Hot Electron Transport and Performance of Semiconductor … · 2012. 7. 25. · Carrier obtained energy from electric field Carrier changed energy and momentum. τ h eF k = − hω

1

Hot Electron Transport and Performance of Hot Electron Transport and Performance of Semiconductor DevicesSemiconductor Devices

Abudukelimu （08D53392）

Supervisor: Professor Hiroshi IwaiCo-Supervisor: Professor Kenji Natori

2012年02月09日(木)

2

Chapter 1 Introduction

Chapter 2 Semiconductor Fundamentals for semi-classicalCarrier transport

Contents

Chapter 3: Carrier Scattering

Chapter 4 Monte Carlo Method for Devices Simulation

Chapter 5 Effects of Scattering Direction on Hot Electron Transport

Chapter 6 Effects of Heat Generation on Hot Electron Transport

Chapter 7 Effects of Hot Phonon on Hot Electron Transport

Chapter 8 Strained Drain and Hot Electron Transport

Chapter 9 Summary

3

Chapter 1 Introduction

1.1 Hot Electron

1.2 Ballistic Transport

1.3 Purpose

1.4 Approach

1.5 Conclusion

4

1.1 Hot ElectronDrift process Scattering processCarrier obtained energy from electric field

Carrier changed energy and momentum.

τh

eFk −= ωh∗=

mkE k 2

22h

ωh≈kE

τ

Drain

Cold Electron

Long Channel Device

Low Electric Field00.02

0.040.06

0.080.1

0 100 200 300X-axis (nm)

Ener

gy (e

V)

Energy Distribution

VD = 0.3 V

100nm 100nm 100nm

n+

1018 cm-3n+

1018 cm-3 1016 cm-3

Source Channel Drain

3*kBT/2 ≈ 40 emV

Flight time

Phonon energy

5

1.1 Hot ElectronHigh Electric Field

ωh>>kE

Injected into the dielectric Lead to impact ionization

Effects of hot electron within channel

http://www.iue.tuwien.ac.at/phd/entner/diss.html

0

0.1

0.2

0.3

0 100 200 300X-axis (nm)

Ene

rgy

(eV

)

VD = 0.3 V

Hot electron is a electron that energy far away thermal energy.

6

1.2 Ballistic TransportNew Device Structures Strain Technology Intrinsic channel, Small size

Reduce the scattering within channel

n+ i n+

Source DrainGate

n+ i n+

Source DrainGate

Surface scattering phonon scattering Impurity scatteringHigh energy scattering

Ballistic transport within channel

Si1-xGex Si1-xGex

Si Strained-Si

Si1-xGex Si1-xGex

Si Strained-Si

nm

IEEE Trans. Electron Devices ED-26, 1677 (1979).Ballistic electron transport could be achieved in GaAs at low temperaturesIEDM Tech. Digest, 532 (1984).provided evidence of quasi-ballistic transport though heavily doped GaAs layersPhys. Rev. Lett. 55, 2200 (1985). Ballistic portions greater than 75% in improved device structures.

Journal of Physics: Conference Series 193 (2009) 012035

Ballistic electrons is 73% for a 50 nm-long channel.

7

1.2 Ballistic Transport

Hot Electron

Channel Drain

Hot Electrons


Hot ElectronsHot Electrons

Source Channel DrainPrevious works

SISPAD 2010 06-A.1, IEEE TRANSACTIONS ON ELECTRON DEVICES, 55, no. 1, 2008.

Thermal Conductivity Temperature Distribution Power Density

Ballistic channel

Ballistic transport greater than 80% or 90% within channel is entirely possible.

8

1.3 PurposePresent Work IS IEF

IS IEF

ID = IS + IEF

3*kBT/2 ≈ 40 emV

Hot electron transport within drain under the effects of various conditions.

1. Effects of Scattering DirectionIsotropic and Anisotropic scattering

2. Effects of Heat GenerationInelastic scattering

3. Effects of Hot phonons g-LO phonon

4. Effects of Strained Drain Strained Channel and Drain

on Hot Electron Transport and Performance of Devices.

Contents

9

1.4 Approach Drift-Diffusion Approach

dxdnqDxExqnJ nnn += )()( µCurrent equations:

Continuity equations

velocity overshoot, parasitic currents, hot electron transport, heat generation.

nn UJqtn +⋅∇=∂∂ 1

Failure of the Drift-Diffusion Approach

Monte Carlo Method

Include various scattering mechanisms.Include band structure.Easy to couple with quantum effective.

10

1.5 Conclusion

Hot electron is a electron that energy far away thermal energy.

Hot electrons motion obviously influence on performance of device.

Ballistic transport within channel is possible.

The role of the hot electron transport within drain on performance

of device will be discuss in detail.

11

Chapter 2 Semiconductor Fundamentals for Semi-Classical Carrier Transport

2.1 Non-Parabolic Band Structure

2.2 Phonon Dispersion

2.3 Density of States

2.4 Effective Mass

2.5 Carrier Dynamics

2.6 Conclusion

12

Full band

non-parabolic

Full band

non-parabolic

parabolic

2.1 Non-Parabolic Band Structure

The non-parabolically band structure is acceptable and is more accurate than parabolic band when energy of carrier is low as our work.

