1. VCU 04/2002 2002/2003 page 1 Cooperative Spin/Nanomagnetic Architectures: A Critical Evaluation Supriyo Bandyopadhyay Dept. of Electrical & Computer Engineering Virginia Commonwealth University Richmond, VA 23284, USA

2. VCU 04/2002 2002/2003 page 2 Why Spin At All? Conventional electronics utilizes “charge” to store, process and communicate information. Example: The MOSFET– when the channel is full of charge, the device is “on” and encodes logic bit 0. When the channel is depleted of charge, the device is “off” and encodes logic bit 1. Switching from one bit to the other involves moving charges in or out of the channel, which causes a current (I) to flow with an associated power dissipation of IV or an energy dissipation of  QV, where  Q is the channel charge. This dissipation is inevitable. Charge, being a scalar, only has magnitude and no direction. Therefore, different logic bits must be encoded in different amounts (or magnitude) of charge. Switching must involve changing the magnitude of the charge, which then invariably causes an energy dissipation of  QV. This is a fundamental shortcoming of all “Charge Based Electronics”.

3. VCU 04/2002 2002/2003 page 3 Spin as a state vector to encode logic bits Spin, unlike charge, is a pseudo vector with a fixed magnitude but variable polarization or “direction”. Place a trapped or localized single electron in a dc magnetic field and the spin polarization becomes bistable: only polarizations parallel and anti-parallel to the field are eigenstates and are stable or metastable. Encode logic bits in these two polarizations. Switch by simply flipping the spin polarization, without physically moving the electron in space and causing a current flow. No  QV dissipation Low energy paradigm 1 0 Global dc Magnetic Field

4. VCU 04/2002 2002/2003 page 4 Do SPINFETs and their cousins cause low energy dissipation as a result? Absolutely not SPINFETs do not utilize the vector nature of spin to reduce energy dissipation It is still very similar to a MOSFET, except that current is modulated (transistor action realized) by changing spin polarization with a gate potential instead of changing carrier concentration in the channel Information is still encoded in charge and current flows so that dissipation is not reduced at all Comparison between SPINFETs and MOSFETs in APL, 85, 1433 (2004) SPINEFT loses

5. VCU 04/2002 2002/2003 page 5 Single Spin NAND gate – no transistor business Nearest neighbor exchange coupling J Inputs applied through local magnetic field; g  B B local >> J J > g  B B global Anti-ferromagnetic ordering in ground state Global field input1input2output 001 110 101 011 Input1Output Input2

6. VCU 04/2002 2002/2003 page 6 Spin wire Nearest neighbor exchange coupling Information replicated in alternate dots Fan out S. Bandyopadhyay, B. Das and A. E. Miller, Nanotechnology, 5, 113 (1994)

7. VCU 04/2002 2002/2003 page 7 The vexing issue of unidirectionality Granular clocking Need 3-phase clock Propagates signal unidirectionally and allows pipelining of data S. Bandyopadhyay, Superlattices and Microstructures, 37, 77 (2005)

8. VCU 04/2002 2002/2003 page 8 Rigorous quantum mechanical calculations of all the ground state configurations in the NAND gate, the gate error probability and energy dissipation can be found in H. Agarwal, S. Pramanik and S. Bandyopadhyay, New J. Phys., 10, 015001.

9. VCU 04/2002 2002/2003 page 9 The Good Energy dissipated in switching a bit is kTln(1/p)… the Landauer Shannon limit! Here p is the bit error probability With p = 10 -9, the energy dissipated is 21 kT. Modern transistors dissipate 40,000-50,000 kT Energy dissipated in the clock can be made arbitrarily small using adiabatic schemes Very low power paradigm (very good) Writing speed determined by  ~ h/(2g  B B local ) = 0.7 psec with InSb q-dots if B local = 1 Tesla. Clock frequency is determined by how fast coupled spin system relaxes to ground state. About 1 nsec. Therefore, clock frequency is ~ 1 GHz.

10. VCU 04/2002 2002/2003 page 10 The Bad Temperature of operation is determined by the requirement 2J =g  B B global = kTln(1/p). With semiconductor quantum dots, J = 1 meV. Therefore, with p = 10 -9, the temperature of operation is 1.1 K (very bad) Room temperature operation requires J=0.3 eV. Maybe possible in molecules but certainly not in quantum dots The global field required is 0.72 Tesla with InSb q-dots (not bad).

11. VCU 04/2002 2002/2003 page 11 What about spontaneous spin flips causing bit errors? … Assume 1 GHz clock. Then for p = 10 -9, we need that the spin-flip time T 1 should be 1 second!

12. VCU 04/2002 2002/2003 page 12 Search for materials with long spin relaxation times Organics have weak spin orbit interaction and hence could have long spin lifetimes…but would it be as long as 1 second above 1.1 K?

