1.
Solid State Physics
UNIST, Jungwoo Yoo
1. What holds atoms together  interatomic forces (Ch. 1.6)
2. Arrangement of atoms in solid  crystal structure (Ch. 1.14)
 Elementary crystallography
 Typical crystal structures
 Xray Crystallography
3. Atomic vibration in solid  lattice vibration (Ch. 2)
 Sound waves
 Lattice vibrations
 Heat capacity from lattice vibration
 Thermal conductivity
(Midterm I)
4. Free electron gas  an early look at metals (Ch. 3)
 The free electron model, Transport properties of the conduction electrons
5. Free electron in crystal  the effect of periodic potential (Ch. 4)
 Nearly free electron theory
 Block's theorem (Ch. 11.3)
 The tight binding approach
 Insulator, semiconductor, or metal
 Band structure and optical properties
6. Waves in crystal (Ch. 11)
 Elastic scattering of waves by a crystal
 Wavelike normal modes  Block's theorem
 Normal modes, reciprocal lattice, brillouin zone
(Midterm II)
7. Semiconductors (Ch. 5)
 Electrons and holes
 Methods of providing electrons and holes
 Transport properties
 Nonequilibrium carrier densities
8. Semiconductor devices (Ch. 6)
 The pn junction
 Other devices based on pn junction
 Metaloxidesemiconductor fieldeffect transistor (MOSFET)
(Final)
All about atoms
backstage
All about electrons
Main character
Main applications
2.
Solid State Physics
UNIST, Jungwoo Yoo
Semiconductors Device
 The pn junction
 Other devices based on pn junction
 Metaloxidesemiconductor field effect semiconductor (MOSFET)
To understand the great majority of semiconductor devices it is necessary to
consider the behavior of charge carriers near a surface or interface. Of particular
importance are the boundary detween an ntype region and a ptype region, the
boundary between a semiconductor and an insulator, and the boundary between
two different semiconductors. This chapter will focus on the understanding the
physics of the devices, rather than the technical applications.
3.
Solid State Physics
UNIST, Jungwoo Yoo
The junction between two metals
If two metals of different work function are brought into contact,
1
1FE
2FE
2
Electron will cross from left to right to occupy the lower energy states available. However, as electrons
cross over there will be an excess of positive charge on the lefthand side and an excess of negative
charge on the righthand side. Consequently, an electric field is set up with a polarity that hinders the
flow of electrons from left to right and encourages the flow of electron from right to left. A dynamic
equilibrium is established when equal numbers of electrons cross in both directions.
The potential difference between the two metals, called the contact potential is equal to the difference
between the two work functions; the potential difference may be obtained by equating the Fermi levels
of the two media in contact
1
FE
2
12
4.
Solid State Physics
UNIST, Jungwoo Yoo
p
The pn Junction with Zero Bias
n
vE
cE
p
vE
cE
n
Particle flow
Hole diffusion
Hole drift
Electron diffusion
Electron drift
Current flow
p n
E



