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. 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

4. 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

5. 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)

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

7. Small devices are better candidates for observing 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 Light. Plant Physiology Information Website. ( ).

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)

12. Resonant Tunneling diode

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

14. 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)

15. 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

16. 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

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. 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)

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

25. 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