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 ?

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

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

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 p/a -p/a y+ y- |U0| k

Interference signatures Yes! There are many examples of quantum interference 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)

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

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

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

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

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

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

Resonant Tunneling diode

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

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

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

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

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

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

Si CMOS surges on

.. Sometimes bafflingly so !

Yet there is a crisis..

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

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

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

Where do we go next? E Dt E Dt 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