1

Welcome to Solid State

Physics!

References:Solid State Physics, Neil W. Ashcroft, N. David

Mermin (1976).

Solid State Physics, Giuseppe Grosso, Giuseppe

Pastori Parravicini (2000).

Introduction to Solid State Physics written by Charles

Kittel, 8th edition (2004).

FUNDAMENTALS OF SOLID STATE

ENGINEERING, 2nd Edition, Manijeh Razeghi(2006).Principles of condensed matter physics, P. M. CHAIKIN, T. C. LUBENSKY (1995).A Theoretical Treatise on the ElectronicStructure of Designer Hard Materials, HÅKAN WILHELM HUGOSSON (2001).

My lectures are on the web

All my lectures in PDF will be on my web site: http://sci.ui.ac.ir/~sjalali

Please download them before class, so you don’t have to take many notes in class.

I’ll be creating and continually modifying them as the term progresses, so it’s best not to download them all the first day, and instead to download each lecture a day or two before class.

Homework

You would give me your homework per week at my officenot in class or under my door.

You can work with others on homework (I encourage you to do so!), but write it yourself.

Evaluation Procedures:

1) Midterm (40% or 45%) + Final (50% or 45%) + Homework (10%)

2) Midterm (25% or 30%) + Final (40% or 35%) + Homework (10%) + Research

(25%)

N.B. Choice is yours to select procedure Number 1 or Procedure Number 2

If you wish to select procedure 2, I would suggest going through the following textbooks:

2

The Importance of Having Class

In the past, people

who have skipped a

lot of classes have

received very bad

grades. Conversely,

people who’ve come

to most or all of the

classes nearly

always receive A’s

and B’s.

You should come to class because there’s a lot that I’ll say that won’t be in the Power Point files. And which will be on the quizzes.

Understanding the ideas of each lecture requires

the knowledge of the previous lectures.

If you keep up, you won’t end up looking like this the night before the exams!

3

The classical ideal gas

Ψ=Ψ EH

VTH +=

(N, V, E)

Ω (E) = E + δδδδE , E

E0

Eδ

∆∆>>

∆>>δ

δ>>

0

0

E

E

EE

E0=

Ω (E) ∝∝∝∝ δδδδE

Ω (E) = ρρρρ(E) δδδδE

Density Of States (DOS)

E

= ΦΦΦΦ (E + δδδδE)

E + δδδδE , E

E+δδδδE

= ΦΦΦΦ (E)

Ω (E) =

=Ω )E(

( ) ( )dE

EdE

Φ=ρ( ) ( ) =Φ−δ+Φ EEE

( ) ( ) =Φ−δ+Φ EEE ( ) EE δρ

E)E(EdE

dδρ=δ

Φ

4

2 2 2 2 2

2

K nE

2m 2mL

π= =

( ) ( ) EEm2h2

LE)E(E 2

1

21

δπ

=δρ=Ω−

?)E( =Φ

n)E( =Φ

)E()mE2(L

n 2/1 Φ=π

=

( ) LE ∝Ω

( )( )

( )1

122

d E LE 2m E

dE 2ρ

π

−Φ= =

n=1n=2n=3n=4

E0

( )2z

2y

2x2

2222

nnnmL2

h

m2

KhE ++

π==

2z

2y

2x nnnnR ++==

( ) 3

23

22

32

23

22

2

LV;h

EmV2

6h

EmL2

3

4

8

1E =

π

π=

ππ×=φ

( ) ( )2

12

3

2

32

2

E2

3Vhm2

dE

EdE

π=

φ=ρ

−

( ) 3

23

22

32

23

22

2

LV;h

EmV2

6h

EmL2

3

4

8

1E =

π

π=

ππ×=φ

( )2z

2y

2x2

2222

nnnmL2

h

m2

KhE ++

π==

( ) 2/12z

2y

2x mE2

LnnnnR

π=++==

( ) E)E(E δρ=Ω 21

23

2

32

2

E2

3Vm2

π=

−

( ) VE ∝Ω

Drude Model

• Linear CaseF = -bv

• Terminal Velocity

• Solution for v0 = 0

b

mgv

bvmgma

T =

=−= 0

( ) ( )τ//11

t

T

mbteve

b

mgv

vm

bg

dt

dv

−− −=−=

−=

Quasi independent electrons

5

Paul Karl Ludwig Drude

(July 12, 1863-July 5, 1906)

2

0

nq

m

τσ =

V

1k lvC

3=

2V

20

mv Ck 1

3 nqσ=

l vτ=

2V

1k v C

3τ=

2B1/ 2mv 3 / 2k T=

V BC 3 / 2nK=

22

B

0

kk 3T

2 qσ

=

A BE N 3 / 2k T=

el A

EC 3 / 2N R

T

∂= =

∂

Arnold Johannes Wilhelm Sommerfeld

(December 5, 1868 - April 26, 1951)

Qu

asi

Fre

e E

lectr

on

s

3F4 / 3 kπΩ =

3F 3

VN 2 4 / 3 k

8π

π= ×

3F 3

N 12 4 / 3 k

V 8π

π= ×

3F2

kn

3π=

FE / N 3 / 5Nε=

2 2F

F

k

2mε =

3 2F

Nk 3

Vπ

=

2

2 3/2 3/23 NE N(3 ) ( )

5 V 2mπ=

2 EP

3 V=

2/3E V

−∝

5/3P V

−∝

6

g( )ε

ε

f ( )ε

εFε

T = 0T <> 0 N( ) f ( )g( )ε ε ε∝

εFε

Bk T

Bk T

Fε

Bk T

Fε

U N=Bk T

FεB3 / 2k T

2B

el

FV,N

3NkUC T

T ε

∂ = =

∂

elC Tγ=