Strain Effects on Bulk <001> Ge Valence Band

1. Strain Effects on Bulk <001> Ge Valence Band EEL6935: Computational Nanoelectronics Fall 2006 Andrew Koehler

2. Outline • Motivation • Background • Strain • Germanium • Simulation Results and Discussion • Summary • References

3. 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?

4. Solution: Novel Materials

5. 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

6. 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 Normal Stress Component Normal Strain Component Shear Stress Component Shear Strain Component

7. What is Strain? Elastic Stiffness Coefficients (1011N/cm2) Compliance Coefficients (10-11cm2/N)

8. Strain Effect on Valence Band

9. 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???

10. 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

11. 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

12. Ge vs Other Semiconductors • nMOS: GaAs is the best material • pMOS: Ge is the best material

13. 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

14. 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

15. k ∙ p method • Schrodinger equation • Written in terms of unk(r)

16. Unstressed Band Structures Silicon Germanium

17. Biaxial Compression 1 GPa Silicon Germanium

18. Longitudinal Compression 1 GPa Silicon Germanium

19. Band Splitting Biaxial Compression Longitudinal Compression Ge Ge Si Si

20. Silicon Mass Change • Longitudinal Compression In-Plane Out-of-Plane 80%

21. Germanium Mass Change • Longitudinal Compression In-Plane Out-of-Plane 90%

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

23. 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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