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 PHYSICS FOR COMPUTER
SCIENCE AND INFORMATION
TECHNOLOGY
21PH101

UNIT V

NANO DEVICES AND INTRODUCTION

TO QUANTUM COMPUTING

Department: FIRST SEMESTER – CSE, IT

Batch/Year : 2021-2022 / I

Created by : DEPARTMENT OF PHYSICS, RMDEC

Date : 10-01-2022
 TABLE OF CONTENTS

S. No. CONTENTS PAGE

1 Course Objectives 7

2 Syllabus 8

3 Course Outcomes 9

4 CO - PO/PSO Mapping 10

5 Lecture Plan 11

6 Activity Based Learning 12

Lecture Notes: Unit – V Nano Devices and Introduction to

Quantum Computing
5.1 Introduction to Nanomaterials 13

5.2 Electron Density in Bulk Materials 14

5.3 Size Dependence of Fermi Energy 15

5.4 Quantum Confinement 17

5.5 Quantum Structures 19

7
5.6 Density of States in Quantum Well 20

5.7 Density of States in Quantum Wire 22

5.8 Density of States in Quantum Dot 24

5.9 Bandgap of Nanomaterials 25

5.10 Tunneling 26

5.11 Quantum Dot Laser 30

5.12 Quantum Computing: Introduction 33

S. No. CONTENTS PAGE

5.13 Differences between Quantum and Classical Computati 35

ons

7 Solved Problems 38

Video Links 39

Quiz 40

8 Assignment 41

9 Part A – Questions with Answers 42

10 Part B – Questions 45

11 Supportive Online Certification Courses 46

12 Real Time Applications in Day to Day Life and to Industry 47

13 Content Beyond the Syllabus 49

14 Prescribed Textbooks and Reference Books 50

15 Mini Project Suggestions 51

 COURSE OBJECTIVES

1. To learn the fundamental concepts of physics and apply this

knowledge to scientific, engineering and technological
problems.

2. To make the students enrich their basic knowledge in

electronics and quantum concepts and apply the same in
computing fields.
 PREREQUISITES

1. Awareness of basic concepts of physics at higher secondary

school level.
2. Fundamental knowledge in mathematics on topics like
calculus (differentiation, integration), trigonometry and
geometry.
3. Trusting your intuition by applying basic common sense
4. Conceptual learning
5. Passion for understanding how things work, enjoy playing
with ideas
 SYLLABUS
COURSE CODE PHYSICS FOR COMPUTER SCIENCE AND L T P C
INFORMATION TECHNOLOGY
21PH101 (Common to CSE & IT) 3 0 0 3

UNIT I LASER AND FIBRE OPTICS 9

     
Population of energy levels – Einstein’s A and B coefficients derivation - Resonant
cavity - Optical amplification (qualitative) - Semiconductor lasers: homojunction and
heterojunction - Engineering applications of lasers in data storage (qualitative).
Fibre optics: Principle, numerical aperture and acceptance angle -V-number - Types
of optical fibres (Material, refractive index and mode) - Losses in optical fibre - Fibre
optic communication - Fibre optic sensors (pressure and displacement).
 
UNIT II MAGNETIC PROPERTIES OF MATERIALS 9
     
Magnetic dipole moment - atomic magnetic moments - Origin of magnetic moments-
Magnetic permeability and susceptibility - Magnetic material classifications-
Diamagnetism – Paramagnetism - Ferromagnetism –Antiferromagnetism -
Ferrimagnetism - Ferromagnetism: Domain Theory- M versus H behaviour - Hard and
soft magnetic materials - Examples and uses - Magnetic principle in computer data
storage - Magnetic hard disc (GMR sensor) - Introduction to Spintronics.
 
UNIT III ELECTRICAL PROPERTIES OF MATERIALS 9
     
Classical free electron theory - Expression for electrical conductivity – Thermal
conductivity expression - Wiedemann-Franz law - Success and failures of CFT -
Particle in a three dimensional box - Degenerate states - Effect of temperature on
Fermi function - Density of energy states and average energy of electron at 0 K -
Energy bands in solids.
UNIT IV SEMICONDUCTOR PHYSICS 9
     
Intrinsic Semiconductors – Energy band diagram - Direct and indirect band gap
semiconductors - Carrier concentration in intrinsic semiconductors- Band gap
determination-Extrinsic semiconductors - n-type and p-type semiconductors
(qualitative) - Variation of Fermi level with temperature and impurity concentration -
Hall effect and its applications.
 
UNIT V  INTRODUCTION TO NANO DEVICES AND QUANTUM 9
COMPUTING
     
Introduction to nanomaterial -Electron density in bulk material - Size dependence of
Fermi energy - Quantum confinement - Quantum structures - Density of states in
quantum well, quantum wire and quantum dot structure - Band gap of nanomaterial-
Tunneling: single electron phenomena and single electron transistor - Quantum dot
laser. Quantum computing: Introduction - Differences between quantum and classical
computation.
 
TOTAL: 45 PERIODS
 COURSE OUTCOMES

On completion of this course, the students will gain knowledge and will be able to

CO1: Know the principle, construction and working of lasers and their
applications in fibre optic communication.

C02: Understand the magnetic properties of materials and their specific

applications in computer data storage.

C03: Analyze the classical and quantum electron theories and energy band
structures.

C04: Evaluate the conducting properties of semiconductors its applications in

various devices.

C05: Comprehend the knowledge on quantum confinement effects.

