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Heterojunction Bipolar TransistorsHeterojunction Bipolar Transistors
forfor
High-Frequency OperationHigh-Frequency Operation
D.L. Pulfrey
Department of Electrical and Computer EngineeringUniversity of British ColumbiaVancouver, B.C. V6T1Z4, Canada
http://nano.ece.ubc.ca
Day 3A, May 29, 2008, Pisa
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OutlineOutline
• What are the important features of HBTs?
• What are the useful attributes of HBTs?
• What are the determining factors for IC and IB?
• Why are HBTs suited to high-frequency operation?
• How are the capacitances reduced?
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Schematic of InGaP/GaAs HBTSchematic of InGaP/GaAs HBT
• Epitaxial structure
• Dissimilar emitter and base materials
• Highly doped base
• Dual B and C contacts
• Identify WB and RB
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HETEROJUNCTION BIPOLAR TRANSISTORS
• The major development in bipolar transistors (since 1990)
• HBTs break the link between NB and
• Do this by making different barrier heights for electrons and holes
• NB can reach 1E20cm-3
e-
h+• Key feature is the wide-bandgap emitter
- this improves fT and fmax
- this allows reduction of both WB and RB SHBT
An example of Bandgap Engineering
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2.5
2
1.5
1
0.5
05.4 5.5 5.6 5.7 5.8 5.9 6 6.1
Lattice Constant, A
Ban
dg
ap, e
V
Si
Ge
GaAs
GaP
AlP
AlAs
InAs
InP90
8070
6050
4030
2010
a = 5.6533 Amatched to GaAs
°
°
a = 5.8688 Amatched to InP
°
Selecting an emitter for a GaAs baseSelecting an emitter for a GaAs base
AlGaAs / GaAs
InGaP / GaAs
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InGaP/GaAs and AlGaAs/GaAsInGaP/GaAs and AlGaAs/GaAs
Draw band diagrams for different emitter
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Preparing to compute IPreparing to compute ICC
• Why do we show asymmetrical hemi-Maxwellians?
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Current in a hemi-MaxwellianCurrent in a hemi-Maxwellian
Full Maxwellian distribution
Counter-propagating hemi-M's for n0=1E19/cm3
/1E20What is the current?
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Density of statesDensity of states
Recall:
In 1-D, a state occupies how much k-space?What is the volume in 3-D?
If kx and ky (and kz in 3-D) are large enough, k-space is approximately spherical
Divide by V (volume) to get states/m3
Use parabolic E-k (involves m*) to get dE/dk
Divide by dE to get states/m3/eV
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VelocitiesVelocities
Turn n(E) from previous slide into n(v) dv using
vR = 1E7 cm/s for
GaAs
Currents associated with hemi-M's and M's
= 1E7 A/cm2 for n0=6E18 /cm3
*
What is Je,total ?
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Collector current: boundary conditionsCollector current: boundary conditions
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Reduce our equation-set for the electron Reduce our equation-set for the electron current in the basecurrent in the base
What about the recombination term?
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Diffusion and Recombination in the baseDiffusion and Recombination in the base
In modern HBTs WB/Le << 1
and is constant
Here, we need:
1016
1017
1018
1019
1020
10-6
10-5
10-4
10-3
10-2
10-1
Doping (cm-3)
Diff
usio
n le
ngth
(cm
)
Le
Lh
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Collector current: controlling velocitiesCollector current: controlling velocities
Diffusion (and no recombination) in the base:
-1
Note:
- the reciprocal velocities
- inclusion of vR necessary in modern HBTs
*
* Gives limit to validity of SLJ10
110
210
30
1
2
3
4
5
6
7
8
9
10x 10
4
WB (nm)
J C
(Acm
-2)
vR
=infinityv
R =1e7 cm/s
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Comparing resultsComparing results
• What are the reasons for the difference?
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Base current: componentsBase current: components
• Which IB components do we need to consider?
(iv)
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Base current components and Gummel Base current components and Gummel plotplot
• What is the DC gain?
