revforAED

Semiconductor Devices

Dr. Kristel Fobelets

Room 714

[email protected]

Course overview

mailto:[email protected]

Aims of the course

Gives sufficient background knowledge into semiconductor devices and technology to understand state-of-the-art micro (nano)

electronics.

Gives an overview of the operation of new field effect transistors which have recently left the

research lab or which are still being investigated.

• Small gate lengths change characteristics in unexpected ways– Short channel effects (SCE)– How to circumvent SCE using “tricks”?

• Are there no other FET structures that can improve on the MOSFET characteristics?– Other materials: GaAs based FETs– FETs based on more than 1 material: hetero-junctions– More than 1 gate – e.g. the finFET– Nanowires with gates all around (see 4rd yr course)

Contents: MOSFETs and beyond

What does the course involve?

• Regular lectures 2hrs/week.– Summary notes → main information (“blue book”)

– Copy of powerpoint slides

• 1 Class in which the questions in the summary notes will be solved.

• Exam 4 questions out of 5• All info available on blackboard

Required background knowledge

• 1st year Electrical Engineering course on Semiconductor devices (K. Fobelets)

• 2nd year Electrical Engineering course on Semiconductor devices (K. Fobelets)

If not, please read the recommended textbooks on solid state physics introduction, pn junction, MOSFET.

Understanding of basic MOSFET operation is essential.

Synopsis of the course

1) Background and Ideal MOSFET – review2) Short channel effects in MOSFETs3) Optimizing FET operation:

1) Schottky gating2) Modulation doping3) Introduction of strain

4) FETs on SOI1) Fully depleted2) Partially depleted

5) Alternative transistor structures: finFETs, nanowire FETs,…

6) Using semiconductors for bio-sensing7) Using semiconductors for energy generation.

Short channel MOSFET

Revision of basic concepts

In semiconductors two types of free charged carriers exist: electrons and holes.

Q1: What are holes?

a) Spherical voids in a semiconductorb) A positively charged Si atom that has lost its electronc) A positively charged particle that is the result of quantum mechanics

Si

Si

SiSi

Si

+Si

Si

Si

Si

Si

Si

SiSi

Si

Si

Si

Si

Si

CThe two charged particles describe together the conduction in semiconductors.

Electron e- with charge q=-e and mass mn = m0 m*n

Hole h+ with charge q=+e and mass mp = m0 m*p

Intrinsic Si

Si

Thermal energy: kT

Si Si Si

Si Si Si Si

Si Si Si Si

Si Si Si Si

Si Si Si Si

Si Si Si Si

Movement: kT

Si Si Si Si

Si Si Si Si

Si Si Si Si

Extrinsic Si

Si B Si Si

Si Si Si Si

Si Si Si Si

NA

Extrinsic Si

Si As Si Si

Si Si Si Si

Si Si Si Si

ND

Obtained by doping

Si

B

As

Covalent bond

Intrinsic silicon (Si) has a small number of both free electrons and holes such that ni=pi.In order to increase the free carrier concentration, the semiconductor can be doped. With donors ND more electrons are created, with acceptors NA more holes are generated.

Q2: When intrinsic Si is doped with donor atoms, which of the following statements is correct?

a) n = p = ni = pi

b) n > ni & p < ni

c) n > p > ni

d) p > n > ni

n: electron concentrationp: hole concentrationni: intrinsic electron concentrationpi: intrinsic hole concentration

Bn > ni & p < ni in an n-type semiconductor.

n-type semiconductorn = ND p = ni

2/ND

p-type semiconductorn = ni

2/NA p = NA By heart

The concept of majority carrier and minority carrier is important in semiconductor devices. Majority carrier is the carrier type in a doped semiconductor with the highest concentration. Minority carrier is the carrier type with the lowest concentration.

Q3: True or False? The holes are the majority carriers in a p-type semiconductor (doped with acceptor atoms NA).

