TFET

SIMULATION OF DOUBLE GATE TUNNEL

FIELD EFFECT TRANSISTOR

REQUIREMENT FOR THE AWARD OF THE AWARD OF THE DEGREE OF

Bechelore of Technology

in

Electronics and Communication Engineering

Rasika Gupta

Beena Kothari

Jyotsana Rawat

Parvati Bhandari

2012

DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

G B PANT ENGINEERING COLLEGE

PAURI GARHWAL (UTARAKHAND)-246194

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

Certificate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Acknowlegement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 MOTIVATION FOR THE PRESENT RESEARCH . . . . . . 1

1.2 NATURE OF THE PROBLEM . . . . . . . . . . . . . . . . . . 3

1.3 RECENT RESEARCH RELEVANT TO THE PROBLEM . 3

1.4 RESEARCH PROBLEM STATEMENT . . . . . . . . . . . . . 5

2. DEVICE DESCRIPTION . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 SEMICONDUCTOR PHYSICS . . . . . . . . . . . . . . . . . . 6

2.1.1 SILICON CRYSTAL STRUCTURE . . . . . . . . . . . . 6

2.1.2 ENERGY BAND THEORY . . . . . . . . . . . . . . . . . 6

2.1.3 ELECTRONS AND HOLES . . . . . . . . . . . . . . . . 7

2.1.4 DOPING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 MOSFET AND ITS CHARACTERISTICS . . . . . . . . . . . 9

2.2.1 OPERATING MODES . . . . . . . . . . . . . . . . . . . . 10

2.3 CMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 SCALING AND POWER DENSITY . . . . . . . . . . . 14

2.4 BAND-TO-BAND TUNNELING TRANSISTOR . . . . . . . 14

Contents iii

2.4.1 PRINCILPLE OF OPERATION . . . . . . . . . . . . . . 15

2.5 ADVANTAGES OF PIN TFET OVER MOSFET . . . . . . . 16

2.6 DEVICE DESCRIPTION . . . . . . . . . . . . . . . . . . . . . . 17

2.6.1 STRUCTURE . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.6.2 DEVICE PARAMETERS . . . . . . . . . . . . . . . . . . 18

2.6.3 WORKING . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.6.4 BAND TO BAND TUNNELING TRANSMISSION . 19

2.6.5 SUB-THRESHOLD SWING IN TUNNEL FETS . . . 22

2.6.6 TUNNEL FET TEMPERATURE CHARACTERIS . . 25

3. DEVICE SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1 SILVACOS ATLAS DEVICE SIMULATOR . . . . . . . . . . . 27

3.1.1 ATLAS INPUTS AND OUTPUTS . . . . . . . . . . . . 27

3.1.2 MODES OF OPERATION . . . . . . . . . . . . . . . . . 27

3.1.3 ORDER OF COMMANDS . . . . . . . . . . . . . . . . . 28

3.2 Comparison between MOSFET and DGTFET Transfer Char-

acteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 DGTFET PARAMETERS OPTIMIZATION . . . . . . . . . . 35

3.3.1 DIELECTRIC CONSTANT OF GATE DIELECTRIC 35

3.3.2 THICKNESS OF SILICON BODY . . . . . . . . . . . . 37

3.3.3 CHANNEL LENGTH . . . . . . . . . . . . . . . . . . . . 38

3.3.4 GATE WORK FUNCTION . . . . . . . . . . . . . . . . . 38

3.3.5 GATE DI-ELECTRIC THICKNESS . . . . . . . . . . . 40

3.4 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.1 STRUCTURE AND PARAMETERS . . . . . . . . . . . 40

3.4.2 ON-CURRENT OF DGTFET . . . . . . . . . . . . . . . 41

3.4.3 TRANS-CONDUCTANCE VS VGS CURVE . . . . . 41

3.4.4 ENERGY BAND DIAGRAMS . . . . . . . . . . . . . . . 41

3.4.5 ELECTRIC FIELD . . . . . . . . . . . . . . . . . . . . . . 41

3.4.6 POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4.7 CURRENT FLOWLINES . . . . . . . . . . . . . . . . . . 45

4. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 FUTURE SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A. DECKBUILD CODING FOR ATLAS . . . . . . . . . . . . . . . . . . . . 52

A.1 Code for ON-current comparison between DGTFET before optimiza-

tion and after optimization . . . . . . . . . . . . . . . . . . . . . . . 52

Contents iv

A.2 Code for contour plots comparison between DGTFET before optimiza-

tion and after optimization . . . . . . . . . . . . . . . . . . . . . . . . 55

List of Figures

2.1 A simple diagram of an isolated si atom and si crystal structure . . . 8

2.2 A basic energy diagram at 0K . . . . . . . . . . . . . . . . . . . . . . 8

2.3 A basic energy diagram at room temperature . . . . . . . . . . . . . . 8

2.4 crystal lattice structure doped with a Boron impurity . . . . . . . . . 9

2.5 Structure of a MOSFET . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 crossection of MOSFET operating in linear region . . . . . . . . . . . 11

2.7 crossection of MOSFET operating in saturation . . . . . . . . . . . . 12

2.8 Structure of a CMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.9 (a) Active power consumption has been increasing with shrinking tech-

nology nodes (b)Standby leakage power also increasing with shrinking

technology nodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.10 Left: Structure of a n-i-p Tunnel FET with external voltage sources.

Right: Band profile of the Tunnel FET in the off-state without applied

VDS. The bandgap blocks any current flow between source and drain.

The Fermi-distributions in source and drain are plotted in gray . . . . 15

2.11 n-FETs. (a) Single-gate. (b) DG. SiO2 and high- gate dielectrics . . . 18

2.12 : Energy band diagrams taken horizontally across the body of a Tun-

nel FET in (a) the off-state where the only current comes from p-i-n

leakage, (b) the on-state with a negative bias on the gate leading to

pFET-type behaviour, and (c) the on-state with a positive bias on the

gate leading to nFET-type behavior. . . . . . . . . . . . . . . . . . . 19

List of Figures vi

2.13 : Band-to-band tunneling can be calculated by approximating the

energy barrier width by a triangular potential energy barrier, where

the electrons must tunnel through the widest distance at the base of

the triangle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.14 Energy band cross section of a Tunnel FET showing the triangular

barrier approximation within the bands, , the screening length , and

the filtering behavior of the device in the on-state . . . . . . . . . . . 22

2.15 Dependence of the Tunnel FET subthreshold slope on gate voltage for

different dielectric constants . . . . . . . . . . . . . . . . . . . . . . . 24

2.16 comparison of IDS-VGS for a conventional MOSFET and a Tunnel FET 24

2.17 Visual definitions of point swing, taken at the steepest point of the

IDS-VGS curve, and average swing, taken as the average from turn-on

to threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.18 Simulated IDS-VGS characteristics for various temperatures for a double-

gate Tunnel FET with dielectric = 21. VDS = 1 V. As temperature

increases, Ioff increases, but Ion changes very little. Inset: Subthresh-

old swing at specific VGS values, vs. temperature in Kelvin. The

swing is only slightly affected by changes in temperature. . . . . . . . 25

3.1 ATLAS Inputs and Outputs . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Comparison of mesh grids when using a multiplier of 5 and 1 . . . . . 30

3.3 ATLAS Mesh and Region Boundaries for a DGTFET . . . . . . . . . 30

3.4 ATLAS Doping Profile of DGTFET . . . . . . . . . . . . . . . . . . . 31

3.5 Some of the mobility models available in ATLAS . . . . . . . . . . . 32

3.6 DGTFET Transfer Characteristics for various Gate Dielectric . . . . 34

3.7 Characteristics of a simplified single-gate NMOSFET for various gate

dielectrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.8 DGTFET Transfer Characteristics for various Gate Dielectric . . . . 36

3.9 DGTFETTrans-conductance (gm) vs VGS Curve for various Dielectrics

(VDS=1V, L=50 nm, tox=3 nm, tsi=10 nm) . . . . . . . . . . . . . . 36

3.10 DGTFET Transfer Characteristics for various tsi . . . . . . . . . . . 37

3.11 DGTFET Trans-conductance (gm) vs VGS Curve for various tsi . . . 37

3.12 DGTFET Transfer Characteristics for various channel lengths, L . . . 38

3.13 DGTFET Trans-conductance (gm) vs VGS Curve for various L (Other

parameters are same as for Fig.6.1) . . . . . . . . . . . . . . . . . . . 38

3.14 DGTFET Transfer Characteristics for various gate work function . . 39

List of Figures vii

3.15 DGTFET Trans-conductance (gm) vs VGS Curve for various gate

work function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.16 DGTFET Transfer Characteristics for various gate dielectric thickness 40

3.17 DGTFET Trans-conductance (gm) vs VGS Curve for various gate di-

electric thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.18 Optimized structure of DGTFET . . . . . . . . . . . . . . . . . . . . 42

3.19 Comparison of ON-Current for optimized DGTFET and DGTFET

before optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.20 Comparison of transconductance vs VGS curve for optimized DGT-

FET and DGTFET before optimization . . . . . . . . . . . . . . . . 43

3.21 Energy Band Diagram of DGTFET before Optimization . . . . . . . 43

3.22 Energy Band Diagram of DGTFET after Optimization . . . . . . . . 43

3.23 Contour plot of Electric Field across DGTFET before optimization . 44

3.24 Contour plot of Electric Field across DGTFET after optimization . . 44

3.25 Contour plot of potential across DGTFET before optimization . . . . 45

3.26 Contour plot of potential across DGTFET after optimization . . . . . 45

3.27 Contour plot of current flowlines in DGTFET before optimization . . 46

3.28 Contour plot of current flowlines in DGTFET after optimization . . . 46

Abstract

The down-scaling of conventional MOSFETs has led to an impending power crisis,

in which static power consumption is becoming too high. In order to improve the

energy-efficiency of electronic circuits, small swing switches are interesting candidates

to replace or complement the MOSFETs used today. Tunnel FETs, which are gated

p-i-n diodes whose on-current arises from band-to-band tunneling, are attractive new

devices for low-power applications due to their low off-current and their potential for

a small subthreshold swing.

