionally successful at this value of VDD. The 6T SRAM of Fig. 1(a) is modified to achieve this 9T cell with a write-assist feature [3, 7] implemented by the addition of M7' and M8' transistors. The inclusion of these two transistors will provide control over feedback in the basic bistable latch comprising M1, M2, M3, and M4 transistors. The gate signal SL and SR of the transistors M7' and M8' provides the required control in achieving the enhanced write-margin. The inclusion of the transistor M9 provides the isolation of read port from the internal storage nodes during the read operation.

      For dynamic read and write operations, precise timing of various signals in Fig. 1(c) is very important. When a 0 has to be written into internal node Q, the WBL is low, WBLB is high, SL is high, SR is low, and WWL is pulsed. This configuration opens the feedback loop, thereby assisting the write operation. When a 1 has to be written into internal node Q, the WBL is high, WBLB is low, SL is low, SR is high, and WWL is pulsed. The internal node QB holds the complement bit of Q node.

      During the read operation, M8' of this 9T SRAM cell is turned off by setting SR to 0V. When the RWL is pulsed, M9 connects QB' to the read port, RBL. As M8' is off, nodes QB and QB' are decoupled. This prevents the voltage rise at node QB' passed from RBL, and inturn passing to the node QB; thus improving the read stability. In hold mode, both SR and SL are kept at VDD to turn ON the feedback loop of the cross coupled inverters. Thus the hold SNM of this 9T SRAM cell is similar to 6T and 8T, but with slight degradation due to stacking.

      Fig. 2 illustrates superimposed voltage transfer characteristics (VTCs) of the two back to back connected inverters. The separatrix of the SRAM cell is defined as the crossover point of Q and QB node voltages through which a 45o line passes through as shown in Fig. 2. The VTCs of Fig. 2 is also called as butterfly curve [4, 5, 7, 8]. The SNM of the SRAM cell is defined as the side of square with smallest diagonal fitted into the eye of the butterfly as shown in Fig. 2.

      As reported by Evert Seevinck et al [8], the SNM of 6T SRAM cell is a lengthy expression with 3 explicit terms; its simplified version is given as:

      6 = ± (2)

      where two terms are implicit in , in this equation. In Equation (2), first term is exclusively VT, the second term is a function of VDD, VT (VTnVTp), CR, and BR; thus is inclusive of VT term again. All these quantities are defined in the earlier section. Thus SNM of 6T SRAM cell is directly proportional to VT and a small fraction ±. The variability of

      VDD, VT, CR, and BR will translate to the variability in the SNM of 6T SRAM cell. Maintaining sufficient cell SNM across PVT (Process-Voltage-Temperature) space and across all the cells is a major challenge in sub-100nm technology nodes [4, 10].

      Fig. 2: Butterfly curve for 6T SRAM cell (when the access transistors are off). Inscribed squares in its eye depicted an SNM 0.4V, at VDD=1V. The separatrix point is where the Q and QB node voltages are same on the line which is drawn through maximum inverter gain of 2 VTC curves at ~0.45V.

   3. N-CURVE METHODOLOGY TO DETERMINE NOISE MARGINS

      The traditional SNM method of analysing the SRAM cell stability is having some limitations. First, the SNM does not provide a simple means of its inline measurement. Secondly, as it involves only the voltage measurements, it does not provide any information on the cell currents during the cell access and hold states. Third, it fails to provide the dynamic characteristics of the cell, related to the read and write access times. Finally, the SNM method is not suitable for measuring large data required for statistical analysis of the SRAM cell characteristics [5, 6, 9].

      The definition of read margin and write margin for the 6T SRAM cell (Fig. 1(a)) based on the NC method, is suitable for inline tester measurements. The NC provides both the current and voltage information, unlike the SNM which provides only the voltage informaion. In this paper the use of NC to understand 6T SRAM cell characteristic follows the analysis and interpretation of NC by Evelyn Grossar et al [6].

      Fig. 3: The N-Curve of 90nm 6T SRAM cell simulated at VDD=1Vfor the circuit of Fig. 1(a).