TRUE

p-type semiconductor

pp

holeconcentration

p-typesemiconductor

np

electronconcentration

p-typesemiconductor

>

n-type semiconductor

nn

electronconcentration

n-typesemiconductor

np

holeconcentration

n-typesemiconductor

>

MAJORITY CARRIERS MINORITY CARRIERS

p-Si

Si B Si Si

Si Si Si Si

Si Si Si Si

NAn-Si

Si As Si Si

Si Si Si Si

As Si Si Si

ND

Depletion

Si

B

As

Si

Si

B

Cap

acit

ive

effe

ct

E+ -

-

-

B- : boron atom ionised

Si

Si

Si

Cap

acit

ive

effe

ct

E- +

As+ : arsenic atom ionised

+

+

The purpose of semiconducting devices is to generate a current/voltage in response to an applied voltage/current. Two different types of current can exist in a semiconductor: drift and diffusion current. The expression of the total current that can flow in a semiconductor is given by the drift-diffusion equation:

Q4: Which statement is true?

a) Term (1) is drift current and (2) diffusion currentb) Term (2) is drift current and (1) diffusion currentc) Only term (1) can exist in a semiconductord) Only term (2) can exist in a semiconductor

dx

xdpeDxExpexJ

dx

xdneDxExnexJ

ppp

nnn

)()()()(

)()()()(

(1) (2)

A

Drift current is proportional to the carrier concentration and the electric fieldDiffusion current is proportional to the carrier gradient.

E(x) Jndrift

Jpdrift

n(x) Jn

diff

p(x) Jpdiff

Motion of free charged carriers in a semiconductor.

Q5: If a p-type semiconductor at room temperature is conducting carriers due to drift, which of the following motion paths would be followed by the holes?

a)

(b)

c)

(d)

E+ - E+ -

E+ - E+ -

B

When carriers move in a semiconductor they are scattered along the way. This means that they will be accelerated by the electric field (in this case) and then interact with atoms, impurities, other carriers that makes them lose some of their kinetic energy = scattering. Therefore the carriers will travel with an average velocity in amplitude and direction.

Review Energy band diagram of

semiconductorWhat does an energy band diagram describe?The total energy of the carrier within the lattice = KE + PE

E

k

Conduction band

Valence band

Ec

EvEg

Free electrons

Free holes

In semiconductor devices the Energy band diagram is simplified

The total electron energy = KE + PE

E

k

Conduction band

Valence band

Ec

EvEg

EConduction band

Valence band

Ec

EvEg

Only electron potential energy = PE is plotted

distance in device, x

+KE

Energy band diagram under electric field E

E

Ec

EvEg

Ec = e- PE → application of electric field will shift Ec at different points in the semiconductor.

x

EEc

Ev

Eg

x

k

E

k

E

e-

AKE

E = 0 E ≠

0

B

Energy band diagrams: Ec, Ev, EF and EG (key components) are based on the quantum mechanical description of the carriers in a semiconductor. Energy band diagrams give a graphical method to estimate the amplitude of conduction in semiconducting devices.

Q6: Sketch the energy band diagram, Ec, Ev, EF, EG of an n-type semiconductor in the point (in k space) where the distance between bottom of conduction band and top of valence band is minimum.

Bottom of conduction bandEc

Top of valence bandEv

Ei

Intrinsic “level”. Is the position of the Fermi level EF when the semiconductor is intrinsic.

EG Bandgap. No energy levels in this energy region.

Position of Fermi level is determined by the doping type and densityFor n-type Si:

D

CFc

D

CCFc

FcC

N

NkTEE

N

N

n

N

kT

EE

kT

EENn

ln

exp

exp

EF

Influence of an electric field on carrier movement in the energy band diagram

• Energy band diagram of a semiconductor under an electric field

E(x) Ec

EvEg

e- opposite direction to electric field.

h+ in direction of electric field.

Applying a bias across the metal-semiconductor junction

Fermi level no longer constant

Apply bias → change PE along junction

EF

Ene

rgy

V>0

eVE

nerg

yEF

V<0

eV

+ -

E

Ec

For a junction with 2 different materials

For instance

metal-semiconductor

Si-SiGe

AlAs-GaAs

Start from the knowledge on workfunctions, f and the energy reference: the vacuum level, Evac.

Evac

Each material has a certain electrical potential that is related to the energy of its charged carriers. This electrical potential for the material is given by the work function, f. For each material the work function is an energy related to a reference vacuum level, Evac.

p-Sie×fp-Si

The position of the Fermi level of each material is defined by the work-function with respect to the reference vacuum level.

EF

metal

e×fm

EF

Same for metal

metal

e×fm

EF

Materials are NOT in contact

Evac

p-Sie×fp-Si

EF

Bringing the materials together

Need to align the Fermi levels via a re-distribution of carriers.Electrons will diffuse from p-Si to metal until the Fermi levels are aligned.This requires energy → change in electric potential of one material with respect to the other.

