Unit – 5 Nanoelectronic devices

UNIT V - NANOELECTRONIC DEVICES


 Density of states
 Resonant Tunneling
 Single Electron Phenomena – SET
 Spintronics
 Carbon Nanotubes (CNTs)

DENSITY OF STATES
Density of states is defined as “The number of states per unit volume in an energy
interval E and E + dE”. It helps us to understand transport properties of materials.
DENSITY OF STATES IN BULK MATERIAL [3 D]
In 3 D structure or bulk structure, no quantization of the particle motion occurs. The particle
is free to move. Electrons in CB and holes in VB free to move in 3D.
Consider an electron in 3 dimensional space. To find the number of quantum states within an
energy interval E and E + dE. Consider a space nx ,n y , n z . Each point with integer values of
the coordinates represents an energy states. Thus ‘n’ represents a vector to a point nx ,ny ,nz
n 2  nx  n y  nz
2 2 2

Number of states in a sphere of radius ‘n’ is

1 4 3
. n
8 3
Only one octant (1/8)th volume of the sphere has positive values of nx ,ny ,nz

Number of states in sphere of radius (n+dn) is

1 4
.  (n  dn)3
8 3
The number of available energy states in an energy interval E and E+dE
1 4 4 
Z ' ( E )dE    (n  dn) 3  n3
8 3 3 
1 4

 .  n 3  3n 2 dn  3ndn 2  dn 3  n 3
8 3

Neglecting higher powers of dn
 Unit – 5 Nanoelectronic devices


1 4
 
Z ' ( E )dE  .  3n 2 dn  n 2 dn      (1)
8 3 2
The energy of a particle
n2h2
E      (2)
8m * L2
m* - effective mass of electron
8m * L2 E
n2       (3)
h2
1
 8m * E  2
n  L      (4)
 h 
2

1
 8m *  2 1  1
dn   2  L E 2 dE      (5)
 h  2
Substituting (3) and (5) in (1)
1
  8m * E  2  8m *  2
1 1
Z ( E )dE    L  2  L E 2 dE
2  h2   h  2
3
  8m *  2 1
Z ( E )dE    L E 2 dE
3

4  h2 
Volume of solid L3=V
3
  8m *  2 1
Z ( E )dE   2  V .E 2 dE    (6)
4 h 
According to Pauli’s exclusion principle, each energy level can accommodate 2 electrons of
opposite spin. Number of states available for electron occupation
3
  8m *  2 1
Z ( E )dE  2    V .E 2 dE
4  h2 
Hence number of states per unit volume is
3
  8m *  2 1
Z ( E )dE   2  E 2 dE
2 h 
The number of states per unit volume per unit energy is
3
  8m *  2 1
Z (E)    E 2
     (7 )
2  h2 
h

Let 2
3
  8m *  2 1
Z (E)   2 2  E 2
2  4  
 Unit – 5 Nanoelectronic devices

3
1  2m *  2 1
Z ( E )  2  2  E 2      (8)
3D

2   
Equation (8) is the density of state in 3 dimension or bulk material.
1
Z ( E )3D  E 2
     (9)

DENSITY OF STATES IN QUANTUM WELL [2 D]

In a two-dimensional structure , there is confinement in one dimension. The particle is free
to move along two dimensions. One dimension is restricted (confined ) and is in nanometre
range. Structure obtained by confining one dimension is the quantum well. Consider a
quantum well of dimensions L , where electrons of mass m* are confined. The two
dimensional density of state is the number of states per unit area per unit energy. Consider an
electron bounded in 2-dimensional space. To find the number of quantum states within an
energy interval E and E + dE. Construct a space of points n x and ny. The space consists of x-y
plane and nx and ny. Coordinates. In 2 dimensional
n 2  nx  n y
2 2

The number of states within a circle of radius ‘n’ is

1 2
n
4

Only one quarter (1/4) th the area has positive values of nx and ny. The number of states
within the circle of radius (n+dn) is

 n  dn 2
1
4
The number of energy states within an energy interval E and E+dE
1

Z ( E )dE   (n  dn) 2  n 2
4

Neglecting higher powers of dn ( i.e dn2 )

