Final m.tech ppt_praveen

Modeling of Silicon Nanowire For Electrical
Mobility and Resistance
By Praveen Dwivedi
M.Tech In VLSI Systems & Technology (V.S.T.)
Under the Guidance of
Dr. Sitangshu Bhattacharya
Assistant Professor
Shiv Nadar University
Tuesday, May 27, 2014 1
School of Engineering, Department of Electrical Engineering
Final Presentation Of M.Tech Thesis

Contents
 Introduction of nanoelectronics.
 Physics of Nanoelectronics.
 My work of M.Tech thesis and Future work.
 References.

1.Introduction of Nanoelectronics.
Nanoelectronics refers to the use of nanotechnology in
electronics components. The term covers a diverse set of
devices and materials which have the common characteristic
that they are very small and the range of this technology lies
between 100 nm to 1nm.

Why we are going beyond CMOS technology or
interested in Nanoelectronics
Problem in nanoscale MOSFET due to Scaling are given below-
1. Sub threshold leakage current.
2. Hot carrier effects.
3. Direct source to drain tunneling.
4. Direct tunneling , gate leakage current.
5. Parasitic resistance, parasitic capacitance.
6. Reverse –biased junction leakage current.

Solution for these given problem
1. New materials , new device architectures and new design are
possible solution to CMOS scaling issue.
2. Noval device and novel material are considered as promising
candidate for beyond technology nodes, including, Planner
DG MOSFET, FINFET, vertical DG MOSFET, Trigate
MOSFET and gate all around devices.
3. New material Si nanowire, Graphene, carbon nanotube.
4. However which device , material will be final winner for
future circuit is still unclear.

Advantages of Nanodevice
1. These nanodevice take the advantage of quantum mechanical
phenomena and ballistic transport characteristics under the
lower supply voltage hence low power consumption.
2. These device offered ultra high density integrated electronics
due to their extremely small size.
Problem- It also increase the defects and variations both during
manufacture and chip operations.

Description of Silicon nanowire according to ITRS
[2,3]
 Potential Value of Material
 Low surface scattering due to one dimensional.
 High control of Leakage by Gate.
 Key challenges
 Nanowires has key challenge to grow in desired location and
desired direction.
 Nanowires has challenge of catalyst compatible with CMOS
processing.
 Challenge for dope nanowires channel and source/ drain regions.
 Challenge to achieve the high, electron and hole mobility on
silicon.
 Challenge in pattern surround gate structure .
[Source-ITRS]

Key Factors (advantages) of Silicon Nanowires
 Cost -effective bottom-up fabrication
 Higher carrier mobility by reduction of scattering due to
crystalline structure.
 Smooth surface and ability to produce radial and axial
nanowires heterostructure.
 Better scalability resulting from the fact that diameter of
nanowires can be controlled down to below 10nm.
[Refe-3]

Physics of Nanoelectronics
 General model of a nanodevice.
 The ballistic and Scattering.
 My work of M.Tech Thesis and future work.

General model of a nanodevice by Landauer-Datta

Filling sate at right and left terminal
 Assume each energy channel is independent
 At one terminal number of
 Filling states from the right contact
0
1 1( ) ( ) ( )N E D E U f E 
0
2 2( ) ( ) ( )N E D E U f E 
0
2
2
( )( ) N E NdN E
dt 


0
1
1
( )( ) N E NdN E
dt 



Steady State
0
1 2
1 2
( )
0
N N N NdN E
dt  
 
  
       0 0
1 1 2 2 2 21 1 1 1 0N N N N      
 
   
 
   
1 20 0
1 2
1 2 1 2
1 1
( ) ( ) ( )
1 1 1 1
N E N E N E
 
   
 
 
1
1
h


 2
2
h




Physics Of Nanoelectronics
 Where and are a unit of time. While and are unit of
energy.
 If = electron density is given by
 Recall that in equilibrium we use
2 1 1 2
1 2
1 2
( ) ( )
( ) ( ) ( )
2 2
D E D E
N E f E f E 
1 2
( ) ( )
( ) ( )
2 2
D E D E
N f E f E dE
 
   

0 0( ) ( )N D E f E dE 

Steady-State Current, I
Contact 1 tries to fill up the
device according to its
Fermi level
Contact 2 tries to fill up
the device according to
its Fermi level
1 2 0F F  Total flux
1 2I qF qF   Current

 equa (1) current under this condition
 After putting all value in the equation in one then final equation for current
is given by
 Then genralised term equation of current is given by
 1 2( )
2
q
I E F F 
0
1
1
( ) ( )
( )
N E N E
F
E