The numerical simulations presented in this thesis have been carried out using

a non-local band-to-band tunneling model in Silvaco Atlas. Numerical simulations

based on correct underlying models are important for emerging devices, since they

can provide insights about optimization before fabrication is carried out, can aid the

understanding of device physics through 1D and 2D cross sections, and can be the

basis for the formation of an accurate compact model.

Certificate

This is to certify that the project entitled SIMULATION OF DUAL GATE

TUNNEL fIELD EFFECT TRANSISTOR being submitted by RASIKA GUPTA,

BEENA KOTHARI,JYOTSANA RAWAT AND PARVATI BHANDARI to Depart-

ment of Electronics and Communication Engineering, G B Pant Engineering College,

Pauri Garhwal (Uttarakhand) for the award of Bachelor of Technology in Electron-

ics and Communication Engineering, is a bonafide work carried out by them under

my guidance and supervision. The results embodied in the report have not been

submitted for the award of any other degree.

I wish them all success in their future endeavours.

Date: 2 June 2012

Place: GBPEC, Pauri

Mr.Balraj Singh

Assistant Professor

Deptt of Electrical & Electronics Engg

G.B. Pant Engineering College

Pauri Garhwal (UK)-246194

Preface

One goal of this thesis is to stay within the framework of what is possible in standard

industrial nano-electronics clean-rooms today, without requiring processes whose

mastery lies many years in the future. For this reason, the focus of this thesis is

on all-silicon devices

The optimization of the static characteristics of a Tunnel FET is carried out,

looking at dielectric constant of gate dielectric (ox), silicon body thickness (tsi),

Channel Length (L), gate work function () and gate dielectric thickness (tox).

Numerical simulations have proven to be an effective means to investigate Tun-

nel FET behaviour and the dependence of its static characteristics on changes in

dimensions, doping, and other parameters. The work presented here can be useful to

other researchers who will be designing and fabricating Tunnel FETs, and developing

analytical and compact models for these devices.

Acknowlegement

This little work of creation would not have been possible without the kind help,

coordination and extended support of some people. Thanks first and foremost to Mr.

Balraj Singh, Asst Professor, the project guide who helped us find this interesting

thesis topic.

We would like to thank Dr. Y. Singh (H. O. D.), ECE Department, for his

guidance, intelligent instructions in the details of semiconductor device operations

and for sharing his knowledge and working with us on several Tunnel FET studies

and publications. His constructive criticism and timely review on the project has

resulted in several improvements in the project. We would like to thank again to

Dr. Y. Singh (H.O.D.) and Dr. A. K. Gautam, Associate Professor, GBPEC for

providing us the facilities and making us strive for the best possible output under

their ardent observations.

Last but not the least we would like to thank our institute G.B.P.E.C, Pauri, for

including such type of curriculum that helped us improves our knowledge.

RASIKA GUPTA

BEENA KOTHARI

JYOTSANA RAWAT

PARVATI BHANDARI

CHAPTER 1

INTRODUCTION

1.1 MOTIVATION FOR THE PRESENT RESEARCH

At present there is a power crisis currently faced by conventional MOSFETs, due

to their ever increasing static power consumption. The reason behind this is that

in previous simulations MOSFET was scaled by keeping the electric fields inside it

unchanged . For this all device dimensions were scaled by 1/, while the doping of the

source and drain regions was increased by a factor of . Applied voltages were scaled

by 1/.

But this scaling [8] rule no longer worked well as due to scaling 1.4 m node changes

to the 65 nm node and supply voltage VDD decreased to about 20

The most important consequence of VDD reducing during device scaling while

VT reduces significantly less, is that the gate overdrive, also goes down. When

gate overdrive decreases, on-current decreases, which negatively affects device per-

formance, the Ion/ Ioff ratio and dynamic speed (Cg VDD/Ion). There are two

possible solutions to this problem of needing a high gate overdrive: either VDD can

stay higher than it should with constant field scaling [?], or VT can be scaled down

more aggressively.

In order to maintain acceptable levels of gate overdrive, VDD scaling has slowed

down drastically. When the supply voltage decreases along with device dimensions,

then the power density remains constant, which means that the energy needed to

drive the chip, and the heat produced by the chip, remain constant. If VDD does not

decrease, and yet device dimensions decrease, and more devices are added to a chip

Chapter 1. INTRODUCTION 2

such that chip size is not significantly reduced, then it can be expected that power

consumption will rise considerably.

Second option for keeping a high gate overdrive: scaling down VT. Is to decrease

sub threshold swing S = dV GS/d(log IDS) and if we want to shift VT by 60 mV,

then the price to pay is an increase of one dynamic, static power and off current. If we

want to decrease VT by shifting the curve left, we pay a price in leakage current [9].

Over the last decades, the continuous down-scaling of metal-oxide-semiconductor

field-effect transistors (MOSFETs) [22] enabled faster and more complex chips while

at the same time the space and power-consumption [23] was kept under control. Since

logic devices operate at a given on/off-current-ratio, the limited sub threshold swing

will prevent further reduction of the operation voltage, which is the main parameter

to reduce the power consumption.

Our report started with the history of transistors that use band-to-band tunnel-

ing [20] current in their on-state, starting from 1978 and continuing to the present

day (2010), showing that the Tunnel FET is still an emerging device with much

unexplored potential.

The basics of semiconductor materials ,then the structure , working and charac-

teristics of MOSFET, tunnel MOSFET and double gate tunnel MOSFET [26] are

discussed.

At this time we would like our computers, appliances, and gadgets to use less

power [22] because its better for the environment. On a more personal level, its

less expensive to use less electricity. On a practical level, its more convenient for

battery-operated gadgets because their batteries will last longer before needing to be

charged. And on a comfort level, it is better when laptops and hand-held gadgets

have a lower power density and therefore produce less heat.

This too has a limit, since we would like our appliances, computers, and gadgets

to stay the same size or shrink, not get larger in order to accommodate a large heat

sink required by the power-hungry chip inside. This give motivation order to circuit

engineers to design circuit that respond to the power crisis, a handful of currently-

used circuit-level solutions will be presented in this section. One efficient solution for

reducing leakage is to cut off the power supply to idle circuit blocks by using sleep

transistors.

Second solution for power crisis is to design conventional MOSFETs with S

60mV/decade [34] at room temperature. Example of small swing device is IMOS

which is a gated p-i-n junction whose gate is offset from one of the junctions such a

very high electric field exists in the non-gated portion of the i-region when the device

is on, leading to avalanche breakdown. The impact ionization [32] process means


that the IMOS can have a very small sub threshold swing and high on-current.

Further researched examples are shown MEM and NEM switches, then Tunnel

Fet and finally double gate Tunnel Fet.

Therefore in our current project we worked on previously designed dual gate

tunnel Fet and then optimized its parameters for better performance .

1.2 NATURE OF THE PROBLEM

Numerical simulations of DG Tunnel FETs [10] such as the ones presented in this

thesis allow the investigation of the device physics, with the possibility to see inside

a device through cross sections in 2D to obtain optimal DGTFET structure for low

power application [30].

1.3 RECENT RESEARCH RELEVANT TO THE PROB-

LEM

Quinn et al. at Brown University were the first to propose the gated p-i-n struc-

ture of a Tunnel FET [32] in 1978, and suggested the usefulness of this device for

spectroscopy.

In 1995, Reddick and Amaratunga at Cambridge, seemingly unaware of all the

previously mentioned work, published measured characteristics of silicon Surface Tun-

nel Transistors [24]. They were motivated by the desire for devices that would be

faster than conventional MOSFETs, as tunneling devices are, and that could be scaled

down more easily without running into problems such as punch-through. They are

sometimes erroneously given credit for being the first to make silicon Tunnel FETs [7].

