IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 10, OCTOBER 2011 3635

Phase-Change Memory RESET ModelBased on Detailed Cell Cooling Profile

K. C. Kwong, Jin He, Member, IEEE, Philip K. T. Mok, Senior Member, IEEE, and Mansun Chan

Abstract—A phase-change (PC) memory model that keeps trackof the detailed cooling profile in the RESET process is describedin this brief. By physically calculating the final crystal fractionresulting from the thermal dynamic of the PC material duringthe RESET process, the final resistance of the memory cell canbe more accurately determined. The proposed model has beenimplemented in Verilog-A language and verified by experimentaldata.

Index Terms—Nonvolatile memory, phase-change memory(PCM).

I. INTRODUCTION

PHASE-CHANGE memory (PCM) is one of the mostpromising alternatives to succeed Flash to be the next-

generation nonvolatile memory [1]–[4]. In addition to produc-tion technology, an accurate PCM model is important to predictthe behavior of actual products. Some preliminary PCM modelshave been proposed in the literature, which focus on the macrooperation of a PCM cells [5]–[9]. An important mechanism,i.e., the cooling profile that determines the final resistance inthe RESET process, has not been fully described. The mainapproach to model the RESET resistance is to calculate itsvalue directly from the quenching time [5] or the currentpulse amplitude [6]. However, all the intermediate temperaturechanges during the cooling process will be ignored by theseapproaches, which sacrifice the accuracy of the final results.

In this brief, a RESET model that keeps track of the tem-perature changes of the PCM cell during cooling is proposed.By including physical effects such as the magnitude of theinput current pulse, the PCM cell dimension, and the thermalproperties of the phase-change (PC) material, the transienttemperature profile can be more accurately simulated. The finalRESET resistances predicted by the model are verified by bothnumerical simulation and experimental data.

Manuscript received February 22, 2011; revised April 11, 2011 and June 22,2011; accepted July 12, 2011. Date of current version September 21, 2011. Thiswork is supported by the General Research Fund provided by the ResearchGrant Council of Hong Kong under Project 611208. The review of this briefwas arranged by Editor J. C. S. Woo.

K. C. Kwong, P. K. T. Mok, and M. Chan are with the Department ofElectronic and Computer Engineering, Hong Kong University of Science andTechnology, Kowloon, Hong Kong (e-mail: eehk@ust.hk).

J. He is with the Department of Electronic and Computer Engineering,Hong Kong University of Science and Technology, Kowloon, Hong Kong, andalso with the Shenzhen System On Chip Key Laboratory, Peking University,Shenzhen 518057, China.

Color versions of one or more of the figures in this brief are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2011.2162843

Fig. 1. PCM cell configuration with the PC material placed between the TECand the BEC.

II. PCM CELL TEMPERATURE

The basic programming operations of PCM, i.e., SET andRESET, depend on the temperature changes inside the cell. Theheat generation of the PCM cell is caused by the joule-heatingeffect to the input current pulse. Fig. 1 shows a generic structureof a PCM cell. The current flows through the PC material, i.e.,from the top electrode (TEC) to the bottom electrode (BEC).According to the cell structure, the power input to the cell atdifferent locations can be expressed as [10]

Pd =I2ρ

2π2a4

(1+

2z2−2x2+r1r2

a2+

r4+r2r1r2

a4

)−1

(1)

where I is the current flowing through the cell, ρ is the resis-tivity of the PC material extracted from I–V measurement, a isthe radius of the BEC, z and x are the distances from the centerof the BEC in z- and x-directions, respectively, r2 = x2 + z2,and r2

1,2 = (a ± x)2 + z2. The total power input to the PCMcell can be calculated by integrating Pd all over the cell. Thetotal power input can be expressed as

Pin = I2

l∫0

w2∫

−w2

ρ

2π2a4

×(

1 +2z2 − 2x2 + r1r2

a2+

r4 + r2r1r2

a4

)−1

dxdz. (2)

The equation only contain the algebraic sum and product ofx and z, which are integrable, despite the long expression.

