pn junction - bu.edu.eg shoubra/electrical... · pn junction dr. abdallah hammad assistant...

PN Junction

Dr. Abdallah Hammad Assistant professor

Faculty of Engineering at Shoubra Benha University

ECE 111

Objective

• band diagram • pn-junction • depletion region • depletion width • built-in potential • biased junction

Selected areas covered in this lecture:

Dr. Abdallah Hammad (2012-2013)

Charter member of the family of all the solid state devices. Basic theory of operation of p-n junctions is essential to the understanding of all the other devices. Many of these devices also contain parasitic p-n junctions. It is essential to understand how these parasitic junctions affect the performance of the main device. What are p-n junctions? In part I of this course we focused on semiconductors which are either n-type or p-type. Now we will study the behavior of samples that are doped with different type of impurities in different parts of the sample.

P-N Junctions - Introduction


P-N Junction formation technology

There are three main methods of formation of p-n junctions: Diffusion

Start with an n-type wafer. Diffuse a p-type impurity at a high temperature. Or start with a p-type wafer and diffuse an n-type impurity. In both cases a p-n junction is formed near the surface of the wafer. Typical junction depths are a few microns.

Ion implantation Start with an n-type wafer and shoot ions of a p-type impurity. Ion energies typically 50 - 200 KeV. Alternatively, implant ions of an n-type impurity into a p-type substrate.

Epitaxy Start with an n-type wafer. Deposit a thin layer of p-type Si epitaxially (single crystal Si).

The first two techniques are extensively used in Si technology. Epitaxial junctions are more common in GaAs technology.


Step junction versus linearly graded junction

Step junction: If the conductivity type changes abruptly at some plane, then the junction is called a step junction or abrupt junction. Epitaxial method results in abrupt junctions. The plane x= xj at which the conductivity type changes is called the junction-plane or the metallurgical junction.

X<Xj, NA > ND (usually ND on the p-side is very small) X> Xj, ND >NA (usually NA n-side is very small)


Linearly graded junctions: Diffused junctions are generally linearly graded junctions. The plane X=Xj at which ND = NA is called the junction plane.

» For x < Xj, NA > ND (p-type) » For x > Xj, ND > NA (n-type) » At X=Xj, n= p= ni. Hole concentration (p= NA-ND)

increases linearly to the left of Xj. Electron (n= ND-NA) concentration increases linearly to the right of Xj


abrupt junction

p-type

NA

n-type

ND


pn-junction in thermal equilibrium

EFno

EC

EV

Ei

p-type

EFpo

n-type

EC

EV

Ei

Eg

EFno

EC

EV

Ei

p-type

EFpo

n-type

EC

EV

Ei

before connection

connection


0=dx

dEFfor thermal equilibrium consequence: the Fermi levels in the p- and n-type semiconductors must be equal

requirement of thermal equilibrium

EFn

EC

EV

Ei

ener

gy

EFp

EC

EV

Ei

biqV built-in potential (diffusion potential)

After connection


depletion region

EF

EC

EV

Ei

ener

gy

EF

EC

EV

Ei

char

ge d

ensi

ty

DqN

AqN−


depletion region ch

arge

den

sity

DqN

AqN−

depletion region

neutral region neutral region

metallurgical junction


depletion region po

tent

ial

char

ge d

ensi

ty

DqN

AqN−

E-fie

ld

biV


At equilibrium condition the drift current due to the electric field must exactly cancel the diffusion current due to the concentration gradient

0p p pdpJ qμ p qDdx

= − =E

0=+=dxdnqDnqμJ nnn E

Thermal equilibrium condition

1D Poisson’s equation:

[ ])()()()(

)()()(2

2

xnxpxNxNεq

εxρ

dxxd

dxxψd

AD

s

−+−−=

=−=−=E ψ - electrostatical potential

ρ

εs - space charge density

- semiconductor permittivity


εqN

dxxd

dxxψd A−=−=

)()(2

2 E for 0<≤− xxp

for nxx ≤<0ε

qNdx

xddx

xψd D=−=)()(

2

2 E

Poisson’s equation for abrupt junction

junction potential

DqN

AqN−

biV

nxpx−

x

x

x

ψ

ρ

E

0)(=

dxxdE


electric field distribution

DqN

AqN−

biV

nxpx−

x

x

x

εAqN

dxxd −

=)(E

1)( EE +−= xqNx A

ε

pA xqN

ε−=1E

( )pA xxqNx +−=

ε)(E

ψ

ρ

E


electric field distribution

DqN

AqN−

biV

nxpx−

x

x

x

εDqN

dxxd

=)(E

2)( EE += xqNx D

ε

nD xqN

ε−=2E

( )nD xxqNx −=

ε)(E

ψ

ρ

E


maximum electric field

nD

pA xqNxqN

εε−=−== )0(max EE

pDpA xNxN =consequence:

nx xpx−

potential distribution

dxsdx )()( ψ

−=E

∫−= dxxs )()( Eψ



DqN

AqN−

biV

nxpx−

x

x

x

( )dxxxqNx pA∫ +=

εψ )(

1

2

2ψ

ε+

+= xxxqN

pA

2

2

1pA xqN

εψ =

0)( =− pxψwith

( )22

)( xxqNx pA +=ε

ψ

ψ

ρ

E

0px x− < <



DqN

AqN−

biV

nxpx−

x

x

x

( )dxxxqNx nD∫ +=

εψ )(

2

2

2ψ

ε+

−=

xxxqNn

D

2

2

2nD

bixqNV

εψ −=

bin Vx =)(ψwith

( )22

)( xxqNVx nD

bi −−=ε

ψ

ψ

ρ

E

0 nx x< <


built-in potential

( )22

)( xxqNx pA +=ε

ψ( )22

)( xxqNVx nD

bi −−=ε

ψ

for 0=x both expressions

must give the same value:

22

22)0( p

An

Dbi xqNxqNV

εεψ =−=

( )22

2 pAnDbi xNxNqV +=ε


depletion width

( )22

2 pAnDbi xNxNqV +=ε nDpA xNxN =

+=

+=

A

DDn

A

nDAnDbi N

NNqxN

xNNxNqV2

22

2

22 εε

biDAD

An V

NNNN

qx 2

2+

=ε

pnd xxx +≡

biAAD

Dp V

NNNN

qx 2

2+

=ε

+=

+

= A

D

ApnA

D

pADbi N

NNqxxN

NxN

NqV2

222

22 εε


depletion width

biDAD

An V

NNNN

qx 2

2+

=ε

biAAD

Dp V

NNNN

qx 2

2+

=ε

( )

( )( )

biAD

DA

ADDA

DADAbi

biADA

Dbi

DAD

A

biADA

Dbi

DAD

Apnd

VNNNN

qNNNNNNNNV

q

VNNN

Nq

VNNN

Nq

VNNN

Nq

VNNN

Nq

xxx

+=

+++

=+

⋅+

⋅+

++

+=+=

εε

εε

εε

222

222

22

22

22

2222

( )bi

AD

DAd V

NNNN

qx +

=ε2


one-side abrupt junction

if

D

bind qN

εVxx 2=≅

( )bi

AD

DAd V

NNNN

qx +

=ε2

np xx <<


potential vs. carrier concentration

=−= 2ln

i

ADpnbi n

NNq

kTψψV

The derivation will be done in the lecture:


E [eV]

x

qVbi EFn EFp

EC

EV

EFi pqψ−

nqψ

n-type p-type

P N

unbiased junction

EFp EFn

x

q(Vbi-VF) E [eV]

EC EFi

n-type

p-type

P N + - IF

-qVF forward-biased junction


p n + - IR EV q(Vbi+VR)

E [eV]

EFp

EC

EFn qVR

reverse-biased junction

generalized depletion layer width

( )B

bid qN

VVεx −=

2

NB – lightly doped bulk concentration V - positive for FB, negative for RB


pn junction - bu.edu.eg shoubra/electrical... · pn junction dr. abdallah hammad assistant...

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