Heterojunction Bipolar Transistors for High-Frequency Operation

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2 Νοε 2013 (πριν από 3 χρόνια και 1 μήνα)

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1


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

pulfrey@ece.ubc.ca

http://nano.ece.ubc.ca

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 I
C

and I
B
?



Why are HBTs suited to high
-
frequency operation?



How are the capacitances reduced?


3

Schematic of InGaP/GaAs HBT



Epitaxial structure



Dissimilar emitter and base materials



Highly doped base



Dual B and C contacts



Identify W
B

and R
B

4

HETEROJUNCTION BIPOLAR TRANSISTORS



The major development in bipolar transistors (since 1990)




HBTs break the link between N
B

and





Do this by making different barrier heights for electrons and
holes




N
B

can reach 1E20cm
-
3


e
-

h
+



Key feature is the wide
-
bandgap emitter

-

this improves f
T

and f
max

-

this allows reduction of both W
B

and R
B

SHBT

An example of Bandgap Engineering

5

Selecting an emitter for a GaAs base

AlGaAs / GaAs

InGaP / GaAs

6

InGaP/GaAs and AlGaAs/GaAs

Draw band diagrams for different

emitter

7


Preparing to compute I
C




Why do we show asymmetrical hemi
-
Maxwellians?

8

Current in a hemi
-
Maxwellian

Full Maxwellian distribution

Counter
-
propagating hemi
-
M's for
n
0
=1E19/cm
3

/
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 k
x

and k
y

(and k
z

in 3
-
D) are large enough, k
-
space
is approximately spherical

Divide by V (volume) to get states/m
3

Use parabolic E
-
k (involves m*) to get
dE/dk

Divide by dE to get states/m
3
/eV

10

Velocities

Turn n(E) from previous slide into n(v) dv using



v
R
= 1E7 cm/s for GaAs

Currents associated with hemi
-
M's and M's

= 1E7 A/cm
2

for n
0
=6E18 /cm
3

*

What is J
e,total

?

11


Collector current: boundary conditions

12

Reduce our equation
-
set for the electron current
in the base

What about the recombination term?

13


Diffusion and Recombination in the base

In modern HBTs

W
B
/L
e

<< 1


and

is constant

Here, we need:

14


Collector current: controlling velocities

Diffusion (and no recombination) in the base:

-
1

Note:

-

the reciprocal velocities

-

inclusion of v
R

necessary in modern
HBTs

*

*
Gives limit to validity of SLJ

15


Comparing results



What are the reasons for the difference?

16


Base current: components



Which I
B

components do we need to consider?

(iv)

17


Base current components and Gummel plot



What is the DC gain?

I
C

(A/cm
2
)

V
BE

(V)

I
B

(injection)

I
B

(recombination)

I
C

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( V
Terminals
, t')

q(x, y, z, t' )


f( V
Terminals
, t < t')

20

Small
-
signal circuit components

g
m

= transconductance

g
o

= output conductance

g


= input conductance

g
12

= reverse feedback conductance

21

Recall

g
12
=dI
b
/dV
ce

next

22

Small
-
signal hybrid
-


equivalent circuit

What are the parasitics?

23


HBT Parasitics



C
EB

and R
B2

need explanation

24

y

Base
-
spreading resistance

25


Capacitance

V

+

+

-

-

Generally:

Specifically:

1

2

26

E

B

C

QNE

QNC

QNB


V
BE

+




Q
E,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 V
BE

(with E & C at AC
ground).



It can be regarded as a parallel
-
plate cap.

W
B2

W
B1

What is the voltage dependence of this cap?


Emitter
-
base junction
-
storage capacitance

27

E

B

C

QNE

QNC

QNB


V
BE

+




Q
E,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 V
BE

(with E & C at AC
ground).



It’s not a parallel
-
plate cap, and we only count one
carrier.


Emitter
-
base base
-
storage capacitance: concept

28

B

QNB

n(x)

x

n(W
B
)

W
B

For the case of no recombination
in the base:

What is the voltage dependence of C
EB,b

?


Emitter
-
base base
-
storage capacitance: evaluation

29


Base
-
emitter transit capacitance: evaluation

Q = 3q

q
e

=
-
2q



What are
q
0

and q
d
?



Where do
they come
from ?

30

f
T

from hybrid
-
pi equivalent circuit



g
0

and g


set to 0



f
T

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.

31


Extrapolated f
T



Assumption:



Conditions:



Current gain:



Extrapolated
f
T
:

32


Improving f
T



III
-
V for high g
m



Implant isolation to reduce C




Highly doped sub
-
collector and supra
-
emitter to reduce R
ec



Dual contacts to reduce R
c



Lateral shrinking to reduce C's

33

Designing for high f
T

values

Why do collector delays
dominate ?

34

How does Si get
-
in on the act?

35

Developing an expression for f
max


Assumption and
conditions:

36

Improving f
max




Pay even more
attention to R
b

and C


Final HF question:

How far behind are
Si MOSFETs?

37

HF MOS

What is this?