strain effects on bulk ge valence band eel6935: computational nanoelectronics fall 2006 andrew...
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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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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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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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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