session 0: solid state physics from atom to transistoree.sharif.edu/~sarvari/25772/pssd000.pdf ·...
TRANSCRIPT
From Atom to Transistor
Session 0: Solid State Physics
1
1.
2.
3.
4.
5.
Objective
To Understand: how “Diodes,” and “Transistors” operate!
2
np np+ p-
p
n+ n+
1.
2.
3.
4.
5.
21 Century Alchemy!
3
Art of VLSI design is:
to put together materials with different resistivity's next to each
other to perform a certain task.
�
Ohm’s law
� � �� → � � �
� resistivity
Resistivity is characteristic of the material
Co
nd
uct
or
Insu
lato
r
��� � 10��������� � 10������Al , Cu SiO2
1.
2.
3.
4.
5.
Periodic Table of Elements
4
Abbreviated Periodic TableBohr Atomic Model
wave-particle duality
� � � �⁄
de Broglie standing wave
�� � !"
Energy Bands:
#�
#$
#%#&
1.
2.
3.
4.
5.
Bohr Atomic Model
5
Single atom:
#�
#$
#%#&
Pauli exclusion principle
#�$
#$$
#%�
#��
#$�
#%$
2 atoms: N atoms:
#�$#��
#�'⋮
#$$#$�
#$'⋮
2N
ele
ctro
ns
forbidden
energies
all
ow
ed
en
erg
ies
1.
2.
3.
4.
5.
Materials
6
�����Insulator
EG (Si) = 1.1eV
EG (Ge) = 0.7eV
EG (SiO2) = 9eV
Conductor Semi-conductor10�$ 10)
2N
sta
tes
Valance band
Conduction band
N electrons
#*
empty seat / filled seat
Conduction band
Valance band
2N
sta
tes
1.
2.
3.
4.
5.
Intrinsic Semiconductor
7
+4 +4+4
+4 +4+4
+4 +4+4
Si
Valance
electrons
Covalent
bands
1.
2.
3.
4.
5.
Intrinsic Semiconductor
8
+4 +4+4
+4 +4+4
+4 +4+4
Si
Valance
electrons
Covalent
bands
!+�+
electron density
hole density
free electron
hole
!+ � �+ � !�
!�,-.%++/ � 10�+���% ≪ ! 12 � 2 4 10$%���%
� useless!!
1.
2.
3.
4.
5.
n-type Semiconductor
9
+5 +4+4
+4 +4+4
+4 +4+4
P
Valance
electrons
Covalent
bands
!+�+ � !�$
Donor: P , As , Sb
free electron for
each dopant !+ � 56
567�8910�:���% ☺
Si
!+�+
electron density
hole density
! 12 � 2 4 10$%���%
1.
2.
3.
4.
5.
p-type Semiconductor
10
+3 +4+4
+4 +4+4
+4 +4+4
B
Valance
electrons
Covalent
bands
!+�+ � !�$
Acceptor: B , Ga , In
hole for each
dopant !+ � 5�
5�7�8910�:���% ☺
Si
!+�+
electron density
hole density
! 12 � 2 4 10$%���%
1.
2.
3.
4.
5.
Energy Diagrams
11
�
Kinetic Energy
Potential Energy
1.
2.
3.
4.
5.
Energy Diagrams
12
1.
2.
3.
4.
5.
Energy Diagrams
13
#
;
1.
2.
3.
4.
5.
Density of States
14
Azadi stadium Boxing stadium
In Stadium: Number of available seats could be a function of
distance from the center so ….
5: number of available states for the electrons could be function
of “Energy” : 5 #
Seats are not the same for fans so empty states for electrons!
1.
2.
3.
4.
5.
Fermi Function
Probability of Electron Distribution
151
<=#> � 11 ? @=A�AB> C-⁄
If we are 3kT away from the Fermi energy then we might use
Boltzmann approximation:
#D is called the Fermi energy or the Fermi level.
0.5
#
<=#>
<=#> � @�=A�AB> C-⁄
< # � 1 E @�=AF�A> C-⁄# E #G ≫ IJif
# E #G ≪ EIJif
#G#G ? IJ#G ? 2IJ#G ? 3IJ
#G E 3IJ#G E 2IJ#G E IJ@�=A�AB> C-⁄ 5 # < # � # of electrons at energy E
5 # 1 E < # � # of holes at energy EJ � 0J
1.
2.
3.
4.
5.
Materials
16
�����Insulator
EG (Si) = 1.1eV
EG (Ge) = 0.7eV
EG (SiO2) = 9eV
Conductor Semi-conductor10�$ 10)
2N
sta
tes
Valance band
Conduction band
N electrons
#*
empty seat / filled seat
Conduction band
Valance band
2N
sta
tes
1.
2.
3.
4.
5.
Electron / Holes : Intrinsic
17
#L
#M
#5L=#>
intrinsic
#G � #�<=#>
5 # . <=#>
5M=#>
#
5 # 1 E < #
5 # < # � # of electrons at energy E
5 # 1 E < # � # of holes at energy E
!+ � O 5 # . < # P# Q
AR
�+ � O 5 # 1 E < # P#Q
AR
1.
