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Simulation of Enhanced Hole Ballistic Velocity in Asymmetrically Strained Germanium Nanowire Trigate p-MOSFETs James Teherani , Winston Chern Profs. Dimitri Antoniadis, Judy Hoyt 2013 International Electron Devices Meeting, Washington DC

slide-1
SLIDE 1

Simulation of Enhanced Hole Ballistic Velocity in Asymmetrically Strained Germanium Nanowire Trigate p-MOSFETs

James Teherani, Winston Chern

  • Profs. Dimitri Antoniadis, Judy Hoyt

2013 International Electron Devices Meeting, Washington DC December 11th, 2013

1

slide-2
SLIDE 2

2 4 6 8 10 500 1000 1500 2000

eff (cm

2/Vs)

Ninv (10

12 cm

  • 2)

High Hole Mobility in Strained Ge

2

  • Strain-induced high hole mobility and ballistic velocity can be used to

increase current drive and decrease power consumption of p-FETs.

James T. Teherani, MIT

NW (w=49 nm) Chern, IEDM 2012 QWFET (biaxial strain) Pillarisetty, IEDM 2010 Planar (biaxial strain) Chern, IEDM 2012 NW (w=40 nm) Ikeda, VLSI 2013 HfO2

G D S

Experimental Data

Chern, IEDM 2012

slide-3
SLIDE 3

2 4 6 8 10 500 1000 1500 2000

eff (cm

2/Vs)

Ninv (10

12 cm

  • 2)

High Hole Mobility in Strained Ge

3

  • Strain-induced high hole mobility and ballistic velocity can be used to

increase current drive and decrease power consumption of p-FETs.

James T. Teherani, MIT

NW (w=49 nm) Chern, IEDM 2012 QWFET (biaxial strain) Pillarisetty, IEDM 2010 Planar (biaxial strain) Chern, IEDM 2012 NW (w=40 nm) Ikeda, VLSI 2013 HfO2

G D S

Experimental Data

Chern, IEDM 2012

Silicon Hole Universal

slide-4
SLIDE 4

2 4 6 8 10 500 1000 1500 2000

eff (cm

2/Vs)

Ninv (10

12 cm

  • 2)

High Hole Mobility in Strained Ge

4

  • Strain-induced high hole mobility and ballistic velocity can be used to

increase current drive and decrease power consumption of p-FETs.

  • This work explains mobility results through QM simulations and

extends analysis to ballistic velocity.

James T. Teherani, MIT

NW (w=49 nm) Chern, IEDM 2012 QWFET (biaxial strain) Pillarisetty, IEDM 2010 Planar (biaxial strain) Chern, IEDM 2012 NW (w=40 nm) Ikeda, VLSI 2013 HfO2

G D S

Experimental Data

Chern, IEDM 2012

Silicon Hole Universal

slide-5
SLIDE 5

Mobility, Current, and Ballistic Velocity

5 James T. Teherani, MIT Lundstrom, EDL 1997

Long-channel device (drift-diffusion):

𝐽𝐸,𝑡𝑏𝑢 =

𝐷𝑝𝑦𝑋 2𝑀 𝜈 𝑊 𝐻𝑇 − 𝑊 𝑢ℎ 2

𝜈 =

𝑟𝜐 𝑛∗

Short-channel devices (ballistic transport):

𝐽𝐸,𝑡𝑏𝑢 = 𝐷𝑝𝑦𝑋 𝑊

𝐻𝑇 − 𝑊 𝑢ℎ ∙ 1 − 𝑠 𝑑

1 + 𝑠

𝑑

𝑤𝜄 𝑤𝜄 =

2𝑙𝑈 𝜌𝑛∗

slide-6
SLIDE 6

Mobility, Current, and Ballistic Velocity

6 James T. Teherani, MIT Lundstrom, EDL 1997

Long-channel device (drift-diffusion):

𝐽𝐸,𝑡𝑏𝑢 =

𝐷𝑝𝑦𝑋 2𝑀 𝜈 𝑊 𝐻𝑇 − 𝑊 𝑢ℎ 2

𝜈 =

𝑟𝜐 𝑛∗

Short-channel device (ballistic transport):