Z ( E )dE  2ndn   ndn    (10)
4 2
Substituting (4) and (5) in (10)
 Unit – 5 Nanoelectronic devices

1 1
  8m * E   8m *  2 1  1
2
Z ( E )dE    L 2  L E 2 dE
2  h2   h  2
  8m * 
Z ( E )dE    L dE
2

4  h2 
Let A= L2 area of the circle
  8m * 
Z ( E )dE    A.dE      (11)
4  h2 
According to Pauli’s exclusion principle each energy level can accommodate 2 electrons.
  8m * 
Z ( E )dE  2    A.dE
4  h2 
Number of states per unit area per unit energy
  8m * 
Z (E)   
2  h2 
h

2
  8m * 
Z ( E )dE   
2  4 2  2 
 m* 
Z (E)   2 
  
The density of states in 2 dimension is
m*
Z (E)2D 
 2 for E ≥ E0 ------------(12)
Where E0 – ground state of quantum well
m*
 2 
Z (E)2D   ( E  En )      (13)
n

Where En are the energies of the quantised states and 𝝈 (E-En) is the step function.
Density of states in 2D is constant with respect to energy ,
Z ( E ) 2 D  E D  cons tan t    (14)
DENSITY OF STATES IN QUANTUM WIRE [1D]
In a one dimensional structure there is a confinement in two directions. The carriers can move
in only one dimension. Two dimensions are reduced to nm range. The structure produced is
quantum wire or nano wire. Semiconductor wires surrounded by a material with large band
gap. Consider a quantum wire ( one dimensional wire) in which motion along x-direction only
is allowed. Density of states is defined as the number of available states per unit length per
unit energy. The electron in the wire can move in 1D along the x-plane with co-ordinates nx
n 2  nx
2

The number of available energy states in an interval of length is

Z ( E )dE  n  dn  n  dn
 Unit – 5 Nanoelectronic devices

Substituting in eqn (5)

1
 8m *  2 1  1
Z ( E )dE   2  L E 2 dE
 h  2
According to Pauli’s exclusion principle , each energy level can accommodate 2 electrons of
opposite spin.
Number of states available for electron occupation,
1
 8m *  2 1  1
Z ( E )dE  2 2  L E 2 dE      (15)
 h  2
Number of states per unit length per unit energy
1
 8m *  2 1
Z ( E )dE   2  L.E 2 dE
 h 
1
 8m *  2  1
Z ( E )   2  E 2
 h 
1
 8m *  2  1
Z ( E )   2 2  E 2
 4  
1
(2m*) 2  12
Z ( E )  E      (16)

Density of states in 1 D ( quantum wire)
1
(2m*) 2  12
Z ( E ) 
1D
E      (17)

If the electron has potential energy E 0, then
2m * ( E  E0 ) 1
Z (E) 1D

 E ≥ E0
1 2m *
Z ( E )1D 
 ( E  E0 )
for E ≥ E0 ----(18)
The density of state in one dimensional system has functional dependence on energy
1
Z ( E )1D  E 2

For more than one quantized state, one dimensional density of state is ,
1 2m *
Z ( E )1D  
 n ( E  E0 )
 ( E  En )

Where, En are energies of quantised states (E-En) is the step function.

DENSITY OF STATES IN QUANTUM DOT [ZERO DIMENSION]
 The process of size reduction in which all three dimensions are in nm range is called
quantum dot
 Electrons and holes are confined in all the three dimensions by a surrounding material
with a large band gap.
 Unit – 5 Nanoelectronic devices

 Quantum dots have discrete energy levels

 In zero dimensional system (quantum dot), the electron is confined in all three spatial
dimensions and hence no motion of electron is possible.
 Each quantum state of a zero dimensional system can be occupied by only 2 electrons.
 The density of states for a quantum dot is a delta function.
Z ( E )0 D  2 ( E  E0 )    (20)
 For more than one quantum state , the density of state is
Z ( E ) 0 D   2 ( E  E0 )    (21)
n

