Department of Electrical, Computer and Information Technology Islamic Azad University of Qazvin

1. Department of Electrical, Computer and Information Technology Islamic Azad University of Qazvin Subject: presentation an article Student:Framarzaghaei Master:Dr. Dr. Shah-Hosseini

2. S. Lin, Y.B. Kim and F. Lombardi, "Design of a Ternary Memory Cell Using CNTFETs,” IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 11, NO. 5, SEPTEMBER 2012 • Abstract, Index Terms • INTRODUCTION • CARBON NANOTUBE FIELD-EFFECT TRANSISTOR • TERNARY LOGIC DESIGN • Review of Ternary Logic • Ternary Inverter • PROPOSED CELL DESIGN • EVALUATION • Static Noise Margin • Power Consumption • Area • CONCLUSION

3. Abstract—This paper presents a novel design of a ternary memory cell using carbon nanotube field-effect transistors (CNTFETs). Ternary logic is a promising alternative to conventional binary logic because it allows simplicity and energy efficiency in modern digital design due to the reduced circuit overhead in interconnects and chip area. In this paper, a novel design of a ternary memory cell based on CNTFETs is proposed; this cell uses a transmission gate for the write operation and a buffer for the read operation to make them separate. Chirality of the CNTFETs is utilized for threshold voltage control, thus avoiding the use of additional power supplies.

4. Extensive simulation results using SPICE are reported to show that the two memory operations of the proposed ternary cell perform correctly at 0.9 V power supply. The static noise margin and read/write delay of the proposed ternary memory cell are also very good; by utilizing the latest CNTFET layout design tools, it is shown that the proposed ternary memory cell achieves a significant saving in area (41.6%) compared with its CMOS ternary counterpart at 32 nm. Index Terms—Carbon nanotube field-effect transistor, multiplevalued memory design.

5. INTRODUCTION TRADITIONALLY, digital computation is performed using two-valued logic, i.e., there are only two possible values (0 or 1, true or false) in the Boolean (binary) space. Multiplevalued logic (MVL) has attracted considerable interest due to its potential advantages over binary logic for designing high performance digital systems [1], [2]. Theoretically, MVL has the potential of improving circuit performance for applications, such as arithmetic and digital signal processing. [1] M. Mukaidono, “Regular ternary logic functions - ternary logic functions suitable for treating ambiguity,” IEEE Trans. Comput., vol. C-35, no. 2, pp. 179–183, Feb. 1986. [2] K. C. Smith, “The prospects for multi-valued logic: A technology and applications view,” IEEE Trans. Comput., vol. C-30, no. 9, pp. 619–634, Sep. 1981.

6. Compared to a binary design, a ternary logic (or three-valued logic) implementation requires fewer operations, less gates, and signal lines; hence, it is possible for ternary logic to achieve simplicity and energy efficiency in digital design, because this type of logic reduces the complexity of interconnects and chip area [3]. In a ternary system, it only takes bits to represent an n-bit binary number; with more and more information and complex computation in today’s computers, ternary logic systems are capable of providing significant power and area efficiency compared to traditional binary systems. Furthermore, serial and serial–parallel arithmetic operations can be carried out faster if ternary logic is employed. [3] P. C. Balla and A. Antoniou, “Low power dissipation MOS ternary logic family,” IEEE J. Solid-State Circuits, vol. 19, no. 5, pp. 739–749, Oct. 1984.

7. Extensive research on the design and implementation of ternary logic using complementary metal-oxide semiconductor (CMOS) can be found in the technical literature [3], [4]. Chip area and power dissipation can be reduced by more than 50% using an efficient MVL implementation for a signed 32-bit multiplier compared to its fastest binary counterpart [5]. MVL modules have been inserted in binary CMOS ICs to enhance performance[6]. [3] P. C. Balla and A. Antoniou, “Low power dissipation MOS ternary logic family,” IEEE J. Solid-State Circuits, vol. 19, no. 5, pp. 739–749, Oct. 1984. [4] A. Heung and H. T.Mouftah, “Depletion/enhancement CMOS for a lower power family of three-valued logic circuits,” IEEE J. Solid-State Circuits, vol. 20, no. 2, pp. 609–616, Apr. 1985. [5] A. Raychowdhury and K. Roy, “Carbon-nanotube-based voltage-mode multiple-valued logic design,” IEEE Trans. Nanotechnol, vol. 4, no. 2, pp. 168–179, Mar. 2005. [6] D. A. Rich, “A survey of multi-valued memories,” IEEE Trans. Comput., vol. 35, no. 2, pp. 99–106, Feb. 1986.