C06: Apply optical, magnetic, conducting properties of material, quantum

concepts at the nanoscale in various applications.
 CO – PO/PSO MAPPING

PO PO PO PO PO PO PO PO PO PO PO PO
COs
1 2 3 4 5 6 7 8 9 10 11 12

CO1 3 2 3 2 - - - - - - - -

CO2 3 2 3 2 - - - - - - - -

CO3 3 2 3 2 - - - - - - - -

CO4 3 2 3 2 - - - - - - - -

CO5 3 2 3 2 - - - - - - - -

CO6 3 2 3 2 - - - - - - - -
 LECTURE PLAN

No. Mode
Actual Taxono
S.N Topics to be of Pertaini Propos of
Lecture my
o. Covered Perio ng CO ed Date Deliver
Date Level
ds y
PPT,
Introduction to
1 1 CO5 K1 Chalk &
nanomaterials
Talk
Electron density in
PPT,
bulk materials
2 1 CO5 K2 Chalk &
Size dependence of
Talk
Fermi energy
Quantum
confinement and PPT,
3 quantum structures 1 CO5 K2 Chalk &
Density of states in Talk
quantum well
Density of states in PPT,
4 quantum wire and 1 CO5 K2 Chalk &
quantum dot Talk
Bandgap of PPT,
5 nanomaterial 1 CO5 K1 Chalk &
Tunneling Talk
Single electron
PPT,
phenomenon and
6 1 CO6 K1, K2 Chalk &
single electron
Talk
transistor
PPT,
7 Quantum dot laser 1 CO6 K2 Chalk &
Talk
Introduction to PPT,
8 quantum 1 CO6 K1 Chalk &
computing Talk
Differences
PPT,
between classical
9 1 CO6 K2 Chalk &
and quantum
Talk
computations
 ACTIVITY
Is measuring an art or a science?
The purpose of this activity is to help students understand the concepts of accuracy
and precision and how they are important in measurements at the nano-scale.
https://nnin.org/sites/default/files/files/Measure_art_science_TG.pdf
https://nnin.org/sites/default/files/files/Measure_art_science_SG.pdf

Nanoparticles: Land to Ocean

Part 1
Pollution, both macroscopic and microscopic, is an important environmental issue for
aquatic ecosystems. For this lab, students will model how nanoparticle pollution
travels from land to water. This activity is designed to help students understand the
effect that nanoscale pollutants have on aquatic ecosystems.
https://nnin.org/sites/default/files/files/Part1_Runoff_Lab_TG.pdf
https://nnin.org/sites/default/files/files/Part1_Runoff_Lab_SGAnswers.pdf
Part 2
Students will test the effects of silver nanoparticles on aquatic organisms and discuss
the effects on a global scale.
https://nnin.org/sites/default/files/files/Part2_Colloidal_Silver_Lab_TG.pdf
https://nnin.org/sites/default/files/files/Part2_Colloidal_Silver_Lab_SGAnswers.pdf

Small Scale Sculpting

This activity is analogous with some nanofabrication processes. This lab will help
students understand some of the challenges encountered while making
semiconductor chips and waveguides, both of which are found in electronic circuits.
https://nnin.org/sites/default/files/files/Garza_Part2_Etch_Chalk_Lab_TPG_0.pdf
https://nnin.org/sites/default/files/files/Garza_Part2_Etch_Chalk_Lab_SW_GuiInq_0.
pdf
5.1 INTRODUCTION TO NANOMATERIAL
Nanomaterials are structures that possess at least one external dimension measuring
1–100 nm. The dramatic changes in properties of nanomaterials when the size is
reduced from macro to nano scale is called size effects. By changing the size of
nanomaterials, it is possible to tune their properties. They have reduced
imperfections when compared to the bulk structures. Nanoscale materials have far
larger surface areas than similar masses of larger-scale materials. As surface area
per mass of a material increases, a greater amount of the material can come into
contact with surrounding materials. As the size of the particle is lesser then de-
Brogile wavelength, the electron and hole get confined, which leads to quantum
confinement effects. These factors can in turn enhance their chemical and physical
properties such as surface energy, reactivity, strength, optical, magnetic, electrical,
mechanical and ionic characteristics. They can occur naturally (e.g., volcanic ash,
soot from forest fires), be created as the by-products of combustion reactions (e.g.,
welding, diesel engines), or be produced purposefully with specific with physico-
chemical properties to perform a specialised function.

5.1.1 NANOELECTRONIC DEVICES

The term nanoelectronics refer to the use of nanotechnology in electronic

components. These components are often only a few nanometers in size.
Nanoelectronics is concerned with nanometre scale electronic devices, circuits,
communication and sensor systems.

Nanoelectronics covers a diverse set of devices and materials, with the common
characteristic that they are so small that physical effects alter the materials'
properties on a nanoscale – inter-atomic interactions and quantum mechanical
properties play a significant role in the workings of these devices. At the nanoscale,
new phenomena take preference over those that hold influence in the macro-world.
Quantum effects such as tunneling and atomistic disorder dominate the
characteristics of these nanoscale devices.
5.2 ELECTRON DENSITY IN BULK MATERIAL
The bulk material is a collection of atoms having properties that are from individual
atoms. The material which is having grain size of 1-100 nm is called nanomaterial
that can exhibit unique, optical, mechanical, magnetic, conductive and absorptive
properties different from that of bulk materials. It is to be noted that the
nanomaterial differ from bulk materials in the number of available energy states. In
a bulk material, the states within each energy sublevel are so close that they
combine into band.

The total number of electron states, , with energies upto , can be determined based
on quantum mechanics using the following equation

[ ]
3
π 8 𝑚 2 3 /2
𝑁 = 𝐸 𝑉
3 h
2
…(5.1)

where is the mass of the electron

is the volume of the solid
is the Planck’s constant

The number of energy states per unit volume is expressed as

[ ]
3/ 2
𝑁 π 8 𝑚
𝑛= = 𝐸3 /2
𝑉 3 h
2 …(5.2)

Differentiating above equation with respect to E, we get density of states

Density of states is the number of energy states per unit volume per unit energy

…(5.3)
𝑑𝑛
𝑍 ( 𝐸 ) =
𝑑𝐸

[ ]
3/ 2 …(5.4)
π 8 𝑚 1/ 2
𝑍 ( 𝐸)= 𝐸
2 h2
The above eqn. (5.4) represents that (i.e., Density of states for a bulk material is
directly proportional to the square root of energy)
𝑛e  =∫ 𝑍 ( 𝐸 ) 𝑑𝐸 𝐹 ( 𝐸 )
Let be the number of electrons per unit volume,

…(5.5)

[ ]
Substitute value in the above equation 3 / 2
π 8𝑚
𝑛𝑒 =∫ 𝐸 1/ 2 𝑑𝐸 𝐹 ( 𝐸 )
2 h
2 …(5.6)

The effect of temperature on Fermi function can be given by the following equation
1
𝐹 ( 𝐸 )= …(5.7)
1+ exp
( 𝐸 − 𝐸F
𝑘𝐵 T
We know that, Femi energy level is the maximum energy that can be occupied by
)
electrons at 0 K.

