BULK Si (100) VALENCE BAND STRUCTURE UNDER STRAIN

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BULK Si (100) VALENCE BAND STRUCTURE UNDER STRAIN
Sagar Suthram Computational Nanoelectronics Cla
ss Project - 2006
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Outline

• Brief history of MOSFET scaling and need for
  Strained Silicon.
• Understanding Strain.
• Si valence band structure calculation using k.p
  method.
• Si valence band structure calculation using tight
  binding method.
• Strain effects on Si valence and conduction band
  qualitative picture.
• Summary

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MOSFET Scaling History

• Si MOSFET first demonstrated in SSDRC in 1960.
• Improved dramatically due to gate length scaling
  driven by
• Increased density and speed
• Lower costs
• Power improvements
• Semiconductor industry scaled the MOSFET channels
  based on Moores law (1965). Simple geometric
  scaling followed.
• Constant field scaling introduced by Dennard et.
  al. (1974).

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MOSFET Scaling History

• Constant field scaling too restrictive
• Subthreshold nonscaling
• Power-supply voltage not scaled proportional to
  channel length
• Generalized scaling is preferable which allows
  oxide field to increase
• Shape of 2-D electric field pattern preserved
  (channel doping engineering)
• Short channel effects do not become worse

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MOSFET Scaling Limits

• But conventional planar bulk MOSFET channel
  length scaling is slowing
• Increased off-state leakage
• Increased off-state power consumption
• Degraded carrier mobility due to very high
  vertical fields (thin oxides lt2nm)
• Lithographic limitations
• Little improvement in switching performance
• Inability to scale supply voltage and oxide
  thickness

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Continued Transistor Scaling

• No exponential is forever Gordon Moore
• But present scaling limits for Si MOSFET are
  caused by materials and device structure and are
  not hard quantum limits
• Continued scaling requires new materials and
  device structures
• High K dielectrics
• Strained Si
• Novel channel materials (Ge, III-V
  semiconductors)
• Non classical CMOS devices (FinFETs etc.)

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Strained Silicon

• Strained Silicon has been adopted in all advanced
  logic technologies
• Scalable to future generations
• Easily incorporated in existing processes
• Enhances performance even in the ballistic regime
  due to effective mass reduction

90nm INTEL Technology node transistor with
process induced uniaxial stress Thompson 04
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How is strain added to silicon ?

• Uniaxial stress is induced in the following ways
• SiGe source-drain for PMOS
• Tensile nitride capping layer for NMOS

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How is strain added to silicon ?
Biaxial stress is induced by epitaxialy growing a
silicon layer on relaxed SiGe. The lattice
mismatch induces biaxial tensile stress in the
silicon layer.
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Outline

• Brief history of MOSFET scaling and need for
  Strained Silicon.
• Understanding Strain.
• Si valence band structure calculation using k.p
  method.
• Si valence band structure calculation using tight
  binding method.
• Strain effects on Si valence and conduction band
  qualitative picture.
• Summary

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Understanding Strain
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Understanding Strain
Elastic Stiffness Coefficients
Elastic Compliance Coefficients
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Outline

• Brief history of MOSFET scaling and need for
  Strained Silicon.
• Understanding Strain.
• Si valence band structure calculation using k.p
  method.
• Si valence band structure calculation using tight
  binding method.
• Strain effects on Si valence and conduction band
  qualitative picture.
• Summary

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Silicon valence band using k.p
The form of the Schrodinger equation when written
in terms of unk(r) near a particular point k0 of
interest.
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Silicon valence band using k.p

• Luttinger-Kohns model k.p method for degenerate
  bands
• Mainly for silicon valence bands
• Consider the heavy hole, light hole and split-off
  bands as class A and rest of the bands as class B
• Use 2nd order degenerate perturbation theory

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Luttinger-Kohn Hamiltonian
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Valence Band structure
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Valence Band structure
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Valence Band structure
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Outline

• Brief history of MOSFET scaling and need for
  Strained Silicon.
• Understanding Strain.
• Si valence band structure calculation using k.p
  method.
• Si valence band structure calculation using tight
  binding method.
• Strain effects on Si valence and conduction band
  qualitative picture.
• Summary

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Silicon Valence band using tight-binding method

• sp3s tight binding picture used
• 20x20 Hamiltonian including spin-orbit
  interaction considered
• Silicon valence band predominantly composed of
  p-bonding states which are degenerate at the G
  point

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Tight binding Band structure
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Tight binding Band structure
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Outline

• Brief history of MOSFET scaling and need for
  Strained Silicon.
• Understanding Strain.
• Si valence band structure calculation using k.p
  method.
• Si valence band structure calculation using tight
  binding method.
• Strain effects on Si valence and conduction band
  qualitative picture.
• Summary

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Strain effects on silicon valence band

• Splits the degeneracy of the valence band at the
  G point
• The bands are no longer just HH or LH due to the
  strong coupling between the two, but either
  HH-like or LH-like
• Biaxial stress does not warp the bands much due
  to the presence of only a hydrostatic component
  in the strain matrix which maintains the crystal
  symmetry.
• Uniaxial stress warps the bands causing a
  reduction in the effective mass due to the
  presence of a shear term which destroys the
  crystal symmetry

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Summary

• k.p method is emperically based and treats the
  band structure with precision
• k.p is useful for calculating band structure only
  for k values close to the band edge which is
  generally the region of interest
• Tight-binding on the other hand considers the
  microscopic interatomic interactions and hence
  gives a good physical insight into the strain
  effects on the band structure
• We see differences in the exact band structures
  computed by the two methods but they show similar
  trends under the application of strain
• Computing more accurate band structures with the
  tight-binding method involves consideration of up
  to 10 orbitals (sp3d5s) along with spin which
  gets very complicated when the strain effect is
  added

Thank You