𝐽𝐸,𝑡𝑏𝑢 = 𝐷𝑝𝑦𝑋 𝑊

𝐻𝑇 − 𝑊 𝑢ℎ ∙ 1 − 𝑠 𝑑

1 + 𝑠

𝑑

𝑤𝜄 𝑤𝜄 =

2𝑙𝑈 𝜌𝑛∗

slide-7
SLIDE 7

𝒙𝑶𝑿

Experimental Device Fabrication

7

Si

Ge

SiO2 Ge

Ge

Lateral Relaxation HfO2

James T. Teherani, MIT

1) s-GOI Substrate 2) Electron Beam Patterning 3) Dielectric Deposition

  • Begin with biaxially strained Ge on insulator
  • Nanowire patterning creates free surfaces

 lateral strain relaxation

  • Final strain is asymmetric
  • Neither biaxial nor uniaxial

4) Final Device Structure

Ge 10 nm

Biaxial Compression HfO2

G D S

  • W. Chern et al., IEDM 2012
slide-8
SLIDE 8

Asymmetric Strain (1/2)

8 James T. Teherani, MIT

slide-9
SLIDE 9

Asymmetric Strain (2/2)

9 James T. Teherani, MIT

  • 2.4%

1.7%

slide-10
SLIDE 10

Measured & Simulated Strain

10 James T. Teherani, MIT

  • Measured strain from Ge-Ge Raman peak shift
  • Simulated strain from elastic energy minimization (nextnano3)
  • W. Chern et al., IEDM 2012

Xia, Univ. British Columbia

20 40 60 80 100 1.0 1.5 2.0 2.5 3.0

 x

WNW (nm)

Biaxially strained substrate ∆𝜕 = −404 (𝜗𝑦𝑦 + 𝜗𝑨𝑨) 2 𝜗𝑨z=2.56% Simulation Experiment

Average Compressive Lateral Strain, 𝜗𝑦𝑦 (%)

slide-11
SLIDE 11

11 James T. Teherani, MIT

  • Strain shifts the valence band through deformation potentials
  • 150 meV energy shift due to lateral strain relaxation near sidewalls

Impact of Strain on Valence Band

Si

slide-12
SLIDE 12

12 James T. Teherani, MIT

  • Holes cluster near side gate due to
  • Strain relaxation near sidewall  valence band shift
  • Favorable gate electrostatics
  • Few carriers near top gate, Si acts as dielectric due to

large valence band offset with Ge

Hole Density (Ninv=3×1012 cm-2)

Hole Density Across Device

Δ𝐹𝑤 ~770 meV

s-Si s-Ge

Valence Band Offset

HfO2 Si WN

  • J. Teherani et al., PRB 2012
slide-13
SLIDE 13

Quantum Mechanical Simulation Details

13 James T. Teherani, MIT

First Hole Eigenstate

  • Performed 2D numerical simulations

using nextnano3 assuming infinite nanowire length

  • Solved Schrödinger-Poisson equation

using 6x6 k∙p quantization method

E-kz Dispersion for 1st Eigenstate

infinite 2D simulation structure

  • 0.2

0.2

  • 0.15

0.15 Energy (eV) 𝑙𝑨 (1/Å) EF

HfO2 Si

WN

slide-14
SLIDE 14

Inverse Effective Mass Calculation

14 James T. Teherani, MIT

  • Solved Schrödinger-Poisson for 80 eigenstates
  • Strain mixes heavy-hole and light-hole valence bands
  • Small 𝑛∗ for small 𝑙𝑨

(light-hole characteristics)

  • Large 𝑛∗ for large 𝑙𝑨

(heavy-hole characteristics)

E-kz Dispersion for 80 Eigenstates

𝑊

𝐺𝐶 − 0.5 V ⇒

𝑂𝑗𝑜𝑤 = 3 × 1012 cm−2

𝑤 =

𝜖𝐹 𝜖ℏ𝑙 1 𝑛(𝑙) = 𝑤 ℏ𝑙

slide-15
SLIDE 15

Inverse Effective Mass (1/2)

