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EE

Introduction to solid state electronics

Fall 2017

Chapter 5

Junctions

PN junction: Equilibrium conditions

The contact potential

Ec

Ev

EF

Ec

Ev

EF

p n

Particle Flow

Current Hole diffusion Hole drift

Electron drift

Electron diffusion

Before contact

After contact

p (^) n

Ec,p

Ev,p

EF,p

Ec,n EF,n Ev,n

Vn

Vp

Vo

qVo

W x

e

_ _ + +

Energy band

Electrostatic potential

0

PN junction: Equilibrium conditions

The contact potential

At equilibrium: 1. Total hole current across junction = 0

Jp(drift) + Jp(diffusion) = 0

2. Total electron current = 0

Jn(drift) + Jn(diffusion) = 0

 Built-in electric field e in space charge region W

 Equilibrium contact potential difference Vo across W

between n and p regions

Vo = energy per unit charge necessary to align Fermi level

throughout the device

PN junction: Equilibrium conditions

Determination of Vo

o i

A D n n

p n n

p o

n p n p

Vn

Vp

pn

pp

p

p

p p p

V

n

N N

q

kT

p n

p n

q

kT

p

p

q

kT

V

V V p p

kT

q

p x

dp x

dV

kT

q

dx

dp x

dx p x

dV x

kT q

dx

dp x

p x

x

D

dx

dp x

J x q p x x qD

ln ln ln 2

( ) ln ln

e

 e

qVo kT p

qVo kT n n

p

e

n

n

e and

p

p / /

Also  

PN junction: Equilibrium conditions

Space Charge at a junction W

**- - - - - -

• • -**

+ + + + p (^) + + n

-xpo 0 xno x

qND+

-qNA-

Q+=qAxnoND

Q=qAxpoNA_ Charge density

-xpo 0 xno x

Q  Q  qNA xpoA  qNDxnoA

Neutrality:

Gauss law:

Displacement vector ( ) = charge/unit area Poisson’s equation: Derive Gauss law wrt x

e





 

^ 

A

D

D A

q N dx

d

qN dx

d

q p n N N dx

d

e

e

e (^) ( )

Assuming p=n=0 in space charge (depletion) region

0 < x < xno (1)

-xpo < x < 0 (2)

Space Charge at a junction

PN junction: Equilibrium conditions

-xpo < x < 0

0 < x < xno

W V qN x W q N x W

x dx V V

dx

x dV

qN x qN x

N dx

q

d

d q N dx

o o D no A po

xno x (^) po n p

o D no A po

xpo A

o

xno D o

0 0

0

0



 

 





e

e e

e

e

e

e

e

2 2

1 W

N N

V q N N A D

o A D 

-xpo 0 xno x

qND+

-qNA-

Q+=qAxnoND

Q=qAxpoNA_

Charge density

-xpo 0 xno x d e ./dx=-qNA/є

Electric Field W

eo

d e ./dx=+qND/є

p

Potential Vn Vp^ Vo

n

(to prove using xno + xpo = W)

Current in PN junction: qualitative description

Forward & Reverse biased junctions at steady state

Current in PN junction: qualitative description

Forward & Reverse biased junctions at steady state

 V = 0 Vbarrier = Vo I = Idiff – Idrift,gen = 0

 V = Vf Vbarrier = Vo – Vf I = Idiff - Igen = +ive, large

 V = Vr Vbarrier = Vo + Vr I = Idiff – Igen = -ive, small

Current in PN junction: carrier injection

Forward biased PN junction at steady state

At Forward bias:

**- Excess minority carriers diffuse away to reach equilibrium concentration far away from junction

• No drift component
• Pure diffusion current**  qV kT xp Ln n po xp L p po

n n no xn Lp no qV kT xn Lp n xp n x e n e e

p x p x e p e e / / /

/ / /

( ) ( ) ( 1 )

( ) ( ) ( 1 )  

 

    

    



1. Hole diffusion current

( 0 ) ( 1 )

( ) ( ) ( )

/

/

    

     

no qV^ kT p

p n p

p p n

n p

xn Lp p n p

p n

p n p n

p e L

D p qA L

D I x qA

p x L

D p e qA L

D qA dx I x qAD dp x 

Current in PN junction and Quasi-Fermi levels

Forward biased PN junction at steady state

2. Electron diffusion current

Total current at any cross section of the structure is constant I(x) = I(0) = Ip(xn=0) – In(xp=0)

(  0 )      po( qV/^ kT  1 ) n

n p n

n n p n e L

D n qA L

D I x qA

( 1 )

( )( 1 )

/

/

 

  

qV kT o

qV kT po n

n no p

p

I I e

n e L

D p L

D I qA

At reverse bias V = Vr

o qVr kT I  Io e  I ( ^ / 1 )

Current in PN junction:

Forward biased PN junction at steady state

I Ip ( xp)In(xp) I Ip ( xn)In(xn) I

n n p n

qV kT xn Lp no p

p p n

I x I I x

p e e L

D

I x qA

 

p p n p

po qV kT xp Ln n

n n p

I x I I x

n e e L

I x qAD

 

Reverse biased PN junction at steady state

Carrier distribution and Quasi-Fermi levels

po qVr kT p po po

no

qVr kT n no no n x n e n

p x p e p      





( ) ( 1 )

/

/

/

/

  



 qVr kT p po po

qVr kT n no no n x n e

p x p e

In the depletion region:

More depletion than at equilibrium

pn ni^2 e(Fn^ Fp)^ /kT  0

W

Reverse bias breakdown

Mechanisms of Breakdown

1. Zener Breakdown  Very heavy doping at both sides of junction  1. Fermi levels very close to VB in p side and to CB in n side 2. Depletion region width W = very thin 3. Electric field in W reaches ≈ 106 V/cm  Field ionization  Tunneling of electrons from VB of p side to CB of n side  Occurs abruptly at V = Vzener

 Occurs at relatively low value ( Vz = a few volts)

Vz Vr

Zero bias Reverse bias

I-V

Reverse bias breakdown

Mechanisms of Breakdown

2. Avalanche Breakdown  In lightly doped n and/or p-side  Ionization of Si atoms in depletion region by impact with crossing energetic carriers  Carrier multiplication: if P = probability of ionization  nout = nin (1 + P + P^2 + P^3 + ..) = nin /(1-P)  Electron multiplication factor Mn = nout/nin = 1/(1-P)