Graphene and carbon nanotubes show potential for use in terahertz antennas due to their high electron mobility. A quantum mechanical framework is used to model the properties of carbon nanotubes and analyze their behavior as nano antennas. Key findings include that resonant frequency increases with diameter, and relaxation time and chemical potential can be tuned to increase conductivity and antenna performance. Graphene patches and MIMO arrays are also proposed for terahertz communication applications like wireless network-on-chip. Challenges remain around interaction with chip packages and initial beam alignment between mobile stations.

1. GRAPHENE BASED NANO
ANTEENAS FOR TERAHERTZ
COMMUNICATION
CARBON NANO TUBES
DIPOLE ANTEENA
MICROSTRIP(PATCH)ANTEENA
MASSIVE MIMO ANTEENA

2. GRPAHENE ANTEENA V/S METTALIC ANTEENA
•The mobility of electrons in graphene is much
larger as compared to metallic antenna.
•It would be unfeasible to operate metallic
antenna in terahertz band as it required a lot of
power to operate.

3. WHY THERE IS A NEED OF COMMUNICATION
AT TERAHERTZ FREQUENCIES
• As the demand for high data rate was constantly increasing there is a
need to do communication at higher frequencies to allocate more
bandwidth for faster and efficient communication.
• Exploration of new materials has enabled communication at higher
frequencies. Graphene enabled wireless communication to be take
place at Terahertz Band at the nanoscale.
• Communication and coordination between these nanodevices will
lead towards the development of future networks.

4. WHAT NEED TO BE EXPLORED FROM
GRAPHENE
•Specified properties of graphene needs to be
explored which includes relaxation time and
chemical potential.
•Hybrid techniques need to explored to mitigate
the problems raised from using high frequencies
for communication.

5. QUANTUM MECHNICAL FRAMEWORK:CARBON
NANOTUBES AS CARNON NANOANTEENAS
• A quantum mechanical framework is proposed to analyze the properties of graphene derivative
carbon Nano tube(CNTs) which as Nano dipole antennas and antenna parameters are computed
after calculation with Nano patch antenna with similar dimensions and it has been shown that
both the Nano dipole antennas and Nano patch antennas will able to radiate at Terahertz.
• It is still not clear how these nanodevices will communicate using electromagnetic waves as
legacy communications will undergo extreme revision to be used in Nano devices.
• There are several limitations in the legacy communication techniques in terms of size complexity
and energy consumption. Exploration of new materials gave rise to new materials for this purpose
and among all other graphene and its derivatives carbon nano tubes (CNTs) and graphene nano
ribbons(GNR) found to be the most suitable A few initial designed based on graphene as been
proposed so far. Graphene antennas up to micro and macro dimension has been made so far.
• A Quantum mechanical framework based on the tight binding model was introduced to
determine the antenna parameters. Carbon nano tubes (CNTs) can behave either a metallic or
semiconductor depending on its dimension and geometry.
• As we want ultra-thin and ultra-low energy nano devices, so antenna parameters must be
analyzed where more than one conducting band is occupied.

6. Transmission Line Properties of CNTs
• The electronic properties of CNTs depend upon their dimension,
fermi energy and the structure of their edge, which can be mainly
either Zigzag or arm chair depending upon how the graphene is
rolled. Top and bottom edges are arm chair edges where left and
right edges are Zigzag.
• Transmission line properties has been identified which includes
quantum resistance, quantum capacitance and kinetic inductance.

8. ENERGY BAND STRCUTURE OF CARBON
NANOTUBE
• The energy band structure will define how many energy levels an electron will
attain in Carbon Nano Tube (CNT).It is described by Schrodinger equation as
mentioned below.
• Where h is the reduced plunk constant, m0 is the electron mass U (_r) stands for
the potential energy of an electron and ψ (_r) is the energy of electron located at
position (r) and E refers to the total energy that electron have. We have to solve
the Schrodinger equation to find the Eigen values and Eigen functions that satisfy
the boundary equations.
• As it is difficult to solve the equation so they have solved this equation using tight
binding model which will reduced this equation to matrix form which is easy to
solve.