0
2
2
( ) ( )
( )
N E N E
F
E


1 2
2
( ) ( )( )
2
q
I E D E f f
h

 
1 2
2 ( )
( )
2
q D E
I f f dE
h
 

 Transmission coefficient is given by
T(E) is decide the types of transport.
 λ=mean free path or Carrier backscattering length.
 L=channel length
 Diffusive L>>λ then
 Ballistic L<<λ then T=1
 Quasi Ballistic then T<1.
1 2
1 2
2 ( )
( ) ( )
2
2
( ) ( )( )
q D E
I E f f dE
h
q
I T E M E f f dE
h
  
 

 ( )
( )
( )
E
T E
E L




T
L


L 

Types of Transport
 0.1mm → Drift-diffusion.
 10 →Drift –diffusion+ Velocity saturation .
 0.1 →Boltzmann for velocity saturation.
 10nm →Quasi –ballistic .
 1nm → Quantum mechanical.
5/27/2014 17
m
m

Conductance and Resistance of Ballistic and
Diffusive case
 Ballistic conductance is given by
 According to relation
 After solving above equation then ballistic conductance is
given by
 Then ballistic resistance is given by
5/27/2014 18
2
02
( ) ( )
q f
G T E M E dEV
h E


 
  
 

2
2
( ) ( )ball
q
G M E T E
h

2
1 12.8
( ) 2
ball
F
h K
R
M E q M

 
0
( )F
f
E
E





2D Diffusive resistor
5/27/2014 19
2
02
( ) ( )
fq
G T E M E dE
h E


 
  
 

( )
( )
( )
F
F
E
T E
E L




( )
( )
F
ball
F
E
G G
E L




1
F
Ball
E
L
R R

 
   
 

Final Equation
2
2
2
2
( ) ( )
1
2 ( )
1
2
y z
q
G T E M E
h
h
R
q T E
w w h
L q T



   
    
  
( )
( )
( )
E
T E
E L




2 mv 

Scattering
• Scattering is a general physical process where some forms
of radiation, such as light, sound, or moving particles, are
forced to deviate from a straight trajectory by one or more
paths due to localized non-uniformities in the medium through
which they pass.
• Scattering may also refer to particle-particle collisions
between molecules, atoms, electrons, photons and other
particles.
NanoScale Electro thermal Laboratory Department of Electrical Engineering

Lattice Scattering
• Because much of the scattering in semiconductor is due to
lattice vibrations, it is important that we understand their basic
properties. If an atom is displaced from its equilibrium
position , the bonding forces tend to push it back , so it
oscillates about its equilibrium site.

Types of Scattering
• Intravalley Scattering –This types scattering assume that the
initial and final states of electron are within the same valley.
• Intervalley scattering - An electron can be scattered from
one valley to another one both by acoustic and optical
phonons.
This scattering process is subdivided into
f -type and g-type process .
 A process is refereed to as f-type if the initial and final
orientation are different otherwise as g-type process.

g and f- Scattering

Calculation of Electrical Resistance & Mobility
• We address a physics based analytical model of electrical resistance and
mobility in an n-silicon nanowire (sinw) under influence of intra
and intervalleyscattering (IVS) to detremine Role of First Order Intervalley
Scattering in Determining Electrical Resistance of Silicon Nanowire.
• Transmission coefficient under the scattering is given by
• G= Scattering contribution due to g-type scattering.
• F= Scattering contribution due to f-type scattering.
• A=Intravalley scattering contribution by acoustic phonons.
1
1
T
G F A

  
2
1
2
y zw w h
L q T

   
    
   2
1
2 ( )
h
R
q T E

1
2
D
L qT
n h
 

Fig.1 Resistance vs Width

Fig.2 Resistivity vs Temperature

Fig.3 Resistance vs length

Fig. 4 Resistance vs Electric Field

Fig.5 Resistance vs Temperature

Mobility Part
• In This work we used that given relation for calculating the
mobility of silicon nanowire.
Mobility for silicon nanowires
Where
L = length of silicon nanowire.
= Carrier density for one dimension material.
T = Transmission Coefficient .
1
2
D
L qT
n h
 
1Dn

Fig. 1. Variation of mobility over temperature under three different
scattering conditions

Fig. 2 Variation of mobility over length of silicon nanowires under the
scattering of intervalley+intravalley, intervalley, intravallley scattering
• .