15 James T. Teherani, MIT

𝜈 = 𝑟𝜐 𝑛∗

slide-16
SLIDE 16

Inverse Effective Mass (2/2)

16 James T. Teherani, MIT

Inverse effective mass

  • Peaks near the sidewalls
  • Same location as hole density peak
  • Dips in center of device where

higher 𝑙𝑨 states are occupied

Inverse Effective Mass As Function of Position

HfO2 Si WN 𝜈 = 𝑟𝜐 𝑛∗

Ninv=3×1012 cm-2

slide-17
SLIDE 17

Inverse Effective Mass (2/2)

17 James T. Teherani, MIT

Inverse effective mass

  • Peaks near the sidewalls
  • Same location as hole density peak
  • Dips in center of device where

higher 𝑙𝑨 states are occupied

𝜈 = 𝑟𝜐 𝑛∗

Inverse Effective Mass As Function of Position

HfO2 Si WN

Ninv=3×1012 cm-2

slide-18
SLIDE 18

Planar Simulations

18 James T. Teherani, MIT

To understand nanowire results, we performed a simulation experiment in which we changed strain in planar structures.

slide-19
SLIDE 19

Impact of Strain on E-k Dispersion (1/3)

19 James T. Teherani, MIT

Strained Ge Biaxial Compression

110

𝜗𝑦𝑦

110

𝜗𝑨𝑨 (transport direction)

slide-20
SLIDE 20

Impact of Strain on E-k Dispersion (2/3)

20

Lateral strain relaxation (𝜗𝑦𝑦)

  • Significantly reduces 𝑛∗ in the

transport direction

James T. Teherani, MIT

Strained Ge Biaxial Compression

110

𝜗𝑦𝑦

110

𝜗𝑨𝑨 (transport direction)

  • 2.4%
slide-21
SLIDE 21

Impact of Strain on E-k Dispersion (3/3)

21

Lateral strain relaxation (𝜗𝑦𝑦)

  • Significantly reduces 𝑛∗ in the

transport direction

Vertical strain relaxation (𝜗𝑧𝑧) (out-of-plane strain)

  • No effect

Strained Ge Biaxial Compression

110

𝜗𝑦𝑦

110

𝜗𝑨𝑨 (transport direction)

James T. Teherani, MIT

1.7%

  • 2.4%
slide-22
SLIDE 22

22 James T. Teherani, MIT

1/𝑛𝑨 and 𝑤𝜄 significantly increase as 𝜗𝑦𝑦 is reduced

Mass Decrease with 𝜗𝑦𝑦 (1/3)

𝜗𝑦𝑦

(transport direction)

𝜗𝑨𝑨

𝜈 = 𝑟𝜐 𝑛∗

𝑂𝑗𝑜𝑤 = 2.5 × 1012 cm−2

slide-23
SLIDE 23

23 James T. Teherani, MIT

1/𝑛𝑨 and 𝑤𝜄 significantly increase as 𝜗𝑦𝑦 is reduced

Mass Decrease with 𝜗𝑦𝑦 (2/3)

𝜗𝑦𝑦

(transport direction)

𝜗𝑨𝑨

𝑤𝜄 = 2𝑙𝑈 1/𝑛𝑨 /𝜌

𝜈 = 𝑟𝜐 𝑛∗

𝑂𝑗𝑜𝑤 = 2.5 × 1012 cm−2

slide-24
SLIDE 24

24 James T. Teherani, MIT

1/𝑛𝑨 and 𝑤𝜄 significantly increase as 𝜗𝑦𝑦 is reduced

𝜗𝑦𝑦

(transport direction)

𝜗𝑨𝑨

𝑤𝜄 = 2𝑙𝑈 1/𝑛𝑨 /𝜌

𝜈 = 𝑟𝜐 𝑛∗

Mass Decrease with 𝜗𝑦𝑦 (3/3)

𝑂𝑗𝑜𝑤 = 2.5 × 1012 cm−2

slide-25
SLIDE 25

↓ 𝜗𝑦𝑦 in Experimental NWs

25 James T. Teherani, MIT

Lateral strain 𝜗𝑦𝑦 decreases with decreasing NW width

𝑥𝑂𝑋

slide-26
SLIDE 26

Increased Mobility for Narrow NWs (1/3)

