Strain Effects on Bulk Ge Valence Band eel6935: Computational Nanoelectronics

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Strain Effects on Bulk <001> Ge Valence Band

  • EEL6935: Computational Nanoelectronics

  • Fall 2006

  • Andrew Koehler


  • Motivation

  • Background

    • Strain
    • Germanium
  • Simulation Results and Discussion

  • Summary

  • References


  • 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?

Solution: Novel Materials

History 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

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

What is Strain?

Strain Effect on Valence Band

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???

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

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

Ge vs Other Semiconductors

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

k ∙ p method

  • k ∙ p method was introduced by Bardeen and Seitz

  • Kane’s model takes into account spin-orbit interaction

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

k ∙ p method

  • Schrodinger equation

  • Written in terms of unk(r)

Unstressed Band Structures

Biaxial Compression 1 GPa

Longitudinal Compression 1 GPa

Band Splitting

Silicon Mass Change

Germanium Mass Change


    • Strain
    • Germanium
    • Strained Germanium Compared to Silicon
      • Unstressed
      • Band Splitting
        • Biaxial Compression
        • Longitudinal Compression
      • Mass Change - Longitudinal Compression
        • In-Plane
        • Out-of-Plane


  • 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

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


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