Chapter 2 Basic Physics of Semiconductors
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Transcript of Chapter 2 Basic Physics of Semiconductors
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1
Fundamentals of Microelectronics
CH1 Why Microelectronics?
CH2 Basic Physics of Semiconductors
CH3 Diode Circuits
CH4 Physics of Bipolar Transistors
CH5 Bipolar Amplifiers
CH6 Physics of MOS Transistors
CH7 CMOS Amplifiers CH8 Operational Amplifier As A Black Box
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2
Chapter 2 Basic Physics of Semiconductors
2.1 Semiconductor materials and their properties
2.2 PN-junction diodes
2.3 Reverse Breakdown
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CH2 Basic Physics of Semiconductors 3
Semiconductor Physics
Semiconductor devices serve as heart of microelectronics.
PN junction is the most fundamental semiconductor
device.
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CH2 Basic Physics of Semiconductors 4
Charge Carriers in Semiconductor
To understand PN junctions IV characteristics, it is
important to understand charge carriers behavior in solids,
how to modify carrier densities, and different mechanisms
of charge flow.
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CH2 Basic Physics of Semiconductors 5
Periodic Table
This abridged table contains elements with three to fivevalence electrons, with Si being the most important.
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CH2 Basic Physics of Semiconductors 6
Silicon
Si has four valence electrons. Therefore, it can form
covalent bonds with four of its neighbors.
When temperature goes up, electrons in the covalent bond
can become free.
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CH2 Basic Physics of Semiconductors 7
Electron-Hole Pair Interaction
With free electrons breaking off covalent bonds, holes are
generated.
Holes can be filled by absorbing other free electrons, so
effectively there is a flow of charge carriers.
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CH2 Basic Physics of Semiconductors 8
Free Electron Density at a Given Temperature
Eg, or bandgap energy determines how much effort isneeded to break off an electron from its covalent bond.
There exists an exponential relationship between the free-
electron density and bandgap energy.
3150
3100
32/315
/1054.1)600(
/1008.1)300(
/2
exp102.5
cmelectronsKTn
cmelectronsKTn
cmelectronskT
ETn
i
i
g
i
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CH2 Basic Physics of Semiconductors 9
Doping (N type)
Pure Si can be doped with other elements to change itselectrical properties.
For example, if Si is doped with P (phosphorous), then ithas more electrons, or becomes type N (electron).
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CH2 Basic Physics of Semiconductors 10
Doping (P type)
If Si is doped with B (boron), then it has more holes, or
becomes type P.
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CH2 Basic Physics of Semiconductors 11
Summary of Charge Carriers
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CH2 Basic Physics of Semiconductors 12
Electron and Hole Densities
The product of electron and hole densities is ALWAYS
equal to the square of intrinsic electron density regardless
of doping levels.
2
innp
D
i
D
A
i
A
N
np
Nn
N
nn
Np
2
2
Majority Carriers :
Minority Carriers :
Majority Carriers :
Minority Carriers :
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CH2 Basic Physics of Semiconductors 13
First Charge Transportation Mechanism: Drift
The process in which charge particles move because of anelectric field is called drift.
Charge particles will move at a velocity that is proportional
to the electric field.
Ev
Ev
ne
ph
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CH2 Basic Physics of Semiconductors 14
Current Flow: General Case
Electric current is calculated as the amount of charge in v
meters that passes thru a cross-section if the charge travel
with a velocity ofv m/s.
qnhWvI
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CH2 Basic Physics of Semiconductors 15
Epnq
qpEqnEJ
qnEJ
pn
pntot
nn
)(
Current Flow: Drift
Since velocity is equal to E, drift characteristic is obtainedby substituting V with E in the general current equation.
The total current density consists of both electrons andholes.
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CH2 Basic Physics of Semiconductors 16
Velocity Saturation
A topic treated in more advanced courses is velocitysaturation.
In reality, velocity does not increase linearly with electricfield. It will eventually saturate to a critical value.
E
v
Ev
bv
bE
sat
sat
0
0
0
0
1
1
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CH2 Basic Physics of Semiconductors 17
Second Charge Transportation Mechanism:
Diffusion
Charge particles move from a region of high concentrationto a region of low concentration. It is analogous to an everyday example of an ink droplet in water.
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CH2 Basic Physics of Semiconductors 18
Current Flow: Diffusion
Diffusion current is proportional to the gradient of charge
(dn/dx) along the direction of current flow.
Its total current density consists of both electrons and
holes.
dxdnqDJ
dx
dnAqDI
nn
n
)(dxdpD
dxdnDqJ
dx
dpqDJ
pntot
pp
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CH2 Basic Physics of Semiconductors 19
Example: Linear vs. Nonlinear Charge Density
Profile
Linear charge density profile means constant diffusion
current, whereas nonlinear charge density profile means
varying diffusion current.
L
NqD
dx
dnqDJ
nnn
dd
n
nL
x
L
NqD
dx
dnqDJ
exp
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CH2 Basic Physics of Semiconductors 20
Einstein's Relation
While the underlying physics behind drift and diffusion
currents are totally different, Einsteins relation provides a
mysterious link between the two.
q
kTD
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CH2 Basic Physics of Semiconductors 21
PN Junction (Diode)
When N-type and P-type dopants are introduced side-by-
side in a semiconductor, a PN junction or a diode is formed.
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CH2 Basic Physics of Semiconductors 22
Diodes Three Operation Regions
In order to understand the operation of a diode, it is
necessary to study its three operation regions: equilibrium,
reverse bias, and forward bias.