13. VCU 04/2002 2002/2003 page 13 Progress to date - experimental T 1 time measured 1 second at 100 K. Largest reported in any system. Nature Nanotech., 2, 216 (2007). T 2 time measured as 2 nsec at room temperature in Alq 3 using ESR. At least 10 times larger than in inorganic materials. Possible phonon bottleneck effect.

14. VCU 04/2002 2002/2003 page 14 Conclusions regarding SSL Very low power Very low bit error probability Synthesis difficult, but has been repeatedly demonstrated by many groups Single spin reading and writing repeatedly demonstrated by many groups Requires low temperature because we cannot make the exchange interaction very large Best platform may be organic semiconductors because of the very long spin relaxation time

15. VCU 04/2002 2002/2003 page 15 Other collective spin (or magnetic) approaches Magnetic quantum cellular automata (originally Cowburn and Welland) Spin wave based cellular non-linear networks (Khitun and Wang)

16. VCU 04/2002 2002/2003 page 16 Magnetic quantum cellular automata Shape anisotropy ensures that magnetization can point to the left (logic 0) or right (logic 1) Apply a magnetic pulse (field pointing right) to set all dots to logic 1. Apply an oscillating ac field whose negative phase represents logic 0 and positive phase logic 1. At the negative amplitude, the magnetization switches and points to left. DC component negative If the initial magnetic pulse sets all dots to logic 0, then ac field has no effect The magnetic pulse and the ac field are the two inputs. State of the dots is output. Realize the AND operation. Cowburn and Welland, Science, 287, 1466 (2000) Input 1 Input 2 Output

17. VCU 04/2002 2002/2003 page 17 Magnetic quantum cellular automata This is a single gate, NOT a circuit or architecture. No information “propagates” here Hence, no issue of unidirectional signal propagation from one gate to another

18. VCU 04/2002 2002/2003 page 18 Magnetic quantum cellular automata: Another gate and NOT a circuit The oscillating magnetic field cannot flip the magnetization of the elongated dot which is immune to its influence If the elongated dot is in logic state 1, the oscillating magnetic field switches circular dots to state 1 during positive phase and state 0 in negative phase If elongated dot in 0, then oscillating magnetic field switches circular dots to state 0 in negative phase, but cannot switch to state 1 in positive phase since weaker in positive phase. Another AND gate Input 1 Output + phase - phase + phase

19. VCU 04/2002 2002/2003 page 19 Signal propagation issues This too is an isolated gate and not a circuit Hence no issue of unidirectional signal propagation, and no issue of pipelining data There is some recognition of signal propagation issues and a solitary wave is mentioned, but it really has no relevance to the ideal operation of the gate Its only utility is that if a cell gets stuck in its previous state (stuck-at-1 or stuck-at-0 fault), then the solitary wave can push it out of that state and provide some protection against faults Misnomer: Should call it a nanomagnetic AND gate. Not relevant to architectures

20. VCU 04/2002 2002/2003 page 20 Magnetic quantum cellular automata circuits (Scaled up version of SSL) Csaba, Porod, Lugli, Csurgay, Int. J. Circuit Theory and Applications, 35, 281 (2007) More of a circuit with signal propagation issues Nanomagnetic dashes have shape anisotropy which makes magnetization bistable. Encode logic 0 and 1 1 0

21. VCU 04/2002 2002/2003 page 21 Magnetic quantum cellular automata Scaled up version of Single Spin Logic where the entire nanomagnet (consisting of about 10,000 spins) acts as a giant spin Ground state is anti- ferromagnetic Majority logic gate designed based on anti-ferromagnetic ordering Top view of majority logic gate

22. VCU 04/2002 2002/2003 page 22 Signal propagation First apply a dc magnetic field to magnetize all dashes to the right Then an input is applied to the leftmost dot Next one flips, and then the next one, in a domino like fashion Unidirectional propagation happens since there is an asymmetry between the state of the left neighbor and the state of the right, with the influence from left being stronger because of shape anisotropy that makes the vertical axis the easy axis of magnetization and the horizontal axis the hard axis Initializing clock Input applied Shift register

23. VCU 04/2002 2002/2003 page 23 The clock Global clock, not granular… saves a lot of fabrication complexity The price….. Non- pipelined architecture The clock signal cannot reset all dash states until the final output has been produced New input cannot be provided until the output has been produced Initializing clock

24. VCU 04/2002 2002/2003 page 24 What is a reasonable clock frequency? The time to switch a nanomagnet is about 1 nsec Therefore, the minimum clock period is N nsec, where N is the number of cells in a line Claim is that nanomagnets can be produced with a density of at least 10 10 cm -2, so that in a 10 cm 2 chip, the longest line will have 3.16x10 5 cells Therefore, the clock period is longer than 0.3 milliseconds Clock frequency is limited to 3 kHz with this density… all because of non-pipelining