)1()(2 *

22

kk

k

EEkmkE

αγ +=

= h

2

0

*

)1(1mm

E g

−=α

First conduction band near minimum Density of States

Parabolic band

Non-parabolic bandConduction band of bulk Silicon

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

∆ΓΛ

JAP 75, no.1, 297 (1994)

13

0

0.3

0.6

0.9

0 0.3 0.6 0.9

0

20

40

60

Reduced wave vector qa/2π

Ener

gy (e

V)

Freq

. (10

14 ra

d/s)

g-typef-type

TALA

TOLO

0

0.3

0.6

0.9

0 0.3 0.6 0.9

0

20

40

60

Reduced wave vector qa/2π

Ener

gy (e

V)

Freq

. (10

14 ra

d/s)

g-typef-type

TALA

TOLO

∑ −∆∆= )( ... abemtVAQ ωω hh

20 ckksq ++= υωω

Phonon frequency for intravalley acoustic phonon scattering

Heat generation rate

2.2 Phonon Dispersion

1. E. Pop, et al., J. Appl. Phys. 96, 4998 (2004).2. C. Canali, et al., Phys. Rev. B 12, 2265 (1975).3. M. H. Jorgensen, Phys. Rev. B, 18, 5657, (1978).4. R. Brunetti, et al., J. Appl. Phys., 52, 6713 (1981).5. T. Yamada, et al., IEEE Trans. Electron Devices, 41,

1513 (1994).

Phonon dispersion curves for Silicon

Type E(meV) ref.1 ref. 2 ref. 3 ref. 4 ref. 5 ref. 1 (108 eV/cm)f1 TA 19 0.15 – 0.3 2.5 0.5 f2 LA/LO 51 3.4 4.3 2 – 3.5 f3 TO 57 4 2 2 8 1.5 g1 TA 10 0.5 0.65 0.5 – 0.3 g2 LA 19 0.8 – 0.8 4 1.5 g3 LO 62 3 7.5 11 8 6

Phonon energy and Deformation Potential for intervalley phonon scattering

Intervalley Scattering of g- and f- type

Heat generation is the process of phonon emission and absorption.

14

2.3 Density of States

kx

ky

kz

kx

ky

kz

Ellipsoidal constant energy surface with a weakly and strongly curved dispersion along the kx, ky, and kz axis.

The density of states describes the states of carriers in the bands and their dependence on energy.

∫ ∇= )(41)( 3 kE

dsENk

k π

EmmEN tl2

322)(hπ

=

2.4 Effective Mass

Conductivity Effective Mass )1(32)1(3

11tlc mmm +=

Density of States Effective Mass 3/12)( tld mmm =

15

2.5 Carrier Dynamics

Hdtdk ∇−=

h1 Hdt

drk∇−=

h1

∗=mkhυ **

l

l

t

t

mk

mk hh +=υ )(41

1* kmk

αγυ

+= h

the potential energy of carriers varies slowly, the quantum effects such as tunneling and reflection can be ignorable,

Carriers group velocity

2.6 Conclusion

The topics, which are indispensable for the understanding of semiclassical carrier transport, are briefly described. The semiclassical transport approach is applicable when the applied potentials vary slowly on the scale of an electron’s wavelength. The non-parabolic band is available when carrier energy is low.

16

Chapter 3 Carrier Scattering

3.1 Theory of Scattering

3.2 Ionization Impurity Scattering

3.3 Phonon Scattering

3.4 Impact Ionization

3.5 Wave Vector after Scattering

3.6 Conclusion

17

3.1 Theory of Scattering

Scattering rate

Transition rate

Dirac notation

Overlap integral

Fermi’s Golden Rule

)(|'|'2)',( '2 ωδπ hm

h kk EEkHkkkS −><=

)',(

)(')(|'|'

'

'

kkIU

drrHrkHk

kk

kk

−

Ω

=

>=< ∫ ψψ

∫Ω= drrurukkI kk )()()',( *'

∫Ω⋅⋅−

− = dretrUeU rikrikkk

''' ),(

θπ

πddkkkSkW ∫∫

∞Ω=003 ')',(

)2()(

1)',( ≈kkI for parabolic band

18

3.2 Ionization Impurity Scattering (anisotropic)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2

Energy (eV)

Scattering rate (s-1) ×1014

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.5 1 1.5 2

Energy (eV)

Scattering rate (s-1) ×1014

3.2.1 Brooks-Herring Approach Impurity concentration <= 1018 cm-3

1/qD is the Debye length)4(1)(2)( 2222

42

DDs

kI

qkqENeZNkW

+=

επ

h TkneqBs

D ε0

2=

Scattering rate for the ionized impurities when NI = 1018 cm-3 .

The low energy carriers have the week influence on performance of devicetheir scattering would

have to be processed consuming computational time.

Hot Electrons


Hot ElectronsHot Electrons


19

3.2 Ionization Impurity Scattering (isotropic) 3.2.2 Kosina’s Approach

0

0 .8

1 .6

2 .4

3 .2

0 0 .3 0 .6 0 .9 1 .2 1 .5

Elect ron Energy (eV)

Scattering rate (10141/s)

Impurity concentration > 1018 cm-3

Scattering will be reduce, but isotropic scattering will be increase.

Kosina’s approach is more accurate than Brooks-Herring Approach

Reduce the small angle scattering

)1)1(ln(41)()( 2 b

bbk

kCkW +−+=

)()(2)( 2

02

42

keZNkC

s

I

υεεπh= 22 /4 skb β= )(

)(2/1

2/1

0

22

ηη

εεβ FF

Tkne

nBss

−=

Solid-State Electronics 42, no. 3, 331 (1998). Scattering rate when NI = 1020 cm-3

20

3.3 Phonon Scattering in Silicon

Unite Cell Unite Cell Unite Cell

a a

m1 m2

Equilibrium

Acoustical Vibration

Optical Vibration

Unite Cell Unite Cell Unite Cell

a a

m1 m2

Equilibrium

Acoustical Vibration

Optical Vibration

Vibrations in a crystal

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

Acoustic: same direction.Optical : opposing direction.

