P-N Junctions

Physical aspects of pn junctions

Mathematical models

• Depletion capacitance• Breakdown characteristics

• Basis for other devices Circuit Symbol

+ V -

PHYSICAL ASPECTS OF THE PN JUNCTION

Metallurgical Junction

p-type semiconductor n-type semiconductor

iD+ -vDDepletion region

x

p-type semicon- ductor

n-type semicon- ductor

iD+

-W1 0

W

-Dv -

W2Fig. 1.2-1

P-N Junctions

N-typeN

D

P-typeN

A

P-N Junctions

N-typeN

D

P-typeN

A

P-N Junctions

N-typeN

D

P-typeN

A

Depletion Layer or Region

P-N Junctions

N-typeN

D

P-typeN

A

Depletion Layer or Region

ChargeDensity

qND

-qNA

P-N Junctions

N-typeN

D

P-typeN

A

Depletion Layer or Region

ChargeDensity

qND

-qNA

BandDiagram

Electrostatics in PN Junction

ChargeDensity

qND

-qNA

x

Q = x

Electrostatics in PN Junction

ChargeDensity

qND

-qNA

x

xElectric Field

Gauss' Law in 1 Dimension: Electric Field = Q /

Q = x

Electrostatics in PN Junction

Vbi = Built

in Voltage

ChargeDensity

qND

-qNA

x

x

x

Electric Field

ElectronPotential

Gauss' Law in 1 Dimension: Electric Field = Q /

Q = x

Why is this the Equilibrium Condition?

Vbi = built-in voltage

= kT ln ( )NAN

D

ni2

Why is this the Equilibrium Condition?

Vbi = built-in voltage

= kT ln ( )NAN

D

ni2

Too much Vbi

Too little Vbi

P-N Junctions --- Diodes

N-typeN

D

P-typeN

A

First-Principles Model

P-N Junctions --- Diodes

N-typeN

D

P-typeN

A

First-Principles Model

P-N Junctions --- Diodes

N-typeN

D

P-typeN

A

First-Principles Model

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

10

20

30

40

50

60

70

80

90

100

Diode voltage (V)

Dio

de

cu

rre

nt

(nA

)

P-N Junctions --- Diodes

N-typeN

D

P-typeN

A

First-Principles Model

Applying Voltage to a Diode

- V +F

P

FN

Forward Bias

Forward Bias

Applying Voltage to a Diode

- V ++ V -F

P

FN

FN

FP

Forward Bias

Reverse Bias

Capacitance in pn Junctions

W1 =

2si(o-vD)NDqND(NA+ND)

W2 = 2si(o-vD)NAqND(NA+ND)

o = kTq ln

NAND

ni2 = UT ln

NAND

ni2

Capacitance in pn Junctions

W1 =

2si(o-vD)NDqND(NA+ND)

W2 = 2si(o-vD)NAqND(NA+ND)

o = kTq ln

NAND

ni2 = UT ln

NAND

ni2

Cj = AsiqNAND2(NA+ND)

1o-vD

= Cj0

1 - vDo

Capacitance in pn Junctions

W1 =

2si(o-vD)NDqND(NA+ND)

W2 = 2si(o-vD)NAqND(NA+ND)

o = kTq ln

NAND

ni2 = UT ln

NAND

ni2

Cj = AsiqNAND2(NA+ND)

1o-vD

= Cj0

1 - vDo

-3 -2.5 -2 -1.5 -1 -0.5 0 0.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Diode voltage (V)

Ca

pa

cita

nce

(fF

) Cj0

Breakdown Voltage

Breakdown Voltage

Caused byAvalancheMultiplication

Due to reachinga critical electric field