8. Ternary memory systems, which allow three logic levels instead of the two of a binary memory, have been studied for years. There are many designs for implementing combinational ternary logic circuits with CMOS technology [3], [4]; however, the design of a simple and robust CMOS ternary memory cell has been very challenging and mostly elusive. For example, the designs of [23] use multiple supply voltages to achieve the ternary design. [3] P. C. Balla and A. Antoniou, “Low power dissipation MOS ternary logic family,” IEEE J. Solid-State Circuits, vol. 19, no. 5, pp. 739–749, Oct. 1984. [4] A. Heung and H. T.Mouftah, “Depletion/enhancement CMOS for a lower power family of three-valued logic circuits,” IEEE J. Solid-State Circuits, vol. 20, no. 2, pp. 609–616, Apr. 1985. [23] H. T. Mouftah and I. B. Jordan, “Design of ternary COS/MOSmemory and sequential circuits,” IEEE Trans. Comput., vol.C-26, no. 3, pp. 281–288, Mar. 1977.

9. However, additional supplies introduce significant complexity in power grid design and are often very costly. In the design of [24], only one power supply is used, but this design requires multiple threshold voltages (in which one threshold voltage level needs to be very close to the power supply); therefore, it is difficult to implement it using today’s CMOS fabrication process. The design of a ternary memory cell in [25] uses a transistor of large size; this makes such ternary design inappropriate for high density integration. [24] U. Cilingiroglu and Y. Ozelci, “Multiple-valued static CMOS memory cell,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 48, no. 3, pp. 282–290, Mar. 2001. [25] Z. Kamar and K. Nepal, “Noise margin-optimized ternary CMOS SRAM delay and sizing characteristics,” in Proc. IEEE Int. Midwest Symp. Circuits Syst., Aug. 2010, pp. 801–804.

10. The carbon nanotube field-effect transistor (CNTFET) is a promising alternative to a traditional bulk silicon transistor for low-power and high-performance designs due to the ballistic transport and the low OFF-current properties [8]–[10]. Moreover in a CNTFET, the threshold voltage is determined by the CNT diameter; therefore, a multi-threshold design can be accomplished by employing CNTs with different diameters (chirality) in a CNTFET. [8] J. Appenzeller, “Carbon nanotubes for high-performance electronics—progress and prospect,” Proc. IEEE, vol. 96, no. 2, pp. 201–211, Feb. 2008. [9] H. Hashempour and F. Lombardi, “Device model for ballistic CNFETs using the first conducting band,” IEEE Des. Test Comput., vol. 25, no. 2, pp. 178–186, Mar./Apr. 2008. [10] Y. Lin, J. Appenzeller, J. Knoch, and P. Avouris, “High-performance carbon nanotube field-effect transistor with tunable polarities,” IEEE Trans. Nanotechnol, vol. 4, no. 5, pp. 481–489, Sep. 2005.

11. The design of a ternary logic family using CNTFETs has been proposed in [11]; the basic ternary gates/operators (inverters, NAND, NOR) have been presented. Ternary arithmetic circuits such as a full adder and multiplier have been designed as examples of the application of a ternary gate technique. Simulation results have confirmed [11] that significant power and delay improvements are possible by utilizing this ternary logic family at both gate and circuit levels. The authors of [11] show that a design approach using the CNTFETbased ternary logic is a viable solution for low-power and highperformance VLSI design in the nanoscaled ranges. [11] S. Lin,Y. B. Kim, and F. Lombardi, “The CNTFET-based design of ternary logic gates and arithmetic circuits,” IEEE Trans. Nanotechnol., vol. 10, no. 2, pp. 217–225, Mar. 2011.

