Final m.tech ppt_praveen

82
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 12/30/21 1 School of Engineering, Department of Electrical Engineering Shiv Nadar University Final Presentation Of M.Tech Thesis

description

This is my final M.Tech Thesis Presentation. Under this ppt i have discussed my M.Tech thesis work.

Transcript of Final m.tech ppt_praveen

Page 1: Final m.tech ppt_praveen

Tuesday, April 11, 2023 1

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

School of Engineering, Department of Electrical Engineering Shiv Nadar University

Final Presentation Of M.Tech Thesis

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Contents

Introduction of nanoelectronics.

Physics of Nanoelectronics.

My work of M.Tech thesis and Future work.

References.

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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.

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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.

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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.

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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.

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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]

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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]

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Physics of Nanoelectronics

General model of a nanodevice.

The ballistic and Scattering.

My work of M.Tech Thesis and future work.

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General model of a nanodevice by Landauer-Datta

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Filling sate at right and left terminal

Assume each energy channel is independent At one terminal number of

Filling states from the right contact

01 1( ) ( ) ( )N E D E U f E

02 2( ) ( ) ( )N E D E U f E

02

2

( )( ) N E NdN E

dt

01

1

( )( ) N E NdN E

dt

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Steady State

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01 2

1 2

( )0

N N N NdN E

dt

0 01 1 2 2 2 21 1 1 1 0N N N N

1 20 01 2

1 2 1 2

1 1( ) ( ) ( )

1 1 1 1N E N E N E

11

h

22

h

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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 EN E f E f E

1 2

( ) ( )( ) ( )

2 2

D E D EN f E f E dE

0 0( ) ( )N D E f E dE

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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

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Physics Of Nanoelectronics

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

qI E F F

01

1

( ) ( )

( )

N E N EF

E

0

22

( ) ( )

( )

N E N EF

E

1 2

2( ) ( )( )

2

qI E D E f f

h

1 2

2 ( )( )

2

q D EI f f dE

h

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Physics Of Nanoelectronics

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 ( )( ) ( )

22

( ) ( )( )

q D EI E f f dE

hq

I T E M E f f dEh

( )

( )( )

ET E

E L

TL

L

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Types of Transport

0.1mm → Drift-diffusion.

10 →Drift –diffusion+ Velocity saturation .

0.1 →Boltzmann for velocity saturation.

10nm →Quasi –ballistic .

1nm → Quantum mechanical.

m

m

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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

202

( ) ( )q f

G T E M E dEVh E

22( ) ( )ball

qG M E T E

h

2

1 12.8

( ) 2ballF

h KR

M E q M

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0 ( )F

fE

E

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2D Diffusive resistor

202

( ) ( )fq

G T E M E dEh E

( )

( )( )

F

F

ET E

E L

( )

( )F

ballF

EG G

E L

1F

BallE

LR R

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Final Equation

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2

2

2

2( ) ( )

1

2 ( )

1

2y z

qG T E M E

hh

Rq T E

w w h

L q T

( )( )

( )

ET E

E L

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2 mv

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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.

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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.

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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.

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g and f- Scattering

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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

1T

G F A

2

1

2y zw w h

L q T

2

1

2 ( )

hR

q T E

1

2

D

L qT

n h

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Fig.1 Resistance vs Width

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Fig.2 Resistivity vs Temperature

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Fig.3 Resistance vs length

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Fig. 4 Resistance vs Electric Field

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Fig.5 Resistance vs Temperature

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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 .

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1

2

D

L qT

n h

1Dn

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

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

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• .

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

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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.

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2 4

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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.

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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.

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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).

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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).

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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.

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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.

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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).

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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).

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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 .

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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

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What are our options :

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

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Advantages of Non-Equilibrium Green’s FunctionMethod

:

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.

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Nonequilibrium Green’s Function Method :

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Fig.1 Current vs Voltage

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Fig.2 Resistance vs Voltage

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Fig3. Conductance vs Voltage

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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.

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My Result

• Thank You

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Content

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

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2

2

2

2( ) ( )

1

2 ( )

1

2y z

qG T E M E

hh

Rq T E

w w h

L q T

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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

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( )2

TD el ox GS T DS

B L

vI T WC V V V

k T

q

( )2

elD ox T GS T

el

TI WC v V V

T

NanoScale Electro thermal Laboratory Department of Electrical Engineering Shiv Nadar University

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• 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.

Tuesday, April 11, 2023NanoScale Electro thermal Laboratory Department of Electrical Engineering Shiv Nadar University

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1

1T

G F A

2

1

2y zw w h

L q T

2

1

2 ( )

hR

q T E