26 James T. Teherani, MIT

1/𝑛𝑨 and 𝑤𝜄 increase as 𝑥𝑂𝑋 ↓

𝑥𝑂𝑋

slide-27
SLIDE 27

Increased Mobility for Narrow NWs (2/3)

27 James T. Teherani, MIT

1/𝑛𝑨 and 𝑤𝜄 increase as 𝑥𝑂𝑋 ↓

𝑥𝑂𝑋

2 4 6 8 500 1000 1500

eff (cm

2/Vs)

Ninv (10

12 cm

  • 2)

1.8×

Si Hole Universal Biaxial Ge NW (w=49 nm) W. Chern et al., IEDM 2012

slide-28
SLIDE 28

Increased Velocity for Narrow NWs (3/3)

28 James T. Teherani, MIT

1/𝑛𝑨 and 𝑤𝜄 increase as 𝑥𝑂𝑋 ↓

𝑥𝑂𝑋

slide-29
SLIDE 29

𝐽𝐸,𝑡𝑏𝑢 = 𝐷𝑝𝑦𝑋 𝑊

𝐻𝑇 − 𝑊 𝑢ℎ ∙ 1 − 𝑠 𝑑

1 + 𝑠

𝑑

𝑤𝜄 𝐽𝐸,𝑡𝑏𝑢 = 𝑅 ∙ 𝐶𝑤𝜄

Drive Current Improvement

29 James T. Teherani, MIT

  • 𝑤𝜄 improvement of 2.8× with respect to unstrained Si
  • 𝑤𝜄 improvement of 1.6× with respect to 1% uniaxial Si
  • 𝐶 also improves as strain splits bands and reduces scattering
  • Reduced backscattering inferred from highly enhanced experimental s-Ge

hole mobility

⇒ 𝑱𝑬 improvement of at least 2× with respect to 1% uniaxial Si

inversion charge ballisticity ballistic velocity

slide-30
SLIDE 30
  • Asymmetric lateral strain in NW device structure
  • Significant lateral relaxation for small nanowire widths

Summary

30 James T. Teherani, MIT

slide-31
SLIDE 31
  • Asymmetric lateral strain in NW device structure
  • Significant lateral relaxation for small nanowire widths
  • Inverse effective mass peak near sidewalls
  • Same location as hole density peak

Summary

31 James T. Teherani, MIT

slide-32
SLIDE 32
  • Asymmetric lateral strain in NW device structure
  • Significant lateral relaxation for small nanowire widths
  • Inverse effective mass peak near sidewalls
  • Same location as hole density peak
  • Significant decrease in 𝑛∗ with lateral strain

relaxation

Summary

32 James T. Teherani, MIT

slide-33
SLIDE 33
  • Asymmetric lateral strain in NW device structure
  • Significant lateral relaxation for small nanowire widths
  • Inverse effective mass peak near sidewalls
  • Same location as hole density peak
  • Significant decrease in 𝑛∗ with lateral strain

relaxation

  • 2.8× increase in 𝑤𝜄 with respect to unstrained Si
  • 1.6× increase in 𝑤𝜄 with respect to 1% uniaxial Si
  • 𝐽𝐸 increase of at least 2× with respect to 1%

uniaxial Si

Summary

33 James T. Teherani, MIT

slide-34
SLIDE 34
  • Asymmetric lateral strain in NW device structure
  • Significant lateral relaxation for small 𝑥𝑂𝑋
  • Inverse effective mass peak near sidewalls
  • Same location as hole density peak
  • Significant decrease in 𝑛∗ with lateral strain

relaxation

  • 2.8× increase in 𝑤𝜄 with respect to unstrained Si
  • 1.6× increase in 𝑤𝜄 with respect to 1% uniaxial Si
  • 𝐽𝐸 increase of at least 2× with respect to 1%

uniaxial Si

Summary

34 James T. Teherani, MIT

slide-35
SLIDE 35

35

Slides available at: http://teherani.mit.edu/

James T. Teherani, MIT