IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006 2715

A Heat Interaction Investigation inThermally Assisted MRAM

Z. Y. Liu, G. C. Han, and Y. K. Zheng

Data Storage Institute, Singapore 117608, Singapore

Joule heating has been used to help the magnetic switching of the magnetic layer in magnetic random access memory cells with in-creased temperature. In this paper, the heat interaction is investigated for different cell dimensions and aspect ratios. It is found that theheat interaction becomes significant when the cell spacing is below the critical spacing (CS). We also find that the aspect ratio also playsan equally important role in determining the CS.

Index Terms—Heat, interaction, magnetic random access memory (MRAM).

I. INTRODUCTION

I N magnetic random access memory (MRAM) technology,the thermal effect has been used to help the magnetic

switching in the thermally assisted MRAM (TAMRAM). If thetemperature is above a certain temperature, either the Curiepoint for a ferromagnetic (FM) material or Neel point for anantiferromagnetic (AFM) material, the writing current can besignificantly reduced [1]–[3]. The temperature distribution inthe free layer (recording layer) as a function of time and cur-rent has been widely investigated. It shows that the increasedtemperature can successfully help to reverse the magnetizationof the recording layer within the writing cycle [2]. A double-barrier structure has also been proposed to improve the Jouleheating efficiency and increase the breakdown voltage [3]. In-creasing storage density requires smaller cell sizes and smallerspacing between the cells, hence a substantially reduced drivencurrent is needed to minimize the load of the select transistorand the power dissipation [4]. Much work has been focusedon the thermally assisted effect from various heating sources.As the cell spacing becomes smaller as the density increases,the joule heat generated within one cell may affect the adjacentcells; thus, the thermal interaction effect should be considered.In this paper, the cell spacing, cell size, and cell aspect ratio aretaken into account to investigate the thermal interaction effect.Also, the three-dimensional finite-element method is used forthe thermal analysis.

II. MODEL

The typical structure of the TAMRAM in this simulation isshown in Fig. 1. The TAMRAM is comprised of a bottom lead,a connecter (C1), an antiferromagnetic (AFM) layer (AFM1), aferromagnetic (FM) layer (FM1), a barrier layer AlOx, an FM2,an AFM2, a connector (C2), and a top lead. AFM2 has a lowerNeel temperature than AFM1. The FM2, which is adjacent to theAFM2 with a thickness of 2 nm, serves as the storage layer. Theheating power is assumed to come from only the barrier layer(AlOx), which has a thickness of 1 nm for simplification. Thetunneling current through the junction heats the FM and AFM

Digital Object Identifier 10.1109/TMAG.2006.879724

Fig. 1. Side view of MRAM cell structure enclosed by insulation material.

Fig. 2. Schematic for thermal interaction investigation (a is long axis length,b is short axis length, gx is spacing at long axis direction, and gy is spacing inshort axis direction).

layer. The temperature of the central plane of the FM layer isused in all our results of this paper, using a reference tempera-ture of 300 K. The AFM layers and the connectors between thebarrier and the lead (Cu) play an important role in dissipatingthe heat. The cell is enclosed by a low-k insulation material tominimize heat loss. A cell with an elliptical shape, shown inFig. 2, is used to produce more stable magnetization. Three as-pect ratios of , and are used in this paper. ( islong axis length; is short axis length.)

The general governing equation in transient heat conductionis

(1)

0018-9464/$20.00 © 2006 IEEE

2716 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006

TABLE IMATERIAL PROPERTIES USED

with , and being the local density, heat capacity,thermal conductivity, temperature, and heat rate, respectively.The heat rate can be expressed by

(2)

where is the current density and is thelocal resistivity .

The material properties used in this paper areshown in Table I.

To simplify the process, the half-symmetric geometry is usedin this paper, so all the following temperature results are pre-sented only for the half-axis. The main cell dimensions usedhere are a long axis length of and nmand AR , and , respectively. The current ampli-tude through the cell is 90 A (for nm) from the tenthto twentieth nanosecond. The same current density is used forthe cells with other sizes.

III. DISCUSSION

A typical structure of nm/50 nm was used toderive the main results here. The time dependence of temper-ature with different cell spacings along the short and long axesis shown in Fig. 3(a) and (b). Although having the same trendof temperature rising with time, it clearly shows the differencebetween varying long and short axes spacing. Fig. 3(b) showsthat changing the long axis spacing does not have much effecton the temperature profile; while the effect is significant whenspacing changes along the short axis, as shown in Fig. 3(a). Ahighest temperature difference of about 30 K between gyand nm has been observed. It can be understood as follows:the heat is easier to dissipate along the short axis direction forthe elliptical cell and so is the effect to the neighbor cell.

