Scaling Limits of CapacitorlessDouble Gate DRAM Cell

Nauman Butt and Muhammad A. AlamSchool of Electrical and Computer Engineering

Purdue UniversityWest Lafayette, IN 47906, U.S.A.

Abstract- In this paper, we consider the scaling ofCapacitor-less Single Transistor (IT-OC) DRAM byclassical (CL) and quantized-ballistic (QB) methods toestablish that (1) it may be difficult to scale IT-OC cellbelow 30nm channel length even with ultrathin (< 3nm)body because of the quantum confinement effects, (2)cumulative drain disturb time must be limited to ensurereasonable retention times, (3) the surround gatestructures such as silicon nanowires (as IT-OC cells)are expected to have more significant confinementeffects, and (4) practical considerations such as theprocess variations in cell geometry and single eventsupsets are likely to remain important scaling concerns.

Keywords-capacitorless; double gate; scaling; quantumconfinement, simulation

I. INTRODUCTIONIn classical DRAM cells, the logic level is indicated by

charge (Q) stored on a capacitor node (1C) that is accessedby a pass transistor (IT). Since, Q = CV, high performanceIT-IC DRAM cells require larger capacitance (C) andhigher voltage (V), opposite to the scaling trend of logictransistors. To remain relevant, DRAM designers havepioneered use of high-k dielectrics (e.g., Ta2O3, A1203, etc.),extreme capacitor geometry (e.g., trench, fin, stack, etc.),and innovative circuit techniques (e.g., hyperpage mode,etc.) [1]. Despite this comprehensive approach, however, theviability and scaling ofDRAM capacitor below 65 nm nodeis not assured. A novel 1 T-OC DRAM cell utilizes thefloating body charging of an SOI transistor to replace thetraditional DRAM capacitor and therefore is sometimesperceived to be more scalable than IT-IC cells [2, 3]. Forthis DRAM cell, a logic state is defined by creating anexcess or a shortage of the majority carriers inside the bodyof the transistor which cause a threshold voltage shift (AVt)below or above its equilibrium value. The state is read bysensing the drain current which has two different levelscorresponding to the two states. A high density 1T-OCDRAM would be very attractive for embedded DRAMapplications as well as for the stand alone DRAM products.

Several designs of IT-OC cells have been proposed whichare based on both partially depleted (PD) and fully depleted(FD) SOI technologies [2-4]. Although removal of externalcapacitor reduces area overhead and reduces processcomplexity, the scaling of 1 T-OC has its own specificchallenges. For example, when the channel length (L,h) isscaled down, the short channel effects like drain inducedbarrier lowering (DIBL) results in an increased junctionleakage current which rapidly reduces the stored chargefrom the floating body. For a scalable design, the cell musthave a strong gate control for which a surround gate ordouble gate (DG) geometry with ultathin body (tbody) isdesirable. Smaller tbody not only reduces DIBL but alsoprovides higher body coefficient- defined as the differentialchange of threshold voltage for a differential change infloating body potential. Despite these advantages, however,our analysis in this paper demonstrates that the quantummechanical charge confinement in the body becomesignificant at tbody < 3nm and offset the above mentionedadvantages of small tbody. Thus the 1 T-OC cell scaling isactually more difficult than perceived by the classicalanalysis, as discussed below. This paper is divided into fivesections: Section II describes the cell operation and SectionIII explains the simulation models. Section IV illustrates theconsiderations for cell scaling and design. Finally, ourconclusions are summarized in Section V.

