Reverse biased PN junction- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

bias RV Vtotal bi RV V V

WW

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n

0

( )

0

ap p

s

dn n

s

eNx x x x

E xeN

x x x x

a dmax p n

s s

eN eNE x x

2 1s bi R an

d d a

V V Nx

e N N N

2 s bi R d a

d a

V V N N

e N N

a p d nN x N xn pW x x

1 dn

a

NW x

N

d an

a

N Nx

N

2 1s bi R a d a

d d a a

V V N N NW

e N N N N

Reverse biased PN junctionenergy diagram

cE

cEvE

vE

FiE

FiE

FnE

FpE

ReV

total bi ReV e V V

Voltage-dependent capacitor

px

nx

with RV

with R RV dV

Voltage-dependent capacitor

px

nx

with RV

with R RV dV

dQ

dQ

differential R

dQC'

dV

nd

R R

dxdQC' eN

dV dV

deN

aeN

Example 5.5 Consider a gallium arsenide PN junction at room temperature. Determine the junction capacitance with a reverse bias voltage of 5 V.

& 15 3 16 3a dN 1 10 cm N 2 10 cm

2cross-sectional area A 410 cm

a dBbi 2

i

N NTV ln

e n

15 16

bi 26

1 10 2 10V 0.0259 ln 1.12V

1.8 10

Example 5.5 Consider a gallium arsenide PN junction at room temperature. Determine the junction capacitance with a reverse bias voltage of 5 V.

& 15 3 16 3a dN 1 10 cm N 2 10 cm

2cross-sectional area A 410 cm

s a d

bi R a d

e N NC A

2 V V N N

19 9 15 16

415 16

13.11.6 10 10 10 2 10

36C 102 1.12 5 10 2 10

0.380 pF

Forward biased PN junction

p n

DV

appliedE

space charg eE

- +

Basic model – thermal equilibrium

FE

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- - - - - -

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

p n+-

cE

cE

vE

vE

FiEbi biE eV

FiEbi biE eV

bi biE eV

FneVFpeV

Reverse biased PN junctionenergy diagram

cE

cEvE

vE

FiE

FiE

FnE

FpE

ReV

totaleV

Forward biased PN junctioncE

cE

vE

vE

FiE

FiE

FnEFpE

DeV

bi DeV eV

Schottky barrier junction

metal surface

Schottky barrier junctionEnergy levels before joining

metal surface

cE

vE

FiE

FE

FE

Schottky barrier junctionThermal equilibrium

cE

vE

FiE

FE

nx

W

bi biE eVSchottky barriermetal surface

FE -

electrons depart leaving a region of ions – Fermi energies lineup

Schottky barrier junctionReverse bias conditions

cE

vE

FE

nx

W

bi ReV eV

metal surface

FE

Schottky barrier

Schottky barrier junctionForward bias conditions

cE

vE

FE

DeV

metal surface

FE

Schottky barrierDV

electrons can easily move creating a current

Characteristics of a Schottky diode and a PN junction diode

VDVT

D sI I e 1

reverse

saturation current

thermal potential

BT

TV

e

Example 5.7 A silicon PN junction is forward biased at room temperature. Determine the voltage that is required to induce a particular diode current.

IV DD lnV IT s

VDVT

D sI I e 1

saturation current 14sI 5 10 A

desired current 3DI 4.25 10 A

VDVT

sI e

IDV V lnD T Is

3

14

4.25 10V 0.0259 lnD 5 10

0.652V

02

20

1 expB e

eVn e

Td V

dx

2

2

dVU

dx

d V dU dV dUU

dx dV dx dV

0

0

1 expB e

eVn e

TUdU dV

0

0

1 expB e

eVn e

TUdU dV

20

10

exp2

B e

B e

n e TU eVV C

e T

01

0

2expB e

B e

n e TdV eVU V C

dx e T

00 1

0

2expx B e

appliedB e

n e T eVV V V C dx

e T

00 1

0

2expx B e

appliedB e

n e T eVV V V C dx

e T

1applied

B e

eV

T

0

0

2n eVdVU

dx

00

00

2

applied

L

V

n edVdx

V0

0

2 appliedV

Ln e

You think that you had a bad day.

Simple three-dimensional unit cell

a

b

c