Fig. 4 shows the temperature distribution in the central planeof the FM layer along the long axis [Fig. 4(a) and (b)] and shortaxis [Fig. 4(c) and (d)], respectively, after the 90- A currentpulse is applied. In Fig. 4(a), the gx is fixed at different spacingsof 20 and 100 nm, with varying gy. It is very clear that the cellwith spacing gx of 20 nm has a significant interaction effecton the neighbor cell as compared to that of the spacing gx of100 nm. For a spacing of 20 nm, the temperature even at thecenter between neighbor cells keeps high above 400 K, while itcan reach near 300 K for a spacing of 100 nm. It is also notedthat the spacing gy effects the amplitude of the temperature too.

Fig. 3. Temperature dependence on time and cell gap for cell dimensions ofa=b = 100 nm/50 nm with current amplitude of I = 90 �A from tenth totwentieth nanosecond. (a) Different cell spacing along short axis. (b) Differentcell spacing along long axis.

Fig. 4. Temperature profile for cell dimension of a=b = 100 nm/50 nm.(a) Long axis (gx is fixed at 20 and 100 nm). (b) Long axis (gy is fixed at 20and 100 nm). (c) Short axis (gx is fixed at 20 and 100 nm). (d) Short axis (gy isfixed at 20 and 100 nm).

The larger the gy, the lower the temperature is at all locationsalong the long axis, though the temperature stabilizes when gyreaches 100 nm. Fig. 4(b) shows a similar effect along the longaxis, where gx is varied while gy is fixed with 20 and 100 nm,respectively. Fig. 4(c) and (d) gives the results on the short axis;they have the same trend, but with less interaction for differentspacing, regardless of either fixed or varying spacing. This isalso due to the aspect ratio effect.

LIU et al.: HEAT INTERACTION INVESTIGATION IN THERMALLY ASSISTED MRAM 2717

Fig. 5. (a) Cell FM layer average temperature as a function of the cell spacingalong long axis (fixed cell spacing along short axis). (b) Cell FM layer averagetemperature as function of cell spacing along short axis (fixed cell spacing alonglong axis). Both use cell dimension of a=b = 100=50 nm.

The average temperature at different gx for a fixed gy isshown in Fig. 5(a). It demonstrates that the average temperatureis stable when the spacing is greater than 100 nm. The sameconclusion is seen for Fig. 5(b), where gx is fixed with varyinggy. From the figures, we can see that for a cell dimension of

nm and AR , the interaction will disappear ata critical spacing (CS) of 100 nm, regardless of whether weconsider the long axis or short axis direction.

We extend our work to other sizes and aspect ratios. Fig. 6(a)shows the CS along the long axis direction, with a dependenceon the cell size and aspect ratio. The larger the cell size, thelower the CS; the higher the aspect ratio, the lower the CS. Forexample, the CS decreases to about 20 nm for a cell with sizeof nm and AR . The CS along the short axis alsodemonstrates a similar trend [Fig. 6(b)] except that it decreasesat a faster speed.

Fig. 6. Critical spacing as function of cell size and aspect ratio. (a) Long axisdirection. (b) Short axis direction.

IV. CONCLUSION

The thermal interaction can be quite significant when thespacing between neighbor MRAM cells is reduced to a certainlevel, depending on the cell size and aspect ratio. In this paper,we demonstrate that narrower cell spacing brings an incrementof the cell temperature. The effect is more significant for spacingvarying along the short axis direction. The critical spacing isabout 100 nm for a cell with a size of long axis length at 100 nmand aspect ratio at 0.5. The CS goes down with a larger cell sizeand aspect ratio.

REFERENCES

[1] R. S. Beech, J. A. Anderson, A. V. Pohm, and J. M. Daughton, J. Appl.Phys., vol. 87, pp. 6403–6405, 2000.

[2] J. G. Deak, J. Appl. Phys., vol. 97-10E316-3, pp. 10E316–1, 2005.[3] J. Wang and P. P. Freitas, IEEE Trans. Magn., vol. 40, no. 5, pp.

2622–2624, Nov. 2004.[4] R. Sinclair and A. Pohm, Proc. Non-Volatile Memory Technology Symp.,

pp. 110–117, Nov. 2004.

Manuscript received March 13, 2006 (e-mail: Liu_zhiyong@dsi.a-star.edu.sg).