+
+
+
w
p
n
Electrostatic potential
pne 0
5.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
The behavior of pn junction results from the effect on the electron energy
levels in the region of the junction as described following
p
n
0e
eoI
hoI
6.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
The total potential difference required to produce a uniform chemical potential
(often called builtin potential, which is necessary to maintain equilibrium at the
junction)
AD NNn
Tk
V
TkE
C
B
BG
eNp
eNn
/
/)(
Consider n type, for some range of T, all donors and acceptors are ionized
AD
C
BGn
NN
N
TkE lna
D
C
BG
N
N
TkE ln~
Consider p type, for some range of T, all donors and acceptors are ionized
DA NNp
A
V
B
DA
V
Bp
N
N
Tk
NN
N
Tk ln~lna
7.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
A
V
B
D
C
BGpn
N
N
Tk
N
N
TkEe lnln
The total potential difference required to produce a uniform chemical potential
(often called builtin potential, which is necessary to maintain equilibrium at the
junction)
VC
AD
BG
NN
NN
TkE ln
TkE
VCi
BG
eNNnpn /2
Law of mass actiona
2
ln
i
ADB
n
NN
e
Tk
322
m10
DA NN
at T = 300 K for Si and Ge ?
316
m102
in 319
m102
in
(take , and intrinsic carrier concentrations at RT for Si and Ge
are
(Si) (Ge)
a eV7.0~ eV3.0~(Si) (Ge)
8.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
The width of depletion layer and the variation of the electrostatic potential )(x
Start on two assumption
1) The boundary between the n and p regions is sharp
2) The majority carrier concentrations decrease very rapidly from their ‘bulk’ value
at the edges of the depletion layer
0x
p=type n=type
DN
AN
AeN
DeN
x
x
pn,
)(x
Then the charge density near the junction
)(x DeN
AeN
0
0 xwp
nwx 0
elsewhere
pw nw
9.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
The width of depletion layer and the variation of the electrostatic potential )(x
)(x DeN
AeN
0
0 xwp
nwx 0
elsewhere
0
2
2
)(
x
dx
d
From Poisson’s equation
a
dx
d
E
)(
0
p
A
wx
eN
)(
0
D
D
wx
eN
0 xwp
nwx 0
E should be continuous at x=0
a nDpA weNweN (charge neutrality)
10.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
The width of depletion layer and the variation of the electrostatic potential )(x
Integrating the electric field
a )(x
2
0
)( p
A
wx
eN
2
0
0 )( n
D
wx
eN
0 xwp
nwx 0
The depletion layer is wider in more lightly doped junctions
should be continuous at x=0)(x
2
0
0 )(
2
nDpA wNwN
e
nDpA weNweN
a
2
00
)(
2
DAD
A
n
NNeN
N
w
2
00
)(
2
DAA
D
p
NNeN
N
w
321
m10~~
DA NN
323
m10~~
DA NN
a
μm1~np ww
μm1.0~np ww
11.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
DN
AN
AeN
DeN
x
x
pn,
)(x
pw nw
)(xE
0
)(x
0
12.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
The values of n, and p at any point being determined by the position of the
chemical potential relative to the conduction and valence band edges respectively
Tk
V
TkE
C
B
BG
eNp
eNn
/
/)(
a
]/)(exp[)(
]/)(exp[)(
0
0
Tkxepxp
Tkxenxn
B
B
Where and are the concentrations of electrons and holes at points where
is zero.
0n 0p
)(x
The rapid falloff in majority carrier concentrations at the edges of the depletion
layer occurs because is small compared to the total energy difference
across the junction
TkB 0e
13.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with Zero Bias
In equilibrium, the current density due to diffusion and due to the electric field
must cancel each other.
a 0
Ene
x
n
eD ee
0)drift()diffusion( JJ
]/)(exp[)(
]/)(exp[)(
0
0
Tkxepxp
Tkxenxn
B
B
Differentiating n )(xn
xTk
e
x
n
B
And
x
E
a
e
TkD B
e
e
e
TkD B
h
h
Einstein relation
14.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
p n



+
+
+
Forward bias
p n



+
+
+
reverse bias
Applied voltage appears across t
he depletion layer
The total potential difference across the depletion layer is
Vpn 0
Forward bias reduces the total potential difference whereas reverse bias increase p
otential difference
15.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
p n