Intravalley optical

Conduction band for silicon

21

3.3 Phonon Scattering (Acoustic phonon) 3.3.1 Intravalley scattering by Acoustic Phonon

3.3.1.1 Elastic Acoustic phonon scattering

)(2)(2

kL

B ENC

TkkWh

Ξ=

π

3.3.1.2 Inelastic Acoustic phonon scattering

32

2/3*

4)2(

)(hπ

kk

EmEN =

32

2/3*

4)2(

)(hπ

kk

EmEN =

0 0.2 0.4 0.6 0.8 1

Energy (eV)

Scattering rate (s-1) 1000

100

10

1

1011

32

2/3*

4)2(

)(hπ

kk

EmEN =

0 0.2 0.4 0.6 0.8 1

Energy (eV)

Scattering rate (s-1) 1000

100

10

1

1011

R is the radius of the spherical Wigner-Seitz cell

dqqINk

mkW qqqs

d 32

2)2

121(1

4)( m

h+Ξ= ∫ωπρ

)]cos()[sin()(

33 sss

sq qRqRqR

qRI −=

Energy (eV)0 0.2 0.4 0.6 0.8 1

1013

1012

1011Scat

teri

ng r

ate

(1/s

)

EmissionAbsorption

Energy (eV)0 0.2 0.4 0.6 0.8 1

1013

1012

1011Scat

teri

ng r

ate

(1/s

)Energy (eV)

0 0.2 0.4 0.6 0.8 1

1013

1012

1011Scat

teri

ng r

ate

(1/s

)

EmissionAbsorption

TkB<<ωhat room temperature

22

)()21

21)(()(

2

ijkijij

ijij ENnZD

kW ωωρωπ

hm ±+=

1)/exp(1)( −= Tkn

Bijij ωω

h

0 0.2 0.4 0.6 0.8 1

Energy (eV)

Scattering rate (s-1)

EmissionAbsorption

1000

100

10

1

1011

3.3 Phonon Scattering (Optical phonon)

3.3.2 Intervalley scattering by Optical Phonon

'k 'k

k kq q

θ θ

'θ'θ

Absorption Emission The band valleys of silicon

[100]

[010]

[001]

f

g

Intervalley scattering

23

3.4 Impact Ionization

2])([)( thEkEPkW −=

P = 6.25×1010 eV2 s-1

Eth =1.1 eV for unstrained Silicon

1 1.1 1.2 1.3 1.4 1.5

Energy (eV)

1011

107

105

109

1 1.1 1.2 1.3 1.4 1.5

Energy (eV)

1011

107

105

109

Impact ionization is the process that the carriers with enough kinetic energy knock bound carriers out of its bound state to create other carriers and lose their kinetic energy, which requires a large electric field.

24

3.5 Wave Vector after Scattering

φ

θk’

k

φ

θk’

k12 rπφ =

φθ cossin'' kk x =φθ sinsin'' kk y =

θcos'' kk z =

221cos r−=θ3.5.1 Isotropic Scattering (impurity scattering when ND = 1020 cm-3 and Phonon scattering)

3.5.2 Anisotropic Scattering (impurity scattering when ND <= 1018 cm-3 )

2)2)(1(1

21cos3

3

Dqkr

r

−+−=θ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+−

++

−++

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

θφθφθ

cossinsincossin

0

'

'

'

22

2222

2222

'

'

'

kkk

kk

k

kk

kk

kkk

kk

kk

k

kk

kkk

kk

kk

k

kkk

zyx

y

yx

zy

yx

x

x

yx

zx

yx

y

z

y

x

42 rπφ =rzk

Lxk

Lyk r

xk

ryk

rzk

ββ

α

α

25

3.6 Conclusion

The method employed is based on Fermi’s Golden Rule. The scattering rates are evaluated directly from the transition rate. Scattering mechanisms identified in this chapter were limited to those that are rather important for the carrier transport in common semiconductors.The full band numerical treatment of the scattering mechanism is essential for the very high energies carriers in devices.

26

Chapter 4 Monte Carlo Method for Devices Simulation

4.1 Procedure of Monte Carlo Method4.2 Drift Process4.3 Scattering Process4.4 Monte Carlo Devices Simulation4.5 Conclusion

27

4.1 Procedure of Monte Carlo Method

Start

t1=tt2=scattering time

t2>t+Δt

τ= t+Δt- t1

Drift(τ)

End

τ= t2- t1

Drift(τ)Scattering

t1=t2t2= new scattering time

Start


t2>t+Δt

τ= t+Δt- t1

Drift(τ)

End

Start


t2>t+Δt

τ= t+Δt- t1

Drift(τ)

End

τ= t2- t1

Drift(τ)Scattering


τ= t2- t1

Drift(τ)Scattering


r=rand()

Start

End

)(11 kEr Λ≤

)(22 kEr Λ≤

)( knn Er Λ≤

NO

NO

NO

YES

YES

YES

φ θ

φ θ

φ θ

r=rand()

Start

End

)(11 kEr Λ≤

)(22 kEr Λ≤

)( knn Er Λ≤

NO

NO

NO

YES

YES

YES

φ θ

φ θ

φ θ

φ

θk’

k

φ

θk’

k

∑=

=ΓN

jkj EW

0)(

Γ=Λ∑

=

n

jk

kn

EWE 1

)()(

EMC Simulation Scattering Process

Total scattering rate

28

Impurity Scattering rate W1Acoustic scattering rate W2Optical scattering rate W3Impact ionization W4

