1
Device Physics
박 기 찬
2
Contents
- Energy Band
- Carrier Action
- p-n Junction
- Metal-Semiconductor Contact
- Metal-Insulator-Semiconductor Capacitor
- MOSFET
3
Energy Band
- Atomic bonding and energy band
- Fermi level and carrier concentration
4
Atomic Bonding and Energy Band
5
Periodic Table of Elements
6
Electronic Energy Levels in Si Atom
7
sp3 Hybridized Atomic Orbitals
Tetrahedron
s orbital px orbital py orbital pz orbital
sp3 hybrid orbital
8
Crystal Structures
9
Energy Band Split
10
Insulator, Semiconductor, Metal
Insulator Semiconductor Metal
11
Electron Energy in Solid
Insulator, Semiconductor Metal
EVAC
EC
EF
EV
work functionionizationpotential
Eg
electron affinity work function
12
Energy Band and Bond Model
T = 0 K T > 0 K
For an intrinsic
silicon,
n = p = ni = 1010 cm-3
@ 300 K
13
Concept of Hole
The movement of a valence electron into the “empty state” is equivalent to the
movement of the positively charged “empty state” itself.
This is equivalent to a positive charge (“hole”) moving in the valence band.
14
Temp. Dependence of Bandgap
Energy bandgap decreases as temperature rises.
15
N-Type Doping
A substitutional phosphorous atom (donor)
with five valence electrons replaces a silicon
atom and a negatively charged electron is
donated to the lattice in the conduction band.
T = 0 K
T > 0 K
16
P-Type Doping
A boron atom (acceptor) with three valence
electrons substitutes for a silicon atom and an
additional electron is accepted to form four
covalent bonds around the boron leading to
the creation of positively charged hole in the
T = 0 K
T > 0 Kvalence band.
17
Donor vs. Acceptor
Donor Acceptor
Filled with Electron 0 6̶
Empty + 0
18
Impurity Levels
19
Fermi Level and Carrier Concentration
20
Fermi Level
F(E) gives the probability that an available energy state at E is occupied by an
electron at absolute temperature T.
k is Boltzmann’s constant ( k = 8.6210-5 eV/K = 1.3810-23 J/K ).
EF is called the Fermi level.
For an energy state at E equal to the Fermi level EF, the occupation probability
is 1/2.
Electrons in solids obey Fermi-Dirac statistics.
The distribution of electrons over a range of allowed energy levels at thermal
equilibrium is governed by the equation,
21
Fermi-Dirac Distribution
22
Carrier Concentration
Number of electrons in the conduction band is given by the total number of states
multiplied by the occupancy , integrated over the conduction band.
> 3 ,
so Boltzmann statistics apply.
23
Distribution of Electrons and Holes
24
Distribution of Electrons and HolesN-type semiconductor P-type semiconductor
25
Fermi Level Position vs. Doping
26
Carrier Concentration
Number of electrons in the conduction band is determined by the position of
with respect to .
27
Mass Action Law
2inpn for nondegenerate semiconductor
28
Intrinsic Carrier Concentration
,
29
Temperature Dependence of ni
30
Donor and Acceptor Level
31
Carrier Conc. vs. Temperature
for nondegenerate semiconductorDD NNnRT ,@
32
Fermi Level Position vs. Temp.
33
Carrier Action
- Drift and diffusion
- Recombination and generation
34
Drift and Diffusion
35
Drift of Carriers
Typical random behavior of a hole in a semiconductor (a) without an electric field
and (b) with an electric field.
Vth = 107 cm/s @ 300K
36
Drift Velocity
Drift velocity of an electron with an applied electric field.
37
Mobility
38
Temperature Effect on Mobility
RT@
Mobility decreases
as temperature
rises.
39
Impurity Effect on Mobility
RT@
RT@
40
Drift Currents
Electrons and hole flow in opposite directions when under the influence
of an electric field at different velocities.
The drift currents associated with the electrons and holes are in the same
direction.
41
Resistivity
EqpΕqn
qpvqnv
JJJ
pn
dpdn
pn
conductivity
42
Resistivity vs. Dopant Concentration
43
Velocity Saturation in High E-field
At low electric fields, .
The mobility is independent of the
electric field.
When the fields are sufficiently large,
however, nonlinearities in mobility and,
in some cases, saturation of drift
velocity are observed.
→ saturation velocity @ RT:
44
Band Bending
(a) Carrier kinetic energies
(b) Electron potential energy
P.E. of charge Q = QV
(c) Electrostatic potential (Voltage)
q
EP
Q
EPV
....
!!!1
1..
dx
dE
qdx
dV
EEqq
EPV
C
refC
45
Diffusion of Carriers
46
Diffusion of Carriers
The flow or flux of carriers proportional to the concentration gradient (Fick’s law).
is call the diffusion coefficient.
This flux of carriers constitutes a diffusion current,
47
Total Current in Semiconductor
Einstein relation
The total conduction current is given by the sum of electron and hole currents.
Each carrier current is composed of both drift and diffusion currents.