At 0 K, if E< F (E) =1

[ ]
3 𝐸𝐹 1
𝜋 8𝑚
0

𝑛𝑒 =
2 h
2
2
∫ 𝐸 2 …(5.8)
𝑑𝐸
0

[ ]
𝜋 8𝑚
3
2
𝐸 3/
𝐹
2
…(5.9)
𝑛𝑒 = 0

2 h
2
3/2
In a conductor at T=0 K, the electron density is given by the number of free
electrons,

[ ]
3
𝜋 8 𝑚 2 …(5.10)
𝑛𝑒 = 𝐸3
𝐹
/2
3 h
2 0

5.3 SIZE DEPENDENCE OF FERMI ENERGY

Considering distribution of energy, solids have thick energy bands, whereas atoms
have thin, discrete energy states.

Free electron concentration of a conductor is given by

[ ]
𝜋 8 𝑚
3 …(5.11)
2 3 /2
𝑛𝑒 = 𝐸 𝐹0
3 h
2
From the above equation,

[ ]
2 3
3 / 2 3 𝑛𝑒 h 2
𝐸 𝐹0 =
𝜋 8 𝑚 …(5.12)

Fermi energy at 0 K

[ ]
2
3 3 h2 2 / 3
𝐸 𝐹0 = 𝑛𝑒
𝜋 8 𝑚 …(5.13)

Here,

[ ]
2
3 3 h2
=constant
𝜋 8 𝑚 …(5.14)

Then, eqn. (5.13) becomes

𝐸 𝐹0 ∝ 𝑛2
𝑒
/ 3
…(5.15)

Electron density ( is the total number of free electrons ( per unit volume
N e
n e = …(5.16)
V
Equation (5.15) becomes,

𝐸 𝐹0 ∝ 𝑛𝑒
2/ 3
∝ ( 𝑁 𝑒
𝑉 …(5.17) )
Equation (5.17) approximately becomes

𝐸 𝐹0 ∝ ( 𝑁 𝑒
𝑉 )
…(5.18)

does not vary with the size of the material,

for silver particle = a brick of silver

Hence, we can say that the energy states will have the same energy for small
volume and large volume of atoms. But for small volume of atoms we get larger
spacing between states. This is not only for conductors, but also for semiconductors
and insulators too.

Let us consider that the energy states upto are occupied by free electrons (N).

The average spacing between energy states is given by

𝐸 𝐹
∆ 𝐸 ≈ …(5.19)
0

𝑁 𝑒
 Fig. 5.1 Size dependence of Fermi energy

Comparing equations (5.18) and (5.19)

1 …(5.20)
∆ 𝐸 ∝
𝑉
Thus, the spacing between states is inversely proportional in the volume of the solid.

If particle size is reduced in nano order, energy states become discrete and
separation between states increases when particle size decreases.

The energy sublevel and the spacing between energy states within it will depend on
the number of atoms as shown in Fig. 5.1.

5.4 QUANTUM CONFINEMENT

The quantum confinement effect is observed when the size of the particle is too
small to be comparable to the wavelength of the electron. To understand this effect
we break the words like quantum and confinement, the word confinement means to
confine the motion of randomly moving electron to restrict its motion in specific
energy levels (discreteness) and quantum reflects the atomic dimension of particles.
So as the size of a particle decrease till we reach a nanoscale the decrease in
confining dimension makes the energy levels discrete and this increases or widens
up the band gap and ultimately the band gap energy also increases.
 Fig. 5.2 Quantum confinement

Electrons are confined if the size of material of the order of the de-Broglie
wavelength. To confine an electron of wavelength,, a material should have a
characteristic dimension at least half of its wavelength
𝜆 h
𝐷= =
2 2 𝑚𝑣
SIZE EFFECTS BAND GAP OF QUANTUM DOT

QD exhibit unique electronic properties intermediate between semiconductor and

discrete molecule. Eg., Fluorescence, Nano crystal produce varying colours
depending on the size of particles.

The above diagram shows as the size of the crystal decreases the bandgap
increases.

The more energy needed to excite dot. Also more energy is released when returning
to ground state. Therefore there is shift from red to blue in emitted light. Thus same
material can emit any colour by changing quantum dot size. The emitted wavelength
depends on the size of the quantum dot.

There are three types of quantum confinements, are

(i) Quantum well in which one-dimension is in nanoscale to create quantum

confinement, eg., thin film. It is also called two dimensional nanomaterial.

(ii) Quantum wires in which two-dimensions are in nanoscale to create quantum

confinement and one-dimension is free. It is also called one dimensional
nanomaterial. Examples nanorods and nanotubes.
 Fig. 5.3 Quantum Confinement 0D, 1D, 2D, 3D

(i) Quantum dot is one in which all three-dimensions are in nanoscale to create
quantum confinement. It is also called zero dimensional nanomaterial. Metal
particles with size 1-10 nm diameters behave like quantum dots.

5.5 QUANTUM STRUCTURES

 Quantum structured material (also referred as nanostructure) are the materials
which are having size (one or more dimensions) smaller than 100 nm.
 When one-dimension is reduced below the constrain limit, electrons can move
freely in other two-dimensions. This kind of structure is known as quantum well.
 When two-dimensions are reduced below the quantum structure limit, electron
can move freely in only one-dimension. Such materials are called quantum wires,
e.g., nanotubes and nanowires.

Fig. 5.4 Quantum structures

 When all three-dimensions of material are minimized below the constrain limits,
electrons are confined in all three-dimensions. This kind of material is called
quantum dot.
 In quantum wells and quantum wires there is at least one-dimension in which the
electrons are free to move. Hence they are called partial confinement structures.
 Quantum dots exhibit total confinement; they are called complete confinement
structures.
 They are used for high-density data storage, chemical sensing, optics,
telecommunications, and quantum computing.

5.6 DENSITY OF STATES IN QUANTUM WELL

Density of state of quantum well is defined as the number of available states per
unit area per unit energy interval.