= W1+W2+W3+W4

4.2 Drift Process 4.3 Scattering Process

Drift process Scattering Process

Γ−= )ln(rτ

Γ

kkk ∆+=

Γ+++<

Γ++<

Γ+<

Γ<

1234

123

12

1

WWWWrelseif

WWWrelseif

WWrelseif

Wrif Impurity Scattering

Acoustic Scattering

Optical Scattering

Impact Scattering

kkE∇=h1υ

τh

eFk −=∆

υτ ×=s

29

4.4 Monte Carlo Devices simulation

Start

config

initial

emc

renew

charge

poisson

t<tmax

End

YesNo

Start

config

initial

emc

renew

charge

poisson

t<tmax

End

Start

config

initial

emc

renew

charge

poisson

t<tmax

End

YesNo

particle i

(x,y)

(x, y)

source gate drain

particle j

particle i

(x,y)

(x, y)

source gate drain

particle j

Could-in-cell method

Finite difference method

The particle refection and the particle exit

x’ = x, y’ = y + (y - ymax)

kx’ = kx , ky’ = ky , kz’ = kz

Simulation process

Self consistently coupled with Poisson’ equation.

30

4.4 Monte Carlo Device simulation

j-1

i - 1 i i + 1

∗j

j+1

Cell Grid Point

j-1

i - 1 i i + 1

∗j

j+1

Cell Grid Point

))(()1,1()1,1()1,1(

))(()1,()1,()1,(

))((),1(),1(),1(

))((),(),(),(

2

112

12

112

ji

ji

ji

ji

yyxxjiAjiNjin

yyxxjiAjiNjin

yyxxjiAjiNjin

yyxxjiAjiNjin

−−++++=++

−−++=+

−−++=+

−−=

++

+

++

Charge Distribution Solution of Poisson Equation

)],.(),,(),(),([)],,()([ tjiptjinjiNjiNqtjix AD +−−−=∇⋅∇ φε

]),(),([)22

(( ,,21,,1,

2,1,,1

,,1

,nji

njiAD

nji

nji

nji

nji

nji

nji

jinji

nji pnjiNjiNq

yxt +−−−

∆+−

+∆

+−−∆+= −+−++ φφφφφφεφφ

Electric Field Calculation

),(),( yxyxE φ−∇=

yjiE

xjiE

jijiy

jijix

∆−

−=

∆−

−=

−+

−+

2),(

2),(

1,1,

,1,1

φφ

φφ

Could-in-cell method

31

4.5 Conclusion

MC simulation is acceptable for many cases that semiconductor device simulation.The use of non-parabolic band enables to simulate the carrier transport in

the device when the energy of carrier is lower than band gap.The non-parabolic band device simulation is more faster than full-band

simulation.The non-parabolic band Monte Carlo simulation can be applied to the engineering of low-voltage nanoscale devices and materials that require detailed knowledge of carrier transport include electron-phonon interaction.

32

Chapter 5 Effects of Scattering Direction on Hot Electron Transport

Scattering Conditions

(A) Ballistic

(B) Elastic and inelastic scattering

(C) Elastic phonon scattering

Current Velocity Effects of elastic and inelastic phonon scattering


Elastic scattering Hot electron

ωhInelastic scattering

ConclusionElastic phonon scattering can enhance the backward flow of hot electrons.

Inelastic phonon scattering can suppress the backward flow of hot electrons.

T. Kurusu, and K. Natori: Jpn. J. Appl. Phys. 45 (2006) 1548.

Rebound of hot electronsElastic--- acoustic ; inelastic---- optical

isotropic scattering

5.1 Introduction

33

5.2 Results and Discussion (1)

n+

100nm 40nm 100nm

n+i


(Ballistic)40nm n+

100nm 40nm 100nm

n+i


(Ballistic)40nm

0

0 .7

1 .4

2 .1

2 .8

0 80 160 240X-axis (nm)

Velocity (107 cm/s) Ba l .

Aco. Imp.Aco.

0

2

4

6

0 0 .3 0 .6 0 .9 Vo ltage (V)

Current (A/cm) Ba l .

Aco. Imp.Aco.

0

0 .7

1 .4

2 .1

2 .8

0 80 160 240X-axis (nm)


Aco. Imp.Aco.

0

2

4

6

0 0 .3 0 .6 0 .9 Vo ltage (V)


Aco. Imp.Aco.

0

0 .7

1 .4

2 .1

2 .8

0 80 160 240X-axis (nm)

Velocity (107cm/s Ba l .

Pho.

Pho. Imp.

0

2

4

6

0 0 .3 0 .6 0 .9

Vo ltage (V)

Current (A/cm)

Ba l .Pho.Pho. Imp.

0

0 .7

1 .4

2 .1

2 .8

0 80 160 240X-axis (nm)

Velocity (107cm/s Ba l .

Pho.

Pho. Imp.

0

2

4

6

0 0 .3 0 .6 0 .9

Vo ltage (V)

Current (A/cm)

Ba l .Pho.Pho. Imp.

Source:acoustic/optical phonon, ionized impurity.

Drain:(A) ballistic; acoustic; acoustic+impurity(B) ballistic; phonon; phonon+impurity

Original of this workInvestigate effects of ionized impurity scattering at different doping concentration.

Velocity distribution I-V characteristics

Ballistic channel diode

ResultsIonized impurity scattering has a weak influence on hot electron transport at low doping concentrations.

