Ultra Low Power
Logic Design with Electron Spin
While Moore's Law states that the number of transistors
that can fit on an integrated circuit should double every
two years, this is getting harder and harder to achieve,
as transistors reach atomic dimensions. One of the biggest
problems is the way power dissipation increases as more
transistors are added. But the researchers have come up
with an entirely new logic circuit family based on magnetic
semiconductor devices.
Unlike traditional integrated circuits, which consist of
a collection of miniature transistors operating on a single
piece of semiconductor, these 'spin logic circuits' exploit
the quantum physics phenomenon of spin, another fundamental
property of the electron in addition to charge property.
The device called Quantum Dot which houses a single electron
can be configured in a logic circuit that is capable of
performing all the necessary Boolean logic and can be cascaded
to develop sophisticated function units. These 'spintronic'
logic devices successfully perform the same operations as
a conventional CMOS circuits, but with fewer devices and
more computing power.
Conventional charge based Logic Design result in enormous
power dissipation since information is stored at two different
charge levels. Charge being a scalar has only magnitude.
So logic levels can solely be defined only by presence or
absence of charge. In order to charge or discharge capacitor
to define logic 0 or logic 1 current has to flow which result
in power dissipation. However we can use spin degree of
freedom of an electron to define the logic. Spin being a
vector, electron has fixed magnitude but can be polarized
in any direction to get bistability. A single electron in
a Quantum well can be oriented to have either UP spin or
DOWN spin with external magnetic field to define logic 0
or logic 1.Switching can be done just by flipping the direction
without actually causing the motion of the charge. This
results in considerable saving of energy.
However there is still power dissipation involved in flipping
the Spin which is gµB, where B is the global magnetic field
which is required to maintain spin polarization bistable,
g is the Lande g factor and µ is the Bohr Magneton . The
external field required to orient electron spin depends
on acceptable error probability in the Logic Design. Magnetic
Field “B” can be made extremely small to reduce power dissipation.
However this results in frequent flipping of Spin resulting
in error. In order to encode bits reliably spin polarization
should not flip frequently. This is important because we
cannot refresh spin bits frequently as it results in power
dissipation. Hence it is required that the Spin relaxation
be long enough. If the electron polarized in particular
direction is housed in a Quantum Dot the relaxation time
in quiet high. Because of weak spin orbit interaction Quantum
Dots are generally fabricated with InP or GaAs.
Universal Logic Gate Design with Single Spin
We can realize any logic gate or entire combinational
circuit with two dimensional array of Quantum Dots containing
single electron. The Quantum Dots interact through nearest
neighbor exchange interaction. Through nearest neighbor
interaction what we understand is that the wave function
of electron in one Quantum Dot overlap with the wave function
of electron only in its nearest neighbor Quantum Dot. Certain
Quantum Dots in the array are defined as input ports and
the spins of the electrons in these input ports are defined
by local Magnetic Field. Nearest neighbor interactions and
the states of input spins determine the spin state of other
Quantum Dots in the array. By properly arranging Quantum
Dots in two dimensional array we can ensure that the output
takes the values determined by the Truth Table for the logic
gate being implemented. We show below implementation of
Universal NAND gate with Quantum Dots.
Fig.1.Nand Gate Implementation with Quantum Dots
As shown in the figure above NAND gate can be implemented
with three Quantum Dots.Dots A and B define input port and
Quantum Dot C between A and B define the output. Global
Magnetic Field B determine the Quantization Axis for the
Spin i.e. Spin in any Dot may be either parallel or Antiparallel
to this. Parallel is defined as logic 1 and Antiparallel
state is defined as logic 0.As defined earlier only nearest
neighbor interactions are strong.If we apply logic inputs
to Dot A and B and allow the system to relax to thermodynamic
ground state the logic output in Dot C is always conforms
to the truth table of NAND operation of Inputs A and B.
Once we have NAND gate any arbitrary circuit can be implemented.
One severe drawback with this design is unidirectionality
in time is not possible since exchange interaction is bidirectional.
So Clock pads which are not shown in the above figure are
used to raise or lower the barrier height between the Dots.
If the barrier height is increased by applying voltage at
the clock pad then there is no wavefunction overlap and
hence the Dots are isolated.If the barrier is lowered again
by applying voltage at the clock pad then the overlap of
wavefunctions take place through exchange interaction. Hence
Unidirectionality is ensured.
Fig.2. Quantum Dots with Clock PADS to control the barrier
height
How to read and write Single Spin
The next issue is how to align spin of electron housed in
Quantum Dot to define Logic 0 or Logic 1.This is done by
local magnetic fields generated by inductors which will
orient the spin parrel to the field and hence write the
logic. Reading the bit information from the output is slightly
complex and is generally done by highly precise magnetic
resonance force microscopy.
Major recent advancements in manipulating single spin of
an electron in Quantum Dot has made it possible to realize
Ultra Low Power Logic Gates. Practical implementation may
take some time but Spintronics will surely replace traditional
Silicon Based Electronics in some near future.
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