Contact potential or built-in potential: SipmV 0

Change in relative electric potential

metal

e×fm

EF

Evac

p-Sie×fp-Si

EF

Junction is formed

Contact potential or built-in potential:

SipmeVe 0

Evac

junction

metal

e×fm

EF

Evac

p-Sie×fp-Si

EF

Drawing the remainder of the energy band diagram.


SipmeVe 0

Evac

junction

Ec

EG

EvConduction band Ec

Doping gives distancebetween Ec and EF

EG gives distancebetween Ec and Ev

Valence band Ev

Doing the same with alternative explanation and using n-Si

1. The potential energy of the electrons Ec (holes, Ev) of different semiconductors can be related to each-other via the workfunction, f of each material

Evac

e×fm1 e×fm2

Ene

rgy

axis

: E

Distance axis: x

EF1

EF2

Ec2

Ev2

n-Simetal

Material 1 Material 2

2. Electrons and holes want to lower their energy if states are available to move to (this is as long as EF1-EF2 ≠ 0) → diffusion.

Ene

rgy

axis

: E

Distance axis: x

EF1

EF2

Ec2

Ev2

n-Simetal

Material 1 Material 2

e-

BUTItot=0

becauseVext=0

Jndiff

Jndriftneeds

electric field

Eint

Jndrift

Einte-

Why do the bands bend?

When an electric field E appears then the potential energy Ec, Ev, of the carriers changes.

3. Electron and hole diffuse (until EF1=EF2). Causes an internal electric field (contact potential) that makes the same amount of carriers drift back → Itot=0.

Ene

rgy

axis

: E

Distance axis: x

EF1 EF2

Ec2

Ev2

n-Simetal

Einte-

Bands bend

e-

E-field points towards increasing Ec

More electrons at interface in this case.

kT

EENn Fc

C exp

4. Due to the diffusion of carriers (from metal to Si in this case) there is an increase in electrons at the metal/Si boundary.

Ene

rgy

axis

: E

Distance axis: x

EF1 EF2

Ec2

Ev2

n-Simetal

Fc EEn

• Back to p-Si

metal

EF

Evac

p-Si

EF

Applying a voltage, Vext.


SipmeVe 0

Evac

Ec

Ev

EG

+ -

eVext

E0

Eext

Etot

extSipmext VeVVe )( 0

metal

EF

Evac

p-Si

EF

Applying a voltage, Vext.

Different reference nodeEvac

Ec

Ev

EG

+ -

E0

Eext

Etot

eVext

For a homojunction same material different doping

e.g.

p-Si – n-Si

p-GaAs – n-GaAs – p-GaAs

It is possible to start from the knowledge on workfunctions, f and the energy reference: the vacuum level, Evac. The workfunction is dependent on the doping concentration!

Evac

n-Sie×fn-Si

EF

p-Si

e×fp-Si

EF

Evac

p-Si

e×fp-Si

EF

Evac

n-Sie×fn-Si

EF

Evac

p-Si

EF EF

Depleted region on both sides

Ec

Ev

Ec

Ev

e×fp-Si

Evac

n-Sie×fn-Si

Evac

SinSipeVe 0

For a homojunction same material different doping

e.g.

p-Si – n-Si

p-GaAs – n-GaAs – p-GaAs

If workfunctions, f not given, then start from V=0V and thus Fermi level EF constant.

p-Si

EF

n-Si

EF

Depleted region on both sides

Ecp

Evp

Ecn

Evn

cncp EEeVe 0

Fermi-Dirac statistics + density of states imposes a variation of the carrier concentration as a function of energy

EF

Electron energy

Hole energy

Ec

Ev

eV0

Electron diffusion Electron drift

Hole diffusionHole drift

n-type p-type

Operation of MOSFET

Using energy band diagrams

S DG

MOSFET: VGS = VDS = 0

EF

n+ n+p

V0: Potential barrier between supply of electrons from source into channel. The drift and diffusion across this interface is equal and opposite → no net current through.

channel

Ec

Ev

V0

Remember: No bias Equilibrium imposes that drift is equal to diffusion

no net current across the potential barrier

EF

Electron energy

Hole energy

Ec

Ev

eV0



source channel

S DG

MOSFET: VGS = 0 ; VDS > 0

EF

n+ n+p

Applying VDS has caused a voltage drop across the channel and channel-drain junction, but did not change the barrier height V0 between source and channel. Thus no net current can flow through that junction. (see previous slide)

channel

Ec

Ev

V0

In order to allow current, the potential barrier between source and

channel needs to be lowered.

