Principles of Semiconductor Devices-L30
Principles of Semiconductor Devices-L30
Principles of Semiconductor Devices-L30
www.nanohub.org
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Outline
1. Introduction
2. Equilibrium solution for heterojunction
3. Types of heterojunctions
yp j
4. Conclusions
“Heterostructure Fundamentals,” by Mark Lundstrom, Purdue
University, 1995.
Herbert Kroemer, “Heterostructure bipolar transistors and integrated
circuits,” Proc. IEEE , 70, pp. 13‐25, 1982.
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How to make a better Transistor
Polysilicon Emitter
Heterojunction bipolar transistor
2 − Eg , B β
n N C , B NV , B e ( Eg , E − Eg , B ) β
i, B
2
= − Eg , E β
≈e
n i, E N C , E NV , E e
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Heterojunction Bipolar Transistors
i) Wide gap Emitter HBT
p+
n n
base n+
emitter collector
EG1>EG2 EG2 EG2
ii) Double Heterojunction Bipolar Transistor
p+
n n
base n+
emitter collector
EG1>EG2 EG2 EG3>EG2
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Mesa HBTs
p+
n n
base n+
emitter collector
EG1>EG2 EG2 EG3>EG2
Mesa HBT
n
p+ base
n‐collector
ll
n+
semi‐insulating substrate
i i l ti bt t
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Applications
1)) Optical fiber communications
p
‐40Gb/s…….160Gb/s
2) Wideband, high‐resolution DA/AD converters
and digital frequency synthesizers
‐military radar and communications
3) Monolithic, millimeter‐wave IC’s (MMIC’s)
‐front ends for receivers and transmitters
future need for transistors with 1 THz power‐gain cutoff freq.
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Background
A heterojunction bipolar transistor
Kroemer
Kroemer
Schokley realized that HBT is possible, but Kroemer really
provided the foundation of the field and worked out the details
provided the foundation of the field and worked out the details.
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Outline
1. Introduction
2 Equilibrium solution for heterojunction
2. Equilibrium solution for heterojunction
3. Types of heterojunctions
4. Conclusions
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Topic Map
Equilibrium DC Small
Small Large
Large Circuits
signal Signal
Diode
Schottky
BJT/HBT
MOS
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Bandgaps and Lattice Matching
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Band Diagram at Equilibrium
∇ • D = q ( p − n + N D+ − N A− ) Equilibrium
∂n 1
= ∇ • J N − rN + g N
∂t q
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N‐Al0.3Ga0.7As: p‐GaAs (Type‐I Heterojunction)
ND NA
Vacuum Level
Vacuum Level
χ2
χ1 EC
EF EG ≈ 1.42 eV
EV
EG ≈ 1.80 eV
Ab t j ti HBT
Abrupt junction HBT
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Built‐in Potential: Boundary Condition @Infinity
Δ1 + χ1 + qVbi = Eg ,2 − Δ 2 + χ 2
qVbi
χ2
χ1 EC
Eg,2
EF Δ1
Δ2 EV
qVbi = Eg ,2 − Δ 2 − Δ1 + χ 2 − χ1
N AND
= k BT ln − Eg ,2 / k B T
+ ( χ 2 − χ1 )
NV ,2 NC ,1e
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Interface Boundary Conditions
E field
E‐field
Position
xn xp
κ1ε 0 E ( 0 ) = κ 2ε 0 E ( 0
− +
)
dV dV
κ1ε 0 = κ 2ε 0
dx 0− dx 0+
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Analytical Solution for Heterojunctions
Charge
E ( 0− ) =
qN D xn
xn xp ks , E ε 0
x
E (0 )=
+
qN A x p
k s , Bε 0
E‐field
⇒ N D xn = N A x p
x
E ( 0− ) xn E ( 0+ ) x p
Vbi = +
Potential 2 2
2
qN D xn 2 qN A x p
x = +
2 k s , E ε 0 2 k s , Bε 0
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Base Emitter Depletion Region
ND NA
xn xp
2ε 0 κ s , Eκ s , B N B
N E xn , BE = N B x p , BE xn = Vbi
q N E (κ s , E N B + κ s , B N E )
Vbi =
qN E xn , BE 2
+
qN B x p , BE 2 2ε 0 κ s , Eκ s , B N E
xp = Vbi
2κ s , Eε 0 2κ s , Bε 0 q N B (κ s , E N B + κ s , B N E )
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Outline
1. Introduction
2 Equilibrium solution for heterojunction
2. Equilibrium solution for heterojunction
3. Types of heterojunctions
4. Conclusions
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P‐Al0.3Ga0.7As : n‐GaAs (Type I junctions)
E0 Vacuum level
χ1 qV (x) qVBI
EC El
V jP
EG ≈ 1.80
1 80 eV
V ΔEC χ2
V jn
EF EC
EV
EG ≈ 1.42 eV
ΔEV EV
Depletion layer Depletion layer 18
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(AlInAs/InP) Type II Junctions
ND NA
Vacuum level
Vacuum level
χ2
χ1 EC
EF
EV
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N‐Al0.3Ga0.7As : n‐GaAs Junctions
‘Isotype Heterojunction’
EC EC
EG ≈ 1.42 E
eV
V
EG ≈ 1.80 eV EV
EV
Depletion Layer Accumulation Layer
E0 Field‐free vacuum level
χ1
EC
χ2
EG ≈ 0.72
0 72 eV
V
E FP
EV
EC
E Fn
EG ≈ 0.36 eV
EV
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P‐GaSb : n‐InAs (Type III)
EC ΔEC = 0.87 eV
EG ≈ 0.72 eV
EF EC
EV EG ≈ 0.36 eV
EV
Accumulation Layer! Accumulation Layer!
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Conclusion
1. Heterojunction transistors offer a solution to the
limitations of poly Si bipolar transistors
limitations of poly‐Si bipolar transistors.
2. Equilibrium solutions for HBTs are very similar to those of
normal BJTs.
3. Depending
Depending on the alignment, there could be different
on the alignment, there could be different
types of heterojuctions. Each has different usage.
4 We will discuss current transport in HBTs in the next class.
4. We will discuss current transport in HBTs in the next class
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