Lecture 28

Lecture 28

OUTLINE

The BJT (cont’d)

• Small-signal model

• Cutoff frequency

• Transient (switching) response

Reading: Pierret 12; Hu 8.8-8.9

Small-Signal Model

Transconductance:

vber gmvbe

C

E

B

E

C

+

Common-emitter configuration,forward-active mode:

kTqVFFC

BEeII /0

qkT

IeI

dV

d

dV

dIg CkTqV

FFBEBE

Cm

BE

//

0

“hybrid pi” BJT small signal model:

EE130/230A Fall 2013 Lecture 28, Slide 2

R. F. Pierret, Semiconductor Device Fundamentals, Fig.12.1(a)

Small-Signal Model (cont.)

, mFBE

CFBED

C

FF

gdV

IdC

I

Q

BE

F

dV

dQC BED,

BEdep

s

W

AC

,BEJ,

m

dc

dc

m

BE

C

dcBE

B

gr

g

dV

dI

dV

dI

r

11

BEDBEDBEJ CCCC ,,,

where QF is the magnitude of minority-carrier charge stored in the base and emitter regions

forward transit time


ExampleA BJT is biased at IC = 1 mA and VCE = 3V. dc = 90, F = 5ps, T = 300K. Find (a) gm , (b) r , (c) C .

Solution:

(a)

(b) r = dc / gm = 90/0.039 = 2.3 k

(c)

siemens)(milliqkTIg Cm mS 39V

mA39

mV 26

mA 1)//(

ad)(femto fargC mF fF 19F109.1039.0105 1412


Cutoff Frequency, fT

The cutoff frequency is defined to be the frequency (f = /2) at which the short-circuit a.c. current gain equals 1:

CBEJFTac qIkTC

f/2

1at 1

,

CBEJFdc

BEJmFdcm

mm

b

c

bemc

bbbe

qIkTCj

Cgjg

g

Cjr

g

i

i

vgi

Cjr

iiv

//1

1

//1)(

/1admittanceinput

,

,

vber gmvbe

C

E

B

E

C

+


fT is commonly used as a metric for the speed of a BJT.

Si/SiGe HBT by IBM

For the full BJT equivalent circuit: ceBCJCBCJBEJF

T rrCqIkTCCf

,,, /2

1

To maximize fT:

• increase IC

• minimize CJ,BE, CJ,BC

• minimize re, rc

• minimize F


Base Widening at High IC: Kirk Effect

• At very high current densities (>0.5mA/m2), the density of mobile charge passing through the collector depletion region exceeds the ionized dopant charge density:

sat

CCCCdepsatC v

JqNqnqNqnvJ ,

increasing IC

For a NPN BJT:

The base width (W) is effectively increased (referred to as “base push out”)

F increases and hence fT decreases.

•This effect can be avoided by increasing NC increased CJ,BC , decreased VCE0

EE130/230A Fall 2013 Lecture 28, Slide 7 C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 8-18

Summary: BJT Small Signal Model

vber gmvbe

C

E

B

E

C

+

Hybrid pi model for the common-emitter configuration, forward-active mode:

m

dc

gr

mFBEJ gCC ,

qkT

Ig C

m /


BJT Switching - Qualitative


R. F. Pierret, Semiconductor Device Fundamentals, Figs. 12.3-12.4

Turn-on Transient Response

•The general solution is:

•Initial condition: QB(0)=0 since transistor is in cutoff

B

BBB

B QI

dt

dQ

BtBBBB AeItQ /)(

)1()( / BtBBBB eItQ

rL

CC

rt

tBBB

t

B

C

ttR

V

tteItQ

ti

B

01)(

)(

/

where IBB=VS/RS

BBB

LCCBr

IRV

t

/

1

1ln

EE130/230A Fall 2013 Lecture 28, Slide 10 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 12.5

Turn-off Transient Response

• The general solution is:

• Initial condition: QB(0)=IBBB

B

BBB

B QI

dt

dQ

BtBBBB AeItQ /)(

BtBBBB eItQ /1)(

sdt

tBBB

t

B

sdCC

C

tteItQ

ttI

tiB

/1)(

0

)(

BBB

tCCBsd

II

t1

ln


Reducing B for Faster Turn-Off• The speed at which a BJT is turned off is dependent on the

amount of excess minority-carrier charge stored in the base, QB, and also the recombination lifetime, B.

– By reducing B, the carrier removal rate is increased

Example: Add recombination centers (Au atoms) in the base


Schottky-Clamped BJT• When the BJT enters the saturation mode, the Schottky

diode begins to conduct and “clamps” the C-B junction voltage at a relatively low positive value. reduced stored charge in quasi-neutral base


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Lecture 28