VD = 0.3 V

ND = 1018 cm-3

34


Rebound Hot electron Absorb

ωhInelastic scattering

Acoustic phonon scattering impurity scattering


Scattering rate

Distribution of electrons

Rebound of hot electrons

S C D S C D

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

0 0.1 0.2 0.3Energy (eV)

Scat

teri

ng r

ate

(s-1

)

Opt. Emi.Opt. Abs.Aco.Imp.

Reason of these results is that ionized impurity scattering is an anisotropic scattering with a high preference for forward scattering at low doping concentrations.

35

0

4

8

12

16

0 0 .3 0 .6 0 .9

Voltage (V)


Aco.

Aco. Imp.

0

0 .6

1 .2

1 .8

2 .4

0 80 160 240X-axis (nm)


Aco.Aco. Imp.

0

4

8

12

16

0 0 .3 0 .6 0 .9

Voltage (V)


Aco.

Aco. Imp.

0

0 .6

1 .2

1 .8

2 .4

0 80 160 240X-axis (nm)


Aco.Aco. Imp.


0

4

8

12

16

0 0 .3 0 .6 0 .9Voltage (V)


Pho.

Pho. Imp.

0

0 .6

1 .2

1 .8

2 .4

0 80 160 240

X-axis (nm)

Velocity (107cm/m) Ba l .

Pho.Pho. Imp.

0

4

8

12

16

0 0 .3 0 .6 0 .9Voltage (V)


Pho.

Pho. Imp.

0

0 .6

1 .2

1 .8

2 .4

0 80 160 240

X-axis (nm)

Velocity (107cm/m) Ba l .

Pho.Pho. Imp.


VD=0.3V VD=0.3V

ResultsIonized impurity scattering severely degrades the peak of the mean velocity of electrons in the channel and the steady-state current.

ReasonIonized impurity scattering approaches isotropic characteristics and enhances the scattering of hot electrons in the backward direction.

S C D

Isotropic anisotropic

S C D

Isotropic anisotropic


ND = 1020 cm-3

Kosina’s Approach

0

0 .8

1 .6

2 .4

3 .2

0 0 .3 0 .6 0 .9 1 .2 1 .5

Electron Energy (eV)

Scattering rate (10141/s)

36

At low doping concentrations, ionized impurity scattering has a weak influence on hot electron transport because of its anisotropic characteristics with a high probability for forward-scattering events.

ionized impurity scattering approaches the isotropic state at sufficiently high doping concentrations, and increases the scattering of hot electrons in the backward direction, severely degrading the peak of the mean velocity of electrons in the channel and the steady-state current.

Therefore, The scattering direction is an important factor for hot electron transport.

The peak of the mean velocity of electrons in the channel and the steady-state current are decreased if the rebound of hot electrons in the backward direction is increased in the drain region.

5.3 Conclusion

37

Chapter 6 Effects of Heat Generation on Hot Electron Transport

2001, IEDM, pp. 31.1.1

Power density Temperature distribution

Proceedings of the IEEE2006, pp. 1587

6.1 Introduction

(Ballistic)(Ballistic)

Ballistic channel diode

Hotspots distribution

JAP 97, 023702 (2005)

Original of this work

Investigate effects of inelastic scatterings on hot electron transport.

38

n+

100nm 40nm 100nm

n+i


(Ballistic)40nm n+

100nm 40nm 100nm

n+i


(Ballistic)40nm

Source:intravalley/intervalley phonon

Drain:(A) intravalley phonon (B) intervalley phonon

0

2

4

0 0.3 0.6 0.9

0

0.7

1.4

2.1

0 80 160 240

X-axis (nm)

Vel

ocity

(107

cm/s)

Inter.Intra.

Drain Voltage (V)

Cur

rent

(A/c

m)

Inter.Intra.

0

2

4

0 0.3 0.6 0.9

0

0.7

1.4

2.1

0 80 160 240

X-axis (nm)

Vel

ocity

(107

cm/s)

Inter.Intra.

Drain Voltage (V)

Cur

rent

(A/c

m)

Inter.Intra.Inter.Intra.

Ballistic Si n+-i-n+ diode Velocity distribution I-V characteristics

ReasonIntravalley acoustic phonon scattering has a low heat generation.

Heat Generation rate at VD = 0.3 V

Intravalley acoustic phonon scattering seriously degrade the mean velocity of electrons in the channel and the drain current.


-1

0

1

2

3

4

0 60 120 180 240

X-axis (nm)

Hea

t gen

. rat

e(1

028eV

/cm

-3/s

) Inter.Intra.

-1

0

1

2

3

4

0 60 120 180 240

X-axis (nm)

Hea

t gen

. rat

e(1

028eV

/cm

-3/s

) Inter.Intra.

39

0

2

4

0 0.3 0.6 0.9

0

0.7

1.4

2.1

0 80 160 240

X-axis (nm) Drain Voltage (V)

Inter. Intra.Intra.

Inter. Intra.Intra.

Cur

rent

(A/c

m)

Vel

ocity

(107

cm/s

)

0

2

4

0 0.3 0.6 0.9

0

0.7

1.4

2.1

0 80 160 240

X-axis (nm) Drain Voltage (V)

Inter. Intra.Intra.

Inter. Intra.Intra.

Cur

rent

(A/c

m)

Vel

ocity

(107

cm/s

)

-1

0

1

2

3

4

0 60 120 180 240

X-axis (nm)

Hea

t gen

. rat

e(1

026eV

/cm

-3/s

) Inter. IntraIntra.