RESONANT TUNNELING
When electron (wave) incident with energy equal to energy level of a potential well of
thin barrier, then the tunneling reaches its maximum value. This is known as resonant
tunneling.
The phenomenon in which the tunneling current reaches peak value, when the energy
of incident electron wave is equal to quantized energy state of the quantum well formed by
the double symmetric barriers is known as resonant tunneling. An interesting phenomenon
occurs when two barriers of width a separated by a potential well of small distance L. This
leads to the concept of resonant tunneling. The barriers are sufficiently thin to allow tunneling
and the well region between the two barriers is also sufficiently narrow to form discrete
(quasi-bound) energy levels. The transmission coefficient of the double symmetric barrier
becomes unity. (ie.,T = 1 ), when the energy of the incoming electron wave (𝐸) coincides with
the energy of one of the discrete states formed by the well.

Double barrier junction with no applied bias.

SPINTRONICS
The spin of the electron can be used rather than its charge to create a remarkable new
generation of “SPINTRONICS DEVICES”. NANO TECHNOLOGY deals with spin
dependent properties instead charge dependent properties.
PRINCIPLE
• Every electron exists in one of the two states spin up and spin down with spins either
positive half or negative half.
• The two possible states represent “0” and “1”
• Information stored into spins as a particular spin orientation(up or down)
 Unit – 5 Nanoelectronic devices

SPIN VALVE
A spin valve is a device, consisting of two or more conducting magnetic materials,
whose electrical resistance can change between two values depending on the relative
alignment of the magnetization in the layers. The resistance change is a result of the giant
magneto resistive effect. The magnetic layers of the device align "up" or "down" depending
on an external magnetic field. A spin valve consists of a non-magnetic material sandwiched
between two ferromagnets, one of which is fixed (pinned) by an antiferromagnet which acts
to raise its magnetic coercivity and behaves as a "hard" layer, while the other is free
(unpinned) and behaves as a "soft" layer. Due to the difference in coercivity, the soft layer
changes polarity at lower applied magnetic field strength than the hard one. Upon application
of a magnetic field of appropriate strength, the soft layer switches polarity, producing two
distinct states: a parallel, low-resistance state, and an antiparallel, high-resistance state.

SPIN-FET
In the spin-FET source and drain are ferromagnetism, connected by a narrow semiconductor
channel. The spins of electrons injected into the semiconductor, are set parallel to the
magnetization source. Ferromagnetic contacts contain mostly spin-polarized electrons. The
ferromagnetic source contact injects spin-polarized electrons into the semiconductor region.
Because of the non-zero spin-orbit interaction the electron spin precesses during the
propagation through the channel. At the drain contact only the electrons with spin aligned to
the drain magnetization can easily leave the channel and contribute most to the current. Hence
the net spin polarization is reduced. In order to solve this problem an electric field is applied
perpendicularly to the plane of the film by depositing a gate electrode on the top to reduce the
spin orbit coupling effect.
• Vg = 0 injected spins which are transmitted through the 2DEG (2 Dimensional
electron Gas) the layer starts precessing before they reach the collector, thereby
reducing the net spin polarization.
• When Vg>>0 the path of the electron is controlled with electrical field there by spins
to reach at the collector. Hence the current in the collector can be modulated.
 Unit – 5 Nanoelectronic devices

SINGLE ELECTRON PHENOMENON

Transistor operations, such as amplifiers, switches, electrometers, oscillators are
operated using single electron or Quantum dot, this is known as single electron phenomena.
To get this single electron phenomena the following conditions are
followed:
 Single electron or Quantum dot should be kept isolated.
 No addition of electron or deletion of electron to quantum dot.
 There should be no tunnelling.
These conditions can be achieved by coulomb blockade effect.
Coulomb blockade effect
The prohibition (or) suppression of tunneling is called Coulomb blockade effect. We know
that Coulomb force are electrostatic, so when two charges are near one another they exert Coulomb
forces upon each other. If two charges are same the force is repulsive. In quantum dot, the charges
are all negative electrons trying to bring them forcefully together create Coulomb force, so it repels.
This is coulomb blockade effect, it presents tunneling to and form a quantum dot. This effect is
measured as