Energy of electron in a quantum well of sides with quantum state,

…(5.21)
𝑛2 h 2
𝐸 = ∗ 2
8
where where and are the quantum 𝑚
numbers. 𝐿

Rearranging the above eqn. (5.21) we get,

…(5.22)
2 8 𝑚 ∗ 𝐿2
𝑛 = 2
𝐸
h

Fig. 5.5 Quantum well

Differentiating the eqn. (5.22) we get
8 𝑚∗ 𝐿 2
2 𝑛𝑑𝑛= 2
𝑑𝐸
…(5.23)
h
Number of available energy levels between and in the circle is equal to the area of
one quadrant circle between the radius and.
1 1
𝑁 ( 𝐸 ) 𝑑𝐸=
4
( 𝜋 ( 𝑛+ 𝑑𝑛 ) − 𝜋 𝑛 )= 𝜋 (𝑛 + 𝑑𝑛 +2 𝑛𝑑𝑛−
2 2
4
2 2
𝑛
2
…(5.24))

Neglecting eqn. (5.24) becomes

𝜋
𝑁 ( 𝐸 ) 𝑑𝐸 = ( 2 𝑛𝑑𝑛 )
…(5.25)
4
Substituting eqn. (5.23) in the above eqn. (5.25), we get

( )
∗ 2
𝜋 8𝑚 𝐿
𝑁 ( 𝐸 ) 𝑑𝐸 = 𝑑𝐸
…(5.26)
4 h
2

According to Pauli’s exclusion principle, number of energy state is given by

′ 𝜋 8 𝑚∗ 𝐿 2 4 𝜋 𝑚∗ 𝐿 2
𝑁 ( 𝐸 ) 𝑑𝐸=2 × × 𝑑𝐸= 𝑑𝐸
…(5.27)
4 h
2
h
2

Density of energy states is the number of energy state per unit area .
𝑤𝑒𝑙𝑙 𝑁 ′ ( 𝐸 ) 𝑑𝐸
𝐷𝑠 𝑑𝐸 = …(5.28)
𝐿2
𝑤𝑒𝑙𝑙 4 𝜋 𝑚∗
𝐷𝑠 𝑑𝐸 = 𝑑𝐸
…(5.29)
h2
On substituting` , eqn. (5.29) becomes
𝑤𝑒𝑙𝑙 𝑚∗
𝐷𝑠 = 2
for 𝐸 ≥ 𝐸
…(5.30)
𝑜
𝜋 ℏ
where is the ground state energy of the quantum well system.
∗
𝑚
𝐷 𝑠
𝑤𝑒𝑙𝑙
=
𝜋 ℏ 2 ∑ 𝜎( 𝐸−𝐸 𝑛)
…(5.31)
𝑛
The bottom of the conduction band set as the origin of energy . If energy is higher
than , more than one sub-band should be there, with at least two values and .
 Fig. 5.6 Density of states in quantum well
On substituting` , eqn. (5.29) becomes

𝑤𝑒𝑙𝑙 𝑚∗
𝐷𝑠 = 2
for 𝐸 ≥ 𝐸
…(5.30)
𝑜
𝜋 ℏ
where is the ground state energy of the quantum well system.
∗
𝑚
𝐷 𝑠
𝑤𝑒𝑙𝑙
=
𝜋 ℏ
2 ∑ 𝜎( 𝐸−𝐸 …(5.31)
𝑛 )
𝑛
The bottom of the conduction band set as the origin of energy . If energy is higher
than , more than one sub-band should be there, with at least two values and .

Thus the density of states of quantum well increases by a factor each time the
energy become higher than the bottom of a new sub-band (, , , ...). So that it exhibit
a stair-case like shape as shown in Fig. 5.6.

5.7 DENSITY OF STATES IN QUANTUM WIRE

Consider the one dimensional system, the quantum wire, in which only one direction
of motion is allowed. e.g along x-direction.

Density of state of quantum wire is defined as the number of available states per
unit length per unit energy interval.

…(5.32)
𝑤𝑖𝑟𝑒 2 × 𝑑𝑛
𝐷 𝑠 =
𝐿
 Fig. 5.7 Density of states in quantum wire
Energy of electron

𝑛2 h 2 …(5.33)
𝐸 = ∗ 2
8 𝑚 𝐿

( )
∗ 2 1/ 2
8 𝑚 𝐿 …(5.34)
1/ 2
𝑛= 2
𝐸
h

( ) ( )
∗ 1 /2 ∗ 1 /2
𝐿 8𝑚 − 1 /2 𝐿 8𝑚 …(5.35)
𝑑𝑛= 𝐸 𝑑𝐸 = 𝑑𝐸
2 h2 2 𝐸 h2
Equation (5.32) becomes

( )
∗ 1/2
8𝑚
𝐷
𝑤𝑖𝑟𝑒
𝑠 = 𝐸
− 1/ 2
( h= 2 𝜋…(5.36)
ℏ)
h2

( )
1/ 2
𝑤𝑖𝑟𝑒 8 𝑚∗ −…(5.37)
1 /2
𝐷 𝑠 = 𝐸
( 2 𝜋 ℏ )2

𝑤𝑖𝑟𝑒 ( 2 𝑚∗ )1 / 2 …(5.38)
𝐷 𝑠 = 𝐸− 1 /2
𝜋 ℏ

𝐷𝑠 𝑤𝑖𝑟𝑒
=
1 √ 2 𝑚…(5.39)
∗

𝜋 ℏ √¿ ¿ ¿
By taking as the ground state energy,

𝐷𝑠 𝑤𝑖𝑟𝑒
=
1
𝜋 ℏ √ 2 𝑚∗
𝐸 − 𝐸0
…(5.40)
for 𝐸 ≥ 𝐸 𝑜
5.8 DENSITY OF STATES IN QUANTUM DOT
In quantum dot, electrons are confined in all the three-dimensions. So there is only
one level is possible with 2 states; corresponding to up spin and down spin.

Therefore, density of states for quantum dot is given by

𝐷𝑠
𝑑𝑜𝑡
=2 √(𝐸 0 )
− 𝐸…(5.41)

=∑ 2 𝛿 √( 𝐸 − 𝐸
𝑑𝑜𝑡
𝐷𝑠 0 )
…(5.42)
𝑛
The energies are discrete bunches of varying densities. So they appear as dots in the
graph.

Fig. 5.8 Density of states in Quantum dot

Fig. 5.9 Density of states in Bulk, Quantum well, Quantum wire and
Quantum dot
Applications:
1. It is used in quantum dot laser, quantum dot memory device, quantum dot
photo- detector and quantum cryptography.
2. It is also used in LED display, amplifier, biological sensor, tumor targeting and
diagnostics.
3. New generation semiconductor laser consists of several million nano-sized
crystals called quantum dots in the active region and act as light emitters.