25. VCU 04/2002 2002/2003 page 25 Granular versus global clock Magnetic quantum cellular automata can be operated with a granular clock (see Behin-Aein, Salahuddin and Datta, arXiv:0804.1389). This will increase speed since it will allow pipelining. However, the penalty is generating a local magnetic field around each clock. Harder than the scheme in SSL

26. VCU 04/2002 2002/2003 page 26 Other problems In SSL, the nearest neighbor interaction is exchange which can be turned on or off by lowering or raising an electrostatic potential barrier between the neighboring cells. This requires a local electrostatic potential which can be applied via a simple gate pad. In magnetic quantum cellular automata, the nearest neighbor interaction is dipole-dipole which cannot be turned on or off by lowering or raising an electrostatic potential barrier between neighboring cells. We need a local magnetic field to orient the magnetization of the selected nanomagnet. Much harder to generate a local magnetic field than to generate a local electric field.

27. VCU 04/2002 2002/2003 page 27 The Killer… Clock Synchronization for a Vector Clock SSL uses a scalar clock … potential MQCA uses a vector clock… magnetic field The timing and direction of the field has to be synchronized across the entire chip. Possible, in principle, for granular clock, but very difficult. Impossible for global clock Misalignment problem will cause many cells to not flip, leading to severe bit errors The only reported experiment reports a failure rate of 25%! A bit error probability of 25% cannot be handled. It has to remain on the order of 10 -6 or less This problem alone can make MQCA impractical

28. VCU 04/2002 2002/2003 page 28 What about energy dissipation? Energy dissipation to flip a nanomagnet with 10 4 spins is NOT 10 4 times the energy dissipated in flipping a single spin Because of interactions between spins, it is much less. Salahuddin and Datta (APL, 90, 093503 (2007)) show that it is only about 35 times that of a single spin flip… Good news. At room temperature, energy dissipated per bit flip is about 800 meV. Compare that with SSL where at 1.1 K, it was 2 meV. If MQCA were operated at 1.1 K, the energy dissipated per bit flip would have been ~ 4 meV. Thus, in terms of energy dissipation, MQCA is only slightly worse than SSL!

29. VCU 04/2002 2002/2003 page 29 The good, the bad and the ugly Good Low energy, ~35 kT to switch. Also room temperature operation Bad Slow, few kHz clock if globally clocked. Granular clocking is hard Ugly Error probability very high because of the misalignment problem (synchronization of a vector clock). Bit error probability in the only experiment reported (Science, 311, 205 (2006)) was about 25%. We need it to be 10 -6 or less.

30. VCU 04/2002 2002/2003 page 30 Another problem with dipole-dipole interaction Dipole-dipole interaction is long-range (polynomial decay with distance instead of exponential decay). Second nearest neighbor interaction is not that much weaker than nearest neighbor interaction. Increases error probability.

31. VCU 04/2002 2002/2003 page 31 The Spin Wave Bus: Another architecture with actual signal propagation Information transmitted by spin waves without charge transfer. Hence no current flows. Is it energy efficient as a result? Depends on the dissipation of spin waves that carry information Supposedly reduces interconnect problem. But this requires selectively directing the wave which will require a waveguide Phase logic: phase is a continuous variable which can degrade due to dephasing. How is signal restoration performed. Need a “phase-device” with non-linear characteristic

32. VCU 04/2002 2002/2003 page 32 Spin bus devices Signal restoration at logic nodes requires a device with a non-linear characteristic for spin wave phase Otherwise, use only for analog applications Analogous to SAW devices Input Output

33. VCU 04/2002 2002/2003 page 33 Other issues Spin waves decay because of magnon emission (scattering with phonons is a secondary issue, primary issue is emission of magnons which carry away energy). Some amplification is necessary. What is a “spin-wave- amplifier”? There are no local interconnects, only global interconnects via a spin wave bus, but how is selective coupling to devices accomplished? What is the coupling efficiency?

34. VCU 04/2002 2002/2003 page 34 CONCLUSIONS Single spin logic is low energy consuming, high speed (granular clock and pipelined) and high density. Fabrication challenging and low temperature operation Magnetic quantum cellular automata can be operated at room temperature and low energy (not as low as SSL, but low). Cannot be “granular clocked”, at least not easily and hence non-pipelined and very slow. May be impractical because of large bit error probability Spin wave bus may be low energy consuming but not as low as SSL or even MQCA. Room temperature operation possible. Probably reasonably fast. Not suitable for digital processing, may work well for analog processing