      Fig. 3 shows a NC simulated for 90nm 6T SRAM cell with high VT transistors, at VDD=1V. For plotting the NC for the cell structure of Fig. 1(a), the bias conditions are: the BL, BLB and WL are all clamped at VDD to configure the cell in read operation mode. The cell is connected to a variable voltage source V2 delivering current i(V2), shown dotted in Fig. 1(a). The V2 is swept from 0V to 1V. The current that is sourced from or sunk into V2 during the sweep operation results in an I-V relation in the form of NC, as shown in Fig. 3

      In three points A, B and C of the N-curve in Fig. 3 the current injected into the storage node is zero. The A and C points correspond to the two stable points of the butterfly curve of Fig. 2, and the point B corresponds to the separatrix (0.45V). When the points A and B are very close, the cell is at the edge of destructive read. The voltage difference between points A and B is called static voltage noise margin SVNM indicates the maximum tolerable DC noise voltage by the cell before its contents flip (i.e. the static read margin). The peak cell current between the points A and B is the maximum current the cell conducts before flipping, is called

      static current noise margin SINM. By using the combined SVNM and SINM metrics, the read stability criterion for the cell is defined properly. The area under the NC between the point A and B is called the static power noise margin SPNM, which signifies the power consumed during read operation.

      The region of NC between the points B and C in Fig. 3, defines the write-margin of the SRAM cell. The voltage difference between the points B and C is called the write trip voltage WTV. The value of WTV indicates static write margin. The maximum magnitude of the negative current between the points B and C is called the write trip current WTI. The area under the NC between the points B and C is called the write trip power WTP, which signifies the power consumed during the write operation.

   4. RESULTS AND DISCUSSION

      We have performed power analysis of 6T SRAM cell (Fig. 1(a)), in terms of SPNM and WTP both as functions of various cell transistor widths. This study is performed using SmartSpice circuit simulator of SimuCad EDA tool from Silvaco. For all the circuit simulations (at VDD=1V), we have used generic 90nm process design kit (PDK). For power analysis, we have used NC method which involves extraction of NC parameters: SVNM, SINM, WTV and WTI (as defined earlier). Using the NC parameters we calculate the SPNM and WTP, as a measure of read and write power margins, respectively. Calculation of SPNM and WTP is done by evaluating the area under NC between the points A and B, and B and C, respectively as shown in Fig. 3.

      Fig. 4 shows two sets of NCs corresponding to two different values of the pull up and access transistor widths Wpu and Wac, respectively, with Wpu=Wac in both cases. For Wpu=Wac=0.4m, Wdn is varied from 0.4m to 2m, in steps of 0.4m, resulting in 5 NCs labelled Case-1 in Fig. 4. A second set of NCs labelled Case-2 are obtained with Wpu=Wac=2m, with Wdn varied over the same range and step size as in Case-1. In Case-1 it is noticed that 3 out of 5, NCs have well defined NC parameters with 2 curves not showing positive peaks, and hence we cannot extract SVNM and SINM for them. In Case-2 we have all the 5 NCs showing well

      defined positive and negative peaks for which we have extracted all the NC parameters. The gate length Lg=90nm for all the cell transistors in both the cases.

      0.4m Wdn 2m @ Wpu = Wac = 0.4m (CR, BR 1): Case-1

      0.4m Wdn 2m @ Wpu = Wac = 2m (CR, BR 1): Case-2

      200

      ) A

      u

      ( 100

      t n e r u 0

      r

      c

      e

      r -100

      c

      u o s

      g -200

      n i c r

      f -300

      o

      e d

      No -400

      0.0 0.2 0.4 0.6 0.8 1.0

      Node forcing voltage-V2 (V)

      Fig. 4: Two sets of N-curves corresponding to two values of the width of pull up and access transistor. Each set is obtained by varying the width of the pull down transistor from 0.4m to 2m in steps of 0.4m.