5.9 BANDGAP OF NANOMATERIALS

Fig. 5.10 Bandgap of nanomaterials

The bandgap gets bigger as the material gets smaller. Once the volume is reduced
from that of a solid, which has bands for sublevels, to that of a nanomaterial, which
has distinct splits in each sub level, the band gap will widen even if only a few atoms
are removed. This allows us to tune the electronic and optical characteristics of a
nanomaterial.
As soon as an electron is excited across the bandgap into the conduction band, it
hardly stays there for a long. It releases its energy in the form of a photon as it
drops back to the valence band. The energy of this photon is equal to the energy of
the electron loses its transition which is equal to the band gap energy.
Thus, if we change a material’s bandgap energy, we change the electromagnetic
radiation it emits. This phenomenon is especially used in optical applications.

5.10 TUNNELING
It is a quantum mechanical effect in which particles have a finite probability of
crossing an energy barrier, such as the energy needed to break a bond with another
particle, even though the particle's energy is less than the energy barrier.

Consider a particle with energy E in the inner region of a one-dimensional potential

well V(x). A potential well is a potential that has a lower value in a certain region of
space than in the neighbouring regions.

In classical mechanics, if E < V (the maximum height of the potential barrier), the
particle remains in the well forever; if E > V, the particle escapes.

In quantum mechanics, the situation is not so simple. The particle can escape even
if its energy E is below the height of the barrier V, although the probability of escape
is small unless E is close to V. In that case, the particle may tunnel through the
potential barrier and emerge with the same energy E.

5.10.1 SINGLE ELECTRON PHENOMENON

Single electron phenomenon is based on the tunneling of one electron at a time in

semiconductor quantum structures. The condition for the single electron
phenomenon to occur is to isolate a quantum dot.

Fig. 5.11 Quantum tunneling

There are two rules to ensure the isolation of quantum dots for the single electron
phenomenon to occur. They are:

Rule 1: The Coulomb blockade

Rule 2: Overcoming quantum uncertainty

RULE 1: THE COULOMB BLOCKADE

Coulomb blockade prevents unwanted tunneling and thereby ensures the isolation of
quantum dot.
𝑒2
𝐸𝐶 = ≫ 𝑘𝐵 𝑇
…(5.43)
2 𝐶 𝑑𝑜𝑡

RULE 2: OVERCOMING QUANTUM UNCERTAINTY

According to energy-time uncertainty principle,
h
Δ 𝐸𝐶 Δt > …(5.44)
2
where is the uncertainty in the energy stored in the capacitor, is the charging time
of the capacitor and is the Planck’s constant.

Since the quantum dot is a tiny capacitor of capacitance , the charging time of the
capacitor is nothing but just the time constant.
Δt = 𝑅𝑡 𝐶 𝑑𝑜𝑡
…(5.45)
where is the tunneling resistance which is in series with the .

Now, allowing for maximum uncertainty in the energy stored on the capacitor, we
get the uncertainty in the energy stored on the capacitor is equal to the energy
stored on the capacitor itself, i.e.,
Δ 𝐸C = 𝐸𝐶
𝑒2
Δ 𝐸C = …(5.46)
2 𝐶 𝑑𝑜𝑡

Now, on substituting Eqn. (5.45) and (5.46) in Eqn. (5.44) we get

𝑒2 h
𝑅 𝑡 𝐶 𝑑𝑜𝑡 >
2 𝐶 𝑑𝑜𝑡 2
After solving, we get the relation for tunneling resistance as
h
𝑅𝑡 > 2
𝑒
Substituting the values of x J s and x C we get
h
2
= 25. 878 k Ω
𝑒
This high resistance is like a thick insulating medium surrounding the quantum dot.
Thus we keep the quantum dot electronically isolated.

Conditions for Isolating the Quantum dots or Preventing Unwanted

Tunneling

The two conditions for isolating the quantum dots and / or preventing the quantum
dots from unwanted tunneling are.
𝑒2
≫ 𝑘𝐵 𝑇
2 𝐶 𝑑𝑜𝑡
h
𝑅𝑡 >
𝑒2
When the above conditions are met, and the voltage across the quantum dot is
scanned, then the current jumps in increments every time the voltage changes by
𝑒
Δ 𝑉 =
𝐶 𝑑𝑜𝑡

5.10.2 SINGLE ELECTRON TRANSISTOR

A transistor made from a quantum dot that controls the current from source to drain
one electron at a time is called single electron transistor (SET).

Difference between Ordinary and Single Electron Transistor

The single electron transistor (SET) is built like a conventional FET. The difference is
that instead of a semiconductor channel between the source and drain electrodes,
there is a quantum dot.
Working of Single Electron Transistor

1. 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. 5.12 (a)].
2. SET in ON mode. At the lowest setting, i.e., electron tunnel one at a time from
the source to the drain via the quantum dot [Fig. 5.12 (b)].

Fig. 5.12 Working of a Single Electron Transistor

3. Once the electron is in the quantum dot, the quantum dot’s potential energy rises
[Fig. 5.12 (c)].

4. Until the electron in the quantum dot leaves, no further electron can tunnel into
the quantum dot.

5. The electron then tunnels through the coulomb blockade on the other side to
reach the drain at the lower potential energy [Fig. 5.12 (d)].

6. With the dot being empty, the potential energy gets lowered again and the
process repeats [Fig. 5.12 (e)].

5.11 QUANTUM DOT LASER

In principle, QD lasers can be treated in a similar way as quantum well (QW)
lasers and the laser structure is fabricated in a similar way, the only difference being
that the optically active medium consists of QDs instead of QWs.

Quantum dots

Rapid growth in semiconductor structure has resulted in reducing three dimension to

two dimension system, one dimension system and finally to zero dimension system.
 It represents ultimate reduction in dimensionality of semiconductor devices.

 It is 3-dimension structure with nanometer scale confining electron and hole.

 It is operated at a level of single electron i.e., ultimate limit of electronic device.

Quantum dots are tiny particles or nano crystals of semiconducting material with
diameter in the range of 2-10 nm (10 to 50 atoms).
 Quantum dot is a nanostructured semiconductor.

 It has a size equal or less than the size of de Broglie wavelength (or mean free
path) of an electron within it .
 We know in nanomaterial, energy levels are discrete.