In 1997, Koga and Toriumi at Toshiba proposed a post-CMOS three-terminal

silicon tunneling device [15] with the same structure as a Tunnel FET, though the

experimental results which were presented showed a device that was forward-biased.In

2000, Hansch et al. at the University of the German Federal Armed Forces in Munich

showed experimental results from a reverse-biased vertical silicon tunneling transistor

[32], with a highly-doped boron delta-layer [17] to create an abrupt tunnel junction,

and noted the saturation behaviour in the ID-VG characteristics.

In 2004, band-to-band tunneling was demonstrated in carbon nanotube (CNT)

FETs [14] by Appenzelleret al. In order to create the energy bands necessary for

tunneling, a back gate and a top gate were used. The researchers claimed that the

one-dimensionality of the CNTs led to extremely different band bending conditions


than those in 3D semiconductors. A subthreshold swing [16] smaller than the 60

mV/dec limit of conventional MOSFETs was reported for the first time.

In 2006, Zhang et al. at Notre Dame remarked once again what others before

them had noticed that theoretically, it is indeed possible for Tunnel FETs to have

a sub-threshold swing lower than 60mV/dec [33]. The structure they studied was

a gated p-n diode, but the general equations they put forth, and the band-to-band

tunneling behaviour, would be the same as for a gated p-i-n structure.

In 2007, Verhulst et al. at IMEC showed by simulation that shortening Tunnel

FET gate length [29], so that the gate covers the source-side junction where tunneling

takes place, but does not cover the majority of the intrinsic region, has the benefits of

decreasing off-current (tunneling through the drain-side junction) and reducing speed,

with a small or no reduction in the on-current, depending on the device design. In

the same year, Toh at the National University of Singapore published a study of

double-gate Tunnel FET silicon body thickness optimization, in which he showed an

optimal device thickness for maximum on-current.

There were also some fabricated Tunnel FET results in 2009. Sandow et al.

from Forschungszentrum Jlich published experimental data for p-type Tunnel FETs

on SOI [9] [21], showing the effects of varying source and drain doping levels, gate

dielectric thickness, and device length.

Luisier et al. at Purdue University did an atomistic study of InAs Tunnel FETs

[16], in which they found that subthreshold swings of less than 60 mV/decade at room

temperature could only be attained if single-gate body thicknesses were less than 4

nm, and double-gate body thicknesses [1] were less than 7 nm, or for nanowires

[31]of less than approximately 10 nm diameter. Looking at more exotic material

systems, Tunnel FETs could one day be fabricated on grapheme nanoribbons [31],

which are basically unrolled single-walled carbon nanotubes [14]. The simulated

transfer characteristics presented in represent the extremely optimistic upper bounds

of possible device performance and reach a simulated subthreshold swing of 0.19

mV/dec.

In 2010, Kathy Boucart and Adrian Mihai Ionescu, Member, IEEE proposed and

validated a novel design for a double-gate tunnel field-effect transistor (DG Tunnel

FET) [5], for which the simulations show significant improvements compared with

single-gate devices using an SiO2 gate dielectric. Showing an ON-current as high as

0.23 mA for a gate voltage of 1.8 V, an OFF-current of less than 1 fA (neglecting gate

leakage), an improved average sub-threshold swing of 57 mV/dec, and a minimum

point slope of 11 mV/dec.


1.4 RESEARCH PROBLEM STATEMENT

The work accomplished in this dissertation has been carried out in terms of the

following intermediate stages as follows: 1. Simulation of Dual Gate TFET device

structure. 2. Optimization of device parameters to improve sub-threshold swing and

ON-current.

CHAPTER 2

DEVICE DESCRIPTION

2.1 SEMICONDUCTOR PHYSICS

When discussing basic electrical properties, materials can be broken into three basic

categories: insulator, conductor and semiconductor. Semiconductors are the most

intriguing type of material and have lead the way for the many of the advancements

of technology in society. The most basic intrinsic semiconductor is silicon and it will

be used to demonstrate basic semiconductor physics and operation [2].

2.1.1 SILICON CRYSTAL STRUCTURE

The Periodic Table shows that Silicon (Si) is a Group IV element. By being a Group

IV element when isolated it has 4 electrons in its outer most shell [11].

These electrons are called valance electrons and when perfect pure Silicon crys-

tal structure occurs these electrons are shared between atoms next to each other

producing a bonded diamond structure. This bonded pure intrinsic Silicon is an

ideal structure at zero Kelvin with no impurities or crystal defects. To understand

what happens when temperature increases or impurities are added knowledge of band

theory is required [11].

2.1.2 ENERGY BAND THEORY

Energy band theory is an important concept in explaining how electrons react to

different conditions within a crystal structure. The spread of energies of electrons can

Chapter 2. DEVICE DESCRIPTION 7

Fig. 2.1: A simple diagram of an isolated si atom and si crystal structure

be described by a set of allowed states that are called energy bands [Ref.fig2.2]. These

energy bands consist of a lower band of energy states called the valence band, an

upper band of energy states called the conduction band and the energy gap between

these states, which is called the bandgap [Ref.fig2.2]. Electrons must either exist

in the Conduction Band or the Valence Band. Different elements have different

value bandgaps and these different bandgaps greatly affect these elements electrical

properties. The Fermi level (EF) is also used in the band diagram and it denotes the

average energy level for electrons. In an intrinsic semiconductor EF is usually placed

in the center of the bandgap. Elements with larger bandgaps are insulators, with no

bandgaps or negative band gaps are conductors and semiconductors fall in between

the two . For a material to conduct electricity it must have electrons in the conduction

band or holes in the valance band. Electrons naturally gravitate towards lower energy

levels and when an element is at zero Kelvin the valance band is completely full of

electrons and the conduction band is completely void of electronics [2].

Fig. 2.2: A basic energy diagram at 0K


Electrons in the conduction band are called free electrons. These electrons are

free to move and allow electricity to conduct through the material. Semiconductors,

like silicon, at room temperature have a limited population of free electrons that

can be artificially increased or decreased to change the materials ability to conduct

electricity.At room temperature the free electrons in the conduction band at equilib-

rium are caused by thermal generation. Thermal generation is the lattice vibrations

that apply enough energy for electrons to jump the bandgap and become free in the

conduction band [11].

Fig. 2.3: A basic energy diagram at room temperature

2.1.3 ELECTRONS AND HOLES

When an electron is excited and moves from the valance band to the conduction band

the absences of the electron in the bond is called a hole. These electrons and holes

provide a method of current flow through a semiconductor. When a hole is created a

free electron will move and fill it. When the electron moves to fill the hole it leaves a

hole behind. This gives the appearance of a hole moving in the opposite direction of

the electron. This apparent movement is called hole flow. When an electric field is

applied to a semiconductor the electrons will move towards the negative side of the

field and the holes will move towards the positive side [11].

2.1.4 DOPING

The electrical properties of pure Si can be greatly changed by introducing small

amounts of impurities. Since Si is a Group IV, and has 4 valance electrons, it forms

strong covalent bonds with the other Si atoms in the diamond lattice. During a

covalent bond two atoms supply electrons to fill each others valance band. This


forms a strong bond because both atoms treat the shared electrons as there own .

If a Group III atom, such as Boron (B), is added as a dopant to a pure Si lattice

it will change the electrical properties of the semiconductor. Boron only has three

electrons in its valance shell when it bonds with four Si atoms in the lattice one of

the covalent bonds will be missing an electron which will be a hole. Nearby electrons

can tunnel into this hole and this will make a hole away from the original B impurity.

This action is repeated until a free hole is created. Since the B atom creates this hole

that will accept an electron therefore it is called an acceptor. This doping produces

a p-type extrinsic semiconductor [11].

Fig. 2.4: crystal lattice structure doped with a Boron impurity

Intrinsic Silicon can also be doped with a Group V element such as Arsenic

(As).Since As has five valance band electrons when it bonds with four Si atoms in

the lattice structure there is one extra electron which is not used in the covalent

bonds. This extra electron continues to orbit the As within the Si lattice structure.

It takes very little energy to free the extra electron and it is usually freed by the

thermal energy of atomic vibrations at room temperature. Since As donates an

electron to the conduction band it is called a donor. This type of doping produces

an n-type material.

2.2 MOSFET AND ITS CHARACTERISTICS

A MOSFET is based on the modulation of charge concentration caused by a MOS

capacitance. The structure of a MOSFET is shown in Figure 3.5. The MOSFET has

two terminals, called source and drain, which are connected to highly doped regions

which are separated by a region called the channel. These regions are either p- or n-

type, but they must both be of the same type. The highly doped regions are denoted


by a + following the type of doping as shown in the Figure5 and are separated by a

doped region of opposite type, known as the body or substrate. This region is not so

highly doped. The third electrode in the MOSFET, called the gate, is located above

the body and insulated from all of the other regions by an oxide (usually an oxide of

Si) [2].

Fig. 2.5: Structure of a MOSFET

The source is so named because it is the origin of the charge carriers (electrons

for n-channel, holes for p-channel) that flow through the channel; similarly, the drain

is where the charge carriers leave the channel. The MOSFET can be of n-channel or

p-channel depending on the doping material in the source and drain of the MOSFET.

The MOSFET can be of two types; Depletion MOSFET and Enhancement MOSFET.

