Strain Effects on Bulk Strain Effects on Bulk <001> Ge Valence Band<001> Ge Valence BandEEL6935: Computational NanoelectronicsFall 2006

Andrew Koehler

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Andrew Koehler

OutlineOutline

• Motivation • Background

– Strain– Germanium

• Simulation Results and Discussion• Summary• References

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Andrew Koehler

MotivationMotivation

• Moore’s Law– ~ 0.7X linear scale factor– 2X increase in density / 2

years– Higher performance (~30%

/ 2 years)

• Approaching Fundamental Limits– “No Exponential is

Forever”

• What is the solution?

Ultimate

CMOS

Current

CMOS

Energy kTln(2) kT(104~105)

Channel

Length1 nm 100 nm

Density 1014/cm2 109/cm2

Power 107 W/cm2 100 W/cm2

Speed 0.01 ps 1 ps

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Solution: Novel MaterialsSolution: Novel Materials

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Andrew Koehler

History of StrainHistory of Strain

1954: Piezoresistance in silicon was first discovered by C. S. Smith

(resistance change due to applied stress)

1980s: Thin Si layers grown on relaxed silicon–germanium (SiGe) substrates

1990s: High-stress capping layers deposited on MOSFETs were investigated as a technique to introduce stress into the channel

1990s: SiGe incorporated in the source and drain areas

2002: Intel uses strained Si in P4 processor

00

0 11

R

R

R

RR

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What is Strain?What is Strain?

• Stress: Limit of Force/Area as Area approaches zero

• Strain: Fractional change in length of an object Distortion of a structure caused by stress

0A

FLim

A

0

0

a a

a

xx

yy

zz

yz

zx

xy

2

2

2

xx

yy

zz

yz

zx

xy

Normal Stress

Component

Shear Stress

Component

Normal Strain

Component

Shear Strain

Component

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What is Strain?What is Strain?

11 12 12

12 11 12

12 12 12

44

44

C C C 0 0 0

C C C 0 0 0

C C C 0 0 0

0 0 0 C 0 0

0 0 0 0 C 0

0 0 0

xx

yy

zz

yz

zx

xy

44

2

2

0 0 C 2

xx

yy

zz

yz

zx

xy

11 12 12

12 11 12

12 12 12

44

44

S S S 0 0 0

S S S 0 0 0

S S S 0 0 0

2 0 0 0 S 0 0

0 0 0 0 S 02

0 0 2

xx

yy

zz

yz

zx

xy

440 0 0 S

xx

yy

zz

yz

zx

xy

C

S

Elastic Stiffness Coefficients (1011N/cm2)

Compliance Coefficients (10-11cm2/N)

c11 c12 c44

Si 1.657 0.639 0.7956

Ge 1.292 0.479 0.670

s11 s12 s44

Si 0.768 -0.214 1.26

Ge 0.964 -0.260 1.49

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Strain Effect on Valence BandStrain Effect on Valence Band

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History of GermaniumHistory of Germanium

1959: First germanium hybrid integrated circuit demonstrated.- Jack Kilby, Robert Noyce

1960: High purity silicon began replacing germanium in transistors, diodes,

and rectifiers

2000s: Germanium transistors are still used in some stompboxes by musicians who wish to reproduce the distinctive tonal character of the "fuzz"-tone from the early rock and roll era.

2000s: Germanium is being discussed as a possible replacement of silicon???

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Why Did Si Replace Ge?Why Did Si Replace Ge?

• Germanium’s limited availability• High Cost• Impossible to grow a stable oxide that could

– Passivate the surface– Be used as an etch mask– Act as a high-quality gate insulator

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Novel Materials to the RescueNovel Materials to the Rescue

• High-k Dielectric– Used as gate oxide– eliminate the issue that germanium’s native oxide is not

suitable for nanoelectronics

• Atomic Layer Deposition (ALD)– HfO2– ZrO2– SrTiO3, SrZrO3 and SrHfO3– ALD WN/LaAlO3/AlN gate stack

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Ge vs Other SemiconductorsGe vs Other Semiconductors

nMOS: GaAs is the best material pMOS: Ge is the best material

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Future of Ge in NanoelectronicsFuture of Ge in Nanoelectronics

• Researchers Believe – Combination of a Ge pMOS with a GaAs nMOS could

be a manufacturable way to further increase the CMOS performance.