At the same time, the heat will be mainly dissipated alongthe thickness of the PCM cell where the PC material is in

0018-9383/$26.00 © 2011 IEEE

3636 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 10, OCTOBER 2011

Fig. 2. Comparison of heat loss rate in the x-direction, keeping x = 0 withincreasing z, and z-direction, keeping z = 0 with increasing x, (normalizedby the radius of the BEC, a) together with the thermal simulation result of thegeneric PCM structure.

Fig. 3. Numerical simulation and model calculation on the temperature distri-bution of the PCM cell in the z-direction at x = 0, together with the modelingequation.

contact with the metal electrode (i.e., z-direction) due to thelow thermal conductivity of the PC material and the insulatorsurrounding it in the x-direction. As demonstrated in Fig. 2, theoverall heat loss rate in the x-direction is only 20% of that inthe z-direction.

After such simplification, a lumped thermal resistance modelcan be used to calculate the heat lost from the cell [8], i.e.,

Pout = k ·(

V

l

)· ∇T (t) ≈ k ·

(V

l

)· dTPCM(z)

dz

= k ·(

V

l

)·(

ΔT (t)l

)(3)

where k is the thermal conductivity that is assumed to beconstant [11], [12], V is the volume of the cell, l is the cellthickness, TPCM(z) is the temperature of PC material along thez-direction, as shown in Fig. 3, and ΔT (t) is the temperaturerise in the active region caused by the input current. Aftersolving the energy equation, we obtain

V cΔT (t) =∫

(Pin − Pout)dt (4)

Fig. 4. Temperature profile of the PCM cell with a sequence of input currentpulses.

and the temperature rise within the cell can be calculated as

ΔT (t) =l2

kV

{Pin − e[−

kt

l2c+ln[Pin]]

}(5)

where c is the heat capacity of the PC material. The program-ming of the cell is determined by the cell temperature, whichis the sum of the surrounding temperature Tsur and the inducedtemperature, i.e.,

T (t) = Tsur + ΔT (t). (6)

The temperature profile of the PCM cell corresponding to achain of input current pulses is shown in Fig. 4.

III. ANNEALING FACTOR AND CELL RESISTANCE

RESET occurs when the PC material in a PCM cell cooleddown from a molten state and the process is sensitive to the ther-mal profile. The RESET model considering only the quenchingtime and the amplitude of the programming current pulse isnot sufficient. RESET occurs when the temperature drops fromthe melting point to the glass transition point [7]. Measuringthe quenching time (which is the period that the temperatureof the PC material drops from the melting point to the glasstransition point) during the RESET alone cannot fully predictthe final RESET resistance. It is because the transient thermaldynamic inside the cells is affected by both the input currentpulse amplitude and profile. An annealing factor that accountsfor the integrated temperature change over time during coolingis introduced and is given by [13]

H =

tglass∫tmelt

T (t)dt (7)

where tglass and tmelt are the times that the PCM achieves theglass transition point and the melting point, respectively. Theannealing factor records how much heat energy has been inputto the cell during cooling for nucleation [14]. A long quenchingtime usually results in a larger annealing factor. Based on the

KWONG et al.: PCM RESET MODEL BASED ON DETAILED CELL COOLING PROFILE 3637

Fig. 5. RESET programming characteristic of the PCM cell. Programmingcurrent pulses with a fixed quenching time (90 ns) and different amplitudes areapplied to the cell. The RESET resistance is then obtained by using a smallreading current pulse.

anneal factor, we can find out the amount of crystallization bycalculating the crystal fraction, which is given by

Cfract =[1 + e

Hth−H

h

]−1

(8)

where h is the sensitivity of the PC material to the temperaturechange and Hth is the annealing factor that the PCM cellachieves 50% crystallization. While it has been shown that thecrystal fraction of the PC material is exponentially dependenton the total thermal budget, (8) is actually a semi-empiricalfunction with fitting parameters based on experimental data.The corresponding cell resistance after RESET programmingcan be then calculated as [15]

RRESET = Rcry + (1 − Cfract) ∗ (Ramo − Rcry) (9)

where Ramo and Rcry are the PCM resistance in perfect amor-phous state and in perfect crystallize state, respectively.