ε – permittivity,
d - diameter of the dot,
G - geometrical form, (for disk like quantum dot G=4, for spherical G=2π).
Therefore the energy required to add negatively charged electron to the dot is known as the charging
energy

Inference:
From equation (2) we can see that EC is inversely proportional to the dot’s capacitance. In that
case a large capacitor can quite easily accommodate another electron without too much energy is
required.
The coulomb blockade can prevent unwanted tunneling, when the charging energy is much
higher than the thermal energy of an electron. Due to thermal vibrations of the atoms in the
lattice, these free electrons will get extra energy to go to higher bands. The extra energy is equal to
KBT. With this extra energy, an excited electron might be able to tunnel through a small barrier.
 Unit – 5 Nanoelectronic devices

Condition for coulomb blockade

The condition of the coulomb blockade is

Rules for single electron phenomena to occur

There are two rules for preventing electrons from tunneling back and forth from quantum dot.
Rule 1: The coulomb blockade
Rule 2: Overcoming uncertainty
Rule 1: The coulomb blockade
We know that the coulomb blockade can prevent unwanted tunneling. Hence we can keep the
quantum dots isolated.

Rule 2: Overcoming uncertainty

To keep electrons from tunneling freely back and forth to and from the dot. To ensure this, the
uncertainty of the charging energy must be less than the charging energy itself.

Working
The purpose of the SET is to individually control the tunneling of electrons into and out of the quantum
dot.
 To do this we must first stop random tunneling by choosing the right circuit and materials. To
control tunneling we apply a voltage bias to the gate electrode.
 There is also a voltage difference between the source and drain that dictates the direction for the
current. The working is similar to the working of FET, where the gate voltage creates an electric
field that alters the conductivity of the semiconducting channel below it, enabling current to flow
from source to drain.
 By applying a voltage to the gate in an SET creates an electric field and change the potential energy
of the dot with respect to the source and drain. This gate voltage controlled potential difference can
make electrons in the source attracted to the dot and simultaneously electrons in the dot attracted to
the drain.
 For current flow, the potential difference must be large enough to overcome the energy of the
coulomb blockade.
The energy E needed to move a charge, Q across a potential difference, V is given by

E = VQ
Where, Q is the charge of the electron
Hence we get the energy needed equal to the energy of the coulomb blockade E=Ec. Voltage that will
move the electron onto or off the dot is

V= =
within this voltage the electron can tunnel
Working
The SET in “OFF” mode. The corresponding potential energy diagram shows that it is not energetically
favorable for electrons in the source to tunnel to the dot.
Fig (a). The SET in “ON” mode. At the lowest setting, electrons tunnel one at a time, via dot, from
source to drain.
Fig (b). This is made possible by first applying the proper gate voltage, V gate = e/2Cdot . So that the
potential energy of the dot is made low enough to encourage an electron to tunnel through the Coulomb
blockade energy barrier to the quantum dot.
 Unit – 5 Nanoelectronic devices

Fig (c). Shows, once the electron is on it, the dots potential energy rises, the electron then tunnels
through the Coulomb blockade on the other side to reach the lower potential energy at the drain.
Fig (d). With the dot empty and the potential lower again, the process repeat. Fig (e)

ADVANTGES
• No wire is needed between arrays.
• Size of each cell can be small as 2.5nm.
• Can be used for quantum computer.
• Suitable for high density memory.
Limitations
• In order to operate the SET circuit at room temperature the size of the quantum dot should be
smaller then 10nm
• It is very hard to prepare by traditional optical lithography and semiconductor process.
Hint: lithography- printing on a smooth surface.
USES
• Mass Data storage
• Sensor Technology
• Digital electronic circuits
• AND and NOR gates
• SET can be used as temperature probe at very low temperature
 Unit – 5 Nanoelectronic devices

CARBON NANOTUBES (CNT)

Definition
Carbon nanotubes (CNTs) are molecular – scale tubes of graphitic carbon with outstanding
properties. They are among the stiffest and strongest fibres researched till date, with
remarkable electronics properties and applications. The hexagonal lattice of carbon is
graphite. A single layer of graphite is called graphene.

