Reply to Comment on Acoustically assisted spin-transfer-torque switching of nanomagnets: An energy-efficient hybrid writing scheme for non-volatile memory [Appl. Phys. Lett., 103, 232401 (2013)]

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This is a reply to a comment on our work recently posted in arXiv. To our knowledge, this comment has not been published anywhere else. We show that the points raised in the comment are invalid
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    a  r   X   i  v  :   1   5   0   3 .   0   4   1   7   4  v   1   [  c  o  n   d  -  m  a   t .  m  e  s  -   h  a   l   l   ]   1   3   M  a  r   2   0   1   5 Reply to Comment on “Acoustically assisted spin-transfer-torqueswitching of nanomagnets: An energy-efficient hybrid writingscheme for non-volatile memory” [Appl. Phys. Lett., 103, 232401(2013)] Ayan K. Biswas 1 , Jayasimha Atulasimha 2 and Supriyo Bandyopadhyay 11 Department of Electrical and Computer Engineering,Virginia Commonwealth University, Richmond, Virginia 23284, USA 2 Department of Mechanical and Nuclear Engineering,Virginia Commonwealth University, Richmond, Virginia 23284, USA A comment [1] has been posted in arXiv on our work on energy-efficient acoustically-assistedspin-transfer-torque writing of bits in non-volatile magnetic memory [2]. It raises the followingpoints: (1) our acoustically-assisted spin-transfer-torque random access memory (AA-STT-RAM)[2] is less energy-efficient than transistors, (2) our Terfenol-D based AA-STT-RAM is less energy-efficient than a CoFeB based traditional STT-RAM, (3) the surface acoustic wave in our AA-STT-RAM causes some small magnetization rotation even in cells that are not being written into andthat results in 40 kT of standby (static) energy dissipation per cell. This wasted energy makes ourAA-STT-RAM memory cell worse than a transistor in energy dissipation, (4) we under-estimatedthe energy barrier in our elliptical nanomagnet (memory cell) by ∼ 33% because we used a formulathat is valid only when the eccentricity of the ellipse is small, whereas our eccentricity was 0.57(major axis  a  = 110 nm; minor axis  b  = 90 nm, eccentricity =   1 − ( b/a ) 2 ), (5) an AA-STT-RAMcell’s footprint is larger than that of a transistor and hence our memory will be less dense thantransistor-based memory, and (6) the commenter’s “own idea” of writing a bit in a non-volatilemagnetic memory cell with the aid of strain alone and a sensing element [3] is somehow more“attractive” than our acoustically assisted spin transfer torque based writing scheme.We reply as follows: Point (1) is specious. One does not write bits into a single transistorsince it is  volatile  . One should therefore compare our AA-STT-RAM (which is non-volatile) witha transistor-based non-volatile memory cell, e.g. a NAND flash. That dissipates several ordersof magnitude more energy than an AA-STT-RAM and has several orders of magnitude worseendurance as well [4]. There is no comparison between the two.Point (2) is equally specious. Comparing a Terfenol-D based AA-STT-RAM with a CoFeBbased STT-RAM is comparing an apple to an orange. To compare apples with apples, one shouldcompare a Terfenol-D based AA-STT-RAM with a Terfenol-D based STT-RAM, or a CoFeB basedAA-STT-RAM with a CoFeB based STT-RAM, or choose any other material as long as it is thesame for both RAMs. We carried out the analysis for Terfenol-D and found the AA-STT-RAMto be superior to STT-RAM in energy dissipation. Another group carried out the analysis forCoFe independently and they too found that strain-assisted STT-RAM (which is equivalent toAA-STT-RAM) is superior [5]. We have now carried out the analysis for CoFeB and once againfound the AA-STT-RAM to be superior. So far, whenever apples have been compared with apples,the AA-STT-RAM has eclipsed the STT-RAM.1  Point (3) is incorrect. Let us concede for the sake of argument that the SAW wave dissipates 40kT in each cell of an AA-STT-RAM per cycle of   ∼  1 ns duration. The resulting power dissipationis 0.16 nW. This is power dissipated in the cell when it is  not   being written into and hence shouldbe compared to the leakage power (i.e. static power or standby power) dissipation in transistors.For the 22-nm node transistor technology, the leakage current, or