II. CELL OPERATION

The WRITE, READ and HOLD operations of a floatingbody double gate 1 T-OC cell are illustrated in Fig. 1. Thetwo gates are connected to the world lines (WL1 and WL2)while the source/drain are connected to the bit lines (BLIand BL2). The bias conditions for the lines during each ofthe cell operation are also shown. The bias conditions anddoping are similar to those proposed in [2]. The state '1' iswritten by applying a high drain voltage (Vd) of 1.2V. Theimpact ionization creates electron-hole pairs near the drain.The electrons are rapidly swept out of the cell by the electricfield while a portion of holes remains trapped in the body,increasing its concentration above the equilibrium value.The state 'O' is written by applying a positive Vg andsmaller Vd. The holes in the body are pushed out through

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WRITING '1'

WL1_ Vg,top = 1 V

< DCD ~

<o m+++ i

WL2-BIL Vg,bot = -1 V L2

HOLD STATE

WL1_ Vg3top =0V

D 11C)> Il

< <WL2-

BEL Vg,bot=-lVB L2

WRITING 'O'Vg,top = 1 V

<<

BLI Vg,bot = OVBU ~~BL2READINGVg,top = 1 V

n< _excess/II S shortage D CCD of holes

BLI Vg,bot = 1VBL2

negligible for the doping and bias conditions used for thecell operations.

The QB model is based on NANOMOS which is a 2-Dsimulator for fully depleted thin-body DG MOSFET. Itsolves the Schrodinger equation in the transverse (thickness)direction self-consistently with the Poisson equation to getthe quantized conduction sub-bands and the correspondingelectron densities. The classical ballistic model ofNANOMOS is used in which the ballistic transport ofelectrons in the channel direction is solved withoutincluding the quantum tunneling under the barrier. Our QBmodel also includes the quantized valence sub-bands (notimplemented in NANOMOS) with the corresponding holesdensities and the holes transport is treated classically. Thecharge dynamics are then obtained in the transientsimulation which treat SRH and impact ionization similar tothe CL model.

Fig. 1. The phenomena of WRITE, READ, and HOLD areillustrated with corresponding operating voltages. To write,Vg,top is made high; state '1' is written by generating excessholes through impact ionization by applying Vd = 1.2V, state'0' is written by pulling holes out of body by applying smallVd. In hold state, barriers are created by applying negativeVg,bot; retention time is determined by SRH recombinationgeneration rates and source/drain leakage. The threshold shiftcorresponding to excess/shortage of holes distinguishes thestate during READ.

source /body junction and result in a shortage of holes in thebody. This excess or shortage of holes modulates thefloating body potential and consequently the thresholdvoltage (Vt). In the HOLD state, the gate voltages arereduced and small voltage is applied to the source and drain.This creates a large barriers at both the source and drainjunctions of the body. The state written previously isretained for a refresh cycle. The retention time of the stateis determined by SRH recombination/generation (RG) rateand the S/D leakage current. Finally, the state is read bysensing the drain current by applying a small Vd. The draincurrent has distinct levels for each of the two states becauseof the shift in threshold voltage.

III. SIMULATION MODELS

We use device simulator MEDICI to consider classicalcharge dynamics (CL model) and NANOMOS [5] toconsider charge dynamics including the quantumquantization effects (QB model). In CL model, chargedensity is obtained by considering classical bulk conductionand valence bands and the drift-diffusion equation is solvedfor the carrier transport. The non-local model of impactionization is included with soft threshold [6] and SRH R-Gis considered with electron/hole lifetime of 1 microsecond.The band-to-band and trap-assisted tunneling are included inCL model but their contributions were found to be

.EQ3

2(b)0.3r

0.2

0a)0.1

... ... ......V .. V... 1vlt- v- v v- v- v--

V.

v vV V VV

-0.1710-7 -5 -3 - 110 10 10

Time [sec]1 310 10

Fig. 2. Pintg (2a) and AVb (2b) in HOLD state after WRITE '0'plotted as a function of HOLD time in 1 T-OC cell of tbody =10nm with various L,h. The effect of DIBL is prominent insmaller L,h where the AVb gap becomes smaller and results indecreased sense margins.