In the case of depletion type of MOSFET the channel is lightly doped with the same

material as that of source and drain to reduce the threshold voltage. The operation of

both types of MOSFETs is similar and is used depending on the applications. Since

the enhancement MOSFET is common, the operation discussed here are based on

enhancement MOSFET only. The different modes of operation of an enhancement

type MOSFET are discussed below.

2.2.1 OPERATING MODES

In the case of n-channel MOSFET, when there is no voltage applied to the gate there

is no channel formation between source and drain and hence there is no current flow

between them. However, when a positive gate-source voltage is applied, it creates a

channel at the surface of the p- region which is negatively charged, under the oxide.

When a negative voltage is applied between gate and source, the channel disappears

and no current can flow between the source and the drain.


If the MOSFET is a p-channel or p-MOSFET, then the source and drain are P+

regions and the body is an n- region. When a negative gate-source voltage is applied,

it creates a channel which is positively charged at the surface of the nregion, just

below the oxide. The operation of a MOSFET can be divided into three different

regions, depending upon the voltages at the terminals. The three regions of operation

are cutoff, linear and saturation which are explained below [2]

1 Cut-off or subthreshold mode (WhenV GS < V th ) where Vth is the threshold

voltage of the device and VGS is the gate to source voltage)Under these operating

conditions the transistor is turned off, and there is minimal conduction between the

drain and source. However, the Boltzmann distribution of electron energies allows

some energetic electrons at the source to enter the channel and flow to the drain

creating a diffusion current. This subthreshold current is an exponential function of

the gate to source voltage. The current between the drain and source should ideally

be zero when the transistor is being used as a turned-off switch; the weakinversion

current, sometimes called subthreshold leakage is very critical in low power digital

circuit]. However, the subthreshold current or weak inversion region is an efficient

region of operation in some analogue circuits.

2 Triode or linear region ( When V GS > V th and V DS < V GSV TH ) In the

linear region where the gate to source voltage VGS is greater than the threshold

voltage Vth the transistor is turned on, and a channel has been created which allows

current to flow between the drain and source. This condition is depicted in Figure

3.6. The MOSFET operates like a resistor, controlled by the gate voltage relative to

both the source and drain voltages.

Fig. 2.6: crossection of MOSFET operating in linear region


The drain current is given by the relation

Id = nCoxW

L((V gs V th)V ds V ds

2

2)

Where n is the charge-carrier mobility, W is the gate width, L is the gate length

and Cox is the gate oxide capacitance per unit area.

Saturation (WhenV GS < VDS and V DS < V GS V TH ) In this case whenthe drain voltage is increased, a channel has been created, which allows current to

flow between the drain and source. Since the drain voltage is higher than the gate

voltage, a portion of the channel is turned off. The onset of this region is also known

as pinch-off. In this region the drain current is now relatively independent of the

drain voltage and the current is controlled by only the gate to source voltage. This

operating condition is shown in Figure 3.7

Fig. 2.7: crossection of MOSFET operating in saturation

The equation for the current in this region is given by

Id = nCoxW

2L(V gs V th)2

For larger drain biases, the length of the inverted drain region decreases with

increase in drain bias leading to channel length modulation which is discussed later

in this chapter. Channel length modulation leads to an increase of current in the

channel with drain bias and hence a lower output resistance for the MOSFET .

above Equation can be multiplied by (1 + VDS) to take account of the channel

length modulation effect; where is the channel length modulation parameter.


2.3 CMOS

A balance of low power and high throughput are the main goals which the mi-

croelectronics industry must address in satisfying the demand for more advanced

applications in the consumer market sector for portable equipment in the modern

world. The designer can make optimizations at all levels of the design space, which

have a cumulative effect on the overall system power reduction. Much work has been

concentrated on architecture, algorithm, and system-level power minimization. The

technology for IC manufacturing is the only level that the designer has limited con-

trol to meet the constraints. Complimentary Metal Oxide Semiconductors (CMOS)

circuits were invented in 1963 by Frank Wanlass at Fairchild Semiconductor as a low-

power alternative to Transistor Transistor Logic (TTL). The first CMOS integrated

circuits were made by Radio Corporation of America (RCA) in 1968 by a group

led by Albert Medwin . CMOS found applications in the watch industry and in

other fields where battery standby capability was more important than speed. After

around twenty-five years, CMOS has become the predominant technology in digital

integrated circuits and still maintains this position. The main advantages of CMOS

over TTL are its energy efficiency, smaller area occupation, comparable operating

speed and manufacturing costs . CMOS benefits from the geometric scaling of di-

mensions that comes with every new technology node associated with semiconductor

processing. Besides all these advantages, low-power dissipation and larger integration

densities, compared to bipolar junction transistors, has made it the mainstay of the

microelectronics world. CMOS uses a combination of p-type and n-type MOSFETs

on the same substrate to implement logic gates and other digital circuits found in

computers, telecommunications and signal processing equipment. Figure 3.8 shows

the structure of a CMOS [23].

Fig. 2.8: Structure of a CMOS


2.3.1 SCALING AND POWER DENSITY

Generations of CMOS technologies have thrived from scaling transistor dimensions.

While scaling primarily drives cheaper and denser integrated circuits because of the

reduced area, it also drives faster circuits. The increase in circuit density and func-

tionality yields higher computing power at the cost of increased power consumption

per chip. As the number of transistors per unit area increases the rising power density

leads to severe packaging/thermal management concerns. There is also the issue of

increased leakage power and its impact on the battery life of electronic equipment [4].

Fig. 2.9: (a) Active power consumption has been increasing with shrinking tech-nology nodes (b)Standby leakage power also increasing with shrinkingtechnology nodes.

Figure 3.9(a) and 3.9(b) illustrate the increase in active power consumption and

standby leakage (subthreshold leakage) power consumption for various CMOS tech-

nology nodes . The active and standby power is seen to increase steadily with scaling

transistor dimensions. As shown by the equations embedded in the figures both ac-

tive and standby power scale with the operation voltage (Vdd) and can therefore be

reduced by scaling Vdd. Figure 3.10 shows that Vdd scaling has however remained

stagnant at 1V for several technology generations now.

2.4 BAND-TO-BAND TUNNELING TRANSISTOR

Although the principle of band-to-band tunneling [8] was already discovered in 1957

by L. Esaki and the first gated p-i-n structure was proposed in 1978 , the interest in

the first results on TFETs was limited. This changed rapidly after W. Hansch and I.

Eisele et al. started to investigate the TFET in 2000 and J. Appenzeller et al. found

in 2004 that the TFET might provide a means to overcome the 60 mV/dec switching


limit of the classical MOSFET. Following these initial results, several groups started

to study the theoretical aspects of TFET operation. Among those were the impact

of the channel dimensionality , power consumption , phonon scattering [18], tem-

perature dependence, gate overlap , threshold voltage , performance comparison to

CMOS, heterostructure TFETs, strain and general modeling. While Appenzellers

results were obtained with carbon-nanotube FETs [14], the adoption of the operat-

ing principle to silicon FETs seems to be more attractive because the mature silicon

technology

Fig. 2.10: Left: Structure of a n-i-p Tunnel FET with external voltage sources.Right: Band profile of the Tunnel FET in the off-state without appliedVDS. The bandgap blocks any current flow between source and drain.The Fermi-distributions in source and drain are plotted in gray

2.4.1 PRINCILPLE OF OPERATION

The device structure of the TFET resembles that of the MOSFET with one exception.

While in the MOSFET, source and drain are doped with the same type of dopant,

in the TFET, source and drain are of opposite doping types. The device structure

and band profile in equilibrium are drawn in Figure 2.10. In equilibrium, the built-in

potentials of the p-i and n-i junctions result in a staircase-like band-profile. If a small

VDS is applied to the equilibrium state [12], electron and hole currents are blocked by

the built-in potential barriers. This is the off-state of the TFET. Now, if a negative

gate-bias is applied, the bands in the channel move up. For negative VDS, charge

carriers can tunnel through the bandgap at the source/channel junction as soon as

the valence band in the channel is lifted above the conduction band in the source.

This operating mode is the p-channel on-state of the TFET because holes accumulate

in the channel. The n-channel on-state can be created by applying a positive VGS


and negative VDS. In this case, the bands in the channel move down and tunneling

occurs at the channel-drain junction as soon as the conduction band in the channel

is pushed below the valence band in the drain [6].

2.5 ADVANTAGES OF PIN TFET OVER MOSFET

With the continual miniaturization of the MOSFET transistors, power dissipation

in integrated circuits has become a major roadblock to performance scaling [19] .

For more than 30 years, numerous breakthroughs in device and material design have

sustained an exponential increase in system performance. The recent introduction

of high-k gate oxides into semiconductor technology has also allowed much needed

reduction in gate leakage and improved the scalability of future devices. Neverthe-

less, the physical operational principles of conventional MOSFETs, based on the

thermionic emission of carriers over a channel barrier, have imposed fundamental

limits on voltage scaling and the reduction of energy dissipation. The subthreshold

swing (S) of a conventional MOSFET, which determines the ability to turn off the

transistor with the gate gate (VGS), has a fundamental limit of ()2.3BkTq where

kB, T, and q are the Boltzmann constant, temperature, and the electron charge, re-

spectively (S = 60mV/decade at room temperature) [4]. Therefore, the requirement

of achieving a large on-state current (ION), while maintaining a small off-state leak-

age (IOFF), has hindered the scaling of the power supply voltage (VDD) in recent

years . Consequently, a device with S below the aforementioned conventional limit

is desirable for continued voltage scaling, and thereby reducing power dissipation in

circuits.