12. Embedded memory occupies the largest percentage area in today’s high-performance designs and this trend has continued unabated over the years; the demand for larger memories continues also in computer systems. Solutions to store more information are therefore been investigated. The use of a larger basis than binary is one of the possible solutions to meet the demand of increased memory capacity. So together with the previously proposed ternary logic family [11], it is also vital to have a high-performance ternary memory system such that ternary information can be stored and accessed. [11] S. Lin,Y. B. Kim, and F. Lombardi, “The CNTFET-based design of ternary logic gates and arithmetic circuits,” IEEE Trans. Nanotechnol., vol. 10, no. 2, pp. 217–225, Mar. 2011.

13. To the best knowledge of the authors, this paper introduces the first circuit design of a ternary memory cell using CNTs as emerging technology. This ternary cell utilizes the chirality feature of CNTFETs for threshold voltage control, such that there is no need to provide additional power supply levels for ternary operation. The separate features of the proposed circuit for the write and read operations make this design very efficient.

14. The rest of this paper is organized as follows. Section II starts with a brief introduction of carbon nanotube transistors, followed by the review of ternary logic in Section III. A ternary memory cell is then proposed, analyzed, and evaluated with respect to the write and read operations in Section IV. Traditional performance measures for a memory cell design, such as area, power and delay are simulated by HSPICE in Section V, which is followed by conclusion in Section VI.

15. CARBON NANOTUBE FIELD-EFFECT TRANSISTOR CNTFETs utilize semiconducting single-wall CNTs to assemble electronic devices [8]. A single-wall carbon nanotube (or SWCNT) consists of one cylinder only, and the simple manufacturing process of this device makes it very promising as an alternative to today’s MOSFET. An SWCNT can act as either a conductor or a semiconductor, depending on the angle of the atom arrangement along the tube. This is referred to as the chirality vector and is represented by the integer pair (n, m). A simple method to determine if a carbon nanotube is metallic or semiconducting is to consider its indices (n, m): the nanotube is metallic if n = m or n–m = 3i, where i is an integer. Otherwise, the tube is semiconducting. [8] J. Appenzeller, “Carbon nanotubes for high-performance electronics— progress and prospect,” Proc. IEEE, vol. 96, no. 2, pp. 201–211, Feb. 2008.

16. The diameter of the CNT can be calculated based on the following equation [12]–[14]: (1) where a0 = 0.142 nm is the inter-atomic distance between each carbon atom and its neighbor.

17. Fig. 1 shows the schematic diagram of a CNTFET [12]–[14]. Similar to a traditional siliconbased device, the CNTFET has four terminals too. As shown in Fig. 1, undoped semiconducting nanotubes are placed under the gate in the channel region, while heavily doped CNT segments are placed between the gate and the source/drain to allow for a low series resistance in the ON-state [8]. As the gate potential increases, the device is electrostatically turned ON or OFF, i.e., via the gate. Fig. 1. Schematic diagram of a carbon nanotube transistor: (a) cross sectional view and (b) top view. [12] (2008). Stanford University CNFET Model website [Online]. Available: http://nano.stanford.edu/model.php?id=23. [13] J. Deng and H.-S. P.Wong, “A Compact SPICE model for carbon-nanotube field-effect transistors including nonidealities and its application—Part I: Model of the intrinsic channel region,” IEEE Trans. Electron. Devices, vol. 54, no. 12, pp. 3186–3194, Dec. 2007. [14] J. Deng and H.-S. P.Wong, “A Compact SPICE model for carbon-nanotube field-effect transistors including nonidealities and its application—Part II: Full device model and circuit performance benchmarking,” IEEE Trans. Electron Device, vol. 54, no. 12, pp. 3195–3205, Dec. 2007. [8] J. Appenzeller, “Carbon nanotubes for high-performance electronics— progress and prospect,” Proc. IEEE, vol. 96, no. 2, pp. 201–211, Feb. 2008.

18. The current–voltage (I–V) characteristics of the CNTFET are similar to those of a MOSFET. The threshold voltage is defined as the voltage required to turn ON the transistor; the threshold voltage of the intrinsic CNT channel can be approximated to the first order as the half-bandgap that is an inverse function of the diameter [12]–[14]: (2) where a = 2.49 A° is the carbon to carbon atom distance, is the carbon - bond energy in the tight bonding model, e is the unit electron charge, and DCNT is the CNT diameter. [12] (2008). Stanford University CNFET Model website [Online]. Available: http://nano.stanford.edu/model.php?id=23. [13] J. Deng and H.-S. P.Wong, “A Compact SPICE model for carbon-nanotube field-effect transistors including nonidealities and its application—Part I: Model of the intrinsic channel region,” IEEE Trans. Electron. Devices, vol. 54, no. 12, pp. 3186–3194, Dec. 2007. [14] J. Deng and H.-S. P.Wong, “A Compact SPICE model for carbon-nanotube field-effect transistors including nonidealities and its application—Part II: Full device model and circuit performance benchmarking,” IEEE Trans. Electron Device, vol. 54, no. 12, pp. 3195–3205, Dec. 2007.

