Download HBTs

Heterojunction Bipolar Transistors
for
High-Frequency Operation
D.L. Pulfrey
Department of Electrical and Computer Engineering
University of British Columbia
Vancouver, B.C. V6T1Z4, Canada
[email protected]
http://nano.ece.ubc.ca
1
Day 3A, May 29, 2008, Pisa
2
Outline
• 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?
Schematic of InGaP/GaAs HBT
• Epitaxial structure
• Dissimilar emitter and base materials
• Highly doped base
• Dual B and C contacts
• Identify WB and RB
3
4
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
- this allows reduction of both WB and RB
- this improves fT and fmax
• Key feature is the wide-bandgap emitter
An example of Bandgap Engineering
SHBT
e-
h+
Selecting an emitter for a GaAs base
2.5 AlP
AlAs
GaP
Bandgap, eV
2
1.5
GaAs
Si
AlGaAs / GaAs
InP
90
80
1
70
60
50
Ge
40
30
0.5
°
a = 5.6533 A
matched to GaAs
0
5.4
5.5
5.6
5.7
20
10
°
a = 5.8688 A
matched to InP
5.8
°
5.9
6
InAs
6.1
Lattice Constant, A
InGaP / GaAs
5
6
InGaP/GaAs and AlGaAs/GaAs
Draw band diagrams for different emitter
Preparing to compute IC
• Why do we show asymmetrical hemi-Maxwellians?
7
8
Current in a hemi-Maxwellian
Full Maxwellian distribution
Counter-propagating hemi-M's for
n0=1E19/cm3
/1E20
What is the current?
9
Density 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
10
Velocities
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 ?
Collector current: boundary conditions
11
12
Reduce our equation-set for the electron current
in the base
What about the recombination term?
13
Diffusion and Recombination in the base
Here, we need:
10
Diffusion length (cm)
10
10
10
10
-1
Le
Lh
-2
n( x ) 
n ( 0) 
n( x )  n0 B
n ( 0)  n 0 B
n( x )  n
-3
0B
WB
n ( 0)  n 0 B
Le
-4
WB
x L
e
-5
x
WB
WB
-6
10 16
10
10
17
In modern HBTs
WB/Le << 1 
18
10
Doping (cm-3)
10
19
10
and
20
WB
Le
x
WB
is constant
14
Collector current: controlling velocities
*
Diffusion (and no recombination) in the base:
-1
10
x 10
4
9
8
JC (Acm-2)
7
Note:
vR=infinity
vR =1e7 cm/s
6
- the reciprocal velocities
5
- inclusion of vR necessary in modern
HBTs
4
3
2
1
0 1
10
2
10
W B (nm)
10
3
* Gives limit to validity of SLJ
Comparing results
• What are the reasons for the difference?
15
Base current: components
(iv)
• Which IB components do we need to consider?
16
IC (A/cm2)
Base current components and Gummel plot
IC
IB (recombination)
IB (injection)
VBE (V)
• What is the DC gain?
17
18
Preparing for the high-frequency analysis
• Make all these functions of time and solve!
• Or, use the quasi-static approximation
19
The Quasi-Static Approximation
q(x, y, z, t' ) = f( VTerminals, t')
q(x, y, z, t' )  f( VTerminals, t < t')
20
Small-signal circuit components
gm = transconductance
go = output conductance
ib  g  vbe  g12 vce
g = input conductance
g12 = reverse feedback conductance
21
Recall
g12=dIb/dVce
next
Small-signal hybrid- equivalent circuit
What are the parasitics?
22
HBT Parasitics
• CEB and RB2 need explanation
23
Base-spreading resistance
y
24
25
Capacitance
Generally:
Q
C
V
V
+
+
1
-
-
2
Specifically:
Emitter-base junction-storage capacitance
E
WB2
B
26
C
QNB
QNE
QNC
WB1
VBE
C EB, j  
QE , j
VBE
C EB, j 
A
WB
+
• 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.
What is the voltage dependence of this cap?
Emitter-base base-storage capacitance: concept
E
B
C
QNB
QNE
QNC
VBE
C EB,b  
QE ,b
VBE
+
• 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.
27
Emitter-base base-storage capacitance: evaluation
28
B
QNB
For the case of no recombination
in the base:
n(x)


V
1
QE ,b (VBE )  q WB An0 p exp( BE )  n(WB )  qWB An(WB )
2
Vth


n(WB)
x
WB
Take
Q E,b
VBE

dQE ,b
dVBE
Hence C EB,b
n(0,VBE1 )  n0 p exp(VBE1 / Vth )
n(0,VBE , 2 )  n0 p exp(VBE 2 / Vth )
What is the voltage dependence of CEB,b ?
Base-emitter transit capacitance: evaluation
Q = 3q
qe = -2q
• What are
q0 and qd ?
• Where do
they come
from ?
29
fT 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.
30
Extrapolated fT
• Assumption:
• Conditions:
• Current gain:
• Extrapolated
fT:
31
Improving fT
• 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
32
33
Designing for high fT values
Why do collector delays
dominate ?
How does Si get-in on the act?
2.5 AlP
AlAs
GaP
Bandgap, eV
2
1.5
GaAs
Si
InP
90
80
1
70
60
50
Ge
40
30
0.5
°
a = 5.6533 A
matched to GaAs
0
5.4
5.5
5.6
5.7
20
10
°
a = 5.8688 A
matched to InP
5.8
°
Lattice Constant, A
5.9
6
InAs
6.1
34
35
Developing an expression for fmax
Assumption and
conditions:
36
Improving fmax
• Pay even more
attention to Rb and C
Final HF question:
How far behind are
Si MOSFETs?
37
HF MOS
What is this?