Field-effect transistors based on the band-to-band tunneling (BTBT) [20] phe-

nomenon are being actively investigated due to their potential for low standby leakage

. It has been predicted through detailed device simulations that BTBT FETs could

produce subthreshold swings below the thermal limit in conventional semiconductor

materials such as silicon , as well as in carbon nanotube (CNT) based transistors .

Indeed, this has been experimentally demonstrated in CNTs and more recently with

a silicon based BTBT FET . BTBT occurs in two different transistor geometries; a

popular p-i-n geometry (hereafter called the TFET), and the conventional MOSFET

. In the case of CNT-MOSFETs it has been established that BTBT is dominated by

phonon assisted inelastic tunneling that severely deteriorates the device characteris-

tics . On the other hand, phonon scattering has a less dramatic effect on TFETs,

and useful device properties are preserved under practical biasing conditions . The

important task of a comprehensive comparison of device performance between the


p-i-n TFET and the conventional n-i-n MOSFET geometries. Here, we use CNTs

as the model channel material due to many benefits of that system. CNTs [14]

allow one-dimensional carrier transport without depletion capacitance effects, and

high performance transistors that operate near the ballistic limit have already been

demonstrated . They also have a direct energy bandgap and small carrier effective

masses that are favorable for BTBT devices . Furthermore, a detailed simulation

framework has been developed for modeling carrier transport through CNT transis-

tors , and benchmarked against experiments. Therefore, many realistic aspects, such

as the effect of phonon scattering on device performance, have been comprehensively

explored in the case of CNT based MOSFETs as well as TFETs . Previous work has

also compared CNT transistor performance to that of silicon transistors and to that

based on silicon nanowires . Here we use similar device metrics to compare the per-

formance between TFETs and MOSFETs using a uniform simulation environment

for both the devices.

2.6 DEVICE DESCRIPTION

Tunnel FETs, also referred to as TFETs, Surface Tunnel Transistors (STTs) or

Tunneling FETs, are promising devices to complement or even replace conventional

MOSFETs for low-power applications. They offer the potential for a very low off-

current and a small subthreshold swing [16]. Tunnel FETs are interesting as low-

power devices because of their quantum tunneling barrier. When the devices are

turned on, the carriers must tunnel through the barrier in order for current to flow

from source to drain. When the devices are off, the presence of the barrier keeps the

off-current extremely low, several orders of magnitude lower than the off-current of

a conventional MOSFET.

2.6.1 STRUCTURE

Tunnel FETs are gated p-i-n diodes [19], or less commonly, gated p-n diodes. To

switch the device on, the diode is reverse biased, and a voltage is applied to the

gate. In order to be consistent with MOSFET technology, the names of the device

terminals are chosen such that voltages are applied in a similar way for Tunnel FET

operation. Since a reverse bias is needed across the p-i-n structure in order to create

tunneling, and since an NMOS operates when positive voltages are applied to the

drain and gate, the n-region of a Tunnel FET is referred to as its drain, and the p+

region as its source for an ntype device.


Fig.5.1 shows the basic device structure for a typical p-i-n Tunnel FET. The

structure shown is an n-type device, with a p+ source and an n+ drain. In a p-type

Tunnel FET, the source would be doped n+ and the drain would be doped p+.

Fig. 2.11: n-FETs. (a) Single-gate. (b) DG. SiO2 and high- gate dielectrics

2.6.2 DEVICE PARAMETERS

The double-gate n-type Tunnel FETs investigated here have been simulated with

Silvaco Atlas, version 5.11.24.C. In all simulations, junctions were quasi-perfectly

abrupt (junction width 0.5 nm), and the p-type source, intrinsic region, and n-type

drain were doped at 1x1020, 1x1017, and 5x1018 atoms/cm3 respectively. The silicon

body thickness is 10 nm.

The gate dielectric covers the drain, intrinsic region, and source in all simulations.

Three different gate stacks were studied. The first uses 3 nm of SiO2 as a gate

dielectric ( = 3.9). The second employs 3 nm of a high-k dielectric [6] ( = 25),

which could be HfO2 or ZrO2. The third incorporates a gate dielectric with two

components: a 1 nm interfacial layer of oxynitride ( = 5.7) and 2 nm of a high-k

dielectric ( = 25), corresponding to a more realistic fabrication process. All Tunnel

FETs simulated here use a midgap (metal) gate work function of 4.5 eV.

2.6.3 WORKING

When a Tunnel FET is OFF, only p-i-n diode leakage current flows between the source

and drain, and this current can be extremely low (less than a fA/m). Fig.5.2(a) shows

the energy bands horizontally across the body of a Tunnel FET in the off-state [10],

with a reverse bias applied across the p-i-n junction, but no voltage applied to the

gate. When a Tunnel FET is designed with symmetry between the n- and p-sides


(similar doping levels, similar gate alignment, etc.), the device exhibits ambipolar

behavior, whereby the transfer characteristics resemble those of a pFET when a

negative voltage is applied to the gate, and those of an nFET when a positive voltage

is applied to the gate.

Fig.5.2(b)shows the energy bands with a reverse bias applied across the device,

and a negative voltage applied to the gate [10]. The energy bands in the intrinsic

region under the gate are lifted, and the energy barrier is now small enough for band-

to-band tunneling to take place between the valence band of the intrinsic region and

the conduction band of the n+-region.

When a positive voltage is applied to the gate, on the other hand, the energy

bands in the intrinsic region are pushed down, as in Fig. 5.2(c), and tunneling takes

place between the valence band of the p+-region and the conduction band of the

intrinsic region [10]. The energy barrier width for band-to-band tunneling is the

single most important factor that determines the amount of drain current through a

Tunnel FET.

Fig. 2.12: : Energy band diagrams taken horizontally across the body of a TunnelFET in (a) the off-state where the only current comes from p-i-n leakage,(b) the on-state with a negative bias on the gate leading to pFET-typebehaviour, and (c) the on-state with a positive bias on the gate leadingto nFET-type behavior.

2.6.4 BAND TO BAND TUNNELING TRANSMISSION

An expression for the band-to-band tunneling [20] current in Tunnel FETs can be

found by using the WKB approximation and taking the tunnel barrier as a triangu-

larly [28] shaped potential barrier as shown in Fig.5.3 With the WKB approximation,

the band-to-band tunneling transmission is given by


Tt exp

x2

x1

|k(x)| dx (2.1)

where k(x) is the quantum wave vector of the electron inside the barrier. Inside

a triangular barrier, the wave vector is

k(x) =

2m

h2(PE E) (2.2)

Here, PE is the potential energy, and E is the energy of the incoming electron.

When the triangular barrier is drawn at the coordinates shown in Fig.5.3, with the

electron at the energy of the widest part of the triangle (at E=0), then the E term

goes away, and PE can be replaced by the equation for the triangle: Eg/2-qFx, where

Eg is the band gap of the semiconductor material at the tunnel junction, and F is

the electric field. Then,

Fig. 2.13: : Band-to-band tunneling can be calculated by approximating the energybarrier width by a triangular potential energy barrier, where the electronsmust tunnel through the widest distance at the base of the triangle.

k(x) =

2m

h(Eg

2 qFx) (2.3)

Plugging this into Eq.1 gives

Tt exp(2

x2

x1

2m

h2(Eg

2 qFx) dx) (2.4)

The next step is to carry out the integration

Tt exp(42m

3qh(3

2 qFx) 32 ) (2.5)


Looking back at the triangular barrier, we know that at x = x2, (Eg/2 qFx) =

0, and that at x = -x1, (Eg/2 qFx) = Eg, so

Tt exp(42mEg

3

2

3qhF) (2.6)

Eq.6 is a general expression for band-to-band tunneling transmission. This equa-

tion can be improved slightly by making it more specific to tunneling transistors.

Now referring to Fig.5.4, the dimensions of the shaded triangular barrier [27] are a

height of + Eg, and a width of . The magnitude of the electric field corresponds to

the slope of the energy bands, so we can replace the electric field F by y/x = ( +

Eg)/. Since electric field is measured in V/m, and the new term has the units eV/m,

we must also cancel out an electron charge, which gives

IBTB Tt exp(42mEg 3

2

3h(+ Eg)) (2.7)

is the energy range over which tunneling can take place, Eg is the band gap at

the tunnel junction, is a screening length, and m* is the tunneling mass. There

are four important conditions in order for band-to-band tunneling to take place:

available states to tunnel from, available states to tunnel to, an energy barrier that

is sufficiently narrow for tunneling to take place, and conservation of momentum

. In order for band-to-band tunneling to take place in materials with an indirect

band gap such as silicon, crystal phonons [18] are necessary in order to conserve

momentum, and Eg in the numerator of Eq.7 is replaced by Eg-Ep, where Ep is

the phonon energy. The effective mass m* must then change to mrx*, which is the

reduced effective mass in the tunneling direction. If these changes are not made to

Eq.7, band-to-band tunneling current is overestimated for indirect materials.