IV. SIMULATION RESULT

The RESET model is implemented into a SPICE simulationengine using the Verilog-A language. Programming currentpulses with different current amplitudes and quenching timesare applied to the model, and the corresponding results areshown in Figs. 5 and 6, respectively, together with experimentaldata [5] and other RESET models in the literature [5], [6].When current pulses with different amplitudes but a fixedquenching time are applied to the cell, it is observed that highcurrent pulse magnitude gives higher resistance after RESET,as shown in Fig. 5, due to the faster cooling rate. Our modelcan successfully simulate the current amplitude dependence ofthe RESET resistance, whereas other models only predicted theabrupt switching of the cells between two predefined valuesdetermined by the quenching time alone. When current pulseswith fixed amplitude but different quenching times are appliedto the cell, it is observed that a longer quenching time giveslower resistance after RESET, as shown in Fig. 6, due to moretime for the crystallization process. The model in [5] and our

Fig. 6. RESET programming characteristic of the PCM cell. Programmingcurrent pulses with fixed amplitude (700 µA) and different quenching times areapplied to the cell. The RESET resistance is then obtained by using a smallreading current pulse.

brief are able to qualitatively predict such behavior, whereasthe model in [6] has not captured this effect.

V. CONCLUSION

In this brief, we have demonstrated the importance of thedetail cooling profile in determining the final RESET resistancein a PCM cell. By considering the quenching time alone maypartially describe the RESET behavior but cannot capture theeffects of different input pulse magnitudes. A physical modelbased on the effects of the cooling profile on the final crystalfraction of the PC material after the RESET process has beenproposed in this brief to enhance the accuracy of existing PCMmodels.

REFERENCES

[1] M. Gill, T. Lowrey, and J. Park, “Ovonic unified memory—A high-performance nonvolatile memory technology for stand-alone memory andembedded application,” in Proc. ISSCC, 2002, pp. 202–459.

[2] S. Lai, “Current status of the phase change memory and its future,” inProc. IEEE IEDM, 2003, pp. 10.1.1–10.1.4.

[3] S. Tyson, G. Wicker, T. Lowrey, S. Hudgens, and K. Hunt, “Nonvolatile,high density, high performance, PC memory,” in Proc. Aero Space Conf.,2000, vol. 5, pp. 385–390.

[4] A. Redaelli, A. Pirovano, A. Tortorelli, I. Ottogalli, F. Ghetti, A. Laurin,and L. Benvenuti, “Impact of the current density increase on reliability inscaled BJT-selected PCM for high-density applications,” in Proc. IEEEIRPS, 2010, pp. 615–619.

[5] D. Ventrice, P. Fantini, A. Redaelli, A. Pirovano, A. Benvenuti, andF. Pellizzer, “A phase change memory compact model for multilevelapplication,” IEEE Electron Device Lett., vol. 28, no. 11, pp. 973–975,Nov. 2007.

[6] X. Q. Wei, L. P. Shi, R. Walia, T. C. Chong, R. Zhao, X. S. Miao, andB. S. Quek, “HSPICE macromodel of PCRAM for binary and multi-level storage,” IEEE Trans. Electron Devices, vol. 53, no. 1, pp. 56–62,Jan. 2006.

[7] P. Fantini, A. Benvenuti, A. Pirovano, F. Pellizzer, D. Ventrice, andG. Ferrari, “A compact model for phase change memories,” in Proc. IEEESISPAD, 2006, pp. 162–165.

[8] Y.-B. Liao, Y.-K. Chen, and M.-H. Chiang, “An analytical compact PCMmodel accounting for partial crystallization,” in Proc. IEEE EDSSC, 2007,pp. 625–628.