9. ENERGY BAND STRCUTURE OF CARBON
NANOTUBE
• We have to solve this matrix for a unit cell and then expand it along
the Zigzag edge parallel to the x-axis or along the Armchair Edge along
the y axis across the entire Nano structure.
• After applying Tight Binding Model we can get a Hamiltonian matrix
which we solve for unit cell and then expand it across the whole Nano
structure.
• The main point in whole process is to find the energy bands which
are relatively close to zero. These are the first energy states which are
occupied by the electrons when the provided energy will increased.

10. WHAT IS FERMI ENERGY
• Fermi energy is often defined as the highest occupied energy level of a
material at absolute zero temperature. In other words, all electrons in a
body occupy energy states at or below that body's Fermi energy at 0K.
• The fermi energy is the difference in energy, mostly kinetic. In metals this
means that it gives us the momentum of the electrons during conduction.
So during the conduction process, only electrons that have an energy that
is close to that of the fermi energy can be involved in the process.
• As a material's temperature rises above absolute zero, the probability of
electrons existing in an energy state greater than the Fermi energy
increases, and there is no longer any constant highest occupied level, so
while the material's Fermi energy may be useful as a reference, it is not
very useful at real temperatures.

11. Quantum Resistance
• After calculating the energy levels of electron
we shall compute quantum resistance. It can be
computed with the formulae Where h is the
plank constant e is the charge on
electron and m is the number of
conducting bands. At given Fermi energy
level the conducting bands will be
increased with diameter depending
upon the separation of conducting
bands.

12. KINETIC INDUCTANCE
• Inductance has been defined as the resistance to the current charge and
energy stored in the magnetic field when the current passes through it.
• If the current is zero the number of electrons moving from left to right is
same that are moving in opposite direction thus cancel the effect of each
other. To have some current some of the electrons moving in opposite
direction must change their direction from left to right to avoid
cancellation. This will be done moving the electrons to higher levels. Thus
as the current increases the kinetic energy of electrons also increases give
rise to kinetic inductance per unit length is
• Increasing the diameter of Nano tube will increase the number of
conducting band by reducing the kinetic inductance.

13. Quantum Capacitance:
• To add electric charge in the system we have to
add electrons to the available quantized states
above the Fermi level. The extra energy is
modeled as an equivalent capacitance per unit
length as shown below.
• By increasing the diameter of Nano tube
the conducting bands will increased and
quantum capacitance will also increase.

14. LINE IMPEDANCE
• To completely characterize the Nano dipole antenna electrostatic
inductance and electrostatic capacitance has been computed as shown
below.
• The main difference between GNR and CNT is based upon folding the
sheet and leave it open as it will alter the differences in energy bands.

15. FUNDAMENTAL
RESONANT FREQUENCIES
• A carbon Nano tube (CNT) of length of 1
micrometer and resonant frequencies
has been measured. Given a specific
Fermi energy level it has been observed
that by increasing the diameter of
nanotube resonant frequency will
increased non-linearly. This increase is
due to the increase in conducting bands
due to the increase in Nanotube
diameter. However similar behavior has
been observed in GNR Nano patch
antenna as width is increased.

16. INPUT IMPEDANCE & CONTACT RESISTANCE
• The major problem in Nano-structures is the high contact resistance.
As seen above the contact resistance has been reduced by
increasing the nanotube diameter and Nano ribbon width or system
energies. So by increasing the conducting bands the input or contact
resistance will reduced.

17. RECONFIGURIBILITY AND TUNEBILITY OF
GRAPHENE BASED NANO ANTEENA
• In the area of wireless communications graphene shows a great platform to design miniaturized and tunable antennas in
the terahertz band.
• The use of frequency band between 0.1 and 10 THZ was emerged as extremely attractive due to large bandwidth,
however the increase in frequency will increase the propagation losses.
• Grapheme can be used either as a radiating element or supporting element e.g. the feed. But first we consider it as a
radiating element.