The parameter deserves a bit more explanation. It has several different names,

including screening length, natural length, and Debye length, and refers to the spa-

tial extent of the electric field, or the length over which an electric charge has an

influence before being screened out by the opposite charges around it . It can be ex-

pressed in terms of the dielectric constants and thicknesses of the gate dielectric and

semiconductor body of a device, and depends upon gate geometry. The expression

for a double-gate device is

=

sitsitox2ox

(2.8)

where Si and tSi are the dielectric permittivity and thickness of the silicon (or

whatever semiconductor material is used to make the device), and ox and tox are the


dielectric permittivity and thickness of the gate dielectric. For a single-gate device,

the factor of (1/2)0.5 must be removed from the expression, and for a wrap-around

gate, the expression becomes more complicated . These equations for were created to

describe conventional MOSFET behavior, but have also been used for Tunnel FETs.

Fig.5.4 shows how the band-to-band tunneling behavior [7] of the Tunnel FET

acts as a band pass filter that cuts off the low-energy and high-energy tails of the

Fermi distribution of the n+-type source. The Fermi-Dirac distribution and Fermi

level for the source are first drawn at the left within the source, and the low-energy

tail of the distribution is crossed out because no carriers can exist at energies inside

the band gap. Then on the channel side, the source Fermi-Dirac distribution is shown

again, and this time the high-energy tail is crossed out since those energy levels cant

exist inside the band gap of the channel. The result is the version of the distribution

shown at the far right, in which only the electrons in the source within the energy

range are available for tunneling.

Fig. 2.14: Energy band cross section of a Tunnel FET showing the triangular barrierapproximation within the bands, , the screening length , and the filteringbehavior of the device in the on-state

2.6.5 SUB-THRESHOLD SWING IN TUNNEL FETS

The dependence of swing on gate voltage up to the threshold voltage (taken at IDS

= 10-7 A/m) is shown in Fig.5.5, demonstrating two important things. First, the

subthreshold swing of Tunnel FETs is not constant, but rather is a function of gate

voltage. And second, at low gate voltages, it is possible for Tunnel FETs to have a

subthreshold swing less than the 60 mV/decade MOSFET limit at room temperature.

In order to derive an expression for the subthreshold swing of a band-to-band

tunneling device, we can start with the expression given by Sze for the tunneling


current through a reverse-biased p-n junction:

I = aV effF exp(bF) (2.9)

where

a =

Aq3

2m

Eg

42h2(2.10)

and

b =4mEg

3

2

3qh(2.11)

Veff is the bias at the tunnel junction and F is the electric field at the tunnel

junction. When the subthreshold swing is calculated as S = dVGS/d(log IDS), the

result is:

S = ln[1

V effdV eff/dV GS +

F + b

F2dF/dV GS]1 (2.12)

Several conclusions can be drawn from this equation. First, as already illustrated

in Fig 5.6, it should be noted that in sharp contrast with a conventional MOSFET,

the subthreshold swing is a function of VGS. This means that the subthreshold region

does not appear as a straight line when IDS-VGS is plotted on a log-lin scale, and

the swing does not have one unique value [24]. Swing is smallest at the lowest VGS,

and increases as VGS increases. Fig.5.7 shows a comparison of the IDSVGS curves

for a typical conventional MOSFET, and for a typical Tunnel FET.

Due to the changing values of swing along the IDS-VGS curve, it is useful to define

two different types of swing, point swing (Spt) and average swing (Savg). These are

illustrated in Fig. 5.7. Point swing is the smallest value of the subthreshold swing

anywhere on the IDS-VGS curve, typically found right as the device leaves the off-

state and tunneling current starts to flow. Average swing is taken from the point

where the device starts to turn on, up to threshold, often defined using the constant

current technique. Average swing is the more useful value for circuit designers,

though in order to truly utilize the average slope as shown in Fig.5.7, the gate work

function would need to be adjusted in order for the turn-on point to fall right at VGS

= 0 V


Fig. 2.15: Dependence of the Tunnel FET subthreshold slope on gate voltage fordifferent dielectric constants

Fig. 2.16: comparison of IDS-VGS for a conventional MOSFET and a Tunnel FET

Fig. 2.17: Visual definitions of point swing, taken at the steepest point of the IDS-VGS curve, and average swing, taken as the average from turn-on tothreshold.


2.6.6 TUNNEL FET TEMPERATURE CHARACTERIS

The temperature dependence [4] of silicon Tunnel FETs with an SiO2 gate dielec-

tric has been reported in and. Simulations of Tunnel FETs with a high-k dielectric

show the same general trends: the off-current, caused by the generation of carriers in

a reverse-biased junction, increases with temperature, while the on-current, coming

from band-to-band tunneling, changes only slightly, as shown in Fig.5.8. The inset

of Fig. 5.8 shows that the subthreshold swing of the Tunnel FET for fixed values of

VGS is nearly constant as temperature increases, unlike that of a MOSFET, which

degrades proportionally to the increase in temperature, as can be seen in Eq. 5.

Due to rising offcurrent, the average subthreshold swing of Tunnel FETs will signifi-

cantly degrade with increasing temperature, but beyond the leakage level, the current

characteristics remain nearly unchanged.

Fig. 2.18: Simulated IDS-VGS characteristics for various temperatures for a double-gate Tunnel FET with dielectric = 21. VDS = 1 V. As temperatureincreases, Ioff increases, but Ion changes very little. Inset: Subthresholdswing at specific VGS values, vs. temperature in Kelvin. The swing isonly slightly affected by changes in temperature.

The use of a high-k dielectric rather than SiO2 leads to a decrease in the threshold

voltage shift caused by temperature. This is to be expected with the constant current

method of VT extraction, since with a higher dielectric constant, VT falls on a

steeper part [13] of the IDS-VGS curve. While VT/ T is in the range of 1-2 mV/K

for Si/SiO2 Tunnel FETs and MOSFETs, we find that VT/T is 0.2-0.3 mV/K for

Tunnel FETs with a gate dielectric constant of 21. Although subthreshold swing

doesnt degrade with increased temperature, when taken at a fixed value of VGS, it

must be kept in mind that circuit designers dont care about swing at a fixed value of

gate voltage. They would be more interested in average swing, taken from turn-on


up to threshold. Since an increase in temperature has a strong effect on Ioff, as seen

in Fig.5.8, the steepest part of the curve is lost as temperature goes up, and so Savg

will be significantly degraded.

CHAPTER 3

DEVICE SIMULATION

3.1 SILVACOS ATLAS DEVICE SIMULATOR

ATLAS is a physically-based two and three dimensional device simulator [1]. It

predicts the electrical behaviour of specified semiconductor structures and provides

insight into the internal physical mechanisms associated with device operation.

The primary method of interfacing with the ATLAS simulator is using Silvacos

Deckbuild operating environment. Majority of the work in this thesis uses Deckbuild

to create the device to run in ATLAS so that will be the main focus of explanation.

3.1.1 ATLAS INPUTS AND OUTPUTS

ATLAS produces three types of output files: 1.Run-time output file: This file gives

progress and error and warning messages as the simulation proceeds. 2.Log file: This

file stores all terminal voltages and current from the device analysis. 3.Output file:

This file is the solution file, which stores 2D and 3D data relating to the values of

solution variables within the device at a given bias point [1].

3.1.2 MODES OF OPERATION

All simulations in this thesis were run using Deckbuild to provide the device structure

information to the device simulator ATLAS [1]. ATLAS has the ability to run in

several different modes that are with Deckbuild including Interactive Mode, Batch

Mode, No Windows Batch Mode and inside Deckbuild. Inside Deckbuild is the

sukumarHighlight

Chapter 3. DEVICE SIMULATION 28

recommended method by Silvaco and will be the only way ATLAS is run during

this thesis. Each time the designer wants to run ATLAS inside Deckbuild the first

programming line should be:

go atlas

This input will start ATLAS simulator and allow it to input the rest of the

conditions stated in the code in Deckbuild.

3.1.3 ORDER OF COMMANDS

The order in which commands are entered into Deckbuild are very important to

ensure that ATLAS runs the program correctly. ATLAS needs to have the commands

in the proper order or it will give an error message. Silvaco breaks the commands

into five groups and each group will have several statements in that group. The

statements in each group in most cases must be run in order. Fig.4.2 shows the

groups and the order in which they should be inputted into Deckbuild [1].

GROUPS STATEMENTS

Structure Specification Mesh, Region, Electrode, Doping

Material Model Specification Materials, Models, Contacts, Interface

Numerical Method Selection Method

Solution Specification Log, Solve, Load, Save

Result Analysis Extract, Tonyplot

This thesis will use ATLAS five command groups to describe how to use ATLAS

to build and simulate a DGTFET.