48
Einstein Relation
These two equations give the relationship
and similarly for p-type semiconductor,
49
Constancy of Fermi Level
E1/2 = EF
E3/4
E1/4
In Equilibrium, there are no external influences such as electric field and temperature gradient. Accordingly electrons are evenly distributed and do not move macroscopically. Their distribution is determined by their energy and described by
This indicates that the Fermi level is constant in equilibrium.
kTEE
EfFexp1
1)(
Wheat does “evenly distributed” mean?In thermal equilibrium, what is even in a system?→ Temperature!!Regarding the distribution of electrons, “evenly distributed” means that the probability of electron occupation for every state at the same energy level is constant.
50
Diffusion Length
51
Recombination and Generation
52
Carrier Recombination-Generation
Electrons and holes are generated or recombine in pairs.
In equilibrium, the generation and recombination rates are same.
Recombination Generation
Band-to-band
Shockley-Read-Hall(via
traps)
53
Photoluminescence
Optical absorption of a photon with hν1 > Eg : (a) An EHP is created during photon
absorption; (b) the excited electron gives up energy to the lattice by scattering
events; (c) the electron is trapped by the impurity level Et and remains trapped until
it can be thermally reexcited to the conduction band (d); finally direct recombination
occurs giving off a photon (hν2) of approximately the band gap energy.
54
Optical Absorption
lt
x
eII
eIxI
xIdx
xdI
0
0)(
)()(
Optical absorption experiment
Dependence of optical absorption
coefficient α for a semiconductor
on the wavelength of incident light
55
SRH Recombination-Generation
Shockley-Read-Hall statistics
56
Impact Ionization
When the electric field in a semiconductor is increased
above a certain value, the carriers gain enough
energy to excite electron–hole pairs.
Ionization rate a is defined as the number of electron–
hole pairs generated by a carrier per unit
distance traveled.
Multiplication of electrons and
holes from impact ionization, due to
electrons (αn) in this example (αp = 0).
57
Ionization Rate
58
p-n Junction
- Space charge region
- Ideal current equation
- Actual I-V characteristic
59
Space Charge Region
60
Electric Field vs. Charge
Gauss’ law,
Integral form,
Integration over the surface of the cylinder,
If can be
neglected (h << S or 1-D case),
ED
QsdE
E1n E2n
h
S
QsdESEE
surfacelcylindrica
nn 1122
hS
QEE nn 1122
surfacelcylindrica
sdE
hS
QEE nn 1122
61
Space Charge Region
Movement of electrons an holes when
forming the junction
Space charge or depletion region
62
Abrupt p-n Junction
qND
-qNA
63
Built-In Potential
64
E-field in SCR
65
Potential Energy in SCR
The built-in potential is
66
Depletion Width
qND
-qNA
67
p-n Junction under Equilibrium
68
p-n Junction with Bias
69
Depletion Layer Capacitance
)(2 V
Nq
WdV
dQC
bi
S
D
SDD
70
Ideal Current Equation
71
Current Flow under Equilibrium
Electron Drift Flow
Electron DiffusionFlow
72
Current Flow with Forward BiasElectron Diffusion Flow
Electron Drift Flow
73
Current Flow with Reverse BiasElectron Drift
Electron Diffusion Flow negligible due to large energy barrier
Flow
74
Ideal I-V Characteristics
75
Carrier Concentration with Bias
76
Quasi-Fermi Level
77
Derivation of Current Equation
78
Ideal Current Equation
79
Carrier Distribution & Current
80
Actual I-V Characteristic
81
Reverse Breakdown
82
Avalanche Breakdown
83
Breakdown Voltage vs. Doping
84
Edge Effect on Breakdown
85
Tunneling
86
Zener Breakdown
87
Generation Current
The current due to generation in SCR
The total reverse current
88
Recombination Current
The current due to recombination in SCR
The total forward current
89
I-V Characteristic of p-n Junction
90
Metal-Semiconductor Contact
- Potential barrier at MS contact
- I-V characteristic of MS contact
91
Potential Barrier at MS Contact
92
Metal vs. n-type Si : Schottky
93
Metal vs. n-type Si : Ohmic
94
Metal vs. p-type Si : Schottky
95
Metal vs. p-type Si : Ohmic
96
Metal Work Function in Vacuum
97
Schottky Barrier with Bias
98
Equations for Depletion Region
99
Analysis with Interface States
100
Density of Interface States
101
Image-Force Lowering
102
Barrier Lowering by Image Charge
103
Barrier Lowering vs. E-field
104
I-V Characteristic of MS Contact
105
Current Transport
JTE converges to very small
value under reverse bias.
106
Schottky Diode in Forward Bias
The built-in voltage of the
Schottky barrier diode, V(SB), is
about ½ as large as the built-in
voltage of the p-n junction diode,
V(pn).
107
Schottky Contact in Reverse Bias
108
Tunneling Current
109
Ratio of FE and TE Current
110
Ohmic Contact by Tunneling
111
RC vs. Doping
112
RC vs. Doping
Top Related