Fig. 3 Variation of mobility over electric filed under the three scattering

Conclusion
• Scattering is an important phenomenon in a MOSFET which affects the
device performance. Mobility strongly dependents on both intervalley and
intravalley scattering and increase in a parabolic manner under the variation
of gate length. Mobility decreases as the temperature increases and
mobility decreases more rapidly under the influence of intravalley
scattering under the variation of temperature.
• We find that the resistivity in the presence of an external longitudinal
electric field is more dominated by f-processes with allowed first order TA
and TO interactions which suggests that there are electron repopulation
From to the valleys. However for higher cross-sectional dimensions,
the resistance starts to weakly Depending on the electric field.
2
4

Future work
• Based on my M.Tech thesis work I am interested in Non
equilibrium Green’s Function (NEGF) method to calculate the
various electrical parameters of silicon nanowire.

References
1. Jing Wang, “Device Physics and Simulation of Silicon Nanowire Transistors", Ph.D. dissertation, Purdue
University August 2005.
2. Runsheng Wang, Jing Zhuge, Ru Huang, Tao Yu, JibinZou, Dong-Won Kim, Dungun Park, and Yangyuan
Wang, “Investigation on Variability in Metal-Gate Si Nanowire MOSFETs: Analysis of Variation Sources
and Experimental Characterization” IEEE Transactions On Electron Devices, Vol. 58, No. 8,pp.2317-2318,
August 2011.
3. Yong-Bin Kim, “Review Paper: Challenges for Nanoscale MOSFETs and Emerging Nanoelectronics”,
Trans. Electr. Electron.Mater.10(1) 21 (2009), G.-D.Hong et al.
4. Huang R, Wu H M, Kang J F, et al. Challenges of 22 nm and beyond CMOS technology. Sci China Ser F-
InfSci, 2009, 52(9):1491–1533, doi: 10.1007/s11432-009-0167-9.
5. International Technology Roadmap for Semiconductors 2011 Edition Emerging Research Materials pp. 1-
15.
6. International Technology Roadmap for Semiconductors 2011 Edition Emerging Research Devices pp. 1-16.
7. Yuting Wan, Jian Sha, Bo Chen, Yanjun Fang, Zongli Wang, and Yewu Wang “Nanodevices Based on
Silicon Nanowires” Recent Patents on Nanotechnology,pp.1-4,2009 Bentham Science Publishers Ltd.

References
8. Soshi Sato, “A Study on Electrical Characteristics of Silicon Nanowire Field Effect Transistors” Ph.D.
dissertation Tokyo institute of technology, 2008.
9. Allon I. Hochbaum, Renkun Chen, Raul Diaz Delgado, Wenjie Liang, Erik C. Garnett, Mark Najarian3,Arun
Majumdar&Peidong Yang “Enhanced thermoelectric performance of rough silicon nanowires”Vol 451| 10
January 2008|,pp.163-167, doi:10.1038/nature06381.
10. Yonatan Calahorra, “Electrical and Mechanical Propertiesof Silicon Nanowires”, Master of Science
dissertation, Israel Institute of Technology February 2010 pp. 5-30.
11. “Intel reinvents transistors using new 3-D structure” , Available online.
12. Y. Li, K. Buddharaju, B. C. Tinh, N. Singh, and S. J. Lee, “Improvedvertical silicon nanowire based
thermoelectric power generator with polyimide filling”, IEEE Electron Dev. Lett., vol.33, pp. 715-717,
(2012).
13. A. K. Buin, A. Verma, A. Svizhenko and M. P. Anantram, “Significant Enhancement of Hole Mobility in
[110] Silicon Nanowires, Compared to Electrons and Bulk Silicon”, Nano Lett., vol. 8, pp. 760-765, (2008).
14. E. B. Ramayya, D. Vasileska, S. M. Goodnick and I. Knezevic, “Electron transport in silicon nanowires:
The role of acoustic phonon confinement and surface roughness scattering”, J. Appl. Phys., vol. 104, pp.
063711 (1)-(12), (2008).

References
15. D. Yu, Y. Zhang and F. Liu, “First-principles study of electronic properties of biaxially strained silicon:
Effects on charge carrier mobility”, Phys. Rev. B, vol. 78, pp. 245204 (1)-(8), (2008).
16. M. Frey, A. Esposito and A. Schenk, “Computational comparison of conductivity and mobility models for
silicon nanowire devices”, J Appl. Phys., vol. 109, pp. 083707(1)-(6), (2011).
17. S. Jin, Y. J. Park and H. S. Min, “A three-dimensional simulation of quantum transport in silicon nanowire
transistor in the presence of electron-phonon interactions”, J. Appl. Phys.,vol. 99, 123719 (1)-(10),
(2006).
18. A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar and P. Yang,
“Enhanced thermoelectric performance of rough silicon nanowires”, Nature Lett., vol. 451, pp. 163-
167,(2007).