 Effective energy gap of a quantum dot is greater than the energy gap in bulk
material.
 Energy gap can be modified by modifying the size of quantum dot
 Fig. 5.13 Schematic
illustration of a quantum
dot laser based on self-
assembled dots

Fig. 5.14
Construction of QD
Laser

Construction of QD Laser
Typical Quantum dot laser consists of a nanostructured InGaAs semiconductor
sandwiched between two GaAs semiconductors. The various layers from the bottom
up are n-GaAs, n-GaAlAs, intrinsic – GaAs with InGaAs QDs, p-GaAlAs and p-GaAs.
There are metals contacts on substrate and cap layer connects the device to external
circuit. The QD laser is grown on n-GaAs substrate. The top p-metal has GaAs
contact layer. There are also a pair of 2μm thick Al0.85Ga0.15As cladding and the
cladding surrounds 1900 Å thick Al 0.05Ga0.95As waveguide. Highly reflecting ZnSe /
MgF2 coating for layers to increase stimulated emission for laser action are present.
The waveguide consists of a 300 Å thick GaAs with 12 monolayers of In 0.5Ga0.5As
QDs with density 1.5×10 10 cm-2. Quantum dots can have a pyramidal shape of the
order of 10 nm.
Fig. 5.14 shows a simple laser structure, consisting of an active layer
embedded in a waveguide, surrounded by layers of lower refractive index to ensure
light confinement.
 The active material consists of quantum wells or quantum dots where the
bandgap is lower than that of the waveguide material. The active layer (QD or QW)
is embedded in an optical waveguide (material with refractive index smaller than
that of the active layer). Wavelength of the emitted light is determined by the
energy levels of the QD rather than the band-gap energy of the dot material.
Therefore, the emission wavelength can be tuned by changing the average size of
the dots. Because the band-gap of the QD material is lower than the band gap of the
surrounding medium we ensure carrier confinement. A structure like this, were
carrier confinement is realized separately from the confinement of the optical wave,
is called a separate-confinement heterostructure (SCH).
The waveguide formed between cladding layer pass laser to exit faces. Lasing
faces of waveguide are polished to form laser activity. Under forward biased
condition, it emits laser light.

Working
 The bandgap of InGaAs is 0.76 eV.
 The forward bias voltage enables in the electron and hole injection into intrinsic
GaAs layer (active layer) and into the QDs with small E g i.e. electrons migrate
from an n-type to quantum dots and holes migrate from a p-type to the quantum
dots.
 Electron-hole recombination occurs , followed by lasing action. Stimulated
recombination of electron-hole pairs occurs with laser beam emission.
 The difference in band gap EgGaAs < EgGaAlAs and the refractive index nGaAs > nGaAlAs
enables in light confinement and recombination of electrons and holes in the QDs.
 The motion of electrons and holes is restricted and energy levels are discrete.
 Laser emits photons of wavelength

Advantages
 Wavelength can be modified with extremely small order by modifying the size of
the material
 Ultrahigh temperature stability
 Low threshold current density
 Quantum dot lasers operate over a broad spectrum of wavelengths, from 400 nm
to 1.5 µm.
 QD lasers can be switched on and off using less current, and in less time.
Disadvantage:

 Fabrication process complicated.

 Carrier leakage due to finite barrier height.
 Strained well PN junction photo detector leads to shift in wavelength.

Applications

 It is used in CD/DVD/Blu-ray players and laser printers.

 It is used in high-density optical information storage devices.

5.12 QUANTUM COMPUTING: INTRODUCTION

Classical computers carry out logical operations using the definite position of a
physical state. These are usually binary, meaning its operations are based on one of
two positions. A single state - such as on or off, up or down, 1 or 0 - is called a bit.

In quantum computing, operations instead use the quantum state of an

object to produce what's known as a qubit. These states are the undefined
properties of an object before they've been detected, such as the spin of an electron
or the polarisation of a photon. Rather than having a clear position, unmeasured
quantum states occur in a mixed 'superposition', not unlike a coin spinning through
the air before it lands in your hand. These superpositions can be entangled with
those of other objects, meaning their final outcomes will be mathematically related
even if we don't know yet what they are.

The complex mathematics behind these unsettled states of entangled

'spinning coins' can be plugged into special algorithms to make short work of
problems that would take a classical computer a long time to work out. if they could
ever calculate them at all. Such algorithms would be useful in solving complex
mathematical problems, producing hard-to-break security codes, or predicting
multiple particle interactions in chemical reactions.
5.12.1 MAPPING A QUBIT

An ordinary bit must be either 0 or 1; however, a qubit can be in any

combination of 0 and 1 at the same time. Those two parts of the state mesh in a
way described by an abstract angle, or phase. So the qubit’s state is like a point on a
globe whose latitude reveals how much the qubit is 0 and how much it is 1, and
whose longitude indicates the phase. Noise can jostle the qubit in two basic ways
that knock the point around the globe.

5.12.2 OPERATING CONDITIONS OF A QUANTUM COMPUTER

These computers are extremely sensitive and require very specific pressure
and temperature conditions and insulation to operate correctly. When these
machines interact with external particles, measurement errors and the erasure of
state overlaps occur, which is why they are sealed and have to be operated using
conventional computers. Quantum computers must have almost no atmospheric
pressure, an ambient temperature close to absolute zero (-273 °C) and insulation
from the earth's magnetic field to prevent the atoms from moving, colliding with
each other, or interacting with the environment. These systems only operate for very
short intervals of time, so that the information becomes damaged and cannot be
stored, making it even more difficult to recover data.

Fig. 5.15 Qubit states

5.12.3 MAIN USES OF QUANTUM COMPUTING

Computer security, biomedicine, the development of new materials and the

economy, are among the fields that may be revolutionised by advances in quantum
computing. Some of the benefits in different fields are:

 Finance: Companies would further optimise their investments and improve fraud
detection and simulation systems.

 Healthcare: This sector would benefit from the development of new drugs and
genetically customised treatments, as well as DNA research.

 Cybersecurity: Quantum programming involves risks, but also advances in data

encryption, such as the new Quantum Key Distribution (QKD) system. This is a
new technique for sending sensitive information that uses light signals to detect
intruders in the system.

 Mobility and transport: Companies like Airbus use quantum computing to

design more efficient aircraft. Qubits will also enable significant progress in traffic
planning systems and route optimisation.

