Lecture 5: HBT DC Properties

2014-01-28 1 Lecture 5, High Speed Devices 2014

•Basic operation of a (Heterojunction) Bipolar Transistor •Abrupt and graded junctions •Base current components •Quasi-Electric Field

Reading Guide: 143-162: 170-177

Basic Operation of a Bipolar Transistor

2014-01-28 2 Lecture 6, High Speed Devices 2014

N In

P

p+

+ In

0.5

3G

a 0.4

7A

s

n In

0.5

3G

a 0.4

7A

s

Emitter Base Collector

VBC VBE

1) Base-Collector junction reversed biased (very small current)

2) Emitter-Base junction forward biased.

3) Electrons/holes diffuse between emitter and base – controlled by VBE!

4) Electrons flow out of collector – IC(VBE).

5) Some electrons recombine in the base – hole current IB(VBE)

Common Emitter Operation

2014-01-28 3 Lecture 6, High Speed Devices 2014

0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

Vce

(V)

Kolle

kto

rstr

öm

(A

)

VBE=0.781V

VBE=0.798V

VBE=0.810V

VBE=0.816V

VBE=0.0V

VBE

+

-

VCE

+

-

IB

IC VCE(sat)

• VBE is the input voltage • IB the input current • IC the output current How do we calculate: IC(VBE) IB(VBE) Current gain b: IC/IB

-VBC=VCE-VBE

Homo&Graded Short-base Junctions – without recombination

2014-01-28 4 Lecture 5, High Speed Devices 2014

dn(0) dn(XB)=0 Emitter Base Collector

01exp

1exp0

0

0

kT

qVnXn

kT

qVnn

BCB

BE

d

d

No recombination tn ~ ∞ XB,E<<Ln,p

dp(0)

kT

qV

N

n

X

DqAI

kT

qV

N

n

X

DqAI

be

d

WG

i

E

pE

dBp

be

a

NG

i

B

nBdC

exp

exp

2

2

kT

E

N

N

X

X

D

D

I

I g

B

E

B

E

pE

nB

Bp

C expb

From the ni terms

IB usually dominated by recombination!

Large current gain even if NB>>NE

We will see that NB should be high: NB≈ 1020 cm-3

Typical HBT has b ~ 20-100.

x XB 0 XE

Example b for InGaAs/InP HBT – no recombination

2014-01-28 5 Lecture 5, High Speed Devices 2014

kT

E

N

N

X

X

D

D

I

I g

B

E

B

E

pE

nB

Bp

C expb

InP In0.53Ga0.47As

Eg (eV) 1.35 0.76

µn,min (cm2/Vs) 1500

µp,maj (cm2/Vs) 150

ND (cm-3) 1017 -

NA (cm-3) 1019

XE (nm) 150

XB (nm) 30

Base current components

2014-01-28 6 Lecture 5, High Speed Devices 2014

Emitter

SCR

Base

1 2 3 4 5

1. Back injected holes – negligible in a well designed HBT

2. Recombination in the space-charge-zone 3. Recombination in the base bulk region 4. Recombination at base contact interface 5. Recombination at base surface

Collector

IB

Every time an electron is ”lost” – replaced through the base current – IB.

Recombination terms for bulk base

2014-01-28 7 Lecture 5, High Speed Devices 2014

Radiative recombination Shockley-Read-Hall (SRH) Auger

n

AugerSRHrad

nnUUUU

t0

Base: ni<<n<<p

tn: total recombination life time

Radiative SRH Auger

The base of a HBT has high doping level NA > 1019 cm-3. tn can become very short! tn ≈ 1-100 pS for NA = 1019 - 1020 cm-3

InGaAs recombination time (tn)

Homo&Graded Short-base Junctions – with recombination

2014-01-28 8 Lecture 5, High Speed Devices 2014

n(0) n(XB)=0 Emitter Base Collector

01exp

exp1exp0

0

00

kT

qVnXn

kT

qVn

kT

qVnn

BCB

BEBE

No recombination tn ~ 0 XB<<Ln

p(0)