18. CONDCUTIVITY CHEMICAL POTENTIAL &
RELAXATION TIME
• The previous work just suggested the tunebility of graphene in other elements rather than radiating element.
• As discussed in the above related work here conductivity has been defined by Kubo formalism at terahertz frequencies. In
this approach the grapheme sheet would be considered very large in order to avoid the effects of edges.
• Where e is the charge on electron kb is the Boltzmann constant, h is the reduced plank constant ,T is the temperature, EF
is the chemical potential and is the relaxation time.
• The plot of conductivity as a function of above given two variables is given below.

19. CONDCUTIVITY CHEMICAL POTENTIAL &
RELAXATION TIME
• Chemical Potential:
Chemical potential refers to the distribution of electron energies upon which
a quantum state may be acquired or remains empty. The value of chemical
potential can be changes by means of chemical doping or by applying
electrostatic bias. Configurability can be achieved by means of biasing or
chemical doping. As chemical potential is directly proportional to voltage by
a formula given below.
As clearly seen in figure 1, the more is the electric potential the more is the
conductivity.
• Relaxation Time:
The relaxation time is the interval required for material to restore a uniform
charge density after a charge distortion is introduced. By increasing the
relaxation time conductivity and antenna performance will increased.

20. GRAPHENE AS AN RADIATING ELEMENT
• Initial work on graphene was based upon using a graphene as a radiating element where finite size graphene
layers was mounted on a dielectric material and used as an radiating element. The maximum gain and the
simulated radiation efficiency are relatively low in the considered cases around -10db and 4.5% respectively.
The increase in chemical potential as shown above in figure 3 will leads towards the
shift of resonance frequency with out changes in radiation pattern. The efficiency
and gain increased up to 52% and 0.46db but we must provide increase bias.

21. GRAPHENE AS AN RADIATING ELEMENT
• As we increase the relaxation time the antenna maintains the same
resonant frequency but shows stronger resonant behavior. This is due
to the increased movement of electrons which gives higher efficiency
up to 32 % and gain of about -2.34 db.

22. TERAHERTZ SOURCE TECHNIQUES
• A photoconductor has been placed at the gap between the arms of dipole
antenna upon which a light has been thrown with a laser with femto second
pulse. Similarly, if an electrostatic bias is applied it can generate a photo current
with terahertz components that enters the antenna. But an electrostatic bias
would have a double effect because it can raise both the phot current and
antenna efficiency.
• Although the use of photoconductive sources is not suitable for the applications
where area is constrained. So, a high electron mobility transistor has been
suggested with a graphene-based gate. When the voltage is applied it generates
the terahertz plasma wave at the gate which will be fed to the antenna without
contact or mismatch impedance issues.
• Configurability of graphene has been explored by using it to provide frequency
tunebility and not to used it as a radiating element to avoid losses. Graphene will
use to provide tunable frequencies to metallic structure which can radiate at
designated frequency.

23. Wireless Nano-Networks & Wireless Network-on-
Chip & Software-Defined Metamaterials (SDM).
• Wireless Nano-Networks:
Graphene based nanoantenna’s has found its application in the field of wireless Nano-
sensors network. Two of the new area applications that suited graphene terahertz antenna
are Wireless Wireless Network-on-Chip(WNOC) and Software-Defined Metamaterials
(SDM).
• Wireless Network-on-Chip:
As we know multicore processors required on chip network to interconnect the multiple
cores in parallel. Wireless Network-on-Chip support the implementation of multiple wireless
anteenas instead of traditional wires for the communication several cores on a single chip
which suits the area constrained applications. Graphene based terahertz antennas also suits
the communication with high bandwidth typically required from 10-100 Gbps range.
However,the interaction of electromagnetic waves with chip package is a major concern.
Software-Defined Metamaterials (SDM).
• Metamaterials has recently brought innovations in applications but they are limited to
their specific use and purpose.DM enables the configurability of materials by means of
software as we can modify the electromagnetic properties of metamaterials. For this
purpose, controllers may have incorporated with metamaterial which may interact
locally or globally, As the general size of metamaterial building block is Lambda/10,
which incorporates the use of millimeter wave or terahertz frequency. The main
problem arises in software defined materials was the interference between two
adjacent anteenas or between the waves use to communicate.