+
+
+
Forward bias
p n



+
+
+
reverse bias
Applied voltage appears across t
he depletion layer
The width of depletion layer is decreased by forward bias and increased by reverse
bias
The width of depletion layer can be obtained by replacing
2/1
00
)(
)(2
DAD
A
n
NNeN
VN
w
2/1
00
)(
)(2
DAA
D
p
NNeN
VN
w
16.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
p
n
)( 0 Ve
eoI
hoI
Ve
p
n
)( 0 Ve
eoI
hoI
eV
Forward bias Reverse bias
18.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
The electric current through a pn junction produced by the applied bias.
Current in equilibrium, 0eI
Let’s consider for p to n0eI
If the lifetime of the electrons per unit volume on the p side of the junction
is then the recombination and generation rates for electrons on this side of
the junction are both equal to per unit volume.
pn
p
ppn /
is electrons generated within one diffusion length of the depletion layer edge
are likely to diffuse to this edge and cross to the n region before recombination.
0eI
On average a newly generated electron moves a distance of one diffusion lengt
h before recombination.
eL
eIe 0 X(generation rate/volume)X(volume within Le of depletion layer)
AL
n
e e
p
p
Where A is the area of the junction.
19.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
If all the acceptors on the p side are ionized,
Aipip Nnpnn // 22
2/1
pee DL a A
NL
neD
I
Ae
ie
e
2
0
Forward bias reduces the barrier by an amount of eV, whereas the reverse bia
s increase the barrier by an amount of leVl
And the occupancy of electron states within the conduction band is given by
a Boltzmann distribution, which leads to an increase by a factor
in the number of electrons on the n side with sufficient energy to overcome t
he barrier
)/exp( TkeV B
The electron current from n to p increases to )/exp(0 TkeVI Be
The electron current from p to n does not change
Therefore, the net electron current through the junction is given by
1)/exp(0 TkeVII Bee
20.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
The net electron current through the junction
1)/exp(0 TkeVII Bee
A
NL
neD
I
Ae
ie
e
2
0
The hole electron current through the junction
1)/exp(0 TkeVII Bhh
A
NL
neD
I
Ah
ih
h
2
0
The total current is obtained by summing the electron and hole contributions
1)/exp(0 TkeVIIII Bhe
Dh
h
Ae
e
ihe
NL
D
NL
D
AenIII 2
000
TkE
VCi
BG
eNNn /2
21.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
1)/exp(0 TkeVII B
22.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
Some deviations
i) High voltage effect
),2/exp('1)/exp(' 00 TkeVITkeVIIII BBtot
2
0 inI inI '0
ii) The recombination and generation within the depletion layer itself
a Important for low voltage and low current
iii) Reverse breakdown: a sudden increase of current that occurs when
the reverse bias increases through some critical value, ~ 3eV. The top of
valence band on the p side of the junction lies above the bottom of the
conduction band on the n side
a Tunneling through the potential barrier consisting of
the central region of the depletion layer
Mechanism for breakdown in more heavily doped pn junctions where
the depletion layer and hence the potential barrier is narrower.
a Zener breakdown a Zener diodes
23.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
Depending on the level of
doping, the threshold voltage
changes
a Zener diodes
24.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
As breakdown voltage increases, the electric field within the depletion
layer leads to excitation of an electron from the valence band to the
conduction band
a Avalanche breakdown
25.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
For a very heavily deped pn junctions, the Fermi level can lie in the
valence band on the pside and in the conduction band on the n side
a The bottome of the conduction band on the n side is then below the
top of the valence band on the p side even with zero bias
a The depletion layer is very narrow and a large tunneling current can be
observed at small forward bias
a With increasing forward bias further, the overlap in energy between the
conduction on the n side and the valence band on the p side eventually
disappears
a Can introduce negative differential resistance, dV/dI<0
a Tunnel diodes
26.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
27.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
p n



+
+
+
Forward bias
p n



+
+
+
reverse bias
Applied voltage appears across t
he depletion layer
A change in the width of the depletion layer via applied bias
a nDpA dweNdweNd
2/1
0
00
))((2
VNN
NN
dV
dw
eN
dV
d
V
Q
C
DA
DAn
D
a
A voltage variable capacitance ! a Varactor diodes or varicaps
28.
Solid State Physics
UNIST, Jungwoo Yoo
The pn Junction with an applied bias
Recombination of electron and hole in the depletion layer
a Emission of photon
a Light emitting diodes (LEDs)
For a heavily doped junctions,
a Forward bias can induces population inversion
a Stimulated emission
Absorption of photon in the depletion layer
a Create electron and hole
a Builtin potential leads current (Solar cells)
29.
Solid State Physics
UNIST, Jungwoo Yoo
)(0 SMee
mFE
The metalsemiconductor junctions
metal n
vE
cE
n
Consider for ntype and
M
mFE
SM
S
Particle flow
Electron diffusion
Electron drift
metal n
E
  
  
  
+
+
+
w
M
S
Electrostatic potential
)( MB ee
Schottky barrier
The equilibrium potential differnece
can be decresed or increased by the
application of either forward or reverse
bias voltage
e
30.
Solid State Physics
UNIST, Jungwoo Yoo
The metalsemiconductor junctions
metal p
vE
cE
p
Consider for ptype and
M
mFE
SM
S
Particle flow
hole diffusion
hole drift
metal p
E
+ + +
+ + +
+ + +



w
M
S
Electrostatic potential
Schottky barrier
The equilibrium potential differnece
can be decresed or increased by the
application of either forward or reverse
bias voltage
e
mFE
)(0 SMee
31.
Solid State Physics
UNIST, Jungwoo Yoo
p n



+
+
+
Forward bias
p n



+
+
+
reverse bias
Applied voltage appears across t
he depletion layer
The total potential difference across the depletion layer is
V 0
Forward bias reduces the total potential difference whereas reverse bias increase p
otential difference
  
  
  
  
  