19. As DCNT of a (19, 0) CNT is 1.487 nm, the threshold voltage of a CNTFET using (19, 0) CNTs in the channel is 0.293 V [from (2)]. Simulation results have confirmed the correctness of this threshold voltage analysis. As the chirality vector changes, the threshold voltage of the CNTFET will also change. Assume that m in the chirality vector is always zero; then, the ratio of the threshold voltages of two CNTFETs with different chirality vectors is given as (3) Equation (3) shows that the threshold voltage of a CNTFET is inversely proportional to the chirality vector of the CNTs. For example, the threshold voltage of a CNTFET using (13, 0) CNTs is 0.428 V, compared to a (19, 0) CNTFET with a threshold voltage of 0.293 V.

20. Fig. 2 shows the threshold voltage of a P-type CNTFET (PCNTFET) with CNTs of different values of a chirality vector. For an N-type CNTFET (NCNTFET), the threshold voltage distribution is the same as the P-typeCNTFET, but with opposite sign [12]. Fig. 2. Threshold voltage of P-type CNTFET with different chirality vectors.

21. CNTFETs provide a unique opportunity to control the threshold voltage by changing the chirality vector, i.e., the diameter of the CNT [5]. [15], [16] have reported advances in manufacturing processes for well-controlled CNTs. The authors of [17] have demonstrated a post-processing technique to adjust the threshold voltage of multiple-tube CNTFETs. In this paper, a multi-tube CNTFET-based design is utilized when designing the ternary memory cell. [12] (2008). Stanford University CNFET Model website [Online]. Available: http://nano.stanford.edu/model.php?id=23. [5] A. Raychowdhury and K. Roy, “Carbon-nanotube-based voltage-mode multiple-valued logic design,” IEEE Trans. Nanotechnol, vol. 4, no. 2, pp. 168–179, Mar. 2005. [15] Y. Li, W. Kim, Y Zhang, M Rolandi, and D. Wang, “Growth of singlewalled carbon nanotubes from discrete catalytic nanoparticles of various sizes,” J. Phys. Chem., vol. 105, pp. 11424–11431, 2001. [16] Y. Ohno, S. Kishimoto, T. Mizutani, T. Okazaki, and H. Shinohara, “Chirality assignment of individual single-walled carbon nanotubes in carbon nanotube field-effect transistors bymicro-photocurrent spectroscopy,” Appl. Phys. Lett., vol. 84, no. 8, pp. 1368–1370, Feb. 2004. [17] A. Lin, N. Patil, K. Ryu, A. Badmaev, L. G. De Arco,C. Zhou, S. Mitra, and H.-S. P. Wong, “Threshold voltage and on–off ratio tuning for multipletube carbon nanotube FETs,” IEEE Trans. Nanotechnol., vol. 8, no. 1, pp. 4–9, Jan. 2009.

22. TERNARY LOGIC DESIGN In this section, a brief review of the basic principles of ternary logic design inclusive of the ternary inverter of [11] (as basic gate) is presented. • Review of Ternary Logic Ternary logic functions are defined as the functions having significance if a third value is introduced to the binary logic. In this paper, 0, 1, and 2 denote the ternary values to represent false, undefined, and true, respectively. Any n-variable {X1 ,. . .,Xn} ternary function f(X) is defined as a logic function mapping {0,1,2}n to {0,1,2}, where X = {X1 ,. . .,Xn}. [11] S. Lin,Y. B. Kim, and F. Lombardi, “The CNTFET-based design of ternary logic gates and arithmetic circuits,” IEEE Trans. Nanotechnol., vol. 10, no. 2, pp. 217–225, Mar. 2011.