24. GRAPHENE
BASED PATCH
ANTEENA
• A graphene patch antenna was also
considered where it was placed on
the substrate and absorption cross
section has been observed as a
function of frequency. Absorption
cross section is used to quantify the
rate of electromagnetic waves
absorption. Consider the figure
mentioned below.
• As shown in figure,
graphene position was
changed, and absorption
cross section was
observed. Dimensions of
substrate and patch
antenna are mentioned in
table.
Substrate 6 x6 μm and a thickness of 1 μm
Graphene Patch 5 x0.5 μm
Left figure Center
Middle Figure 1.25 μm from the center
Right Figure 2.5 μm from the center

25. ABSORPTION CROSS
SECTION AS A
FUNCTION OF POSITION
• As shown in figure, absorption cross
sections were increased by moving
the graphene patch at right up to 2.5
μm from the center or closer to the
side of the substrate.
• Absorption cross section was also
increased by increasing the size of
substrate as shown below.

26. Absorption Cross Section as
a Function of Chemical
Potential:
• In terms of chemical potential,
there is a trade off between
amount of power an graphene
antenna can absorb and resonant
frequency.
• As shown in figure ,the more is the
electric potential, the more is the
absorption energy and resonant
energy which will reduce their
transmission range. However less
is the electric potential, less is the
energy, and more is the
transmission range.
Color Chemical Potential
Green Line 0ev
Yellow Line 0.5ev
Red Line 1ev
Blue Line 2ev
Gray Dashed Line Metallic antenna modeled as gold antenna

27. Absorption Cross
Section as a Function
of Relaxation Time
• As shown above in the figure,
at relaxation time 10^-14s
there is no radiation from
graphene. As we can move
towards higher relaxation
time resonance phenomena
of graphene will further
increased.
Color Relaxation Time
Yellow dotted line 10^-14s
Green dashed line 10^-13s
Red dot-dashed line 10^-12s
Blue solid line 10^-11s

28. SCHEMATIC DIAGRAM
OF GRAPHENE &
RADIATION PATTERN
• Schematic diagram of the
graphenna in
transmission.The graphenna
is composed of a graphene
patch witha length L = 5 μm
and a width W = 1 μm, and a
pinfeed located at 0.1 μm
from the edge of the
graphenna.The blue circle
shows the plane in which the
radiation diagram is
measured.

29. MIMO BASED GRPAHENE
ANTEENAS
• As graphene propagate around terahertz frequency due to which
the wavelength become very small. The relation between them
are given below.So if we are using traditional omnidirectional
antennas then the range or area of radiation will be very less. To
cater this problem MIMO system for terahertz communication
based upon grapheme antennas has been proposed as shown
below.
• Beams emission from different antennas undergo constructive
and destructive interference to form a direction beam with
increase range.
• As we increase the number of elements the specific range of
beam or radiation area was also increased as shown in graph.

30. PROBLEM STATEMENT & SOLUTION
• As the beam thrown by an antenna is directional so there will be a
delay problem during the initial cell discovery called initial access by
MIMO antennas. It doesn’t matter whether the mobile station will
perform analog beam forming or digital beam forming.
• It would be suggested to use microwave and millimeter wave
antennas in combination and by means of GPS allocation and sharing
there is no need to cover 360 degree which causes delay problem.