  
The metalsemiconductor junctions
32.
Solid State Physics
UNIST, Jungwoo Yoo
Forward bias
reverse bias
The metalsemiconductor junctions
)( 0 Ve
mFE
)( Me
eV
V
V
)( 0 Ve mFE
)( Me
vE
cE
n
V
I
Currentvoltage characteristic
1/
0 TkeV B
eII
Schottky barrier diode
 Typically minority carrier
injection is negligible
33.
Solid State Physics
UNIST, Jungwoo Yoo
mFE
The metalsemiconductor junctions
metal n
vE
cE
n
Consider for ntype and
M
mFE
SM
S
Particle flow
Electron diffusion
Electron drift
metal n
E
+ + +
+ + +
+ + +



w
Barrier for electron to flow is negligible
No depletion layer
M
S
Electrostatic potential
)(0 MSee
)( Me
34.
Solid State Physics
UNIST, Jungwoo Yoo
The metalsemiconductor junctions
metal p
Consider for ptype and SM
Particle flow
Hole diffusion
Hole drift
metal p
E
  
  
  
+
+
+
w
M
S
Electrostatic potential
vE
cE
p
M
mFE
S
)(0 SMee
M
mFE
Barrier for hole to flow is negligible
No depletion layer
35.
Solid State Physics
UNIST, Jungwoo Yoo
The metalsemiconductor junctions
Typical schottky barriers: surface state lead to charges at the metalsemiconductor
interface. These surface states often lies in semiconductor band gap and pin the
Fermi level at a fixed position, regardless of the metal used.
36.
Solid State Physics
UNIST, Jungwoo Yoo
The metalInsulatorsemiconductor junctions
metal nI
metal nI
0 x
eNlog
0 x
eNlog
mFE
vE
cE
n
eV
mFE
vE
cE
n
eV
vE
cE
n
MIS
37.
Solid State Physics
UNIST, Jungwoo Yoo
The metalInsulatorsemiconductor junctions
38.
Solid State Physics
UNIST, Jungwoo Yoo
n n
Transistors
Field effect transistors
Junction gate field effect transistor (JFET)
p
P
Gate
Source Drain
Source Drain
Gate
39.
Solid State Physics
UNIST, Jungwoo Yoo
Transistors
Field effect transistors
Junction gate field effect transistor (JFET)
Gate
Source Drain
n n
p
PSI
GI
DI
40.
Solid State Physics
UNIST, Jungwoo Yoo
n n
Transistors
Field effect transistors
Junction gate field effect transistor (JFET)
Gate
Source Drain
p
PSI
GI
DI
41.
Solid State Physics
UNIST, Jungwoo Yoo
n n
Transistors
Field effect transistors
Junction gate field effect transistor (JFET)
Gate
Source Drain
p
PSI
GI
DI
42.
Solid State Physics
UNIST, Jungwoo Yoo
n n
Transistors
Field effect transistors
Junction gate field effect transistor (JFET)
Gate
Source Drain
p
PSI
GI
DI
At pinchoff voltage, maintains a saturation level defined as since a
very small channel still exists with a current of very high density
DI DSSI
The absence of a drain current would remove the posssibility of different
potential levels through the nchannel material to establish the varying levels
of reverse bias along the pn junction. The result would be a loss of the
depletion region
43.
Solid State Physics
UNIST, Jungwoo Yoo
Transistors
Field effect transistors
Junction gate field effect transistor (JFET)
44.
Solid State Physics
UNIST, Jungwoo Yoo
p
Transistors
Field effect transistors
MOSFET Depletion type
n nn
DI
DSV
GSV
45.
Solid State Physics
UNIST, Jungwoo Yoo
Transistors
Field effect transistors
MOSFET Depletion type
p
n nn
DI
DSV
GSV
46.
Solid State Physics
UNIST, Jungwoo Yoo
Transistors
Field effect transistors
MOSFET Enhancement type
p
n n
DI
DSV
GSV
47.
Solid State Physics
UNIST, Jungwoo Yoo
Transistors
Field effect transistors
MOSFET Enhancement type
p
n nn
DI
DSV
GSV
48.
Solid State Physics
UNIST, Jungwoo Yoo
p
Transistors
Field effect transistors
MOSFET Enhancement type
n n
DI
DSV
GSV
49.
Solid State Physics
UNIST, Jungwoo Yoo
Heterojunctions
GaAs : 1.42 eV
AlAs : 2.16 eV
Ga1xAlxAs
Band gap engineering
vE
cE
p
Ga1xAlxAs Ga1xAlxAsGaAs
50.
Solid State Physics
UNIST, Jungwoo Yoo
Heterojunctions
GaAs : 1.42 eV
AlAs : 2.16 eV
Ga1xAlxAs
Band gap engineering
vE
cE
Ga1xAlxAs Ga1xAlxAsGaAs
ptype P+type ntype
recombination
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