This is done by applying a positive gate voltage

S DG

MOSFET: VGS>Vth 0 ; VDS > 0

EF

n+ n+p

Applying VGS has caused a decrease of the potential barrier between the source and the channel. Now the electrons in the source lying at a higher energy than the potential barrier V0-VSi will be able to diffuse across the source-channel barrier. Once the electrons are in the channel region they drift due to VDS to the drain. A current is flowing.

channel

Ec

Ev

V0V0-Vsi

No bias

EF

Electron energy

Hole energy

Ec

Ev

eV0



source channel

Remember: Forward biasThe potential barrier decreases and thus allows diffusion of

electrons into the channel

EF

Electron energy

Hole energy

Ec

Ev

E(V0-Vf)

Electron diffusionElectron drift


source channel

MOSFET material cross section – low VDS

Currents: apply VDS

VGS>Vth

Linear region or triode regionfor 1 VGS value

MOSFET schematic cross section – VDS<VDsat

Depletion region increases as reverse bias between drain and bulk increases.

Channel gets narrower near drain

Non-linear current region.

What happens at pinch-off?

The channel-drain junction is reverse biased.

A depletion region exists between the channel and the drain.

S DG

n+ n+p

Large part of the VDS will be dropped across the channel-drain depletion region = reverse biased pn diode.

channel

EF

Ec

Ev

V0-Vsi

MOSFET: VGS>Vth 0 ; VDS ≥ VGS-Vthno longer inverted

↓depleted

EF

Ec

Ev

If VDS is increased, most of the extra voltage will be dropped across the channel-drain depletion region.

S DG

n+ n+p

channel

V0-Vsi

MOSFET: VGS>Vth 0 ; VDS ≥ VGS-Vth

EF

Ec

Ev

Negligible change in slope of potential energy Ec in channelNo change in source-channel barrier (controls carrier supply)Thus current remains constant

Remember: Reverse biasThe current in reverse bias is limited by the availability of

minority carriers

EF

Ele

ctro

n en

ergy

Hol

e en

ergy

Ec

Ev

Electron diffusionElectron drift


e(V0+Vr)

Channel Drain

Any extra is made available by source and is controlled by the source channel potential barrier

MOSFET schematic cross section – VDS=VDsat

Constant current region.

Channel is pinched-off at drain because VDS=VGS-Vth

or VDG=Vth (onset of inversion at drain).SATURATION

MOSFET schematic cross section – VDS>VDsat

In ideal long channel device current remains constant after saturation.The supply of carriers is controlled by source-gate voltage.

Gradual channel approximationdrift current only

)()(

)(

xVVVCxne

Adx

dVxneI

thGSox

Valid for low longitudinal electric fieldsstrong inversion VGS>Vth

regionsaturationVVL

WCI

regionlinearVVVL

WCI

VVVV

L

WCI

thGSoxsat

DS

DSthGSoxlin

DS

DSDSthGS

oxDS

2

2

2

2

Ideal n-channel enhancement mode MOSFET characteristics

L

VWCI DSnox

DS 2

2

IDS

VDS

VGS

VDS = VGS –Vth

triode saturation

Output characteristics

2

2DS

DSthGSnox

DS

VVVV

L

WCI

Ideal n-channel enhancement mode MOSFET characteristics

2

2DS

DSthGSnox

DS

VVVV

L

WCI

IDS

VGSVth

VDS1

Transfer characteristics in triode region

thGSDS

thGSDSnox

DS

VVI

VVL

VWCI

@0

IDS

VGSVth

Transfer characteristics in saturation region

thGSDS

thGSnox

DS

VVI

VVL

WCI

@02

2

Conclusion

The simple description of currents in MOSFETs, the gradual channel operation, only describes the drift component of the current. It ignores the fact that n(x) ≠ 0 for VGS < Vth and that VDS can also have an impact on the source-channel barrier.These simplifications are acceptable when the channel length is long and the channel is strongly inverted, but break down for short channel lengths and when operating the MOSFET in the subthreshold regime.

Insight into this topic is give in: short channel effects in MOSFETs.

How to draw an energy band diagram?

• E points into the direction of increasing potential energy• At metal-semiconductor contacts equilibrium is kept, dn

& dp = 0• Diffusion creates internal electric fields: E0 (Vext=0V)

• Relative position of EF defined by workfunction f

• EF constant throughout structure when Vext=0V

• Abrupt junctions• Eg of each material remains the same up to the junction

• e- transfer from high E to low E

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