2.
3.
4.
5.
Electron / Holes : n-type
18
#L
#M
#5L=#>
n-type
#G <=#>5 # . <=#>
5M=#>
#
5 # 1 E < #
5 # < # � # of electrons at energy E
5 # 1 E < # � # of holes at energy E
!+ � O 5 # . < # P# Q
AR
�+ � O 5 # 1 E < # P#Q
AR
!+ ≫ �+
1.
2.
3.
4.
5.
Electron / Holes : p-type
19
#L
#M
#5L=#>
p-type
#G<=#>
5 # . <=#>
5M=#>
#
5 # 1 E < #
5 # < # � # of electrons at energy E
5 # 1 E < # � # of holes at energy E
!+ � O 5 # . < # P# Q
AR
�+ � O 5 # 1 E < # P#Q
AR
�+ ≫ !+
1.
2.
3.
4.
5.
Fermi Energy
20
p-type
# !+
�+
#L
#M#D
#
#D
#
#D
!+!+
�+ �+
n-typeintrinsic
1.
2.
3.
4.
5.
Fermi Energy
21
#G#G
n-typep-type
n-typep-type
#G
1.
2.
3.
4.
5.
Flow of Charge
22
Electric field � gravitational field
#L
#M
SS@�
�T
Drift
DiffusionCharges move to be evenly distributed throughout
space. Similar to perfume in room or heat in a solid
U ∝ S
U' � WX'P!P;
UY � EWXYP�P;
1.
2.
3.
4.
5.
PN Junction
23
#L'
#M'
#G'
n
#LY
#MY#GY
p
1.
2.
3.
4.
5.
PN junctions
24
#L'
#M'
#G'
n
#LY
#MY#GY
p
Z
1.
2.
3.
4.
5.
PN junctions
25
#L'
#M'
#G'
n
#LY
#MY#GY
p
Depletion region
W�[�
1.
2.
3.
4.
5.
PN junctions
26
#L'
#M'
#G'
n
#LY
#MY#GY
p
depletion region
W�[�
U'\]�D^ U'\�DD
UY\�DD UY\]�D^
�
�
1.
2.
3.
4.
5.
PN junctions , Reverse Biased
27
#G'
n
#GY
p
depletion region
�_
U'\]�D^ U'\�DD
UY\]�D^
UY\�DD
�
�
W�_
1.
2.
3.
4.
5.
PN junctions , Forward Biased
28
#G'
n
#GY
p
depletion region
�G
U'\]�D^ U'\�DD
UY\�DD UY\]�D^
�
�
W�G
1.
2.
3.
4.
5.
BJT Electrostatics
29
Under normal operating conditions, the BJT may be viewed electrostatically as
two independent pn junctions
#L`
#M`#G`
Emitter
np+ p-
CollectorBase
pnp
1.
2.
3.
4.
5.
BJT Electrostatics
30
Under normal operating conditions, the BJT may be viewed electrostatically as
two independent pn junctions
#L`
#M`#G`
Emitter
np+ p-
CollectorBase
pnp
1.
2.
3.
4.
5.
BJT Electrostatics
31
#L`
#M`#G`
Emitter
np+ p-
CollectorBasepnp
�A �L
W�AW�L
ab
a
1.
2.
3.
4.
5.
JFET
32
�
n p+
p+
Junction FET
a
Source Drain
Gate
Gate
2c
1.
2.
3.
4.
5.
JFET
33
�n p+
p+
a
2c �6
� � � �a;
�6
�6
;
�6~0
1.
2.
3.
4.
5.
JFET
34
�n p+
p+
a
2c �6
� � � �a;
�6
�6
;
�6 e 0
1.
2.
3.
4.
5.
JFET
35
�n p+
p+
a
2c �6
� � � �a;
�6
�6
;
�6~0
1.
2.
3.
4.
5.
JFET
36
�n p+
p+
a
2c �6
� � � �a;
�6
�6
;
�6~0
1.
2.
3.
4.
5.
JFET
37
�n p+
p+
a
2c �6
� � � �a;
�6
�6
;
�* � 0
�* � E2
�* � E2
�* � E2
1.
2.
3.
4.
5.
Qualitative Theory of the NMOSFET
38
fc8@
p
SiO2
197 �@ X c2!n+ n+
A A’ #L
#M
#GX c2!197 �@
�* � 0�* e 0�* � �-
The potential barrier to electron flow from the source
into the channel region is lowered by applying VGS> VT
1.
2.
3.
4.
5.
Qualitative Theory of the NMOSFET
39p
1 Xn+ n+
�* e �- �6 e �* E �-
�6
�6
�6ghi � �* E �-
p
1 Xn+ n+
�* e �-
p
1 Xn+ n+
�* e �-
�6 � 0
�6 e 0j0 �=j>