5.13 DIFFERENCES BETWEEN QUANTUM AND

CLASSICAL COMPUTATION

S. No. CLASSICAL COMPUTER QUANTUM COMPUTER

It is large scale integrated multi- It is high speed parallel computer

1
purpose computer (CPU) based on quantum mechanics

Information storage is Quantum bit

Information storage is bit based on
2 based on direction of an electron
voltage/charge etc.
spin

Information processing is carried Information processing is carried

3 out by logic gates e.g. NOT, AND, out by Quantum logic gates in
OR etc in sequential basis parallel basis.
S. No. CLASSICAL COMPUTER QUANTUM COMPUTER

Quantum bits or "qubits" are

similar in that for practical
purposes we read them as a
value of 0 or 1, but they can also
hold much more complex
Computer runs on bits that have a
4 information, or even be negative
value of either 0 or 1
values. Before their value is read,
they are in an indeterminate state
called superposition and be
influenced by other qubits (called
entanglement).

Infinite (continuous) number of

possible states.
Discrete number of possible Probabilistic: measurements on
states: 0 or 1. Deterministic: superposed states yield
5 repeated computations on the probabilistic answers (our
same input will lead to the same confidence in these answers
output. builds up through repeated
computations) then reduced to 0
or 1.

Quantum answers (which are in

quantity called amplitudes) are
Only specifically defined results are probabilistic, meaning that
6 available, inherently limited by an because of superposition and
algorithm's design entanglement multiple possible
answers are considered in a given
computation.

Circuit behaviour is governed by Circuit behaviour is governed

7
classical physics explicitly by quantum mechanics

Operations are defined by linear

Operations are defined by Boolean algebra over Hilbert Space and
8
Algebra can be represented by unitary
matrices with complex elements
S. No. CLASSICAL COMPUTER QUANTUM COMPUTER

No restrictions exist on copying or Severe restrictions exist on

9
measuring signals copying and measuring signals

Circuits must use microscopic

Circuits are easily implemented in
technologies that are slow, fragile
10 fast, scalable and macroscopic
and not yet scalable e.g. NMR
technologies such as CMOS
(Nuclear magnetic resonance).
 SOLVED PROBLEMS

1. Calculate the wavelength of radiation emitted by a quantum dot laser

made up of a semiconducting material with band gap energy 2.8 eV.

Solution:
Given data: Band gap, = 2.8 eV

Other useful data: Planck’s constant, = 6.625 x 10 -34 J s

Speed of light, = 3 x 10 8 m s-1
The energy of the radiation emitted from the LED will have an energy equal to the
band gap energy of the semiconductor. So, its wavelength can be found as shown
below
h𝑐
𝜆=
𝐸𝑔 𝑒
6.625 × 10− 3 4 × 3 × 10 8
¿ − 19
2.85 × 1.602 × 10
¿ 4430.8 × 10− 10 m
¿ 4430.8 Å
 OTHER LEARNING MATERIALS

1. Introduction to Nanomaterials

2. Density of States for Quantum Structures

3. Comparison between Bulk semiconductors, Quantum Well, Q

uantum Wire & Quantum Dot for easy visuals

4. Quantum Dot Laser

5. Single Electron Transistor

6. Quantum Computing for Beginners

 COMPREHENSIVE QUIZ

After completing the course, students are instructed to take the following quiz to
quantify their understanding of the concepts on the nanomaterials.

1. https://forms.gle/M3fsKLeg1p38t9A7A

2. https://forms.gle/iJ4m9FJm8zY9e4pa9

RESULTS
Repeat your learning, if your score is less than 60%.
Congratulations, if your score is above 90%.
 ASSIGNMENT

Define Moore’s law and connect the law to the continued miniaturising
in the electronics industry today.
Name the two approaches to the manufacture nanomaterials.
Compare the them.
How are small particle size and large surface area of nanoparticles
related to its properties and future applications?
Basics of Quantum Computing
What’s Next in Quantum Computing?
Quantum computing to new heights in the future
I hope the video helped you to understand more about the fascinating
capabilities of quantum computing. If you are hooked, you can actually
try a real quantum computer via the IBM Cloud. This is done through
the IBM Q Experience platform.
Write your own views on Quantum Computing and your experience with
the IBM Q Experience Platform.

Choose any one of the above mentioned topics and prepare a detailed
report.
 PART A – QUESTIONS WITH ANSWERS

1. What is a quantum well? (CO5,K1)

When two semiconductors of different band gap energies and of thickness

comparable to the electron mean free path alternate to form a synthetically
modulated structure, then such a structure is called quantum well structure.

2. What are Quantum dots? (CO5,K1)

Quantum dots are tiny particles or nano crystals of semiconducting material with
diameter in the range of 2-10nm(10 to 50 atoms).

3. Give the importance of Quantum dots. (CO5,K2)

• It represents ultimate reduction in dimensionality of semiconductor devices.
• It is 3-dimension structure with nanometer sixe confining electron and hole.
• It is operated at a level of single electron i.e., ultimate limit of electronic device.
• It is used gain material in laser. .

4. Give the disadvantage of Quantum dot laser. (CO5,K2)

• Fabrication process complicated.
• Carrier leakage due to finite barrier height.
• Strained wells lead to shift in wavelength.

5. What is the difference between the band gap of a material to the

nanomaterial? (CO5,K1)

In ordinary material band gap will be smaller. For nanomaterial the band gap will be
greater.

6. Define quantum dot laser. (CO5,K1)

A quantum dot laser is a semiconductor laser that uses quantum dots as the active
medium in its light emitting region.
7. What are the applications of the quantum dot laser? (CO5,K2)

It is used in medicine (Optical coherence tomography)

They are used in display technologies, spectroscopy and telecommunication

8. Define density of energy states. (CO5,K1)

It is defined as the number of available energy states per unit volume, per unit energy
in a solid.

9. Whether Fermi energy varies on material’s size? If yes or no, justify your
statement. (CO5,K2)

No, since electron density is the property of the materials, the Fermi energy does not
vary with material size.

Fermi energy is same for a particle of copper as it is for a brick of copper.

10. What will happen to the band gap when the volume is reduced from that
of a solid to a nano material? (CO5,K2)

The band gap gets bigger as the material gets smaller. If the volume is reduced from
that of a solid to that of a nano material, the band gap will wider.

11. What is meant by quantum confinement? (CO5,K1)

The effect achieved by reducing the volume of a solid so that energy level with in it
becomes discrete is called quantum confinement.

12. What is meant quantum confined structure? (CO5,K1)

A quantum confined structure is one which the motion of the electron or holes is
confined in one or more directions by potential barriers.