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e e

Retention time

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IV. SCALING AND OPTIMIZATION OF IT-OC CELL

A. Channel Length Scaling

Fig. 2 illustrates the retention time and the noise marginafter writing a cell of tbody= Onm for various Lch. Theretention time of a state is defined as the time for which thestate can be correctly sensed by the READ operation afterbeing written. The noise margin is the difference betweenthe two states which can be defined in terms of difference inthe threshold voltage (Vt) or the difference in the floatingbody potential (Vb). Fig. 2a shows the integrated holesdensity (Pintg), which is the total number of holes per unitwidth in the body, as a function of hold time after writing.As explained in section II, PHtg decreases during writing 'O'and increases during writing '1'. In the HOLD state, SRHRG and the S/D junction leakage bring Pintg back towards itsequilibrium value. The rates of these two phenomenadetermine the retention time. Fig. 2b shows the shift in thefloating body potential (AVb) during the hold time for thestates. Since the impact ionization is not very high with Vd1.2V, AVb caused by writing 'O' primarily defines the noisemargin. It should be noted that the noise margin becomessmaller for cells with smaller Lch. In particular, AVb goes tozero for Lch = 20nm. This is the consequence of a wellknown short channel effect i.e., DIBL. In DIBL, the bodypotential comes under an increased influence of thesource/drain field and the intrinsic holes concentration in thebody is reduced. This can be seen in Fig. 2a where Pintg isdecreasing with smaller Lch. For Lch < 30, Pintg is reduced toa level that is not enough to create a significant AVb after aWRITE operation.

B. Body Thickness Scaling

There are two ways of reducing the effect of DIBL: (i)increased body doping concentration and (ii) reduced bodythickness, tbody. But the increased body doping causes othertwo problems i.e, it increases the trap-assisted tunneling tothe S/D and it increases the Vt-fluctuation due to randomdoping effects in ultrathin cells [2]. The former reduces theretention time and the latter shortens the noise margin.Reducing body-thickness, on the other hand, provides twoadvantages, i.e., it reduces DIBL an it increases the bodycoefficient (AVt/AVb = -toxfi/tbody, where tox,f is the frontoxide thickness) and hence a given AVb can be translatedinto a bigger AVt. However, cells with very small tbody suffera radical drop in AVb because of the quantum mechanicalconfinement of carriers. The splitting of the bands intoquantized levels results in widening of the band gap and areduction in the intrinsic carrier concentration. As a result,there are not enough holes in the body to cause a significantshift in Vb. Fig. 3 illustrates this in a cell with Lch = 50nmand two different tbody. The conduction and valence bands(first conduction and valence subbands in QB model) alongthe channel direction are plotted along with thecorresponding carrier densities for the two cases. For tbody=5nm, both CL and QB models give almost the same results,

1

-1

-3

c\JE 100*;~ io0-Z10

0 20 40 60 0Xch [nm]

Fig. 3. The conduction & valence bands in the middle (tbody/ 2)of cell with Lch = 50nm plotted along the channel direction fortbody= 5nm (left) & tbody= Inm (right). Dotted and solidlines are result of QB & CL models respectively. The wideningof the band gap can be observed with smaller tbody whichdecreases the equilibrium carrier concentration.

0cin

(d)L h=20nm

10 0 2 6 8 10tbody [nm]

Fig. 4. Change in threshold voltage immediately after WRITE'O' for the cells with various dimensions obtained by QB(squares) and CL (circles) models. The models differsignificantly at tbody < 3nm because of quantum mechanicalconfinement.

whereas in tbody= nm, the QB model shows a widening ofthe band gap and significant reduction in the carrierconcentrations as compared to CL model. Fig. 4 furtherexplains the effect of scaling tbody on the sense margin. Theplots of AVt at the time immediately after writing 'O' areshown as a function of tbody for the cells of different LCh.Both models give similar AVt down to tbody= 3nm. In thisrange, both curves follow the expression: AVt- tbody 1 Fortbody < 3nm, the CL and QB models differ significantlybecause CL model continues to follow the above expressionbut QM model results in a much lower AVt because of thequantum confinement effect. It can be noticed that QB

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model predicts almost zero AVt for Lch= 20nm and tbodyInm.