Structure Specification

Structures of devices to be simulated are entered in plain text into the Deckbuild

input deck. To properly build a device in Deckbuild a designer must define several key

parameters to get an accurate result. The key parameters in the structure command

group include the following; a two or three dimensional grid, called the mesh, the

mesh must be divided into regions, electrode locations and materials must be defined,

doping levels and dopants must be defined. When programming in Deckbuild the

is used to indicate that the line is only a programmers note and not part of the

program [1].

The mesh is the two or three dimensional grid used as the frame work to build

your device. In this thesis all the device designs will be using a two dimensional grid.


The mesh statement will define the boundaries of the device you are building and

the resolution of detail. The first mesh command must be the mesh space multiplier

Command.

meshspace.mult =< value >

This command will tell ATLAS the scaling factor of the mesh. The mesh will be

less dense for a large number and denser for a smaller number. The value for this

is normally set to equal 1. Fig. 4.3 shows an example of a mesh with a space.mult

value of 5 compared to a mesh with a value of 1.

The next step to defining the mesh is to specify the actual grid make up. Mesh

statements are entered in as vertical and horizontal lines in microns and as distance

from the center line. ATLAS will automatically adjust the grids to represent the

desired resolution the user has entered. ATLAS divides the grid using a triangle

format. The user can use a higher resolution over areas of the device that the user

wants more detail. Typically a high grid resolution is used at junctions and material

boundaries. This can be seen in Fig.4.4 which shows the ATLAS mesh and the mesh

statements of a DGTFET. Notice the tighter grid along the junction in the middle

of the device.

After the designer has defined the device mesh, they will next have to define the

regions of the device. The regions will be used to assign materials and properties to

the device. The regions must be defined along the mesh lines and the statements

will be similar to those used for the mesh states. ATLAS allows the user to define

up to 200 different regions for one device. If the designer overlaps any of the two

regions ATLAS will assign the material type to the last region that was defined. The

entire two dimensional mesh area must be defined into regions or ATLAS will not run

successfully. The designer will list the material type when defining a region but to

define the material properties of the material type the design must wait until second

command group. Regions can be defined using cylindrical coordinates but this type

of region definition is not used in this research so it will not be addressed. Fig. 4.4

shows also the ATLAS regions for a DGTFET.

For ATLAS to find the electrical properties of the structure the designer must

define the location of the electrodes. The designer must specify the electrode name

and where it is located. ATLAS requires a minimum of one electrode and has a

maximum limit of 50 electrodes for one device. The electrodes can be specified as

a certain material or you can leave them undefined and ATLAS will use an ideal

conductor.


Fig. 3.1: ATLAS Inputs and Outputs

Fig. 3.2: Comparison of mesh grids when using a multiplier of 5 and 1

Fig. 3.3: ATLAS Mesh and Region Boundaries for a DGTFET


The next action, doping, is one of the most important actions a designer does

to affect the electrical properties of the structure they are designing. Silvaco allow

the designer to specify the type of dopant and the concentration. It also allows the

designer to specify the distribution of the doping material. ATLAS has the ability to

distribute the dopants in a uniform or Gaussian profile. The uniform doping profile

has an easy set of commands to dope the material exactly how the design wishes

it. Fig. 4.5 shows the doping concentration of a DGTFET; notice how the impurity

concentrations change in the junction region

Fig. 3.4: ATLAS Doping Profile of DGTFET

Material Models Specification

Once the designer has defined the structure and the geometry of the device being

designed they can now change the default material properties and choose which

models ATLAS will use to solve the devices electrical characteristics. The first of all

properties investigated will be the contact command. This command is used to tell

ATLAS how to treat the electrode. In the default condition an electrode in contact

is assumed to be ohmic. If the designer wants the electrode to be treated like a

Sckottky contact the design must use the workfunction.

An example of this would be: contact name=gate workfunction=4.8 This com-

mand would treat the contact as Sckottky contact and set the contact named gate to

4.8eV. The designer can also use the contact command to change an electrode from

being voltage controlled and make it current controlled.

An example of this would be: contact name=drain current

This would make the contact named drain a current controlled contact. ATLAS

also has the ability to float contacts, short two contacts together, and make an open

circuit contact.


Since none of these features were used in this research these are not discussed in

detail. The next step in the ATLAS design process is to designate material properties

for the regions that are being used. ATLAS has an extensive library of different

elements, compounds and alloys with their properties already defined. Silvaco allows

the designer to edit these allows or create completely new materials. Some of the

properties defined are bandgaps, mobility and absorption coefficients. An example

of a way to use the material statement to improve the simulation is as follows:

Material Material=Silicon EG300=1.12 mun=1100 This command would set the

bandgap and low field electron mobility for all the silicon in the device. The next

statement to investigate is the models statement. ATLAS has over seventy models

that a designer can choose to use to improve the accuracy of the structure they are

trying to simulate. These models would change the parameters of the device using

the following command statements: models, mobility, impact, and material. Fig. 4.6

shows an example of some of the mobility models available.

Fig. 3.5: Some of the mobility models available in ATLAS

Numerical Method Selection

ATLAS allows several different methods for calculating the solution for semiconductor

device problems. For each model type there are various types of solution techniques

such as Newton and Gummel [1]. The designer should look and see what type

of method the model they are using. Using the wrong method can lead to non-

convergence or incorrect results.


Solution Specifications

ATLAS will calculate AC, DC, small signal and transient solutions. Obtaining a

solution is similar to setting up a test device. Once the command has been made

the user will typically save the results using a log or save command. An example of

solving a DC solution is given below:

solve vcathode=1.0

This will solves a single bias point with 1 volt on the cathode. The designer can

also solve a sweeping bias using the following commands:

solve vcathode=0

solve vanode=-5 vfinal=5 vstep=0.1 name=anode

This will solve the circuit parameters by holding cathode voltage at 0 and sweeping

the anode voltage from -5 to 5 with 0.1 voltage steps. If no solve voltage is designated

Silvaco will put a default of 0. The results can be saved to a log file by using the

following command:

log outfile=simplesidiode-iv.log

This will save a log output file of the results from the voltage sweep in them.

Results Analysis

The primary method when working with ATLAS to view the results of a simulation

is using Tonyplot. Tonyplot is viewing program for ATLAS that allows the designer

to view the structure and log files that are created by ATLAS. The structure files

allow you to view the mesh diagram, doping concentrations, current densities, and

other parameters. The log files allow you to view the results of ATLASs electrical

analysis in a graph format. It can show both log and linear scaling. It can also

produce cylindrical graphs. Tonyplot [1] has the ability to do cutlines to look at a

specific slice of the device and see what is electrical occurring at the slice point or

plane.

All simulations were done in Silvacos ATLAS, version 5.16.3.R, which uses a

nonlocal Hurkx band-to-band tunneling model [1]. The currently used nonlocal model

works by calculating the tunnelling probability from the energy-band diagrams across

the device. The simulations use a very fine mesh across the region where the tunneling

takes place, from which energy band profiles and the energies for which band-to-band

tunneling is permitted, are determined.

All simulations carried out in Silvacos ATLAS are 2-D, and it is informative

to look at vertical cross sections of the energy bands of the Tunnel FET, as well as

contour plots in two dimensions, in order to understand the functioning of the device.


3.2 Comparison between MOSFET and DGTFET Transfer

Characteristics

It can be observed from the following fig. that, the ON-current does not increase

merely proportionally to the increase in the gate capacitance, as it would for a MOS-

FET. A simplified MOSFET 2-D structure has been designed for numerical simula-

tion in order to show the difference between the two. For Tunnel FETs, as we saw in,

the improved coupling between the gate and the tunneling barrier has an exponential

effect rather than a linear one. The ON-current of a Tunnel FET depends on the

width of the energy barrier between the intrinsic and p+ regions, and the current

increases exponentially with a reduction in this barrier width.

Fig. 3.6: DGTFET Transfer Characteristics for various Gate Dielectric

Fig. 3.7: Characteristics of a simplified single-gate NMOSFET for various gate di-electrics.


3.3 DGTFET PARAMETERS OPTIMIZATION

Before investigating the unique properties of Tunnel FETs or looking in detail at

their behaviour, it is important to carefully choose all device parameters such that

characteristics are optimized [3], and to show why each choice was made as it was.

In this chapter, Tunnel FET optimization is explored, considering the following pa-

rameters:

1.Dielectric Constant of Gate Dielectric, ox

2.Silicon Body Thickness, tsi

3.Channel Length, L

4.Gate Work Function,

5.Gate Dielectric Thickness, tox

3.3.1 DIELECTRIC CONSTANT OF GATE DIELECTRIC

An improved on-current and decreased sub-threshold swing can be obtained by the

careful choice of a gate dielectric. As shown in Fig.6.1, current increases as the gate

dielectric constant increases. Here, Si3N4 and two high-k dielectrics with dielectric

constants of 21 and 29 are compared with SiO2, all with a physical thickness of 3

nm. In addition to improved Ion, both the point and average sub-threshold swing

improve as the result of the better gate coupling given by a high-k dielectric [6]. The

off-current is less than 1 fA for all materials.

