VCU

04/2002 2002/2003 page 1

Cooperative Spin/Nanomagnetic Architectures:

A Critical Evaluation

Supriyo Bandyopadhyay Dept. of Electrical & Computer Engineering

Virginia Commonwealth UniversityRichmond, VA 23284, USA

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”.

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 dcMagnetic Field

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

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; gBBlocal >> J

J > gBBglobal

Anti-ferromagnetic ordering in ground state

Global field

input1 input2 output

0 0 1

1 1 0

1 0 1

0 1 1

Input1 Output Input2

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)

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)

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.

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/(2gBBlocal) = 0.7 psec with InSb q-dots if Blocal = 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.

VCU

04/2002 2002/2003 page 10

The Bad

Temperature of operation is determined by the requirement 2J =gB Bglobal = 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).

VCU

04/2002 2002/2003 page 11

What about spontaneous spin flips causing bit errors?

1/1 T Textrinsicp e

… Assume 1 GHz clock. Then for p = 10-9, we need that the spin-flip time T1 should be 1 second!

VCU

04/2002 2002/2003 page 12

Search for materials withlong 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?

VCU

04/2002 2002/2003 page 13

Progress to date - experimental

T1 time measured 1 second at 100 K. Largest reported in any system.Nature Nanotech., 2, 216 (2007).

T2 time measured as 2 nsec at room temperature in Alq3 using ESR. At least 10 times larger than in inorganic materials. Possible phonon bottleneck effect.

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

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)

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

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

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

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

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

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

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 1010 cm-2, so that in a 10 cm2 chip, the longest line will have 3.16x105 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

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

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.

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

tan

where is the ratio of the fields required

to magnetize along easy axis and hard axis

r

r

VCU

04/2002 2002/2003 page 28

What about energy dissipation?

Energy dissipation to flip a nanomagnet with 104 spins is NOT 104 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!

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.

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

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

Out

put

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?

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