𝜁𝐷𝐶 =1

𝐷𝑛𝜏𝑛= 1/𝐿𝑛

𝜕2𝑛

𝜕𝑥2− 𝜁𝐷𝐶

2 𝑛 = 0

𝑛𝑑𝑐 𝑥 = 𝑛 0sinh 𝜁𝐷𝐶(𝑋𝐵 − 𝑥)

sinh 𝜁𝐷𝐶(𝑋𝐵)

sinh 𝑥 =𝑒𝑥 − 𝑒−𝑥

2

cosh 𝑥 =𝑒𝑥 + 𝑒−𝑥

2

x XB 0 XE

𝐼𝐶 = 𝑞𝐴𝑐𝐷𝑛 ∙𝑑𝑛

𝑑𝑥𝑥=𝑋𝐵 𝐼𝐸 = 𝑞𝐴𝑐𝐷𝑛 ∙

𝑑𝑛

𝑑𝑥𝑥=0

Homo&Graded Short-base Junctions: Current gain

2014-01-28 9 Lecture 5, High Speed Devices 2014

dn(0) dn(XB)=0 Emitter Base Collector

dp(0) 𝑛𝑑𝑐 𝑥 = 𝑛 0sinh 𝜁𝐷𝐶(𝑋𝐵 − 𝑥)

sinh 𝜁𝐷𝐶(𝑋𝐵)

sinh 𝑥 =𝑒𝑥 − 𝑒−𝑥

2

cosh 𝑥 =𝑒𝑥 + 𝑒−𝑥

2

𝛼𝑇 =𝐼𝐶𝐼𝐸≈

1

1 +𝑋𝐵2

2𝐷𝑛𝜏𝑛

𝛽 =𝐼𝐶𝐼𝐵≈

1

1 − 𝛼𝑇=2𝐷𝑛𝜏𝑛

𝑋𝐵2 ≡

𝜏𝑛𝜏𝑏

Base Transport Factor:

Common emitter current gain:

High Gain: • Thin Base • High mobility • Long life time

𝜏𝑏 =𝑄𝐵𝐼𝐶

= 𝑞𝐴𝐸 𝑛 𝑥 𝑑𝑥 𝑋𝐵0

𝐼𝐶 Base Transport Factor

𝑑

𝑑𝑥sinh 𝑥 = cosh (𝑥)

cosh 𝑥 ≈ 1 +𝑥2

2+ 𝑂 𝑥4

Ideality Factor – Bipolar Transistor

2014-01-28 10 Lecture 5, High Speed Devices 2014

kT

qV

N

n

X

DqAI be

a

NG

i

B

nBdC exp

2

kT

qVI be

baseB exp,Recombination inside neutral base layer

kT

qVI be

RLOB2

exp,

VBE

log

(I C

,I B)

Recombination inside space-charge region

𝐼𝐵 = 𝐼𝐵,𝑅𝐿𝑂 + 𝐼𝐵,𝑏𝑎𝑠𝑒

Total base current:

1 minute exercise – Gummel Plot

2014-01-28 11 Lecture 5, High Speed Devices 2014

VBE

log

(I C

,I B)

VBE b

How does b vary with Vbe?

Abrupt Junction

2014-01-28 12 Lecture 5, High Speed Devices 2014

kT

E

N

N

X

X

D

D

I

I v

B

E

B

E

pE

nB

Bp

C expb

Electron current set by potential spike and diffusion across base (complicated) Hole curent set by diffusion Potential barrier for electrons ~fbi

Potential barrier for holes ~fbi+Ev

fbi

fbi

Ev

Correction due to limited thermal velocity

2014-01-28 13 Lecture 5, High Speed Devices 2014

Diffusion is due to thermal motion of electrons: vdiff < vthermal

Jdiff = qn(XB)vthermal : Must be some electrons at XB for a diffusion current to flow!

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

7

Vd

iff (c

m/s

)

Base Thickness (nm)

n(0) n(XB)=0?? Base Collector

0,00 BdiffB

B

ndiff XqnvXnn

X

qDJ

thnB

ndiff

vDX

nqDJ

/

0

*

2

m

kTvth

vdiff=Dn/XB

Modern HBTs have XB<30 nm So this correction can be important! However – more complicated math!

vth

Calculation for InGaAs base

n(XB)=0

(1)

(1)

2 minute excercise

2014-01-28 14 Lecture 5, High Speed Devices 2014

0 XB

dn(x)

Consider two HBTs with two different minority carrier concentrations in the base: 1) Are the collector currents the same?

2) Which one has the highest b?

Dn=Dn

tn=tn

(2)

(1)

Base electric field

2014-01-28 15 Lecture 5, High Speed Devices 2014

Introduce an (quasi) electric field in the base region – diffusion and drift For a constant electric field, eB

xn

kT

q

dx

xdnqDJ B

nc

ecc JxJ )(

xX

kT

q

q

kT

qD

Jxn B

B

Bn

c e

eexp1

Same current – smaller n(x) as compared with pure diffusion!

Possible to achieve higher b

Lower QB better high frequency properties!