-1

0

1

2

3

4

0 60 120 180 240

X-axis (nm)

Hea

t gen

. rat

e(1

026eV

/cm

-3/s

) Inter. IntraIntra.


Hot electron

ωh


Intravalley scattering


Hot electron

ωh


Intravalley scattering

Velocity distribution I-V characteristics Heat Generation rate at VD = 0.3 V

Intervalley phonon scattering has high heat generation, obviously suppress the backward flow of hot electrons and increase the drain current.


40

6.3 Conclusion

Intravalley acoustic phonon scattering severely degrades the peak of the mean velocity of electrons in the channel and the drain current because intravalley acoustic phonon scattering has relatively lower heat generation, and most rebounded hot electrons from the drain region can transport with high velocity.

In contrast, most rebounded hot electrons from the drain region transport with low velocity when they are undergoing intervalley phonon scatterings because intervalleyphonon scattering has a relatively higher heat generation.

Therefore, The heat generation is an important factor for hot electron transport.

The heat generation rate can provide one parameter for measuring the influence of inelastic phonon scattering on electron transport.

41

Chapter 7 Effects of Hot Phonon on Hot Electron Transport

7.1 Introduction

)()21

21)(()(

2

ijkqij

ijij ENTNZDkW ωρωπ

hm ±+=

dqqITNkmkW qq

qs

d 32

2)2

121)((1

4)( mh

+Ξ= ∫ ωπρ

Intervalley phonon

Intravalley phonon

1)/exp(1)( −= TkTN

Bqq ωhPhonon occupation for equilibrium condition

0.1

1

10

100

0 0.4 0.8 1.2Energy (eV)

Scat

. rat

e (1

012 1/

s)

Emi.Abs.

Scattering rate Phonon energyElectron

PHYSICAL REVIEL B 39, no. 11, 1989

IEEE TRANSACTIONS ON ELECTRON DEVICES 55, no. 1, 2008

Phonon occupation

Original of this workHot electron transport under the non-equilibrium condition.

42

20 cqqsq ++= υωω

∑ −= )( ...sup

'''absems

simVtNNQ ωω hh

ph

qq

phph

q TNNt

Nτ

)(−−=∂

∂

−

)(6..

3max

2

supTNtqN

nphogenN qsim

phq +=

τπ

7.2 Method

Heat generation Phonon BTE

Non-equilibrium phonon occupation Phogen.

SISPAD 2005, pp. 307IEEE TRANSACTIONS ON ELECTRON DEVICES 55, no. 1, 2008

LO occupation

ωωωτ

∆≈ )(''

LOLOLO g

QNh

)( LOg ω Phonon density of states

ω∆ The spectral width

43

1.0

1.1

1.2

1.3

1.4

Eq. Noneq.

Cur

rent

(103 A

/cm

)

0.0

0.5

1.0

1.5

2.0

0 60 120 180 240X-axis (nm)

Vel

ocity

(107 c

m/s

) Eq.Noneq.

(a) (b)

1.0

1.1

1.2

1.3

1.4

Eq. Noneq.

Cur

rent

(103 A

/cm

)

0.0

0.5

1.0

1.5

2.0

0 60 120 180 240X-axis (nm)

Vel

ocity

(107 c

m/s

) Eq.Noneq.

1.0

1.1

1.2

1.3

1.4

Eq. Noneq.

Cur

rent

(103 A

/cm

)

0.0

0.5

1.0

1.5

2.0

0 60 120 180 240X-axis (nm)

Vel

ocity

(107 c

m/s

) Eq.Noneq.

(a) (b)

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5Time (ps)

Nq


Velocity Current

Phonon occupation

0.1

1

10

100

0 0.4 0.8 1.2Energy (eV)

Scat

. rat

e (1

012 1/

s) Emi.Abs.

Scattering rate

Phonon absorption is

increased as Nq increased.

When the non-equilibrium phonon occupation is considered, the simulation results for the mean electron velocity and the drain current are lower than the corresponding results under the equilibrium condition.

ND = 5×1020 cm-3

44

-0.1

0.3

0.7

1.1

1.5

0 60 120 180 240X-axis (nm)

Eq.Noneq.

Hea

t gen

. rat

e (1

012W

/cm

3 )

0

0.05

0.1

0.15

0 60 120 180 240X-axis (nm)

Ene

rgy

(eV

)Eq.Noneq. (a) (b)

-0.1

0.3

0.7

1.1

1.5

0 60 120 180 240X-axis (nm)

Eq.Noneq.

Hea

t gen

. rat

e (1

012W

/cm

3 )

0

0.05

0.1

0.15

0 60 120 180 240X-axis (nm)

Ene

rgy

(eV

)Eq.Noneq.

-0.1

0.3

0.7

1.1

1.5

0 60 120 180 240X-axis (nm)

Eq.Noneq.

Hea

t gen

. rat

e (1

012W

/cm

3 )

0

0.05

0.1

0.15

0 60 120 180 240X-axis (nm)

Ene

rgy

(eV

)Eq.Noneq. (a) (b)


Mean electron energy mean heat generation

The mean electron energy within the drain region under the non-equilibrium condition is larger than

that under the equilibrium condition.

when the non-equilibrium phonon effect is considered, the heat generation within the drain region is

less than the case under the equilibrium condition.

ConclusionWe conclude that the hot phonon effect should be taken into account in the study of hot electron transport within the drain region when the hot phonon generation has obviously increased.