13. Define the term ‘quantum well, quantum wire and quantum dot.
(April/May 2018) (CO5,K1)

• An electrically isolated region, like a thin film, where electrons are constrained in
one dimension and exhibiting quantum behavior is called quantum well.

• An electrically isolated region, like a nanotube or nanoscale wire, where electrons

are constrained in two dimensions and exhibiting quantum behavior is called
quantum wire.
• An electrically isolated region, like a particle, where electrons are constrained in
all three dimensions and exhibiting quantum behavior is called quantum
dot.Write any two applications of quantum well, quantum wire and quantum dot.

14. List the applications of Quantum well, Quantum wire and Quantum
dot. (CO5,K2)

Quantum well
• They are now widely used to make semiconductor layer and other important
devices.
• They are used for infra-red imaging and photo detectors.

Quantum wire
• Quantum wires can be used for transistors.

• It is used in medical field. Nano bar codes are made different quantum wires of
different metals that have different reflectivity.

Quantum dots
• A quantum dot may be used as a basic building block in making a quantum
computer
• A quantum dot applications are blue laser diode, single electron transistor, light
emitting diode, etc.

15. State any two differences between classical and quantum

computations. (CO5,K2)

S. No. CLASSICAL COMPUTER QUANTUM COMPUTER

Information storage is Quantum

Information storage is bit based on
1 bit based on direction of an
voltage/charge etc.
electron spin

Circuit behaviour is governed

Circuit behaviour is governed by
2 explicitly by quantum
classical physics
mechanics
 PART B – QUESTIONS
1. Discuss in detail quantum confinement and quantum structures in nanomaterials.
(April/ May 2018) (CO5,K1)

2. Discuss density of states in quantum well, quantum wire and quantum dot.
(April/ May 2019) (CO5,K2)

3. Explain with a neat diagram the construction, working and applications of

Quantum dot laser in detail. (CO5,K2)

4. Explain size dependence of Fermi energy and Energy band gap of nanomaterial.
(CO5,K2)

5. Explain in detail the principle and working of a single electron transistor.

(CO5,K2)

6. What are the differences between classical and quantum computations?

(CO5,K2)
 SUPPORTIVE ONLINE CERTIFICATION
COURSES

NPTEL COURSES

1. Nanoelectronics: Devices and Materials: 12 weeks course

2. Nanotechnology, Science and Applications: 12 weeks course

3. Quantum Information and Computing: 8 weeks course

Coursera

Nanotechnology: A Maker’s Course

Udemy

4. Nanotechnology: an Introduction

5. Nanotechnology: A Beginners Guide

REAL TIME APPLICATIONS OF NANOMATERIALS
IN DAY TO DAY LIFE AND INDUSTRY

Sunscreen: Nanoparticles have been added to sunscreens for years to make

them more effective. Two particular types of nanoparticles commonly added to
sunscreen are titanium dioxide and zinc oxide. These tiny particles are not only
highly effective at blocking UV radiation, they also feel lighter on the skin, which is
why modern sunscreens are nowhere near as thick and gloopy as the sunscreens
we were slathered in as kids.

Clothing: When used in textiles, nanoparticles of silica can help to create fabrics
that repel water and other liquids. Silica can be added to fabrics either by being
incorporated into the fabric’s weave or sprayed onto the surface of the fabric to
create a waterproof or stainproof coating. So if you’ve ever noticed how liquid
forms little beads on waterproof clothing – beads that simply roll off the fabric
rather than being absorbed – that’s thanks to nanotechnology.

49
 Computers: Without nanotechnology, we wouldn't have many of the electronics
we use in everyday life. Intel is undoubtedly a leader in tiny computer processors,
and the latest generation of Intel’s Core processor technology is a 10-nanometer
chip. When you think a nanometer is one-billionth of a meter, that’s incredibly
impressive!

Quantum well applications

Quantum Dot Light Emitters

Magnetic Nanowires: Revolutionizing Hard Drives, RAM, and Cancer Treatment

Quantum wire as nanobarcodes

A quantum wire application is nanobarcodes which is used in medical field.

Nanobarcodes are made different quantum wires of different metals that have
different reflectivity. Barcode readout is accomplished by bright field reflectance
imaging, typically using blue illumination to enhance contrast between Au and Ag
stripes.

50
 CONTENT BEYOND THE SYLLABUS

1. Ballistic Conductance in Nanostructures

https://courses.cit.cornell.edu/ece407/Lectures/handout28.pdf

2.Quantum of Conductance
https://nanohub.org/resources/632/download/2004.08.27-l03-ece453
.pdf

3.Carbon Nanotubes
https://www.nanowerk.com/nanotechnology/introduction/introductio
n_to_nanotechnology_22.php
 PRESCRIBED TEXTBOOKS AND
REFERENCE BOOKS
TEXTBOOKS

1. G.W. Hanson, “Fundamentals of Nanoelectronics”, Pearson Education, 2008.

REFERENCE BOOKS

2. N. Garcia and A. Damask, “Physics for Computer Science Students”, Springer-

Verlag, 2012.

3. B. Rogers, J. Adams and S. Pennathur, “Nanotechnology: Understanding Small

System”, CRC Press, 2014.

4. C.P. Williams, “Explorations in Quantum Computing”, Springer-Verlag London,

2011.
 MINI PROJECT SUGGESTIONS

1. Nanoparticles & Light Energy Experiment: Quantum Dots and Colors

2. Nanomaterial Case Study: Nanoscale Silver In Disinfectant Spray

3. Nanomaterial Case Study: A Comparison of Multiwalled

Carbon Nanotube and Decabromodiphenyl
Ether Flame-Retardant Coatings Applied to Upholstery Textiles

4. Nanomaterial Case Studies: Nanoscale Titanium Dioxide In Water Tr

eatment And In Topical Sunscreen

5. Carbon Nanomaterials in Agriculture: A Critical Review

6. Carbon nanomaterials: Production, impact on plant development, ag

ricultural and environmental applications

7. Production and application of carbon nanomaterials from high alkali

silicate herbaceous biomass

8. Food–Materials Nexus: Next Generation Bioplastics and Advanced M

aterials from
Agri-Food Residues

9. Conversion of Industrial Bio-Waste into Useful Nanomaterials

10. Engineered nanomaterials of relevance to human health

 Thank you

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