As shown in Fig.6.2, trans-conductance (gm) also increases as gate dielectric

constant increases. The off-current is less than 1fA for all materials.

The above statements are in full agreement to the equation of band-to-band

tunnelling current.

IBTB Tt exp(42mEg 3

2

3h(+ Eg)) (3.1)

where

=

tsitox2ox

(3.2)

These two figures Fig. 6.1 and 6.2 show that the optimized value for dielectric

constant of gate material can be chosen as 29.


Fig. 3.8: DGTFET Transfer Characteristics for various Gate Dielectric

Fig. 3.9: DGTFET Trans-conductance (gm) vs VGS Curve for various Dielectrics(VDS=1V, L=50 nm, tox=3 nm, tsi=10 nm)


3.3.2 THICKNESS OF SILICON BODY

Tunnel FETS are sensitive to the thickness of silicon body, tsi , which influences the

shape of its IDS-VGS curve as shown in Fig.6.3

Fig. 3.10: DGTFET Transfer Characteristics for various tsi

Fig. 3.11: DGTFET Trans-conductance (gm) vs VGS Curve for various tsi

Several trends can be seen in this figure. First, the off-currents are practically

independent of the thickness. As the film gets thinner than 7 nm, on-current starts

to drop possibly due to the reduced cross-sectional area available for current flow.

Fig. 6.4 showing gm vs VGS curve shows that among all these values of silicon

body thickness maximum trans-conductance is obtained for silicon body thickness

equal to 15 nm and thus is the optimized value of tsi for DGTFET.


3.3.3 CHANNEL LENGTH

A detailed study of the length scaling [25] of Tunnel FETs is conducted, in which

all other parameters stayed constant. It is shown that Tunnel FETs ON-current is

immune to the effects of length scaling as shown in Fig.6.5 . But Fig.6.6 shows that

the trans-conductance value is maximized for channel length of 70 nm.

Fig. 3.12: DGTFET Transfer Characteristics for various channel lengths, L

Fig. 3.13: DGTFET Trans-conductance (gm) vs VGS Curve for various L (Otherparameters are same as for Fig.6.1)

Thus channel length is optimized to length of 70 nm.

3.3.4 GATE WORK FUNCTION

When the impact of the work function of the gate, on the ION in a DMG-DGTFET

is analyzed, it is observed that with the reduction in , the band overlap increases,


Fig. 3.14: DGTFET Transfer Characteristics for various gate work function

Fig. 3.15: DGTFET Trans-conductance (gm) vs VGS Curve for various gate workfunction


and the tunneling width decreases, leading to a significant increase in the tunneling

probability and hence the ON-current is increased as shown in Fig.6.7.

Since, in general, DGTFET suffers from a low ION and high VT , it is desirable

to adjust the device parameters to obtain a maximum ION and a minimum VT .

Therefore, we choose to be the lowest possible value, i.e., 4.4 eV.

3.3.5 GATE DI-ELECTRIC THICKNESS

Tunnel FETs show high sensitivity to changes in gate dielectric thickness. The gate

leakage increases exponentially as the oxide thickness is reduced. This limits the

downscaling [22] thickness to about 3.4 nm 3.5 nm. But to further decrease the

effective oxide thickness alternative high dielectric constant material can be used.

On the other hand, a thin gate oxide reduces the short channel effect and improves

the driving capabilities of a MOS transistor [12].

However a trade off between this benefits and gate leakage is necessary. So opti-

mum value of gate dielectric thickness is chosen as 3 nm as Fig.6.10 shows maximized

value of ON-current and gm for this value of thickness.

Fig. 3.16: DGTFET Transfer Characteristics for various gate dielectric thickness

3.4 RESULTS

3.4.1 STRUCTURE AND PARAMETERS

The following table shows the parameters of the proposed device, Dual Gate TFET

with their optimized values for better performance in terms of low sub-threshold

swing and high ON-current.


PARAMETER

Silicon Body Thickness 15 nm

Gate Dielectric Thickness 3 nm

Gate Dielectric Constant 29

Drain Doping(N+) 5 1018/cm3Source Doping(P+) 1 1020/cm3Intrinsic Region(N) 1 1017/cm3Channel Length 70 nm

Gate Work function 4.4 eV

The following figure shows the optimized structure of DGTFET with ON-current

as high as 0.13 mA for gate voltage of 1.8V and an improved average sub-threshold

swing of 57 mV/dec.

3.4.2 ON-CURRENT OF DGTFET

The following figure shows that the device, DGTFET proposed by us has better

performance in terms of high ON-current. ON-current value for optimized device is

0.13mA which is higher than its value, 0.09mA for the device before optimization.

3.4.3 TRANS-CONDUCTANCE VS VGS CURVE

The following figure shows considerable improvement in terms of trans-conductance

of DGTFET. Before optimization of parameters its value was 1.25e-6 A/V which is

raised to 2.1e-6 A/V by optimizing the already discussed parameters.

3.4.4 ENERGY BAND DIAGRAMS

The following two figures show that the optimized DGTFET has better probability of

band-to-band tunneling as compared to that before optimization due to the reduction

in barrier width after optimization.

3.4.5 ELECTRIC FIELD

Looking first at the x direction component of the electric field across a device which

is ON, we see that the electric field is close to zero nearly everywhere. Between

the intrinsic and p+ regions, where the tunnelling takes place, we see a maximum

positive field throughout the depth of the device.


Fig. 3.17: DGTFET Trans-conductance (gm) vs VGS Curve for various gate di-electric thickness

Fig. 3.18: Optimized structure of DGTFET

Fig. 3.19: Comparison of ON-Current for optimized DGTFET and DGTFET be-fore optimization


Fig. 3.20: Comparison of transconductance vs VGS curve for optimized DGTFETand DGTFET before optimization

Fig. 3.21: Energy Band Diagram of DGTFET before Optimization

Fig. 3.22: Energy Band Diagram of DGTFET after Optimization


Fig. 3.23: Contour plot of Electric Field across DGTFET before optimization

Fig. 3.24: Contour plot of Electric Field across DGTFET after optimization


3.4.6 POTENTIAL

In the potential contour plot for this same device in the same state , we see that the

potential drops abruptly at the tunnel junction, and once again, this holds true for

the entire device depth, not just at the surface.

Fig. 3.25: Contour plot of potential across DGTFET before optimization

Fig. 3.26: Contour plot of potential across DGTFET after optimization

3.4.7 CURRENT FLOWLINES

In the diagrams of current flow lines, shown at the threshold voltage, it is clear that

the current does not stay close to the gate dielectric as in a MOSFET. As the electrons

move from right to left (source to drain) in the Tunnel FET, they move parallel to the

interface through most of the source, then move away from the dielectric interface at

about the location of the tunnel junction and, then, attracted by the positive voltage

on the gate, flow closer to the interface before spreading back out and passing through


the drain parallel to the interface, as they were in the source (electrical contacts are

on the sides of the source and drain).

Fig. 3.27: Contour plot of current flowlines in DGTFET before optimization

Fig. 3.28: Contour plot of current flowlines in DGTFET after optimization

CHAPTER 4

CONCLUSION

Numerical simulations have proven to be an effective means to investigate Tunnel

FET behavior and the dependence of its static characteristics on changes in dimen-

sions, doping, and other parameters.

The work presented here can be useful to other researchers who will be designing

and fabricating Tunnel FETs, and developing analytical and compact models for

these devices.The main accomplishments of this work can be summarized as follows:

The optimization of the static characteristics of Tunnel FETs by the variation

of gate structure (single or double), source, drain, and intrinsic region doping levels,

gate dielectric material, and silicon body thickness was carried out.

The proposed device had a double gate, a high source doping and lower drain

doping to suppress ambipolar behavior, a high-k dielectric of 29, silicon body thick-

ness of 15 nm ,work function of 4.4 eV, oxide thickness of 3 nm and channel length

of 70 nm.

1.Dielectric permittivity constant was investigated and by increasing its value there

was a significant change in on current and trans-conductance.

2.The optimization of work function shows that the increasing value of work function

decreases the threshold voltage significantly.

3.Channel length variation doesnt show much change in Ion current but by increasing

channel length breakdown improves significantly.

4.Oxide thickness reduction increases leakage current so in our proposed device we

had not reduce its value .

Chapter 4. CONCLUSION 48

Our proposed Tunnel FET showed improved characteristics including higher ON-

current, .higher trans-conductance and a lower sub-threshold swing after the modifi-

cations in the design of previously proposed device.

The Tunnel FETs promising behaviour makes it a strong candidate to complement

or replace MOSFET technology, particularly for low power applications.

4.1 FUTURE SCOPE

Since the beginning of this thesis work in early 2005, the progress made with Tunnel

FETs has come a long way. Referring back to the Recent research relevant to the

problem in chapter 1, it can be seen that the majority of Tunnel FET work has been

done in the past few years. but there is still much progress to be made in terms of

optimization to achieve superior device characteristics.

The biggest future ch

TFET

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