Download Solid State Physics

Intro to Semiconductors and p-n
junction devices
Homework: Chapter 11 Krane
Problems: 13, 14, 15, 16, 17, 23, 28, 33, 34, 35
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pn Junction: Band Diagram




Due to diffusion, electrons
move from n to p-side and
holes from p to n-side.
Causes depletion zone at
junction where immobile
charged ion cores remain.
Results in a built-in electric
field (103 to 105 V/cm),
which opposes further
diffusion.
Note: EF levels are aligned
across pn junction under
equilibrium.
EC
EF
EV
n-type electrons
pn regions
“touch” &
free
carriers
move
EF
holes
p-type
pn regions in equilibrium
EC
EF
EV
––
–
+– – ––
+
+ +
+ + +–– –– –
+ ++
++
Depletion Zone
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Forward Bias and Reverse Bias


Forward Bias : Connect positive of the
positive end to positive of supply…negative of
the junction to negative of supply
Reverse Bias: Connect positive of the junction
to negative of supply…negative of junction to
positive of supply.
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PN Junction: Under Bias
• Forward Bias: negative voltage on n-side promotes diffusion of
electrons by decreasing built-in junction potential  higher current.
• Reverse Bias: positive voltage on n-side inhibits diffusion of electrons
by increasing built-in junction potential  lower current.
Equilibrium
Forward Bias
Reverse Bias
p-type
n-type
e–
p-type
n-type
–V
e–
Majority Carriers
p-type
n-type
+V
e–
Minority Carriers
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pn Junction: IV Characteristics

Current-Voltage Relationship
I  I o [e



eV / kT
 1]
Forward Bias: current
exponentially increases.
Reverse Bias: low leakage
current equal to ~Io.
Ability of pn junction to pass
current in only one direction is
known as “rectifying”
behavior.
Forward
Bias
Reverse
Bias
Manifestly not a resistor: V=IR
Not Ohm’s law
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N-channel MOSFET
Gate
Drain
Source
n
gate
oxide insulator
p
n
ID
• Without a gate-to-source voltage applied, no current
can flow between the source and drain regions.
• Above a certain gate-to-source voltage (threshold
voltage VT), a conducting layer of mobile electrons is
formed at the Si surface beneath the oxide. These
electrons can carry current between the source and
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drain.
Metal-Oxide-Semiconductor FET
How does it work? There is no conduction between the source and
drain normally (VGS = 0) because regardless of what voltage VDS
you apply there is a reverse biased PN junction. Even apply a
voltage VGS does not appear from the structure to have an obvious
effect since it is not even attached - there is a thin SiO2
insulating layer in between!
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Metal-Oxide-Semiconductor FET(2)
However when you apply a
positive voltage the oxide
behaves like a capacitor since positive charge
builds up on one side, there
must be an equal and
opposite charge on the
other side.
This charge must come from the substrate. Since it is P-type there are
not many electrons but those that are present are all sucked up to the
gate oxide. This creates a region that is very thin, but very rich in
electrons, converting P-type to N-type locally. This “channel” is
enhanced by applying higher positive biases.
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IG vs. VGS Characteristic
Consider the current IG (flowing into G) versus VGS :
S
IG
V +
IG
G
oxide
semiconductor
D
V
+DS
GS
always zero!
The gate is insulated from
the semiconductor, so there
is no significant steady gate
current.
VGS
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ID vs. VDS Characteristics
Next consider ID (flowing into D) versus VDS, as VGS is
varied:
S
V +
G
oxide
semiconductor
ID
D V
+DS
GS
ID
VGS > VT
zero if VGS <
VT
VDS
Above threshold (VGS > VT):
“inversion layer” of electrons
appears, so conduction between
S and D is possible
Below “threshold” (VGS < VT):
no charge  no conduction
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The MOSFET as a Controlled Resistor

The MOSFET behaves as a resistor when VDS is low:

Drain current ID increases linearly with VDS

Resistance RDS between SOURCE & DRAIN depends on VGS
• RDS is lowered as VGS increases above VT
NMOSFET Example:
ID
VGS = 2 V
VGS = 1 V > VT
VDS
IDS = 0 if VGS < VT
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ID vs. VDS Characteristics
The MOSFET ID-VDS curve consists of two
regions:
1) Resistive or “Triode” Region: 0 < VDS < VGS  VT
VDS 
W 
ID
VGS  VT 
VDS


L 
2 
where k n   n Cox
 k n
2) Saturation Region:
VDS > VGS  VT
kn W
2
VGS  VT 
I DSAT 
2 L
where kn   nCox
“CUTOFF” region: VG < VT
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MOSFET regions of operation
Cutoff: VGS <= VT
ID = 0
Resistive: ID ~
(VGS – VT)VDS
Saturation: ID ~
(VGS – VT)2
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MOSFET Uses
A MOSFET can be used as
A linear amplifier: Input voltage applied between
gate and source; output voltage
appears between source and drain
or
An electronic switch: Switches between no
current conduction between source and drain,
and heavy conduction between source and
drain as voltage applied between gate and
source changes from low to high
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Importance


The transistor is probably the most important
invention of the 20th century….
Transistors are central to the Integrated Circuit,
and therefore, all electronic devices of the
information age, such as: pc’s, cellular phones,
ipods, pda’s, intelligent cars and buildings…….
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