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

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

3. Andrew Koehler 3Motivation 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 EnergykTln(2)kT(10 4 ~10 5 ) Channel Length 1 nm100 nm Density10 14 /cm 2 10 9 /cm 2 Power10 7 W/cm 2 100 W/cm 2 Speed0.01 ps1 ps

4. Andrew Koehler 4 Solution: Novel Materials

5. Andrew Koehler 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. Andrew Koehler 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 Shear Stress Component Normal Strain Component Shear Strain Component

7. Andrew Koehler 7 What is Strain? Elastic Stiffness Coefficients (10 11 N/cm 2 ) Compliance Coefficients (10 -11 cm 2 /N) c11c12c44 Si1.6570.6390.7956 Ge1.2920.4790.670 s11s12s44 Si0.768-0.2141.26 Ge0.964-0.2601.49

8. Andrew Koehler 8 Strain Effect on Valence Band

9. Andrew Koehler 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. Andrew Koehler 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. Andrew Koehler 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. Andrew Koehler 12 Ge vs Other Semiconductors nMOS: GaAs is the best material pMOS: Ge is the best material

13. Andrew Koehler 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. Andrew Koehler 14 k ∙ p method k ∙ p method was introduced by Bardeen and Seitz Kane’s model takes into account spin-orbit interaction –Ψ nk (r) = e ik∙r u nk (r) – u nk (r+R) = u nk (r) – Bloch function n refers to band k refers to wave vector Useful technique for analyzing band structure near a particular point k 0

15. Andrew Koehler 15 k ∙ p method Schrodinger equation Written in terms of u nk (r)

16. Andrew Koehler 16 Unstressed Band Structures Silicon Germanium

17. Andrew Koehler 17 Biaxial Compression 1 GPa Silicon Germanium

18. Andrew Koehler 18 Longitudinal Compression 1 GPa Silicon Germanium

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

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

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

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

23. Andrew Koehler 23References 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).

24. Andrew Koehler 24 THANK YOU