Types of CNTs:
1) Based on rolling a graphite sheet - Arm Chair , Zig Zag and Chiral
2) Based on number of layers - Single walled Nanotubes (SWNTs and Multi walled nanotubes
(MWNTs)
Based on rolling a graphite sheet:

 Arm Chair Structure: When the axis of the tube is parallel to C-C bonds of carbon hexagons, it
is referred as “armchair” structure.
 Zig – zag structure: The axis of the tube will be perpendicular to C-C bonds.
 Chiral structure: The C-C bond is inclined towards the axis of the tube.
Based on number of layers:
 SINGLE WALLED NANOTUBES (SWNTs): SWNT consists of a single graphene cylinders.
 MULTI WALLED NANOTUBES (MWNTs): MWNT comprises of several concentric
graphene cylinders.

SYNTHESIS OF NANOMATERIALS

(i) Top down process

In this process the bulk materials are broken into nano-sized particles.
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 Unit – 5 Nanoelectronic devices

Ex: Mechanical alloying or Ball milling

(ii) Bottom – up process

In this process nano-materials produced by building of atom by an atom
Ex: Chemical Vapour Deposition (CVD)

Chemical Vapour Deposition Method

The deposition of nano films from gaseous phase by chemical reaction on high temperature is known as
chemical vapour deposition. This method is used to prepare nano-materials.
Principle:
In this technique initially the material is heated to gaseous state and then it is deposited on a solid
surface under vaccum condition to form nano powder by chemical reaction with the substrate.
Description and Working:
CVD involves the flow of a gas with diffused reactants over a hot substrate surfaces. The gas that
carries the reactants is called the carrier gas. While the gas flows over the hot solid surface the heat
energy increases chemical reactions of the reactants that form a film during and after the reactions. The
byproduct of the chemical reactions are removed. The thin film of desired composition can thus be
formed over the surface of the substrate.

Advantages:
(i). The CVD method is used to produce defect free nano-particles.
(ii). Due to the simplicity of the experiment the scaling up of the unit for mass production and in
industry is achieved without any major difficulties.

12
 Unit – 5 Nanoelectronic devices

Properties
1. Electrical Properties
 CNTs are metallic or semiconducting depending on the diameter and chirality.
 The energy gap of semiconducting chiral CNTs is inversely proportional to the diameter of the
tube.
 The energy gap also varies along the tube axis and reaches minimum value at the tube ends.
This is due to the presence of defects at the ends due to extra energy states.
2. Mechanical Properties
 The strength of the carbon-carbon bond is very high therefore any structure based on aligned
carbon-carbon bonds will ultimately have high strength.
 Young’s modulus of CNT is about 1.8 TPa. Nanotubes have high tensile strength.
 CNTs can withstand extreme strain
 CNTs can recover from severe structural distortions.
3. Physical Properties
 Nanotubes have a high strength to weight ratio.
 The surface area of nanotubes is of the order of 10-20 m2/g which is higher than that of
graphite.
4. Chemical Properties
 Nanotubes are highly resistant to any chemical reaction.
 It is difficult to oxidize them and the onset of oxidation in nanotubes is 100 degree Celsius
higher than of carbon fibres.
5. Thermal Properties
 Nanotubes have a high thermal conductivity and the value increases with decrease in diameter.
Applications

1. The carbon nanotubes are very light in weight, but they are very strong, hence they
are used in aerospace.
2. They are used in constructing nanoscale electronic devices.
3. CNTs are used in battery electrodes, fuel cells, reinforcing fibres etc.
4. CNTs are used in the development of flat panel displays for computer monitors and
televisions.
5. Semiconducting CNTs are used as switching devices.
6. Semiconducting CNTs are also used as chemical sensors to detect various gases.
7. Light weight CNTs are also used in military and communication system, for protecting
computers and electronic devices.
8. Plastic composite CNTs are used as a light weight shielding materials for protecting
electromagnetic radiation.
9. Nano-tubes can also serve as catalysts for some chemical reactions.
10. The unique properties of CNTs will undoubtedly lead to many more applications in future to
produce nano computers plastic computers etc.,

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