Strain Effects on Bulk 001 Ge Valence Band

Strain Effects on Bulk <001> Ge Valence Band EEL 6935: Computational Nanoelectronics Fall 2006 Andrew Koehler

Outline • Motivation • Background – Strain – Germanium • Simulation Results and Discussion • Summary • References Andrew Koehler

Motivation • Moore’s Law – ~ 0. 7 X linear scale factor – 2 X increase in density / 2 years – Higher performance (~30% / 2 years) • Approaching Fundamental Limits – “No Exponential is Forever” • What is the solution? Andrew Koehler Ultimate CMOS Current CMOS Energy k. Tln(2) k. T(104~105) Channel Length 1 nm 100 nm Density 1014/cm 2 109/cm 2 Power 107 W/cm 2 100 W/cm 2 Speed 0. 01 ps

Solution: Novel Materials Andrew Koehler

History of Strain 1954: Piezoresistance in silicon was first discovered by C. S. Smith (resistance change due to applied stress) 1980 s: Thin Si layers grown on relaxed silicon–germanium (Si. Ge) substrates 1990 s: High-stress capping layers deposited on MOSFETs were investigated as a technique to introduce stress into the channel 1990 s: Si. Ge incorporated in the source and drain areas 2002: Intel uses strained Si in P 4 processor Andrew Koehler

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 Andrew Koehler

What is Strain? Elastic Stiffness Coefficients (1011 N/cm 2) c 11 c 12 c 44 Si 1. 657 0. 639 0. 7956 Ge 1. 292 0. 479 0. 670 Compliance Coefficients (10 -11 cm 2/N) Si s 11 s 12 s 44 0. 768 -0. 214 1. 26 Ge 0. 964 -0. 260 1. 49 Andrew Koehler

Strain Effect on Valence Band Andrew Koehler

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 2000 s: 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. 2000 s: Germanium is being discussed as a possible replacement of silicon? ? ? Andrew Koehler

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 Andrew Koehler

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) – – Hf. O 2 Zr. O 2 Sr. Ti. O 3, Sr. Zr. O 3 and Sr. Hf. O 3 ALD WN/La. Al. O 3/Al. N gate stack Andrew Koehler

Ge vs Other Semiconductors ü n. MOS: Ga. As is the best material ü p. MOS: Ge is the best material Andrew Koehler

Future of Ge in Nanoelectronics • Researchers Believe – Combination of a Ge p. MOS with a Ga. As n. MOS 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 Andrew Koehler

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 k 0 Andrew Koehler

k ∙ p method • Schrodinger equation • Written in terms of unk(r) Andrew Koehler

Unstressed Band Structures Silicon Andrew Koehler Germanium

Biaxial Compression 1 GPa Silicon Andrew Koehler Germanium

Longitudinal Compression 1 GPa Silicon Andrew Koehler Germanium

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

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

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

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

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 Gex. Si 1−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). Andrew Koehler

THANK YOU Andrew Koehler