23. The basic operations of ternary logic can be defined as follows, where Xi,Xj#{0,1,2} [18]: Xi + Xj= max{Xi,Xj } Xi*Xj= min{Xi,Xj } (4) where “−” denotes the arithmetic subtraction, the operations “+,” “*” and “−” are referred to as the OR, AND, and NOT in ternary logic, respectively. The ternary gates are designed according to the convention defined in (4). [18] S. C. Kleene, Introduction to Metamathematics. Amsterdam,, The Netherlands: North Holland, 1952, pp. 332–340. [4] A. Heung and H. T.Mouftah, “Depletion/enhancement CMOS for a lower power family of three-valued logic circuits,” IEEE J. Solid-State Circuits, vol. 20, no. 2, pp. 609–616, Apr. 1985.

24. Ternary Inverter A standard ternary inverter (STI) has been proposed in [11] and shown in Fig. 3; the STI in Fig. 3 consists of six CNTFETs with the following characteristics [11]. The chiralities of the CNTs used in T1/T5, T2/T6, and T3/T4 are (19, 0), (10, 0), and (13, 0), respectively. The diameters of T1/T5, T2/T6, and T3/T4 are 1.487, 0.783, and 1.018 nm, respectively. The threshold voltages of T1, T2, and T3 are 0.289, 0.559, and 0.428 V, respectively. The threshold voltages of T5, T6, and T4 are –0.289, –0.559, and –0.428 V, respectively. Fig. 3. CNTFET-based STI design of [11]. [11] S. Lin,Y. B. Kim, and F. Lombardi, “The CNTFET-based design of ternary logic gates and arithmetic circuits,” IEEE Trans. Nanotechnol., vol. 10, no. 2, pp. 217–225, Mar. 2011.

25. TABLE I LOGIC SYMBOLS When the input voltage changes from low to high (at a power supply voltage of 0.9 V), initially the input voltage is lower than 300 mV. This turns ON both T5 and T6, and both T1 and T2 are turned OFF; the output voltage is 0.9 V, i.e., logic 2. As the input voltage increases beyond 300 mV, T6 is OFF and T5 is still ON. Meanwhile, T1 is ON and T2 is OFF.

26. The diode connecting the CNTFETs T4 and T3 produces a voltage drop of 0.45 V from node n2 to the output and from the output to n1 due to the threshold voltages of T4 and T3. Therefore, the output voltage becomes 0.45 V, i.e., half of the value of the power supply voltage. As shown in Table I, half Vdd represents logic 1. Once the input voltage exceeds 0.6 V, both T5 and T6 are OFF, and T2 is ON to pull the output voltage down to zero. The input voltage transition from high to low is similar to the low to high transition.

27. PROPOSED CELL DESIGN Back to back inverters are used in traditional memory cells as basic components of the storage element for the correct states; access transistors (such as pass or transmission gates) are commonly used to read and write from the back to back inverters. The design requirement for a memory cell is usually specified as follows: when the cell is holding the data (i.e., the access transistors are OFF), the back to back inverters must be able tohold the bi-stable states; when the cell is ready to write or read (i.e., the access transistors are ON), then the access transistors must be able to update the correct state from the wordlines, or pass the current state to the wordlines.

28. The traditional CMOS cell in a binary memory system uses six transistors (6T); two NMOS access transistors and two back to back CMOS inverters. The STI shown in Fig. 3 can be used as a basic storage element of the ternary memory cell. For the read and write operations, single-ended read and write access mechanisms are used as described in more detail next.

29. The proposed ternary memory cell design is shown in the schematic form in Fig. 4; its transistor-level implementation is shown in Fig. 5. As shown in Fig. 4, the proposed memory cell consists of two transmission gates: one connected to wbl for the write operation and one connected to rbl for the read operation. Fig. 4. Proposed CNTFET-based ternary memory cell. Fig. 5. Proposed CNTFET-based ternary memory cell (transistor level implementation).

30. The basic storage element of the proposed ternary memory cell consists of two back to back STIs, whose arrangement is very similar to a conventional binary cell. As shown in Fig. 5, the basic storage element of this ternary memory cell consists of transistors T3–T14; they keep logic “0”, “1”, and “2” when the memory cell is holding data. The threshold voltages of T3 and T9, T4 and T10, T5 and T11 are 0.289, 0.559, and 0.428 V, respectively, [from (2)]. The threshold voltages of the P-type CNTFETs (T7 and T13, T8 and T14, T6 and T12) are −0.289, −0.559, and −0.428 V, respectively.

