Quantum Effects Lead to Phenomena such as: Ultra Thin Oxides Observe: High Leakage Currents Through the Oxide - Tunneling Depletion in Poly-Si metal gate capacitance effect Thickness of Inversion Layer alters t ox GIDL (Gate-Induced Drain Leakage) High Doping - Leads to tunneling DIBL (Drain-Induced Barrier Lowering) Short Channel - Leads to tunneling Take advantage of Quantum Effects Decrease effective mass Change E -vs- k energy band diagram by Induce strain using lattice mismatch between S/Cs Quantum Confinement Gain in Device Efficiency Band gap engineering Use other S/Cs to decrease E g 1 Ultrathin begin to observe quantum effects poly-crystalline Si - V gate V Drain - Channel amorphous Source Contact Insulator source Poly Si Gate Contact - Gate oxide + + + + + + + + + + + + + + channel Si Wafer drain Drain Contact Insulator Crystalline Si C ox okoxa t ox 2 1
E e- E f Flat band What condition is this? 3 E e- Treat as IF a p-n junction Flat band h + flow only one way 4 2
Poly-depletion Poly depletion 5 Depeletion in poly-si C Cox C C 1 x ox, physical D, poly Si 1 Colinge & Colinge, S/C Devices Other: Relativistic Carriers (hot emissionoxide damage) 6 3
Quantization: (cont.) 2D gas in channel Inversion layer thickness is similar to the gate oxide thickness Changes oxide thickness ox tox, eff tox, physical x Si Davies, The Physics of Low Dimensional Semiconductors, (Cambridge, 199) p. 343 Hareland, IEEE Transactions on Electron Devices, 1996 See also: Anderson & Anderson. Fundamentals of Semiconductor Devices, (McGraw Hill, 2005) p. 504-506 7 Quantization: (cont.) - Recall Particle in a Box or Infinite Potential Well or Quantum Well? Chapter 3 of Kasap Ψ and lψl 2 is always zero at the boundary! Energy of electron 0V(x) E 4 E 3 E 2 V = n =4 n =3 n =2 Electron 0 a x 3 2 V =0 4 E 1 n =1 0 1 x x =0 x = a 0 a 0 a Energy levels in the well (x) sin(nx/a) Probability density (x) 2 Electron in a one-dimensional infinite PE well. The energy of the electron is quantized. Possible wavefunctions and the probability distributions for the electron are shown. V = From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005) 4
Quantization: (cont.) 2D gas in channel Inversion layer thickness is similar n ~1 to the gate oxide thickness Changes oxide thickness ox tox, eff t ox, physical x Si Energy States of e - : Bound versus Unbound (continuum) Davies, The Physics of Low Dimensional Semiconductors, (Cambridge, 199) p. 343 9 Tunneling: Fowler-Nordheim (FN) [cold emission oxides] Direct (oxides) Band-to-Band Barrier lowering Drain Induced Barrier Lowering (DIBL) V gate = 0n Drain Contact V g Poly Si Gate Contact - Gate oxide n + source channel p-si Wafer V D =V DD V d Drain Contact n + drain This results because this occurs. Streetman & Banerjee, Solid State Electronic Circuits (Prentice Hall,2000) Muller & Kamins (Wiley-Interscience,2003) Fig. 9.17 p. 452 10 5
Tunneling: Fowler-Nordheim (FN) [cold emission oxides] Direct (oxides) Band-to to-band Barrier lowering Gate Induced Drain Leakage (GIDL) Colinge & Colinge, S/C Devices V gate =0 V g V D =V DD V d Drain Contact n + source Poly Si Gate Contact - Gate oxide channel P-Si Wafer Drain Contact n + drain GIDL Sze, Modern S/C Device Physics (Wiley-Interscience,199) Ch. 3 by SlJ. Hillenius 11 Quantization: (cont.) 2D gas in channel SOI Gate-all-around (GAA) MOSFET: Gate-All-Around (GAA) MOSFET is an SOI transistor in which the gate oxide and the gate electrode are wrapped around the channel region. Fabricated using an SOI CMOS process to which two process steps are added a photolithographic step a wet etch step during which a cavity is formed under previously patterned silicon islands. The remarkable features of this MOSFET are that there are two channels (at the top and the bottom of the silicon film, The entire channel area is surrounded by good-quality gate oxide and the gate electrode. Colinge & Colinge, S/C Devices 12 6
Quantization: (cont.) 2D gas in channel SOI Gate-all-around (GAA) MOSFET: Colinge & Colinge, S/C Devices 13 Bandgap Engineering of Channel Consider: Bandgap, mobility, effective mass,lattice matching, quantum confinement of carriers Lattice Constants: a Si = 5.4309 Å a Ge = 5.6577 Å Cullity, Elements of X-ray Diffraction, 2 nd Ed (197) Appendix 5 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005) 14 7
Bandgap Engineering of Channel Consider: Bandgap, mobility, effective mass, lattice matching, quantum confinement of carriers Lattice Constants: a Si = 5.4309 Å a Ge = 5.6577 Å Cullity, Elements of X-ray Diffraction, 2 nd Ed (197) Appendix 5 Science M. Ieong, B. Doris, J. Kedzierski, K. Rim, M. Yang, Silicon Device Scaling to Sub-10nm Regime (2004) 15 Bandgap Engineering of Channel Consider: Bandgap, mobility, effective mass, lattice matching, quantum confinement of carriers Lattice Constants: a Si = 5.4309 Å a Ge = 5.6577 Å Cullity, Elements of X-ray Diffraction, 2 nd Ed (197) Appendix 5 IBM RJ Antoniadis et al., Continuous MOFET Performance Inc with Scaling - Strain & Channel Matl (2006) 16