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Lesson 2: Review of solid state physics

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(1)

Lesson 2:

Review of solid state physics

(2)

A) Short review of quantum mechanics - De Broglie relation

- Heisenberg uncertainty principle

- Schrödinger wave equation and applications

Time-

dependent

(3)

Time-

independent

Engineering VEngineering the nanostructure electronic properties

Free particle: V=0

Hydrogen atom: V1/r

(4)

Harmonic oscillator: Vr

2

Infinite square well potential: V(z)=0, 0<z<a; V(z)=, z<0, z>a

V

0

0 a

E

z

(5)
(6)

- Fermi-Dirac distribution

It plays a key role in the distribution of electrons in

nanostructures

(7)

B) Free electron model of a solid; Density of states function

(8)

Born-von Karman

conditions

(9)

Density of states

(10)
(11)
(12)

T=0 K

(13)

C) Bloch theorem

Bloch states

(14)

D) Electrons in crystalline solids

Nearly free electron model (perturbation method)

a

(15)
(16)

Metal: no energy gaps (free electrons, parabola) Semiconductors: E

G

~0.7-3 eV

Insulators: E

G

>3 eV

E

G

(17)

Riduzione alla prima zona di Brillouin

(18)

E) Dynamics of electrons in bands

- Equation of motion

(19)
(20)

Crystal momentum

(21)

- Effective mass

(22)
(23)

- Holes

(24)

E) Lattice vibrations (Phonons)

- 1D monoatomic lattice

(25)
(26)

- 1D biatomic lattice

(27)

- Phonons

Riferimenti

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