31. The operation of the proposed memory cell can be described as follows. When the memory cell is holding logic “1”, transistors T3, T5, T6, T7, T9, T11, T12, T13 are ON to hold both nodes q and qb to the value of 1/2 Vdd; When the memory cell is holding logic “0”, transistors T6, T7, T8, T9, T10, T11 are on to hold node q to 0 and node qb to the value of Vdd; When the memory cell is holding logic “2”, transistors T3, T4, T5, T12, T13, T14 are ON to hold node q to Vdd and node qb to 0.

32. The write transmission gate forces the correct data to be written into the back to back STIs. Fig. 5 shows single-ended transmission gates T1 and T2 (with the threshold voltages of 0.289 and −0.289 V); these gates are used for the write operation and ensure that the correct voltage level is written into the memory cell without dropping any threshold voltage. When the write wordlinewwl is high and wwlb is low, the data on the write bitlinewbl is written into the memory cell. The read buffer consists of one P-CNTFET (with the threshold voltage of −0.559 V) and one N-CNTFET (with the threshold voltage of 0.559 V).

33. This read buffer inverts the logic state “0” and “2” stored in node qb. Its operation is as follows. When the cell is storing a “0” (i.e., node qb is Vdd), T15 is ON and a “0” is read by the transmission gates T17 andT18. When the cell is storing a “2” (i.e., node qb is 0), T16 is ON and a “2” is read by the transmission gates T17 and T18. 3) When the cell is storing a “1” (i.e., node qb is 1/2 Vdd), both T15 and T16 are OFF and the bitlinerbl remains at 1/2 Vdd.

34. The addition of the read buffer avoids the read disturb problem [20], thus alleviating the static noise margin (SNM) for the ternary memory (a reduced noise margin has been a major concern in a multi-valued system design). The read operation is performed by the read buffer consisting of transistors T15, T16, T17, and T18, with the threshold voltages of 0.559, −0.559, 0.289, and −0.289 V, respectively. The read bitlinerbl is precharged to 1/2 Vdd in the ternary memory. Both the read and write operations will be discussed in more detail next. [20] E. Seevinck, F. J. List, and J. Lohstroh, “Static-noise margin analysis of MOS SRAM cells,” IEEE J. Solid-State Circuits, vol. SSC-22, no. 5, pp. 748–754, Oct. 1987.

35. A 1×128 ternary memory cell array is simulated to check the functionality of the proposed memory cell. The write operation of the proposed ternary cell is performed as follows: the write bitlinewbl is driven to the logic “0”, or “1”, or “2” and the write wordlineswwl and wwlb are Fig. 6. Write operation of the proposed ternary memory cell. accessed with logic “2” and logic “0”, respectively. HSPICE simulation of the write operation is shown in Fig. 6. As shown in Fig. 6, the write transmission gate (T1 and T2) allows the correct data (from data_in to wbl) to be written into the memory cell (q and qb).

36. The read operation of the proposed ternary cell is performed as follows: rbl is precharged to 1/2 Vdd prior to the read operation, and the read transmission gates (T17 and T18) are accessed to read the correct data from the memory cell. The read operation of the proposed ternary memory cell has been simulated by HSPICE (see Fig. 7) and operates as follows. The ternary memory cell is storing a logic “2”; then, the read bitline rbl is charged to logic “2” when the read wordlinesrwl and rwlb are accessed. The ternary memory cell is storing a logic “0”; the read bitlinerbl is discharged to logic “0” when the read wordlinesrwl and rwlb are accessed. The ternary memory cell is storing logic “1”; rbl remains at logic “1”. A ternary STI is then connected to the read bitlinerbl to sense the voltage at rbl.

37. Fig. 7. Read operation of the proposed ternary memory cell. TABLE II READ AND WRITE DELAY OF THE TERNARY MEMORY CELL

38. Table II summarizes the read and write delays of the ternary memory cell at 0.9 V power supply; the write and read delays have been estimated by the HSPICE simulation as follows. The write delay is estimated as the time required to flip the cell data after the write wordline is turned ON during the write operation. The write delay in HSPICE is measured from the 50% of the write wordlinewwl rising edge to the 50% of the rising/falling edge of the storage node q, as shown in Fig. 6. The read delay is estimated as the time required to sense the cell data to the output after the read wordline is turned ON during read. Therefore, the read delay in HSPICE is measured from the 50% of the read wordlinerwl rising edge to the 50% of the rising/falling edge of the output read_out, as shown in Fig. 7.

