Institute of Solid State PhysicsTechnische Universität Graz

6. pn - Junctions

Nov. 7, 2018

Institute of Solid State Physics

pn junctions Technische Universität Graz

p n

pn junctions are found in:diodessolar cellsLEDsisolation JFETsbipolar transistorsMOSFETssolid state lasers

pn junction

p-type n-type

Ec

Ev

EF

Ec

Ev

EF

isolated semiconductors

exp v Fv

B

E Ep Nk T

exp F cc

B

E En Nk T

valid for both n and p doping

ln cF c B

D

NE E k TN

ln vF v B

A

NE E k TN

pn junction

p-type

n-typeEc

Ev

EF

Ec

Ev

semiconductors in contactelectrons flow from n to p

ln cF c B

D

NE E k TN

ln v

F v BA

NE E k TN

ln cF v g B

D

NE E E k TN

pn junction semiconductors in contact

Abrupt junction: the doping changes abruptly from p to n

Built-in voltage

FE

bieV

cE

vE

p n

FE

bieV

cE

vE

p n

Built-in voltage Vbi

, , , ,

ln lnc vbi g B B

D n A n A p D p

N NeV E k T k TN N N N

, , , ,

ln c vbi g B

D n A n A p D p

N NeV E k TN N N N

ln vF vp B

A

NE E k TN

ln ccn F B

D

NE E k TN

gE

Vbi

, , , ,

ln c vbi g B

D n A n A p D p

N NeV E k TN N N N

, , , ,2ln D n A n A p D p

bi Bi

N N N NeV k T

n

2ln D Abi B

i

N NeV k Tn

for ND,n - NA,n = ND and NA,p - ND,p = NA

22 exp lng ii v c g B

B v c

E nn N N E k Tk T N N

Vbi

Can Vbi perform work?

p n

E

-

-

-

+

+

+

+

+

+

-

-

-

- - - - -

- - - - + + +

+ + +

p and n profiles

exp F cc

B

E En Nk T

exp v F

vB

E Ep Nk T

p

xn

x

-xp

xn

depletion region

depletion approximation

FE

bieV

cE

vE

p n

space charge

x

-xp

xn

NAxp = NDxn

+

-

eND

eNA

FE

bieV

cE

vE

p n

electric field

x

E-xp xn

E pushes the holes towards p and the electrons towards n

dEdx

Ap

eNE x x

Dn

eNE x x

x

-xp

xn

+

-

eND

eNA

maxA pD n eN xeN xE

E

Gauss's law in 1-D is

potential

x

E-xp xn

dV Edx

2

2

02

02

Ap p

Dn n

eN xV xx x x

eN xV xx x x

Ap

eNE x x

Dn

eNE x x

2 2( ) (0) 0 ( )2 2

A Dp p n n

eN eNV x x V V x x

potential

dV Edx

2 2

2 2A p D n

bi

eN x eN xV

electron energies are plotted in band diagram

Depletion width 2 2

2ln2 2

A p D nB D Abi

i

eN x eN xk T N NVe n

A p D n D p A nN x N x N W x N W x W

D Ap n

A D A D

N W N Wx xN N N N

2

2D A

biD A

N NeV WN N

2 D A bi

D A

N N VW

eN N

light doping => wide depletion width

Depletion width

W

Vbi ~ 1V

W ~ 1m

Emax ~ 104 V/cm

vsat ~ 107 cm/sec

The electric field pushes the electrons towards the n-region and the holes towards the p-region.

Diffusion sends electrons towards the p-region and holes towards the n-region.

linearly graded junction

( ) ( )D Ae N x N x eax

2 22

max 2 2 8ea W eaWE dx x E

2 3

2 2 3ea W xV Edx x

3

12bieaWV

x

ND - NA

W/2-W/2

-W/2 W/2

Area = Vbi

Vbi

EF

Ec

Ev

EgeVbi

http://lampx.tugraz.at/~hadley/psd/L6/linearly_graded.html

Isolation

Solar cell

pn

hf > Eg

Light creates an electron-hole pair in the depletion region. The electric field sweeps the electrons towards the n-region and the holes towards the p-region.

Light emitting diode

pn

hf = Eg

Electrons and holes are injected into the depletion region by forward biasing the junction. The electrons fall in the holes. For direct bandgap semiconductors, photons are emitted. For indirect bandgap semiconductors, phonons are emitted.

Heterojunctions

Bipolar transistor

p

MOSFET

functions as a switch~ 1 billion /chip

Metal Oxide Semiconductor Field Effect Transistor

http://en.wikipedia.org/w

iki/Image:M

osfetlinear.sv

Varactor

nj bi RC V V

abrupt: n = 1/2linearly graded: n = 1/3

n = 1/(m+2)

mD A oN N x x

Capacitance-voltage characteristics

-2 F mjCW

2 D A bi

j D A

N N V VW

C eN N

abrupt junction:

a one sided abrupt junction in reverse bias:

2

21 bi

j D

V VC e N

p+ n

specific capacitance

Capacitance-voltage characteristics

a one sided abrupt junction in reverse bias:

2

21 bi

j D

V VC e N

slope gives impurity concentration and the intercept gives Vbi

p+ n2

1

jC

-V

2slopeDe N

-Vbi

diode fabrication