Lecture 3 Notes
8. Micro & Nanoscale Phenomena
8.1 Classical size effects
In section 7, the characteristic length of the box is much longer than the mean free path
. Therefore, the collisions between molecules and the wall are neglected in
our derivation
Lecture 2 Notes
5.1 Heat conduction
Th
Tc
In last lecture, we describe electrons as free electron gas and lattice vibrations as
phonon gas. Basically they are both gases in a box.
5.2 Convection
1) Typically electron velocities are 105-106 m/s, while phon
Lecture 5 Notes
Quick review of Lecture 4
1. Free particles
The energy can be any values determined by the wavelength.
2
2 2
E p 2 / 2m
; k 2/ , = h / 2
2m
2m
2. Quantum well
ENERGY AND
WAVEFUNCTION
U
x
U=0
Energy has discrete levels, and we have one qua
Lecture 9 Notes
3.4 Density of states
(1) Electron in a quantum well
ENERGY AND
WAVEFUNCTION
U
n=
3
n=
2
n=
1
U=0
x
For electrons in a quantum well, the energy has discrete levels as
2
2
E
(n=1,2,)
8m D 2
For wavefunction n,s , we have degeneracy g(n)=
Lecture 10 Notes
Review on previous lectures
kz
k
ky
kx
In above figure, we can find the volume of one state is V (2/ L)3 . In the sphere, the
number of states within k and k+dk is
4 k 2 k
Vk 2 k
,
N
1
in which V=L3 is the crystal volume.
The density of
Lecture 4 Notes
Quick review of Lecture 3
Photon: E h , p h /
.
Assuming t(r,t)=(r)Y(t), we use separation of variables to solve the Schrdinger
equation
2
2m
U i=
2
.
t t The
solutions are
Y C exp i t C exp
1
=
i
t , and
2m
U E 0
2
,
where the eigen
Lecture 1 Notes
1. Overview for nano sciences
1.1 Length scale
1.2 Examples in microtechnology
1.3 Examples in nanotechnology
1.4 Nano for energy (phonon, phonon, electron; wavelength, mean free path)
1.5 Nanoscale heat transfer in devices (e.g., CMOS)
1.
Lecture 6 Notes
Quick review of Lecture 5
In the last lecture, we approximate the potential field as rectangular wells in the crystal.
From periodicity, the Bloch theorem gives additional equations
[x (a b )n ] (x ) e ikn (a b) ,
which is used to determin
Lecture 8 Notes
In the last lecture, we have talked about the primitive unit cell. There is only one lattice
point (equivalently speaking) per primitive unit cell. The smallest space formed by all the
bisecting planes is a Wigner-Seitz cell, as indicated
Lecture 7 Notes
In the last lecture, we have talked about atoms in a one-dimensional chain. We find the
solution as
u j A exp[i(t kja)],
where the frequency is 2
K
sin
ka
.
Na
(j-1)a ja (j+1)a
Note: When k approaches zero for large wavelength, the frequen