39. In Table II, the write delay is very small when the original data in the memory cell is logic “1”, i.e., it is easier for the memory cell to exit the logic “1” state than the logic “0” or “2” state. EVALUATION In this section, a detailed assessment of the proposed memory cell is presented through a simulation by HSPICE. A CMOS ternary memory cell design at 0.18 μm has been proposed in [25]; however, this design uses multiple power supplies and has very large read and write delays (3.9 and 1.23 ns, respectively). Moreover, 30λ and 70λ transistor widths are used in this design leading a very large area and power penalties for a memory cell design. Since there is no CMOS ternary memory cell of similar dimension as a CNTFET, the proposed CNTFET-based ternary memory cell is compared with a binary memory cell at 32 nm CMOS technology for fair comparison. [25] Z. Kamar and K. Nepal, “Noise margin-optimized ternary CMOS SRAM delay and sizing characteristics,” in Proc. IEEE Int. Midwest Symp. Circuits Syst., Aug. 2010, pp. 801–804.

40. Static Noise Margin The stability of a binary memory cell is usually represented by the SNM; the SNM is defined as the maximum value of dc noise voltage that can be tolerated by a memory cell without changing the stored bit [20]. The SNM can be graphically found on the butterfly curve plot by drawing the voltage transfer characteristics (VTC) of the inverter and mirroring the VTC for the same Fig. 8. SNM of the proposed ternary memory cell under process variations. plot. The same approach used on the binary memory cell is also applied to the proposed ternary memory cell shown in Fig. 4; the resulting butterfly plot is plotted in Fig. 8. [20] E. Seevinck, F. J. List, and J. Lohstroh, “Static-noise margin analysis of MOS SRAM cells,” IEEE J. Solid-State Circuits, vol. SSC-22, no. 5, pp. 748–754, Oct. 1987.

41. As shown in Fig. 8, the butterfly plot of the ternary memory cell has two more squares (eyes) than the binary memory cell; the diagonal between the smallest square defines the SNM of the ternary memory cell. Simulation results show that the SNM is 154.2 mV at 0.9 V power supply voltage for the proposed ternary memory cell when the memory cell is storing logic “1”. Since the read and write operations are separated, there is no read-disturb problem in the proposed ternary memory cell. This has been a major concern in a traditional six transistor (6T) binary memory cell (for the 6T memory cell, the read SNM is 100.8 mV at 0.9 V power supply, as shown in Fig. 8). The simulation results for the SNM are consistent with the results of Table II, i.e., the SNM of the logic “1” state is the smallest so it is faster to exit the state “1” than to exit states “2” and “0”.

42. It is widely known that process variations significantly affect performance of nanoscale and MOSFET devices during the fabrication process (such as oxide thickness and gate width). For CNT-based devices, the variations in the oxide and gate width have no negligible impact [27]; due to the nature of CNTFETs, the diameter of the tubes (thus the chirality), the distance between tubes (pitch), and the number of tubes under the gate (that determine the effective width of the transistor) affect CNTFETbased circuits and devices. The Monte Carlo simulation has been performed to assess process variations; for simulation, chirality and pitch are modeled as a ±10% Gaussian distribution with variation at the ± 3σ level. The simulation results are given in Fig. 8. Fig. 8 shows that with process variation, the worst SNM of the proposed CNTFET ternary memory cell is 101.8 mV at 0.9 V power supply, hence close to the 32 nm CMOS binary cell in the ideal case. [27] B. C. Paul, S. Fujitam,M. Okajima, T. H. Lee, H.-S. P.Wong, and Y. Nishi, “Impact of a process variation on nanowire and nanotube device performance,” IEEE Trans. Electron. Devices, vol. 54, no. 9, pp. 2369–2376, Sep. 2007.

