Device Physics
박기찬
1
Contents
- Energy Band
- Carrier Action
- p-n Junction
- Metal-Semiconductor Contact
- Metal-Insulator-Semiconductor Capacitor
- MOSFET
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Energy Band
- Atomic bonding and energy band
- Fermi level and carrier concentration
3
Atomic Bonding and Energy Band
4
Periodic Table of Elements
5
Electronic Energy Levels in Si
Atom
6
sp3 Hybridized Atomic Orbitals
s orbital
px orbital
py orbital
pz orbital
Tetrahedron
sp3 hybrid orbital
7
Crystal Structures
8
Energy Band Split
9
Insulator, Semiconductor, Metal
Insulator
Semiconductor
10
Metal
Electron Energy in Solid
Insulator,
Semiconductor
Metal
EVAC
ionization
potential
electron
affinity
work function
EC
EF
Eg
EV
11
work function
Energy Band and Bond Model
T=0K
T>0K
For an intrinsic silicon,
n = p = ni = 1010 cm-3
@ 300 K
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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.
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Temp. Dependence of Bandgap
Energy bandgap decreases as temperature rises.
14
N-Type Doping
T=0K
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.
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T>0K
P-Type Doping
T=0K
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 valence band.
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T>0K
Donor vs. Acceptor
Donor
Acceptor
Filled with
Electron
0
̶
Empty
+
0
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Impurity Levels
18
Fermi Level and Carrier Concentration
19
Fermi Level
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,
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 = 8.6210-5 eV/K = 1.3810-23 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.
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Fermi-Dirac Distribution
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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.
22
Distribution of Electrons and
Holes
23
Distribution of Electrons and
N-type semiconductor
P-type semiconductor
Holes
24
Fermi Level Position vs. Doping
25
Carrier Concentration
Number of electrons in the conduction band is determined by the position of
with respect to
.
26
Mass Action Law
2
pn  ni for nondegenerate semiconductor
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Intrinsic Carrier Concentration
,
28
Temperature Dependence of ni
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Donor and Acceptor Level
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Carrier Conc. vs. Temperature
@ RT, n  N D  N D
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for nondegenerate semiconductor
Fermi Level Position vs. Temp.
32
Carrier Action
- Drift and diffusion
- Recombination and generation
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Drift and Diffusion
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Drift of Carriers
Vth = 107 cm/s @ 300K
Typical random behavior of a hole in a semiconductor (a) without an electric field
and (b) with an electric field.
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Drift Velocity
Drift velocity of an electron with an applied electric field.
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Mobility
37
Temperature Effect on Mobility
Mobility decreases
as temperature rises.
@ RT
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Impurity Effect on Mobility
@ RT
@ RT
39
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.
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Resistivity
J  Jn  J p
 qnvdn  qpvdp
conductivity
 qn n Ε  qp p E
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Resistivity vs. Dopant Concentration
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Velocity Saturation in High Efield
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:
43
Band Bending
(a) Carrier kinetic energies
(b) Electron potential energy
P.E. of charge Q = QV
V 
P.E. P.E.

Q
q
(c) Electrostatic potential (Voltage)
P.E.
1
  EC  Eref 
q
q
dV 1 dEC


!!!
dx q dx
V 
44
Diffusion of Carriers
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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,
The total conduction current is given by the sum of the drift and diffusion current.
Einstein relation
46
Constancy of Fermi Level
In Equilibrium, there are no external influences such as electric field and temperature
gradient. Accordingly electrons are evenly distributed and do not move macroscopically.
1
Their distribution is determined by their energy and described by f ( E ) 
 E  EF 
1  exp

This indicates that the Fermi level is constant in equilibrium.
 kT 
E1/4
E1/2
= EF
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.
E3/4
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Einstein Relation
These two equations give the relationship
and similarly for p-type semiconductor,
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Diffusion Length
49
Recombination and Generation
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Carrier Recombination-Generation
Recombination
Generation
Band-toband
ShockleyReadHall
(via traps)
Electrons and holes are generated or recombine in pairs.
In equilibrium, the generation and recombination rates are same.
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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.
52
Optical Absorption
dI ( x)
 I ( x)
dx
I ( x)  I 0e x
I t  I 0e l
Dependence of optical absorption
Optical absorption experiment
coefficient α for a semiconductor
on the wavelength of incident light
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SRH Recombination-Generation
Shockley-Read-Hall statistics
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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).
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Ionization Rate
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p-n Junction
- Space charge region
- Ideal current equation
- Actual I-V characteristic
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Space Charge Region
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Electric Field vs. Charge
Q
 2 E2 n  1 E1n   h
S
Gauss’ law,
 D   E  
Integral form,
 E ds  Q
Integration over the
surface of the cylinder,
h
E1n
 2 E2 n  1E1n S    E  d s  Q
cylindrical
surface
E2n
If
S
 E ds
can be
cylindrical surface
neglected (h << S or 1-D
case),
Q
 2 E2 n  1 E1n   h
S
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Space Charge Region
Movement of electrons an holes when
forming the junction
Space charge or depletion region
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Abrupt p-n Junction
qND
-qNA
61
Built-In Potential
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E-field in SCR
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Potential Energy in SCR
The built-in potential is
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Depletion Width
qND
-qNA
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p-n Junction under Equilibrium
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p-n Junction with Bias
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Depletion Layer Capacitance
dQD  S
CD 

dV WD
q S N

2(bi  V )
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Ideal Current Equation
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Current Flow under Equilibrium
Electron Drift
Flow
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Electron Diffusion
Flow
Current Flow with Forward Bias
Electron Diffusion
Flow
Electron Drift
Flow
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Current Flow with Reverse Bias
Electron Drift
Flow
Electron Diffusion Flow negligible
due to large energy barrier
72
Ideal I-V Characteristics
73
Carrier Concentration with Bias
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Quasi-Fermi Level
75
Derivation of Current Equation
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Ideal Current Equation
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Carrier Distribution & Current
78
Actual I-V Characteristic
79
Reverse Breakdown
80
Avalanche Breakdown
81
Breakdown Voltage vs. Doping
82
Edge Effect on Breakdown
83
Tunneling
84
Zener Breakdown
85
Generation Current
The current due to generation in SCR
The total reverse current
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Recombination Current
The current due to recombination in SCR
The total forward current
87
I-V Characteristic of p-n Junction
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Metal-Semiconductor Contact
- Potential barrier at MS contact
- I-V characteristic of MS contact
89
Potential Barrier at MS Contact
90
Metal vs. n-type Si : Schottky
91
Metal vs. n-type Si : Ohmic
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Metal vs. p-type Si : Schottky
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Metal vs. p-type Si : Ohmic
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Metal Work Function in Vacuum
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Schottky Barrier with Bias
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Equations for Depletion Region
97
Analysis with Interface States
98
Density of Interface States
99
Image-Force Lowering
100
Barrier Lowering by Image
Charge
101
Barrier Lowering vs. E-field
102
I-V Characteristic of MS Contact
103
Current Transport
JTE converges to very small
value under reverse bias.
104
Schottky Diode in Forward Bias
The
built-in
voltage
of
the
Schottky barrier diode, Vg(SB), is
about ½ as large as the built-in
voltage of the p-n junction diode,
Vg(pn).
105
Schottky Contact in Reverse Bias
106
Tunneling Current
107
Ratio of FE and TE Current
108
Ohmic Contact by Tunneling
109
RC vs. Doping & Temp.
110
RC vs. Doping
111