C. Design Spacefor the Scaled Cell

Fig. 5 illustrates the design space for the dimensions of1 T-OC cell. The areas bounded by the allowed Lch and tbodydimensions are shown as predicted by the two models whilekeeping AVt > 0.3V. The space above tbody= 3nm is limitedby DIBL for Lch < 40nm. Both models are consistent in thisregime. For example, Lch= 30nm has an upper limit of tbody= 4nm. For tbody < 2nm, the design space from QB model islimited by the quantum confinement whereas the designspace from CL model extends to 1nm. Thus, while CLmodel predicts that Lch < 27nm could be achieved with tbody= lnm, the QB model predicts that the scaling stops for Lch< 27nm because the density of confined holes is so low thatthe cell volume does not have sufficient holes to support anyWRITE operation.

D. Other Considerations

In practice, the drain disturb, process variations andradiation induced soft errors must also be considered in scalingof a 1 T-OC cell. We explore the susceptibility of 1 T-OC cellto drain disturb problem in Fig. 6 and find that thecumulative disturb time must be less than a millisecond fora given cell to hold its charge. This time sets the upper limitof number of write operations in the neighboring cells whichshare a common drain bit-line before the cell in HOLD '0'must be refreshed.

0n0

5 - (UDt-J

.E

o

t\1

10 15 20 25 30 35Lch [nm]

40 45 50

Fig. 5. The allowed design space of IT-OC cell whendimensions are scaled while keeping AV, . 0.3V. The wholearea bound by outer curves (circles) is the result of CL modeland the lightly shaded area is from QB model (squares). Thedark shaded area is where the two models differ due to theeffect of charge confinement. At higher tbody, DIBL limits thedesign space while at tbody < 2nm, quantum confinement limitsthe design.

v 2ms600 aJ0.2ms

&200nsD-.- 400

n.:L2C

zo ~~~~I: "

10- 10 10 10 10Hold Time [sec]

Fig. 6. The effect of WRITE '1' drain disturb on 1 T-OC cellin HOLD '0' with Lch = 50nm and tbody = 10nm. Pintg (left)and - AVb (right) are plotted as a function of hold time forcumulative disturb times of 200ns, 0.2ms and 2ms withhigher values reducing sense margin and retention time.

V. CONCLUSIONS

In this paper, we have systematically analyzed thescaling limits of a novel; (presumably) more scalable doublegate 1 T-OC cell to find that in practice the scaling of thecells may actually be more difficult than previouslypresumed. In contrast to the analysis based on the classicalmodel, the model including the quantum confinement ofcarriers predicts that the confinement effect causes asignificant loss of sense margin between the two states of1 T-OC cell for ultra-thin body (< 3nm). For a slightly greaterbody thickness, both models predict that DIBL limits thechannel length scaling. The trade-off between confinement,body coefficient and DIBL determines the limits of 1 T-OCcell scaling. In practice, other considerations like draindisturb, process variations and single event upset mayfurther restrict scaling. The surround gate geometry for IT-OC cell is expected to be less scalable because of twodimensional confinements. All these have significantimplications for 1T-OC cell as a potential replacement forclassical I T-IC DRAM.

REFERENCES

[1] J. A. Mandelman, R. H. Dennar, G. B. Bronner, J. K. DeBrosse, R.Divakaruni, Y. Li & C. J. Radens, IBMJ. Res. & Dev., Vol. 46, No. 2/3,2002

[2] C. Kuo, T. King and C. Hu, IEEE Transactions on Electron Devices,Vol. 50, No. 12, Dec. 2003

[3] E. Yoshida, T. Miyashita, T. Tanaka, IEEE Electon Device Letters, Vol.26, No. 9, Sep. 2005

[4] S. Okhonin, M. Nagoga, J. M. Sallese, and P. Fazan, IEEE Intl. SOIConf, 2001, pp. 153-154

[5] Z. Ren, R. Venugopal, S. Goasguen, S. Datta, M. Lundstrom,"nanoMOS2.5: A Two -Dimensional Simulator for Quantum Transportin Double-Gate MOSFETs,"IEEE Trans. Electron. Dev., and IEEETrans. on Nanotechnology, joint special issue on Nanoelectronics, Vol.50, pp. 1914-1925, 2003.

[6] C.Jungemann, R.Thoma and W.L.Engl, Solid-StateElectronics, Vol. 39,No. 7, pp.1079-1086, 1996.

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-I

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