• Current Problems– Passivation of interface states– Reduction of diode leakage – Availability of high-quality germanium-on-insulator

substrates

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k k ∙ p method∙ p method

• k ∙ p method was introduced by Bardeen and Seitz

• Kane’s model takes into account spin-orbit interaction– Ψnk(r) = eik∙runk(r)– unk(r+R) = unk(r) – Bloch function

• n refers to band• k refers to wave vector

• Useful technique for analyzing band structure near a particular point k0

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k k ∙ p method∙ p method

• Schrodinger equation

• Written in terms of unk(r)

)()()()(2 0

2

rkErrVm

pnknnk

)(2

)()()(2 0

22

00

2

rum

kkErurVpk

mm

pnknnk

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Unstressed Band StructuresUnstressed Band Structures

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

<--- out of plane (k) channel direction --->

Ene

rgy

(eV

) --

->

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

<--- out of plane (k) channel direction --->

Ene

rgy

(eV

) --

->

Silicon Germanium

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Biaxial Compression 1 GPaBiaxial Compression 1 GPa

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

<--- out of plane (k) channel direction --->

Ene

rgy

(eV

) --

->

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

<--- out of plane (k) channel direction --->

Ene

rgy

(eV

) --

->

Silicon Germanium

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Andrew Koehler

Longitudinal Compression 1 GPaLongitudinal Compression 1 GPa

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

<--- out of plane (k) channel direction --->

Ene

rgy

(eV

) --

->

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

<--- out of plane (k) channel direction --->

Ene

rgy

(eV

) --

->

Silicon Germanium

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Band SplittingBand Splitting

0 0.5 1 1.5 2 2.5 30

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Stress (GPa)

Ene

rgy

(eV

)

0 0.5 1 1.5 2 2.5 30

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Stress (GPa)

Ene

rgy

(eV

)

Ge

Si

Ge

Si

Biaxial Compression Longitudinal Compression

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Silicon Mass ChangeSilicon Mass Change

0 0.5 1 1.5 2 2.5 30.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Stress (GPa)

m*/

m

0 0.5 1 1.5 2 2.5 30.18

0.2

0.22

0.24

0.26

0.28

0.3

Stress (GPa)

m*/

m

•Longitudinal Compression

In-Plane Out-of-Plane

80%

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Germanium Mass ChangeGermanium Mass Change

0 0.5 1 1.5 2 2.5 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Stress (GPa)

m*/

m

0 0.5 1 1.5 2 2.5 30.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Stress (GPa)

m*/

m

•Longitudinal Compression

In-Plane Out-of-Plane

90%

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SummarySummary

– Strain– Germanium– Strained Germanium Compared to Silicon

• Unstressed• Band Splitting

– Biaxial Compression

– Longitudinal Compression

• Mass Change - Longitudinal Compression– In-Plane

– Out-of-Plane

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ReferencesReferences

C. S. Smith, “Piezoresistance effect in germanium and silicon,” Phys. Rev., vol. 94, no. 1, pp. 42–49, Apr. 1954.

R. People, J. C. Bean, D. V. Lang, A. M. Sergent, H. L. Stormer, K. W. Wecht, R. T. Lynch, and K. Baldwin, “Modulation doping in GexSi1−x/Si strained layer heterostructures,” Appl. Phys. Lett., vol. 45, no. 11, pp. 1231–1233, Dec. 1984.

S. Gannavaram, N. Pesovic, and C. Ozturk, “Low temperature (800 ◦C) recessed junction selective silicon-germanium source/drain technology for sub-70 nm CMOS,” in IEDM Tech. Dig., 2000, pp. 437–440.

S. E. Thompson and et al., "A Logic Nanotechnology Featuring Strained-Silicon," IEEE Electron Device Lett., vol. 25, pp. 191-193, 2004.

S. E. Thompson and et al., "A 90 nm Logic Technology: Part I - Featuring Strained Silicon," IEEE Trans. Electron Devices, 2004.

W. A. Brantley, "Calculated Elastic Constants for Stress Problem Associated with Semiconductor Devices," J. Appl. Phys., vol. 44, pp. 534-535, 1973.

Semiconductor on NSM, URL http://www.ioffe.rssi.ru/SVA/NSM/Semicond/.

O. Madelung, ed., Data in Science and Technology: Semiconductors-Group IV elements and III-V Compounds (Springer, Berlin, 1991).

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THANK YOUTHANK YOU