45

Chapter 8 Strained Drain and Hot Electron Transport

8.1 Introduction

IEEE TRANSACTIONS ON ELECTRON DEVICES 56, no. 4, 2009

http://userweb.elec.gla.ac.uk/k/kalna/III-VMOSFETgrant.html

Strained channel

IEDM 2003, pp. 11.6.1

Induce compressive strain in the channel region.

Induce tensile channel strain

Strain

46

8.1 Introduction

JAP 97, 011101 (2005)

Current enhancement Mobility enhancement

Reasons Reduction of the density of states effective mass and scattering.

ProblemsReduction of scattering is not useful for ballistic channel device. Backward flow of hot electrons within drain will reduce drain current.

47

Si1-xGex Si1-xGex

Si Strained-Si

Si1-xGex Si1-xGex

Si Strained-Si

X4

X2

Si Strained-Si

SiX6

Strained-SiX4

X2

∆E

X4

X2

X4

X2

X4

X2

Si Strained-Si

SiX6

Strained-SiX4

X2

∆ESiX6

Strained-SiX4

X2

∆E∆E

(1) Change the lattice constant of material (2) Energy splitting between the valleys

)(]21

21)([)(

2

jiijkijij

jij EENnZDkW ∆−±+= ωωρωπ

hm

2

0

*

)1(1mm

Eg

−=α

0196.0 mmm td ==

xE 67.0=∆

xExE gg 4.0)( −=

(3) Reduce the band gap (4) Reduce the scattering

Eg(x) = 1.11-0.4xEth(x) = 1.1Eg(x)/Eg(0)

8.2 Strained Silicon

0.328m0)( 3/12 == tld mmm

EmEN d32

2/3

4)2()(hπ

=

For bulk silicon

For X2 valleys

48

ScatteringIntervalley/intravalley phonon scattering,Impurity scattering, impact ionization.

SiX6

Strained-SiX4

X2

∆ESiX6

Strained-SiX4

X2

∆E∆E

Si n+-i-n+ diode

Splitting of the valleys

The drain current and the mean velocity of electron within drain, when drain region is strained, are larger than the case that channel region is strained.

Reasons Intervalley phonon scattering is suppressed and the rebound of hot electron in the

backward direction is degraded.

x=0.6∆E=0.402 eV Eg(0.6)=0.842 eVEth(0.6) = 0.842 eV

n+

100nm 20nm 100nm

n+i


(Ballistic)40nm n+

100nm 20nm 100nm

n+i


(Ballistic)40nm


>90%

0

1

2

3

4

5

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

1

2

3

UnStr. Cha. Dra.

Cur

rent

(A/c

m)(a) (b)

0

1

2

3

4

5

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

1

2

3

UnStr. Cha. Dra.

Cur

rent

(A/c

m)

0

1

2

3

4

5

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

1

2

3

4

5

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

1

2

3

UnStr. Cha. Dra.

Cur

rent

(A/c

m)

0

1

2

3

UnStr. Cha. Dra.

Cur

rent

(A/c

m)(a) (b)

-8

-6

-4

-2

0

2

0 50 100 150 200

X-axial (nm)

Ele

ctri

c Fi

eld

104 ( eV/cm)

Unstr.Cha.Dra.

-8

-6

-4

-2

0

2

0 50 100 150 200

X-axial (nm)

Ele

ctri

c Fi

eld

104 ( eV/cm)

-8

-6

-4

-2

0

2

0 50 100 150 200

X-axial (nm)

Ele

ctri

c Fi

eld

104 ( eV/cm)

Unstr.Cha.Dra.

Mean velocity of electrons within drain

Drain currentVD=0.3 V

dmkh=υ

49

Drain Resistance

RD = Q / I2

∑ −= )(1... abemtQ ωω hh

Strained drain has lower resistance than other two cases.

x=0.6∆E=0.402 eV


0

2

4

6

8

10

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

2

4

6

UnStr. Cha. Dra.

Cur

rent

(A/c

m)(a) (b)

0

2

4

6

8

10

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

2

4

6

UnStr. Cha. Dra.

Cur

rent

(A/c

m)(a) (b)

Dra

in R

esis

tanc

e (Ω

.ｃm

)

0

0.3

0.6

0.9

1.2

UnStr. Cha. Dra.Dra

in R

esis

tanc

e (Ω

.ｃm

)

0

0.3

0.6

0.9

1.2

UnStr. Cha. Dra.

Mean velocity of electrons within drain Drain current VD= 1.0 V

50

0

1

2

3

4

5

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

1

2

3

UnStr. Cha. Dra.

Cur

rent

(A/c

m)

0

1

2

3

4

5

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

0

1

2

3

UnStr. Cha. Dra.

Cur

rent

(A/c

m)

Double Gate MOSFET

0

3

6

9

UnStr. Cha. Dra.

0

2

4

6

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

Cur

rent

(A/c

m)

0

3

6

9

UnStr. Cha. Dra.

0

2

4

6

UnStr. Cha. Dra.

Vel

ocity

(106

cm/s

)

Cur

rent

(A/c

m)

VG = 0.3 Vt0x = 6 nm

ResultWe obtained similar results as diode.

n+

100nm 20nm 100nm

n+

Source Gate Drain

40nm i

(Ballistic)n+

100nm 20nm 100nm

n+

Source Gate Drain

40nm i

(Ballistic)

Include quantum correction

8.3 Results and Discussion (3)Mean velocity of electrons within drain

Drain currentVD=0.3 V

Mean velocity of electrons within drain

Drain current

VD= 1.0 V

51

8.4 Conclusion

When the drain region is strained the drain current and the mean velocity of electron in the drain are larger than the case that the channel region is strained because the strained drain can obviously suppress the rebound of electron in the backward direction and degrade the parasitic resistance of drain.

