Quantum Mechanics in today’s world

1. Quantum Mechanics in today’s world • Tunneling • Interference, Entanglement and Phase • Coherence • 3. Quantization and resonance • 4. Macroscopic Quantum Coherence (Spins) • 5. Charge Quantization • 6. Quantum Stat Mech • 7. Quantum Many-Body • 8. QM and Free Will ?

2. 1. Electron Interference • Band-gap [Cancellation] • Interferometers [Oscillation]

3. y+ y- -p/a p/a Why do we get a gap? y+ ~ cos(px/a) peaks at atomic sites y- ~ sin(px/a) peaks in between E Its periodically extended partner k

4. y+ |U0| y- -p/a p/a Let’s now turn on the atomic potential The y+ solution sees the atomic potential and increases its energy The y- solution does not see this potential (as it lies between atoms) Thus their energies separate and a gap appears at the BZ This happens only at the BZ as we have propagating waves elsewhere k

5. Interference signatures Magnetoconductance oscillations in an antidot lattice (Nihey et al, PRL 51, ‘95) Aharonov-Bohm interference in a nanotube (Dai group, PRL 93, 2004) Fano interference between a channel and a quantum dot Atom laser (Ketterle group) Yes! There are many examples of quantum interference

6. Quantum computation schemes thrive on interference! Scheme of a Si-based quantum computer

7. Small devices are better candidates forobserving quantum effects We must thus learn to transform matrices, paying special attention to their off-diagonal components

8. 2. Tunneling Encyclopedia of Nanotechnology pp 2313-2321 Scanning Tunneling Spectroscopy Amadeo L. Vázquez de Parga , Rodolfo Miranda

9. TunnelFETs Abrupt onset Problem: Low ION Heterojunction TFET Higher ION Problem: Traps High IOFF, voltage

10. 3. Quantization and Resonance Chlorophyll Koning, Ross E. 1994. Light. Plant Physiology Information Website. http://plantphys.info/plant_physiology/light.shtml. (4-22-2016).

11. Quantization and Resonance Heme binds oxygen This changes conformation of molecule This changes Fe(II) d6 orbital energy This shifts absorption to higher wavelengths Hemoglobin (Waterman ‘78) http://sites.sinauer.com/animalphys3e/boxex24.01.html

12. Resonant Tunneling diode e1 e2

13. Quantum of Resistance L ~ 10 nm G =(2q2/h) MT = (2q2/h) < vxD > Landauer drain source

14. Landauer Equation EF + qV  L ~ 10 nm I =(2q2/h) MT dE  Landauer EF drain source THEORY EXPT (HRL)

15. Quantum of Conductance G0 = 2q2/h = 77 mA/V EF + qV  I =(q/h) MT dE  EF M = 2, T = 1 EXPT Halbritter PRB ’04 < MT > G = dI/dV = (q2/h) Minimum resistance of a conductor (h/2q2 = 12.9 kW) Modified Ohm’s Law R = r(L + L0)/A

16. Ohm’s Law for the 21st century L ~ 100s nm L > 1 mm L ~ 10 nm Resistor Waveguide drain source • Semiclassical Quantum Classical RQ =(h/q2MT) ROhm = L/sA M = hvD/L s = nq2t/m* T = l/(l+L)

17. 70% of electrons in today’s FETs are ballistic • What does resistance even mean when you’re • ballistic? • How does scattering bring electrons back to • classical Drude’s Law? R = RQ + ROhm

18. U UL UN Applied Laplace potential (e.g. Gate) CQ Neutrality potential CE Electrostatic capacitance quantum capacitance Quantum of Capacitance CQ =q2D The smaller capacitor wins C = CECQ/(CE+CQ)

19. Si CMOS surges on

20. .. Sometimes bafflingly so !

21. Yet there is a crisis..

22. .. including a fundamental one Pentium 2000, 50W/cm2; ~2025, 40MW/cm2 Based on Fundamental considerations alone ! P = ½aCV2f + IOFFV

23. Moore’s law: Alive, but not kicking • Stopped scaling V, f (Dennard) • 18 months  2yrs  3 yrs • SRAM, contacts, oxides • not scaling well • Node isn’t feature size anymore ! Moore’s Law is about complexity / Performance per $$ Metric: Energy x Delay x log(error) x A • Grow in 3D, through Si vias - footprint • Hyperthreading, Multicore • Scale Wafer size P = ½aCV2f + IOFFV

24. Moore’s law: Alive, but not kicking From Ralph Cavin, NSF-Grantees’ Meeting, Dec 3 2008

25. Where do we go next? New Architecture: FinFETs, SOIs, DGMOSFETs, .. New Materials: Strained Si, III-V….. 2-D? New Switching Principles: Nanomagnetic, Neuromorphic (Short channel effects, Error rates) E Dt E Dt