43. Power Consumption Power consumption, especially the standby power consumption, has been a significant concern for memory systems that usually occupy a large area in a chip design. Compared to the high-leakage nano-CMOS device, a CNTFET has a significantly smaller OFF current; therefore, the power consumed when the transistor is OFF is greatly reduced in CNTFET designs [8]. The CNTFET has a significantly higher ON–OFF current ratio compared to the MOSFET in the deep sub-micrometer range. Therefore, the standby power of the CNTFET memory cell is lower compared to its CMOS counterpart. [8] J. Appenzeller, “Carbon nanotubes for high-performance electronics— progress and prospect,” Proc. IEEE, vol. 96, no. 2, pp. 201–211, Feb. 2008.

44. TABLE III STANDBY POWER OF THE TERNARY MEMORY CELL The standby power consumption of the proposed CNTFET-based ternary memory cell is listed in Table III. As shown in Table III, when the ternary memory cell is storing “0” or “2”, the power consumption is less than 1% of the CMOS 6T binary memory cell, but when storing “1”, the standby power of the ternary cell is nine times larger than the CMOS 6T binary memory cell due to the diode-connected T5, T6, T11, and T12 in Fig. 5.

45. Area A system-level CNTFET-based design approach and the layout technique for CNTFET technology have been proposed in [21]. The layout of the proposed ternary memory cell, using the guidelines presented in [21], is shown in Fig. 9. The write bitlinewbl and the read bitlinerbl are connected by the higher layer metal (not shown in Fig. 9). In the CNTFET-based layout, the minimum distance between the PUN (P-CNTFET) and PDN (N-CNTFET) is just limited by lithography (3λ); this is significantly less than the minimum distance between PUN and PDN in CMOS (10λ) [21]. The area of the ternary memory cell is 57λ × 32λ (1824λ2), compared to 1562λ2as the area of the conventional 6T CMOS (binary) memory cell at 32 nm bulk CMOS technology [22]. [21] D. Atienza, S. K. Bobba, M. Poli, G. De Micheli, and L. Benini, “Systemlevel design for nano-electronics,” in Proc. 14th IEEE Int. Conf. Electron., Circuits Syst., Dec. 2007, vol. 1, no. 1, pp. 747–751. [22] Y. Morita, H. Fujiwara, H. Noguchi, Y. Iguchi, K. Nii, H. Kawaguchi, and M. Yoshimoto, “An area- conscious low-voltage-oriented 8T-SRAM design under DVS environment,” in Proc. Symp. VLSI Circuits, Jun. 2007, pp. 256–257.

46. For representing ternary logic without the use of additional power supplies, two 6T binary memory cells can be used. The area of the proposed ternary cell is only 1.168 times larger than the one for a single 6T memory cell, i.e., 41.6% area saving is achieved by the CNTFET-based ternary memory cell design compared to a CMOS ternary implementation for the same function (utilizing two binary 6T cells). Furthermore, one of the attractive features of the CNTFET is that it has been reported to be scalable down to 10 nm channel length or less [12]. Therefore, it is possible for the proposed CNTFET-based ternary memory cell to achieve even smaller area than CMOS technology in the next few years. [12] (2008). Stanford University CNFET Model website [Online]. Available: http://nano.stanford.edu/model.php?id=23.

47. CONCLUSION This paper has presented the first design of a ternary memory cell based on CNTFETs. As the threshold voltage of the CNTFET is a function of the geometry of the CNTFET (i.e., the chirality and diameter), a novel multidiameter (multithreshold voltage) CNTFET-based ternary memory cell design has been pursued in this paper. This memory cell does not require additional power supplies and the read/write operations are correctly executed by introducing in the design a transmission gate and a buffer to make these operations separate.

48. Simulation results using HSPICE have showed that the proposed CNTFET-based ternary cell performs the correct function during the read and write operations. It has also been shown that the proposed ternary cells achieve a high SNM due to the separate read and write operations, more than 90% lower standby power consumption for the “0” and “2” states and low area compared to a conventional binary CMOS implementation. The impact of process variations on stability has also been simulated; simulation results show that the proposed CNTFET-based ternary memory cell with substantial process variations still achieves the same SNM as its CMOS binary counterpart at 32 nm under ideal conditions (i.e., with no process variations). Therefore, the detailed technology assessment of this paper demonstrates that CNTFET is a viable candidate for ternary memory design in the nanoscale era.

49. THEEND