Credit for M.Tech Degree
• First Credit to Shiv Nadar University.
• Major Credit to Sitangshu Sir and his motivation for Ph.D.
• Third Credit to My all Faculty and All friends.

Tuesday, May 27, 2014
NanoScale Electro thermal Laboratory
Department of Electrical Engineering
51

52

Part I
• We determining the mobility of silicon nanowires under the influence of
intra & intervalley scattering has been presented. The relationship of
Landauer transmission coefficient with scattering process has been
derived. This transmission coefficient has been used to determine the
mobility of silicon nanowires. The effect of longitudinal electric field,
temperature and length of silicon nanowire on the mobility of silicon
nanowires has been shown. This study has been done under the influence
of intra+intervalley, intervalley and intravalley scattering. The core aim of
this paper is to show the affects of scattering on the mobility of silicon
nanowire.

My Work for 4th Semester
• In Part 1 We Calculated the mobility of silicon nanowires under the
influence of intra & intervalley scattering has been presented.
• In part 2 we Calculated the current for [100] Oriented silicon Nanowire by
Non equilibrium Green’s Function (NEGF) and Atomistix ToolKit (ATK).

57

58

59

Part II
• Under this work we calculated the Electrical current [100]
Oriented Silicon Nanowire by the Non-equilibrium Green’s
Function Method (NEGF) and Atomistix Tool Kit(ATK).

What is NEGF
• Non equilibrium Green function method which being widely
used in the analysis and design of nanoscale device it provide
a unified description for all kind of device from molecular to
carbon nanotube to silicon nanowire transistor in term of the
Hamiltonian describing the energy level of channel, the self
energy describing the connection to the contact and
describing the interaction inside the channel.
• The NEFG formalism provides a sound conceptual basis for
the development Of quantitative model for quantum transport .

Motivation
 Calculation of current in nanoscale devices
 Scale too small to apply drift-diffusion
 Current is a non-equilibrium quantity
 Schrodinger-Poisson only applicable in equilibrium
 Need a method which can handle:
1. Non-equilibrium conditions
2. Scattering mechanisms
3. 2D/3D and approximate many-body problems

What are our options
:
 Self-consistent quantum drift-diffusion model (complicated)
 Monte Carlo methods (expensive)
 Non-equilibrium Green's function formalism (this is option)

Advantages of Non-Equilibrium Green’s Function
Method
: Incorporation of quantum interference effects such as
tunnelling and diffraction, not possible through the Boltzmann
equation.
 Mathematically accurate approach to include rigorous
scattering (electron-phonon scattering, surface scattering etc).
 Eliminates periodic boundary conditions as outgoing waves
are planar.
 Multiscale formulation: Can be used to solve atomistic
systems to mesoscopic systems.

Nonequilibrium Green’s Function Method
:

Fig.1 Current vs Voltage

Fig.2 Resistance vs Voltage

Fig3. Conductance vs Voltage

Reference
1. NANOSCALE TRANSISTORS Device Physics, Modeling and Simulation by
Mark Lundstrom & Jing Guo.
2. International technology roadmap for semiconductors 2011 edition
emerging research devices.
3. International technology roadmap for semiconductors 2011 edition
emerging research materials.
4. Review Paper: Challenges for Nanoscale MOSFETs and Emerging
Nanoelectronics by gone-Bin Kim.

77

My Result
• Thank You

Content
• Introduction
• Solving the Wave Equation
• Computing n(x)
• Computing ID
• NEGF Formulation
• Scattering
• Summary

80
2
2
2
2
( ) ( )
1
2 ( )
1
2
y z
q
G T E M E
h
h
R
q T E
w w h
L q T



   
    
  

Proposed work for next Semester
• My proposed work for next semester will be determine the
electrical current in an n-silicon nanowire (sinw) under
influence of intra and intervalleyscattering (IVS).
• Current in linear region
• Current under saturation region
( )
2
T
D el ox GS T DS
B L
v
I T WC V V V
k T
q
 
 
 
 
( )
2
el
D ox T GS T
el
T
I WC v V V
T
 
  
 

• Transmission coefficient under the scattering is given by
• G= Scattering contribution due to g-type scattering.
• F= Scattering contribution due to f-type scattering.
• A=Intravalley scattering by acoustic phonons.
NanoScale Electro thermal Laboratory Department of Electrical Engineering Shiv Nadar
University
82
1
1
T
G F A

  
2
1
2
y zw w h
L q T

   
    
  
2
1
2 ( )
h
R
q T E


Final m.tech ppt_praveen

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