EEL 6935 class project

Effect of Inversion layer Centroid on MOSFET capacitance

Srivatsan ParthasarathySWAMP Group

2

Organization

• Introduction Scaling Issues in nanometer MOSFETS Parasitics – the ultimate showstoppers Project relevance

• Simulation Approach Tools of the trade – what we need Bandstructure Self–consistent solution Computing surface potential Capacitance

• Results and Discussion

Part I:Introduction

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Scaling Issues in nanometer MOSFETS

• Phenomenal scaling in last 40 years: LGATE – from 10 μm to ~30 nm ! Major changes in both technology and materials;

• Smart optimizations in device structures• Timely introduction of new processing techniques • New materials (eg. Halo, silicides), but not in channel

• Issues with scaling Parasitics Lesser control on Short Channel effects Decreasing ION/IOFF (more leakage with thin oxide)

Industry is looking at new vectors Strained Si, III-V channel materials, multi-gate architectures

Part 1: Introduction

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Parasitics

Channel Resistance

SeriesResistance

Series Resistance ~ 47% of Channel Resistance

at 45 nm

ITRS Roadmap0

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0 20 40 60 80 100 120

Technology Node

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Parasitics Dominate!

Gate Capacitance

Total ParasiticCapacitance

• Why does gate capacitance reduce? Geometric Scaling

• To first order, Cox is proportional to scaling factor

Quantum effects• Peak of Inversion Charge is not at

Si-SiO2 interface, but instead a few nm inside.

This reduction due to quantum effects cannot be neglected.

Part 1: Introduction

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Project relevance

• Very important to quantify capacitance degradation To build better device models and simulators To compare how novel channel materials compete with

existing technology

Main goal of this project: To quantify the quantum effects leading to reduction in

capacitance using techniques taught in class

Part 1: Introduction

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What I did in the project

• Simulated capacitance degradation for unstrained, planar nMOS Bandstructure - sp3d5s* TB model with SO coupling Self-consistent solution of schroedinger-poisson equation Surface potential calculation Inversion Capacitance = d(QINV)/d(S)

• The TB Hamiltonian can be used 3-5 materials also, but GaAs or other materials was not simulated ( as initially planned) due to lack of time

Part II:Simulation Approach

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Tools of the Trade

• What all do we need? Bulk bandstrcture

• EMA, k•p, TB … which method to choose?• Trade-offs/Advantages in TB

Bandstrcture for M-O-S structure• Different from bulk bandstructure due to confinement

Self-consistent solution of schroedinger-poisson equations

Computing surface potential• How is S related to VGATE ?

Part 2: Approach

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Bandstructure

• Many approaches exist in theory Single/multi-band Effective Mass Approximation (EMA)

• Hartree, Hartree-Fock, Local Density Approximation k•p method - based on the non-degenrate perturbation

theory Empirical and semi-empirical Tight Binding (TB)

• sp3s*, sp3d5s* etc.

Density Functional Theory (DFT)

Which method should I follow?

Part 2: Approach

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Bandstructure (cont.)

• Tight Binding followed in this project

• Main Advantages Atomistic representation with localized basis set It is a real space approach Describes bandstructure over the entire Brillouin zone Correctly describes band mixinga

Lower computational cost w.r.t other method

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Tight Binding Method

• We attempt to solve the one-electron schoredinger equation in terms of a Linear Combination of Atomic Orbitals (LCAO)

1954Slater and Koster

Simplified LCAO Method

1983Vogl et al.

Excited s* orbital

1998Jancu et al.

Excited d orbitals

2003NEMO 3D

Purdue

Ci

orbital

Ci= coefficients i= atomic orbitals (s,p,d)

i

iiiC

site,atomic orbitals,

Rrr

Caution is needed !

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Tight Binding Method (cont.)

• 3 Major assumptions: “Atom-like” orbitals Two center integrals NN interaction

a

(001)

(100)

(010)

(111)

(110)

inbRiR

Type 1

Type 2

• Choice of basis:

Atleast need sp3 for cubic semiconductors

# of neighboring-atom interactions is a choice between computational complexity and accuracy

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Tight Binding Method (cont.)

• The sp3s* Hamiltonian [Vogl et al. J. Phys. Chem Sol. 44, 365

(1983)]

• In order to reproduce both valence and conduction band of covalently bounded semiconductors a s* orbital is introduced to account for high energy orbitals (d, f etc.)

• The sp3d5s* Hamiltonian• [Jancu et al. PRB 57 (1998)]

Many more parameters, but works quite well !

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Tight Binding Method (cont.)

• Hamiltonian in spds* basis:

Hl,l+1

Hl,l-1Hl,l

l+1

l-1

l

1D chain:Hamiltonian is tridiagonal

a

(001)

(100)

(010)

(111)

(110)

Size of each block is 10 x 10

H =

Size of each block is 1 x 1

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Tight Binding Method (cont.)

Each of the elements in the above matrix is a 5 x 5 block

How to treat SO coupling?

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Tight Binding Method (cont.)

• In sp3d5S* TB, SO interaction of d orbitals is ignored, but SO is present for all other orbitals.

• SO interaction happens between orbitals located on the same atom (not neighboring atoms).

Size of each block is 10 x 10 Hamiltonian size is 40 x 40

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Calculated bandstructure

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Applying TB to a MOS structure

Application to finite structure

Size of each block is 10 x 10

11 12

21 22

B

E VH k

V E

Bulk Hamiltonian

2X2 block matrix

Z

X

Type 1

Type 2

11 12

21 22 21

12 11 12TF

E X

X E Y

H k Y E X

MOS Hamiltonian (1D)

NZ X NZ block tridiagonal

NZ Atomic layers

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Applying TB to a MOS structure

Z

X

NX Atomic layers

†

†TB y

A C

C B D

H k D A C

Device Hamiltonian

NX X NX block tridiagonal

Block Size = (NZ Nb) X (NZ Nb)(Nb = 10 for sp3d5)

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Capacitance Calculation

• The schroedinger-poisson equation is solved self-consistently using the method described in the text.

• The total carrier concentration n(z) is calculated as a function of distance by summing up the electron concentration in each energy level.

• For calculating the capacitance, we need to find surface potential at every gate voltage. Ronald van Langevelde,"An explicit surface-potential-based MOSFET

model for circuit simulation", Solid-State Electronics V44 (2000) P409

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Simulation results

0.5

0.6

0.7

0.8

0.9

1

1.1

0.5 1 1.5 2 2.5

Gate Voltage (V)

Su

rfac

e P

ote

nti

al (

V)

Characterization of Inversion-Layer Capacitance of Holes in Si MOSFETs, Takagi et al,TED, Vol. 46, no.7, July 1999.

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Summary

• Quantified the effect of inversion layer capacitance with a good TB model for the Hamiltonian Results agreed with existing published values, so approach

seems to be right. Hamiltonian is not 100% accurate … passivation of surface

states at interface, dangling bonds etc. Simulation was only for a 15 nm “quantum domain”, but still

am able to get good results effectiveness of sp3d5 hamiltonian

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References and Thanks

• Exploring new channel materials for nanoscale CMOS devices: A simulation approach, Anisur Rahman, PhD Thesis, Purdue University, December 2005.

• Characterization of Inversion-Layer Capacitance of Holes in Si MOSFETs, Takagi et al,TED, Vol. 46, no.7, July 1999.

• Ronald van Langevelde,"An explicit surface-potential-based MOSFET model for circuit simulation", Solid-State Electronics V44 (2000) P409

• Dr. Yongke Sun, SWAMP Group, ECE – UF• Guangyu Sun, SWAMP Group, ECE – UF

Questions?