welcome to solid state physics! - university of...
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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=