Transcript Strain Effects on Valence Band for

Strain Effects on Bulk
<001> Ge Valence Band
EEL6935: Computational Nanoelectronics
Fall 2006
Andrew Koehler
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Outline
• Motivation
• Background
– Strain
– Germanium
• Simulation Results and Discussion
• Summary
• References
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Motivation
• 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?
Andrew Koehler
Ultimate
CMOS
Current
CMOS
Energy
kTln(2)
kT(104~105)
Channel
Length
1 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 Materials
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History of Strain
1954:
Piezoresistance in silicon was first discovered by C. S. Smith

1 R  R0 1 R

 R0
 R0
(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
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What is Strain?
•
Stress: Limit of Force/Area as Area approaches zero
F
  Lim
A 0 A
•
Strain: Fractional change in length of an object
Distortion of a structure caused by stress

  xx 



 yy 
 
zz

 
  yz 


  zx 
  xy 


Normal
Stress
Component
Shear
Stress
Component
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a  a0
a0
 xx 
Normal


Strain
 yy 
   Component
zz

 
 2 yz 
Shear


Strain
 2 zx  Component
 2 xy 


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What is Strain?
  xx   C11

 

 yy   C12
   C
 zz    12
 yz   0

 

 zx   0
 xy   0


C12 C12 0
0
0
C11 C12 0
0
0
C12 C12 0
0
0
0
0
0
C 44 0
0
0
0
C 44 0
0
0
0
0
C 44
 xx 
  
  yy 
 zz 


  2 yz 
 2 
  zx 
 2 
  xy 
 S
Compliance Coefficients (10-11cm2/N)
Si
s11
s12
s44
0.768 -0.214 1.26
Ge 0.964 -0.260 1.49
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  C
Elastic Stiffness Coefficients (1011N/cm2)
c11
c12 c44
Si 1.657 0.639 0.7956
Ge 1.292 0.479 0.670
xx   S11

 

yy

  S12
   S
 zz    12
 2 yz   0

 
2

 zx   0
 2 xy   0


S12 S12 0
0
0
S11 S12 0
0
0
S12 S12 0
0
0
0
0
S44 0
0
0
0
0
S44 0
0
0
0
0 S44
   xx 
  
  yy 
   zz 


  yz 
  
  zx 
  
  xy 
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Strain Effect on Valence Band
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History 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?
• 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 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 Semiconductors
 nMOS: GaAs is the best material
 pMOS: Ge is the best material
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Future 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 ∙ 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 ∙ p method
• Schrodinger equation
 p2

 V (r ) nk (r )  En (k ) nk (r )

 2m0

• Written in terms of unk(r)
 p2



 2k 2 

k  p  V (r )unk (r )   En (k ) 

unk (r )
2m0 
 2m0 m0


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Unstressed Band Structures
Germanium
0.1
0.1
0
0
-0.1
-0.1
Energy (eV) --->
Energy (eV) --->
Silicon
-0.2
-0.3
-0.2
-0.3
-0.4
-0.4
-0.5
-0.5
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
<--- out of plane (k) channel direction --->
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0.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
<--- out of plane (k) channel direction --->
0.2
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Biaxial Compression 1 GPa
Germanium
0.1
0.1
0
0
-0.1
-0.1
Energy (eV) --->
Energy (eV) --->
Silicon
-0.2
-0.3
-0.2
-0.3
-0.4
-0.4
-0.5
-0.5
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
<--- out of plane (k) channel direction --->
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0.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
<--- out of plane (k) channel direction --->
0.2
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Longitudinal Compression 1 GPa
Germanium
0.1
0.1
0
0
-0.1
-0.1
Energy (eV) --->
Energy (eV) --->
Silicon
-0.2
-0.3
-0.2
-0.3
-0.4
-0.4
-0.5
-0.5
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
<--- out of plane (k) channel direction --->
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0.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
<--- out of plane (k) channel direction --->
0.2
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Band Splitting
Biaxial Compression
Longitudinal Compression
0.14
0.18
0.16
0.12
Ge
Ge
0.14
0.1
Energy (eV)
Energy (eV)
0.12
0.08
0.06
Si
0.04
0.1
0.08
Si
0.06
0.04
0.02
0
0.02
0
0.5
1
1.5
Stress (GPa)
2
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2.5
3
0
0
0.5
1
1.5
Stress (GPa)
2
2.5
3
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Silicon Mass Change
•Longitudinal Compression
In-Plane
Out-of-Plane
0.9
0.3
0.8
0.28
0.7
0.26
0.5
m*/m
m*/m
0.6
80%
0.24
0.4
0.22
0.3
0.2
0.2
0.1
0
0.5
1
1.5
Stress (GPa)
2
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2.5
3
0.18
0
0.5
1
1.5
Stress (GPa)
2
2.5
3
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Germanium Mass Change
•Longitudinal Compression
In-Plane
Out-of-Plane
0.4
0.18
0.35
0.16
0.3
0.14
90%
0.12
m*/m
m*/m
0.25
0.2
0.1
0.15
0.08
0.1
0.06
0.05
0
0
0.5
1
1.5
Stress (GPa)
2
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2.5
3
0.04
0
0.5
1
1.5
Stress (GPa)
2
2.5
3
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Summary
– 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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References
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 YOU
Andrew Koehler