EE130 Lecture 18, Slide 1Spring 2007

Lecture #18

OUTLINE

• pn junctions (cont’d)

– Deviations from the ideal I-V R-G current series resistance high-level injection

– Narrow-base diode

Reading: Chapter 6.2, 6.3

EE130 Lecture 18, Slide 2Spring 2007

Effect of R-G in Depletion Region

• The net generation rate is given by

• R-G in the depletion region contributes an additional component of diode current IR-G

levelenergy state- trap

and where

)(τ)(τ/)(

1/)(

1

11

2

T

kTEEi

kTEEi

np

i

E

enpenn

ppnn

npn

t

n

t

p

TiiT

dxt

pqAI

GR

x

xGR

n

p

EE130 Lecture 18, Slide 3Spring 2007

• For reverse bias greater than several kT/q,

in

ip

iGR n

p

n

nWqAnI 11

00

ττ2

1 τ where

τ2

Ip

In

EE130 Lecture 18, Slide 4Spring 2007

• For forward biases,

kTqViGR

AWeqAnI 2/

Ip

In

EE130 Lecture 18, Slide 5Spring 2007

Effect of Series Resistance

EE130 Lecture 18, Slide 6Spring 2007

High-Level Injection Effect

• As VA increases, the side of the junction which is more lightly doped will eventually reach HLI:

significant gradient in majority-carrier profile

Majority-carrier diffusion current reduces the diode current from the ideal

pop

non

pp

nn

or

(p+n junction)

(n+p junction)

EE130 Lecture 18, Slide 7Spring 2007

Summary: Deviations from Ideal I-V

Forward-bias current Reverse-bias current

EE130 Lecture 18, Slide 8Spring 2007

Derivation of Narrow-Base Diode I-V

• We have the following boundary conditions:

• With the following coordinate system:

• Then, the solution is of the form:

0)''( cn xxp)1()( / kTqVnonn

Aepxp

pp LxLx eAeAxp /2

/1)(

NEW:x' 0 0 x' '

x' c

EE130 Lecture 18, Slide 9Spring 2007

Applying the boundary conditions, we have:

Therefore

Note that so that

'

//

/'/'/

0 '0 ,)1()'( ''

''

cLxLx

LxxLxxkTqV

nn xxee

eeepxp

PcPc

PcPc

A

pcpc LxLx

n

eAeA

AAp/

2/

1

21

''

0

)0(

2sinh ee

''

'/

0 '0 ,/sinh

/'sinh)1()'( c

Pc

PckTqVnn xx

Lx

Lxxepxp A

EE130 Lecture 18, Slide 10Spring 2007

Excess Carrier Profiles: Limiting Cases

Long base (xc’):

pA

PcPc

pPcpPc

A

PcPc

PcPc

A

LxkTqVn

LxLx

LxLxLxLxkTqV

n

LxLx

LxxLxxkTqV

nn

eep

ee

eeeeep

ee

eeepxp

/'/0

//

/'//'//

0

//

/'/'/

0

)1(

)1(

)1()'(

''

''

''

''

EE130 Lecture 18, Slide 11Spring 2007

Narrow base (xc’0):

pn is a linear function of x

Jp is constant (no recombination)

'/

0'

'/

0

'

'/

0

'1)1(

/

/')1(

/sinh

/'sinh)1()'(

A

A

c

kTqVn

Pc

PckTqVn

Pc

PckTqVnn

x

xep

Lx

Lxxep

Lx

Lxxepxp

A

EE130 Lecture 18, Slide 12Spring 2007

• For a p+n junction, then:

where

)1(

/sinh

/cosh)1(

0

2

0

kTVq

Pc

PckTVq

D

i

P

p

xP

A

A

eI

Lx

Lxe

N

n

L

DqAJAI

Pc

Pc

D

i

P

P

Lx

LxNn

LDqAI

/sinh

/cosh'0 '

'2

Pc

PcPkTqV

npP

npP

Lx

LxxL

epqDJ

x

xpqDJ

A

/sinh

/cosh1

1

)(

/0

2cosh ee

EE130 Lecture 18, Slide 13Spring 2007

0 as sinh Note: 0 as 1cosh 2

• If xc’ << LP:

and

D

i

c

p

c

P

D

i

P

p

c

P

Pc

Pc

Pc

Pc

N

n

x

DqA

x

L

N

n

L

DqAI

x

L

Lx

Lx

Lx

Lx

22

0

2

/

/1

/sinh

/cosh

EE130 Lecture 18, Slide 14Spring 2007

Narrow (Short) Base Diode I-V Equation

Let

and

Then,

region type-p of width

region type-n of width

P

N

W

W

NpPP

PnNN

LxWW

LxWW

11 /0

/2

kTqVkTqV

AP

N

DN

Pi

AA eIeNW

D

NW

DqAnI

EE130 Lecture 18, Slide 15Spring 2007

Summary: Current Flow in pn Junctions

• The diode current is dominated by the term associated with the more lightly doped side:

p+n diode:

pn+ diode:

i.e. current flowing across junction is dominated by carriers injected from the more heavily doped side

sidenshort

siden long

)( 2

2

0

DN

Pi

DP

Pi

nP

NW

DqAn

NL

DqAn

xII

sidepshort

sidep long

)(2

2

0

AP

Ni

AN

Ni

pN

NW

DqAn

NL

DqAn

xII