We conclude that the strained drain is an efficient method to improve the electrical characteristics of ballistic-channel devices.

52

Chapter 9 Summary


Hot electronBallistic

Strained

Intervalley

Drain Current

Inelasticelastic

Hot phonon

53

9.2 For Improved Performance and Future Works

1. Reducing operation voltage to avoid high energy scattering.

2. Controlling the doping concentration to reduce ionized impurity scattering.

3. Reducing phonon scattering by using a materials, which have the low effective mass and deformation potentials.

There are several ways to reduce backward flow of hot electrons from drain region

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

)4(1)(2)( 2222

42

DDs

kI

qkqENeZNkW

+=

επ

h

)(2)(2

kL

B ENC

TkkWh

Ξ=

π32

2/3*

4)2(

)(hπ

kk

EmEN =

0.0

0.5

1.0

1.5

2.0

Si Ge

Cur

rent

(A/c

m)

54

4. Using the strained materials to reduce scattering;

5. Using the materials, which have high phonon energy, to increase the phonon generation in hotspots region and reduce backward flow of hot electrons.

In this work, a simplistic band structure for carriers is employed. In the simulation of the employed device, a bulk regime is used and the low-dimensional structure is not considered. The scattering mechanisms are limited to those that are rather important for low energy carrier transport. To achieve more accurate simulation of the device, there are several points that need to be considered in future works.

(1) If device scale is further reduced, the two-dimensional effects, both related to both the electrostatics and the quantum confinement, are likely to influence significantly the hot electron transport. This is because the final density-of-states will be significantly different and the scattering rates themselves will be different. In bulk devices this may be a secondary consideration, since the quantum confinement is weak in the drain region. But in UTB SOIs or DGFETs the difference may be substantial.


http://nanohub.org/

55

(2) Phonon scatterings are very sensitive to the selection of deformation potential. The arguments about the deformation potentials are very important. One must be fully careful in selection of the deformation potential in future works.

Type E(meV) ref.1 ref. 2 ref. 3 ref. 4 ref. 5 ref. 1 (108 eV/cm)f1 TA 19 0.15 – 0.3 2.5 0.5 f2 LA/LO 51 3.4 4.3 2 – 3.5 f3 TO 57 4 2 2 8 1.5 g1 TA 10 0.5 0.65 0.5 – 0.3 g2 LA 19 0.8 – 0.8 4 1.5 g3 LO 62 3 7.5 11 8 6

(3) Intravalley deformation potential scattering is suppressed by the selection rules along the Delta symmetry line. When the energy of hot electrons are far away from the Delta minima, the electrons interact with optical phonons via non-polar optical scattering in silicon.

(4) The realistic band structure of Si is quite different from any analytical band approximation in the wide range. When hot electrons energy are far away from the minimum point of realistic in the band structure, one should be careful to employ a better band structure model, e.g. the full-band model, in the simulation.

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ

Eg EX

EL

ΓE ΓE

Wave vector

Eg = 1.12 eV

EX = 1.2 eV

EL = 2.0 eV

eVEeVE 2.4 4.3

==

Γ

Γ


56

(5) Because of the thermalization of the energy distribution through the carrier-carrier scattering, hot electrons may easily be affected by the high energy valley carriers, even when a relatively small bias is applied.

(6) Although relatively small biases are applied, impact ionization cannot be ignored because the carrier-carrier scattering can produce significantly high energy electrons above the applied bias near the drain-end of the channel.


57

Q & A

Hot ElectronHot electron is a electron that energy far away thermal energy.

Ballistic TransportBallistic transport greater than 80% or 90% within channel is entirely possible.

PurposeHot electron transport within drain and Performance of device under the effects of various conditions.

Velocity distribution within source and drainEffects of hot electron transport on backward direction.

UTB SOIs or DGFETsEffects of Density of states must be considered in simulation.

58

PublishedA. Abudukelimu et al., “Effects of Scattering Direction of Hot Electrons in the Drain of Ballistic n+–i–n+

Diode”, Japanese Journal of Applied Physics, 50 (2011) 104301.Under revieweA. Abudukelimu et al., “Influence of Heat Generation within Drain Region on Transport of Hot Electrons ”,

Journal of Applied Physics (JAP).A. Abudukelimu et al., “Influence of strained channel and drain on performance of

ballistic channel diode”, Semiconductor Science and Technology.

International ConferenceA. Abudukelimu et al., “Performance of Silicon Ballistic Nanowire MOSFET with Diverse Orientations and

Diameters ”, China Semiconductor Technology International Conference (CSTIC), Mar. 18 - 19, 2010. A. Abudukelimu et al., “The effect of isotropic and anisotropic scattering in drain region of ballistic channel

diode”, International Conference on Solid-State and Integrated Circuit Technology (ICSICT), Nov. 1- 4, 2010.

Domestic Conference• Abudukelimu et al., “バリスティックナノワイヤMOSFETの電流-電圧特性の数値分析”, 70th応用物理

学会学術講演会, Sep. 8~11,2009.

Award2010/06 植之原留学生奨励賞2010/03 Best Student 3rd Place, SEMI ECS Student & Engineer Award.

59

Thank You for Your Attention!

Documents

Hot Electron Transport and Performance of Semiconductor … · 2012. 7. 25. · Carrier obtained energy from electric field Carrier changed energy and momentum. τ h eF k = − hω