off-current, is  ∼  0.7 nA in a 1 µ m gate width transistor for a power supply voltage of 1.5 V (threshold voltage 300 mV) and 0.8 µ A for a power supply voltage of 0.5 V (threshold voltage 100 mV) [7]. The corresponding leakagepowers are 1.05 nW and 400 nW, respectively. Therefore, the standby power dissipation in anAA-STT-RAM cell is almost an order of magnitude  less   than that in a single transistor, let alonea NAND flash cell made of multiple transistors.Point (4) is somewhat orthogonal to the message of our paper. If we rigorously calculate theenergy barrier from Ref. [8] (which is valid for small or large eccentricities), then we will find thatthe energy barrier we used actually corresponds to a major axis dimension of 108 nm (instead of 110 nm) and a minor axis dimension of 93 nm (instead of 90 nm). Since lithographic precision of 2-3 nm is somewhat impractical when delineating the nanomagnets, the dimensions are rounded off to 110 nm and 90 nm. In any case, if the energy barrier increases, then the energy dissipation in both   STT-RAM and AA-STT-RAM will go up, whereas if the energy barrier decreases, the energydissipation in  both   STT-RAM and AA-STT-RAM will go down. Since both types of RAMs areaffected similarly, the comparison between the two (which is the message of the paper) and theconclusion that AA-STT-RAM is superior, is not alteredPoint (5) is a red herring. It is well known that magnets are larger than transistors and cannotbe shrunk beyond the super-paramagnetic limit at the operating temperature. This limitation ismore than offset by the non-volatility, endurance, etc. of magnets that transistors do not possess.Point (6) is orthogonal to our paper. It refers to an idea (that we actually co-authored but didnot pursue further; it is certainly not the commenter’s sole idea) whereby a bit is written into anon-volatile magnetic memory cell with strain alone, without any spin polarized current generatinga spin transfer torque. On the surface, it may appear to be a more energy-efficient strategy forwriting bits than switching with both strain and STT (since strain consumes much less energythan STT to rotate a magnet’s magnetization), but its debilitating drawback is that it requires afeedback/sensing circuit to write bits correctly (i.e. with better than 50% error probability). Whenthe energy dissipated in the feedback circuit is factored in, that scheme may not be any moreenergy-efficient than acoustically-assisted spin-transfer-torque [6] and almost surely will be moreerror-prone since the feedback circuit needs to operate with very precise timing. Fortunately, thereare better ways to write bits in magnetic memory with strain alone [9, 10, 11, 12, 13]. They mayindeed dissipate less energy than acoustically-assisted spin-transfer-torque, but one disadvantagesome of them have is that the writing step must be preceded by a reading step every time. Thatdisadvantage also afflicts the scheme in ref. [3]. However, the acoustically-assisted spin-transfer-torque technique is free of this disadvantage.In conclusion, we find that none of the points raised in Ref. [1] is tenable. References [1] K. Roy, arXiv:1501.05941v1.[2] A. K. Biswas, S. Bandyopadhyay and J. Atulasimha, Appl. Phys. Lett.  103 , 232401 (2013).[3] K. Roy, J. Atulasimha and S. Bandyopadhyay, Sci. Rep., , 3038 (2013).2  [4] T. Perez and C. A. F. De Rose, Technical Report 060, Porto Alegre, 2010([5] A. Khan, D. E. Nikonov, S. Manipatruni, T. Ghani and I. A. Young, Appl. Phys. Lett.  104 ,262407 (2014).[6] S. Bandyopadhyay and J. Atulasimha, Appl. Phys. Lett.  105 , 176101 (2014).[7] H. Iwai, Microelectronic Engr.  86 , 1520 (2009).[8] M. Beleggia, M. De Graef, Y. T. Millev, D. A. Goode and G. Rowlands, J. Phys. D: Appl.Phys.  38 , 3333 (2005).[9] N. A. Pertsev and H. Kohlstedt, Appl. Phys. Lett.  95 , 163503 (2009)[10] S. Giardano, Y. Dusch, N. Tiercelin, P. Pernod and V. Preobrazhensky, Phys. Rev. B.  85 ,155321 (2012).[11] A. K. Biswas, S. Bandyopadhyay and J. Atulasimha, Appl. Phys. Lett.  104 , 232403 (2014).[12] A. K. Biswas, S. Bandyopadhyay and J. Atulasimha, Appl. Phys. Lett.  105 , 072408 (2014).[13] J. J. Wang, J. M. Hu, J. Ma. J. X. Zhang, L. Q. Chen and C. W. Nan, Sci. Rep.  4 , 7507(2014).3
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