[9] K. Sonoda, A. Sakai, M. Moniwa, K. Ishikawa, O. Tsuchiya, and Y. Inoue,“A compact model of phase-change memory based on rate equationsof crystallization and amorphization,” IEEE Trans. Electron Devices,vol. 55, no. 7, pp. 1672–1681, Jul. 2008.

3638 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 10, OCTOBER 2011

[10] B. Rajendran, J. Karidis, M.-H. Lee, M. Breitwisch, G. W. Burr,Y.-H. Shih, R. Cheek, A. Schrott, H.-L. Lung, and C. Lam, “Analyticalmodel for RESET operation of phase change memory,” in Proc. IEEEIEDM, 2008, pp. 1–4.

[11] M. Kuwahara, O. Suzuki, Y. Yamakawa, P. Fons, T. Yagi, N. Taketoshi,K. Tsutsumi, M. Suzuki, J. Tominaga, and T. Baba, “Measurement of ther-mal and optical properties at high temperature for optical disk materials,”in Proc. 1st Int. Symp. Thermal Des. Thermophys. Property Electron.,Tsukuba, Japan, 2008.

[12] J. P. Reifenberg, K.-W. Chang, M. A. Panzer, S. Kim, J. A. Rowlette,M. Asheghi, H.-S. P. Wong, and K. E. Goodson, “Thermal boundary resis-tance measurements for phase-change memory devices,” IEEE ElectronDevice Lett., vol. 31, no. 1, pp. 56–58, Jan. 2010.

[13] K. C. Kwong, J. He, P. K. T. Mok, and M. Chan, “RESET modelingof PCM using thermal budget approach,” in Proc. IEEE EDSSC, 2010,pp. 1–4.

[14] D. W. Oxtoby, “Nuclearion of first-order phase transitions,” Acc. Chem.Res., vol. 31, no. 2, pp. 91–97, 1998.

[15] Y.-B. Liao, J.-T. Lin, and M.-H. Chiang, “Temperature-based phasechange memory model for pulsing scheme assessment,” in Proc. IEEEICICDT , 2008, pp. 199–202.

K. C. Kwong received the B.S. (honors) and M.S.degrees in electronic engineering in 2007 and 2009,respectively, from The Hong Kong University of Sci-ence and Technology, Kowloon, Hong Kong, wherehe is currently working toward the Ph.D. degree inelectrical engineering.

In 2008, during his M.S. study, he was withTaiwan Semiconductor Manufacturing Company,Taiwan, on device scaling and high-performance de-vice research and development. His current researchinterests include characterization and modeling of

novel memory devices.

Jin He (M’04) received the B.S. degree from TianjinUniversity, Tianjin, China, in 1988, and the M.S. andPh.D. degrees from the University of Electron Sci-ence and Technology of China, Chengdu, Sichuan,China in 1993 and 1999, respectively.

From 1999 to 2001, he was a Postdoctoral Re-searcher and then an Associate Professor with PekingUniversity, Beijing, China. From 2001 to 2005, hewas a Visiting Scholar and then a Researcher with theDepartment of Electrical Engineering and ComputerSciences, University of California, Berkeley. Since

August 25, 2005, he has been a Full Professor and the Director of the Nano-scale and Terahertz Device and Circuit Group (Tera-Scale Research Center)with the School of Electronic Engineering and Computer Science, PekingUniversity. From July 2006 to September 2006, he was a Visiting Professorwith the Department of Electronic and Computer Engineering, University ofScience and Technology of Hong Kong. From July to August 2008, he was aVisiting Professor in advanced science of matter with Hiroshima University,Hiroshima, Japan. Since May 2007, he has been a Guest Professor with theChinese Academy of Science, Beijing. Since May 2010, he has been a GuestProfessor with Nantong University, Jiangsu, China. Since October 2010, hehas been the Deputy Director of Peking University Shenzhen System-on-Chip Key Laboratory with the Peking University-Hong Kong University ofScience and Technology, Shenzhen-honggang Institute, Shenzhen, China. Heis a Guest Professor with the Institute of Microsystem of Chinese Academicof Science, China. He has authored or edited three books, published more than130 journal and 170 conference papers, and was an invited speaker of over20 talks to international conferences, societies, universities, and industry. Hewas one of the members of the main contributors of the international standardcomplementary metal–oxide–semiconductor model BSIM4.3.0. He was thecore model developer and framework builder of BSIM5. He is Editor Memberof “Patents on Engineering,” “Open Nano Science Journal,” “Recent Patentson Electrical Engineering,” “The Open Chemical Engineering Journal,” and“Micro and Nanoscale Electronic Technology.”