      (a) (b)

      (c) (d)

      Fig. 5: The parameters extracted for two sets of NCs labelled: Case-1 and Case-2 (Fig. 4) plotted as a function of pull down transistor width. (a) Plots of SVNM and WTV for Case-1, (b) Plots of SINM and WTI for Case-1, (c) Plots of SVNM and WTV for Case-2, and (d) Plots of SINM and WTI for Case-2.

      In Fig. 5 we have plotted the NC parameters extracted from the two sets of NCs labelled Case-1 and Case-2 in Fig. 4 as a function of pull down transistor (M1 in Fig. 1) width Wdn. Fig. 5(a) shows the plots of SVNM and WTV for Case-1, Fig. 5(b) shows plots of SINM and WTI for Case-1, again. Fig. 5(c) shows the plots of SVNM and WTV for Case-2, and in Fig. 5(d) SINM and WTI are plotted for Case-2. From this graph, it is seen that as SVNM increases from relatively smaller value, WTV decreases with Wdn. This trend explains the fact that, as the static read margin increases the static write margin decreases.

      In Fig. 5(c) and (d), trends similar to Fig. 5(a) and (b) are noticed in the plots of SVNM, WTV, SINM, and WTI, but the currents in this case are proportionately high due to larger transistor widths (with Wpu=Wac=2m), with Wdn again in the same range i.e. 0.4mWdn2m and same step size of 0.4m. This study would provide a basis in balancing the static read and write margins of 6T SRAM cells.

      Important point to note from Fig. 5 is that the SVNM and WTV are relatively higher, and SINM and WTI are relatively lower for Case-1, when compared with that in Case-2.

      Fig. 6 is the plot of SPNM and WTP as a function of Wdn, with 0.4mWdn 2m. Fig. 6(a) corresponds to Case-1 and Fig. 6(b) corresponding to Case-2. An important point to note from Fig. 6 is that, as the widths of the transistors are increased the cell power consumption is increasing.

      From Fig. 6 we have calculated the average sensitivity of SPNM to Wdn which is 1.3W/m and 5.5W/m when Wac=Wpu=0.4m and 2m respectively. The average sensitivity of WTP to Wdn is 3.7W/m and 3W/m, when again Wac=Wpu=0.4m and 2m, respectively.

      The above NC technique can also be applied to 8T and 9T SRAM cells that are discussed in earlier section, in a similar manner.

      (a)

      (b)

      Fig. 6: The static power noise margin SPNM and the write trip power WTP for the two sets of N-curves labelled Case-1 and Case-2 in Fig. 4 are plotted as a function of Wdn. (a) SPNM and WTP versus Wdn for Case-1, and (b) SPNM and WTP versus Wdn for Case-2.

   5. CONCLUSIONS

We have performed the extraction of NC parameters (i.e. SVNM, SINM, WTV, and WTI) for 90nm, 6T SRAM cell. The NC based static power noise margin SPNM and static write trip power WTP are considered as metrics to determine the read and write access powers. For 6T SRAM, the sensitivity of SPNM to Wdn is 1.3W/m and 5.5W/m when Wac=Wpu=0.4m and 2m, respectively. The sensitivity of WTP to Wdn is 3.7W/m and 3W/m, again when Wac=Wpu=0.4m and 2m, respectively. These sensitivities highlight the efforts required to determine the right transistor widths to balance and minimize the cell SPNM and WTP, simultaneously. The SPNM and WTP parameters determined in this work, have given a deep insight into the order of worst case power dissipation in the 90nm SRAM cells. We have also reviewed dual port 8T and 9T SRAM cells [3, 6], qualitatively. The qualitative analysis of these two cell architectures has provided a deep insight into their low power

capabilities, especially with a highlight on deep subthreshold operational capability of 9T SRAM cell.

ACKNOWLEDGEMENT

Author would like to acknowledge Visvesvaraya Technlogical University (VTU), Belgaum, Karnataka, for funding this research project. Authors also convey special thanks to Dr. D. Premachandra Sagar, Vice-chairman, Dayananda Sagar group of institutions (DSI) for all his support and constant encouragement for this research work.

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