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CH2 Basic Physics of Semiconductors 23
Current Flow Across Junction: Diffusion
Because each side of the junction contains an excess ofholes or electrons compared to the other side, there existsa large concentration gradient. Therefore, a diffusioncurrent flows across the junction from each side.
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CH2 Basic Physics of Semiconductors 24
Depletion Region
As free electrons and holes diffuse across the junction, a
region of fixed ions is left behind. This region is known as
the depletion region.
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CH2 Basic Physics of Semiconductors 25
Current Flow Across Junction: Drift
The fixed ions in depletion region create an electric field
that results in a drift current.
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CH2 Basic Physics of Semiconductors 26
Current Flow Across Junction: Equilibrium
At equilibrium, the drift current flowing in one direction
cancels out the diffusion current flowing in the oppositedirection, creating a net current of zero.
The figure shows the charge profile of the PN junction.
ndiffndrift
pdiffpdrift
II
II
,,
,,
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CH2 Basic Physics of Semiconductors 27
Built-in Potential
Because of the electric field across the junction, there
exists a built-in potential. Its derivation is shown above.
n
p
p
p
p
x
x
p
pp
p
dpDdV
dx
dpqDpEq
2
1
n
p
p
p
pp
p
pDxVxV
dx
dpD
dx
dVp
ln)()(12
200ln,ln
i
DA
n
p
n
NN
q
kTV
p
p
q
kTV
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CH2 Basic Physics of Semiconductors 28
Diode in Reverse Bias
When the N-type region of a diode is connected to a higherpotential than the P-type region, the diode is under reversebias, which results in wider depletion region and largerbuilt-in electric field across the junction.
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CH2 Basic Physics of Semiconductors 29
Reverse Biased Diodes Application: Voltage-
Dependent Capacitor
The PN junction can be viewed as a capacitor. By varyingVR, the depletion width changes, changing its capacitancevalue; therefore, the PN junction is actually a voltage-dependent capacitor.
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CH2 Basic Physics of Semiconductors 30
Voltage-Dependent Capacitance
The equations that describe the voltage-dependent
capacitance are shown above.
0
0
0
0
12
1
VNNNNqC
V
V
CC
DA
DAsi
j
R
j
j
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CH2 Basic Physics of Semiconductors 31
Voltage-Controlled Oscillator
A very important application of a reverse-biased PN
junction is VCO, in which an LC tank is used in an
oscillator. By changing VR, we can change C, which also
changes the oscillation frequency.
LCf
res
1
2
1
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CH2 Basic Physics of Semiconductors 32
Diode in Forward Bias
When the N-type region of a diode is at a lower potentialthan the P-type region, the diode is in forward bias.
The depletion width is shortened and the built-in electricfield decreased.
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CH2 Basic Physics of Semiconductors 33
Minority Carrier Profile in Forward Bias
Under forward bias, minority carriers in each regionincrease due to the lowering of built-in field/potential.Therefore, diffusion currents increase to supply theseminority carriers.
T
F
fp
fn
V
VV
pp
0
,
,
exp
T
ep
en
V
V
pp
0
,
,
exp
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CH2 Basic Physics of Semiconductors 34
Diffusion Current in Forward Bias
Diffusion current will increase in order to supply the
increase in minority carriers. The mathematics are shown
above.
)1(exp
exp 0
T
F
T
D
pVV
V
VNn )1(exp
exp 0
T
F
T
A
nVV
V
VNp
)(2
pD
p
nA
n
isLN
D
LN
DAqnI )1(exp
T
F
stotV
VII
)1(exp
exp
)1(exp
exp00
T
F
T
D
T
F
T
Atot
V
V
V
V
N
V
V
V
V
NI
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CH2 Basic Physics of Semiconductors 35
Minority Charge Gradient
Minority charge profile should not be constant along the x-axis; otherwise, there is no concentration gradient and nodiffusion current.
Recombination of the minority carriers with the majoritycarriers accounts for the dropping of minority carriers asthey go deep into the P or N region.
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CH2 Basic Physics of Semiconductors 36
Forward Bias Condition: Summary
In forward bias, there are large diffusion currents of
minority carriers through the junction. However, as we godeep into the P and N regions, recombination currents from
the majority carriers dominate. These two currents add up
to a constant value.
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CH2 Basic Physics of Semiconductors 37
IV Characteristic of PN Junction
The current and voltage relationship of a PN junction is
exponential in forward bias region, and relatively constant
in reverse bias region.
)1(exp T
D
SD V
VII
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CH2 Basic Physics of Semiconductors 38
Parallel PN Junctions
Since junction currents are proportional to the junctions
cross-section area. Two PN junctions put in parallel are
effectively one PN junction with twice the cross-section
area, and hence twice the current.
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CH2 Basic Physics of Semiconductors 39
Constant-Voltage Diode Model
Diode operates as an open circuit if VD< VD,on and a
constant voltage source of VD,on if VD tends to exceed VD,on.
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CH2 Basic Physics of Semiconductors 40
Example: Diode Calculations
This example shows the simplicity provided by a constant-voltage model over an exponential model.
For an exponential model, iterative method is needed tosolve for current, whereas constant-voltage model requiresonly linear equations.
S
X
TXDXXI
IVRIVRIV ln
11
mAI
mAI
X
X
2.0
2.2
VV
VV
X
X
1
3
for
for
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CH2 Basic Physics of Semiconductors 41
Reverse Breakdown
When a large reverse bias voltage is applied, breakdown
occurs and an enormous current flows through the diode.
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Zener vs. Avalanche Breakdown
Zener breakdown is a result of the large electric field insidethe depletion region that breaks electrons or holes off theircovalent bonds.
Avalanche breakdown is a result of electrons or holescolliding with the fixed ions inside the depletion region.