Dr. He is Technical Committee Member or Session Chairman of the IEEEInternational School on Quantum Electronics, the Electron Devices and Solid-State Circuits, the International Caracas Conference on Devices, Circuits andSystems, etc. He was selected in the Science and Technology chapter of“Marquis Who’s Who” 2008–2009 edition.

Philip K. T. Mok (S’86–M’95–SM’02) received theB.A.Sc., M.A.Sc., and Ph.D. degrees in electricaland computer engineering from the University ofToronto, Toronto, ON, Canada, in 1986, 1989, and1995, respectively.

Since January 1995, he has been with the Depart-ment of Electronic and Computer Engineering, TheHong Kong University of Science and Technology,Kowloon, Hong Kong, where he is currently a Pro-fessor. His research interests include semiconductordevices, processing technologies, and circuit designs

for power electronics and telecommunications applications, with current em-phasis on power management integrated circuits, low-voltage analog integratedcircuits, and radio-frequency integrated circuit design.

Dr. Mok was the recipient of the Henry G. Acres Medal, the W. S. WilsonMedal, and a Teaching Assistant Award from the University of Toronto, andthe Teaching Excellence Appreciation Award three times from The Hong KongUniversity of Science and Technology. He is also a corecipient of the BestStudent Paper Award in the 2002 and 2009 IEEE Custom Integrated CircuitsConference. In addition, he has been a member of the International TechnicalProgram Committees of the IEEE International Solid-State Circuits Conferencefrom 2005 to 2010, and he has served as an Associate Editor for the IEEETRANSACTIONS ON CIRCUITS AND SYSTEMS—II from 2005 to 2007, theIEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I from 2007 to 2009,and the IEEE Journal of Solid-State Circuits from 2006 to 2011.

Mansun Chan received the B.S. degree from theUniversity of California (UC), San Diego, in 1991and the M.S. and Ph.D. degrees from the UC,Berkeley, in 1994 and 1995, respectively.

During his undergraduate study, he was withRockwell International Laboratory on heterojunc-tion bipolar transistor (HBT) modeling, where hedeveloped the self-heating SPICE model for HBT.His research at Berkeley covered a broad area insilicon devices ranging from process developmentto device design, characterization, and modeling. A

major part of his work was on the development of record breaking silicon-on-insulator (SOI) technologies. He has also maintained a strong interest indevice modeling and circuit simulation. He is one of the major contributorsto the unified BSIM model for SPICE, which has been accepted by mostUS companies and the Compact Model Council (CMC) as the first indus-trial standard metal–oxide–semiconductor field-effect transistor model. Since1996, he has been with the Electrical and Electronic Engineering faculty, TheHong Kong University of Science and Technology, Kowloon, Hong Kong.Between July 2001 and December 2002, he was a Visiting Professor withthe UC at Berkeley and the Codirector of the BSIM program. His researchinterests include nanodevice technologies, image sensors, SOI technologies,high-performance integrated circuits, 3-D circuit technology, device modeling,and nano Biomedical Nano-Electro-Mechanical-Systems technology.

Dr. Chan is a recipient of the UC Regents Fellowship, the Golden KeysScholarship for Academic Excellence, the Semiconductor Research Corpo-ration Inventor Recognition Award, the Rockwell Research Fellowship, theResearch and Development 100 award (for the BSIM3v3 project), the Distin-guished Teaching Award, and other awards.