I C (
A/c
m2 )
VBE (V)
IB (injection)
IB (recombination)
IC
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Preparing for the high-frequency analysisPreparing for the high-frequency analysis
• Make all these functions of time and solve!
• Or, use the quasi-static approximation
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The Quasi-Static ApproximationThe Quasi-Static Approximation
q(x, y, z, t' ) = f( VTerminals, t')
q(x, y, z, t' ) f( VTerminals, t < t')
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Small-signal circuit components
gm = transconductance
go = output conductance
cebeb vgvgi 12
g = input conductance
g12 = reverse feedback conductance
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Recallg12=dIb/dVce
next
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Small-signal hybrid-Small-signal hybrid- equivalent equivalent circuitcircuit
What are the parasitics?
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HBT ParasiticsHBT Parasitics
• CEB and RB2 need explanation
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y
Base-spreading resistanceBase-spreading resistance
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Capacitance Capacitance
V
QC
V
+ +
- -
Generally:
Specifically:
1
2
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E B C
QNE
QNC
QNB
VBE+
BE
jEjEB V
QC
,
,
• QE,j is the change in charge entering the device through the emitter and creating the new width of the depletion layer (narrowing it in this example),
• in response to a change in VBE (with E & C at AC ground).
• It can be regarded as a parallel-plate cap.B
jEB W
AC
,
WB2
WB1
What is the voltage dependence of this cap?
Emitter-base junction-storage capacitanceEmitter-base junction-storage capacitance
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E B C
QNE
QNC
QNB
VBE+
BE
bEbEB V
QC
,,
• QE,b is the change in charge entering the device through the emitter and resting in the base (the black electrons),
• in response to a change in VBE (with E & C at AC ground).
• It’s not a parallel-plate cap, and we only count one carrier.
Emitter-base base-storage capacitance: Emitter-base base-storage capacitance: conceptconcept
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B
QNB
n(x)
xn(WB)
WB
)/exp(),0(
)/exp(),0(
202,
101
thBEpBE
thBEpBE
VVnVn
VVnVn
bEB
BE
bE
BBBth
BEpBBEbE
C
dV
dQ
WAnqWWnV
VnAWqVQ
,
,
BE
bE,
0,
Hence
V
Q Take
)()()exp(2
1)(
For the case of no recombination in the base:
What is the voltage dependence of CEB,b ?
Emitter-base base-storage capacitance: Emitter-base base-storage capacitance: evaluationevaluation
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Base-emitter transit capacitance: evaluation Base-emitter transit capacitance: evaluation
Q = 3q
qe = -2q
• What are q0 and qd ?
• Where do they come from ?
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30fT from hybrid-pi equivalent circuit
• g0 and g set to 0
• fT is measured under AC short-circuit conditions.
• We seek a solution for |ic/ib|2 that has a single-pole roll-off with frequency.
• Why?
• Because we wish to extrapolate at -20 dB/decade to unity gain.
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Extrapolated fExtrapolated fTT
• Assumption:
• Conditions:
• Current gain:
• Extrapolated fT:
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32 Improving fImproving fTT
• III-V for high gm
• Implant isolation to reduce C
• Highly doped sub-collector and supra-emitter to reduce Rec
• Dual contacts to reduce Rc
• Lateral shrinking to reduce C's
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Designing for high fDesigning for high fTT values values
Why do collector delays dominate ?
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How does Si get-in on the act?How does Si get-in on the act?2.5
2
1.5
1
0.5
05.4 5.5 5.6 5.7 5.8 5.9 6 6.1
Lattice Constant, A
Ban
dg
ap, e
V
Si
Ge
GaAs
GaP
AlP
AlAs
InAs
InP90
8070
6050
4030
2010
a = 5.6533 Amatched to GaAs
°
°
a = 5.8688 Amatched to InP
°
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Developing an expression for Developing an expression for ffmaxmax
Assumption and conditions:
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Improving fImproving fmaxmax
• Pay even more attention to Rb and C
Final HF question:
How far behind are Si MOSFETs?
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HF MOS HF MOS
What is this?