Tutorial -7

ELEC4510-fall/2011

huangtongde@ust.hk

PN junction and fabrication-I Grown, alloyed, diffusion, and implantation junction.

Implantation vs. Diffusion

Performed at low temperature, thus immunity to impurity

Abrupt

PN junction and fabrication-II

Fabrication of PN junction and Al electrode deposition Mask used to defined the junction region: SiO2, photoresist

Types of junction

Abrupt Graded

Two proles encountered most often in real devices Easy to analyze from device physics point of view

Good approximation for shallow, high concentration junctions (xj < 1m) and epitaxially grown junctions

Good approximation for deep junctions (xj > 3 m)

The PN Junction Diode

Quick view of PN junction properties: Rectify Increase exponentially at forward bias Saturate at reverse bias

As conduction electrons and holes diffuse across the junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.

Efn Efp

n

p

E-field

Built-in potential

PN junction-physics process

d

c

i

acbi

N

N

n

NN

q

kTVV lnln12

2

d

ckTVq

cdN

N

q

kTVeNNn ln11 N-region

2ln

i

adbi

n

NN

q

kT

2

2

2

ln2i

ackTVq

c

a

i

n

NN

q

kTVeN

N

nn P-region

PN junction-Built-in potential

Recall previous tutorial: built-in potential in non-uniformly doped semiconductor

Built-in potential

(Unit: Volts)

PN junction- Poissons Equation Gausss Law:

s: permittivity (~12o for Si) : charge density (C/cm3)

D x

E ( x ) E ( x + D x )

x

Poissons equation

In the depletion region on the N side:

bxqN

E

qN

dx

dE

si

D

si

D

si

(x)

x -qNA

qND

In the depletion region on the P side:

xaqN

E

qN

dx

dE

si

A

si

A

si

DA bNaN

a

-b

PN junction- E-field in depletion

PN junction- depletion width

W x xno po

x N x Npo a no d

xnoqNa

Esi

dai

da

NNn

NN

q

kTW

11ln

222

Know the E, Vbi,

Try to derive this expression for W

EXAMPLE: A P+N junction has Na=1020 cm-3 and Nd

=1017cm-3. What is a) its built in potential, b)Wdep , c)xN , and d) xP ?

Solution: a) b) c) d)

V 1cm10

cm1010lnV026.0ln

620

61720

2

i

adbi

n

NN

q

kT

m 12.010106.1

11085.812222/1

1719

14

d

bisdep

qNW

m 12.0 depN Wx

0 2.1m102.1 4 adNP NNxx

kTEEkTEE

c

kTEE

cfpfnfpcfnc eeNeNxn

/)(/)(/)(

P )(

kTqV

P

kTEE

P enenfpfn /

0

/)(

0

The minority carrier densities are raised

by eqV/kT

Ec

Efp

Ev

Efn

0N 0P

x

Ec

Efn

Efp

Ev

x

Efn

xN xP

PN junction- Minority Carrier Injection

1)( kT

qV

pppp

a

ennxnn

The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.

The minority-carrier concentrations at the edges of the depletion region are changed by the factor

60 mV rule

np(x)

np0

A

ip

N

nn

2

0 Equilbrium concentration

of electrons on the P side:

edge of depletion region

x'

PN junction- Minority Carrier Injection

kTqVDe/

EXAMPLE: Carrier Injection

A PN junction has Na=1019cm-3 and Nd=10

16cm-3. The applied voltage is 0.6 V. Question: What are the minority carrier concentrations at the depletion-region edges? Solution:

Question: What are the excess minority carrier concentrations? Solution:

-311026.06.0

0 cm 1010)( eenxnkTVq

PP

-314026.06.04

0 cm 1010)( eepxpkTVq

NN

-31111

0 cm 101010)()( PPP nxnxn-314414

0 cm 101010)()( NNN pxpxp

PN junction- Minority Carrier Injection

p

p

p

L

xx

npppL

xpqD

L

expqD

dx

xpdqDxJ

p

n

)(= )(=

)()(

)()(=)()( npnnpppn XJxJxJxJJ

The current flowing across the junction is comprised of hole diffusion and electron diffusion components:

Negligible drift current

n

n

n

L

xx

pnnnL

xnqD

L

exnqD

dx

xndqDxJ

n

p

)(= )(=

)()(

1= 1=

2 kT

qV

pd

p

na

ni

kT

qV

p

np

n

pnaa

eLN

D

LN

DqAne

L

pD

L

nDqAAJI

PN junction- Injected minority carrier distribution

Ideal diode equation:

Questions

As the mid-term approaches, I received lots of emails asking question in notes and HW

In order to give you more detailed explanation, please bring your questions and discuss with me after tutorial