1. Department of Electronics
Nanoelectronics 02
Atsufumi Hirohata
Department of Electronics
12:00 Wednesday, 18/January/ (D/L 036)

2. Quick Review over the Last Lecture
Nano-scale miniaturisation :
reduction of ( effective electron paths )
reduction of ( electron scattering )
( faster ) operation
nano-fabrication ;
( complicated ) processes
( higher ) cost
( larger ) distributions in device properties
( leakage ) current
( Joule ) heating
electron ( confinement )
Electron transport :
( diffusive ) transport
 ( electron scattering )
( ballistic ) transport
 ( negligible electron scattering )

3. Contents of Nanoelectronics
I. Introduction to Nanoelectronics (01)
01 Micro- or nano-electronics ?
II. Electromagnetism (02 & 03)
02 Maxwell equations
03 Scalar and vector potentials
III. Basics of quantum mechanics (04 ~ 06)
IV. Applications of quantum mechanics (07, 10, 11, 13 & 14)
V. Nanodevices (08, 09, 12, 15 ~ 18)
Lecture notes and files can be found at

4. 02 Maxwell Equations Electromagnetic field
Origins of an electromagnetic field
Boundary conditions of an electromagnetic field

5. Maxwell Equations Maxwell equations are proposed in 1864 :
E : electric field, B : magnetic flux density,
H : magnetic field, D : electric flux density,
J : current density and  : charge density
Supplemental equations for materials :
 Definition of an electric flux density
 Definition of a magnetic flux density
 Ohm’s law *

6. Maxwell Equations - Origins of an electromagnetic field
For a time-independent case,
 Ampère’s law
 Biot-Savart law H i i dH
Gauss law : E
An electrical charge induces an electric field.

7. Maxwell Equations - Boundary conditions of an electromagnetic field
Faraday’s law of induction : N S N S
current
force
magnetic field
Gauss law for magnetism :
Conservation of magnetic flux *

8. Maxwell Equations in Free Space
In free space (no electron charge, and ,  and  : constant),
By differentiating the first equation with t and substituting the second equation,

9. Maxwell Equations in Free Space (Cont'd)
Here, the left term can be rewritten as
Similarly,
For an ideal insulating matrix,
Electric field
Magnetic field
Propagation direction
 Electromagnetic wave
propagation speed :
in a vacuum, *

10. Electromagnetic Wave *

11. Essence of the Maxwell Equations
Maxwell equations unified electronics and magnetism :
Electronics
Magnetism
Electron charge
Source
Magnetic dipole moment
Force (Coulomb’s law)
Field
Potential
Flux (Gauss’ law)
 Further unification with the other forces
 Einstein’s theory of relativity

12. Michelson-Moley Experiment
In 1881, Albert A. Michelson and Edward W. Morley precisely designed
experiment to prove the presence of Ether :
Ether was believed exist as a matrix to transfer an electromagnetic wave.
 No interference between
parallel / perpendicular to Ether flow
 No sign of Ether
 No relative speed ! *

13. Einstein's Theory of Relativity
In 1905, Albert Einstein proposed the theory of special relativity :
Lorentz invariance for Maxwell’s equations (1900)
Poincaré proved the Lorentz invariance for dynamics.
 Lorentz invariance in any inertial coordinates
Speed of light (electromagnetic wave) is constant. *

14. Unified Theory beyond the Maxwell Equations
Big bang and Grand Unification Theory
Gravity
Weak nuclear force -decay
Big bang
Weinberg-Salam Theory
Maxwell Equation
Electromagnetic force
Strong nuclear force nucleus *