Lecture 9 OUTLINE pn Junction Diodes – Electrostatics (step junction) Reading: Pierret 5; Hu...

Lecture 9

OUTLINE• pn Junction Diodes– Electrostatics (step junction)

Reading: Pierret 5; Hu 4.1-4.2

pn Junctions• A pn junction is typically fabricated by implanting or diffusing

donor atoms into a p-type substrate to form an n-type layer:

EE130/230A Fall 2013 Lecture 9, Slide 2

• A pn junction has a rectifying current-vs.-voltage characteristic:

C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-2

C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-1

Terminology

Doping Profile:

Lecture 9, Slide 3EE130/230A Fall 2013

Net

R.F. Pierret, Semiconductor Fundamentals, Figure 5.1

Idealized pn Junctions

Lecture 9, Slide 4

• In the analysis going forward, we will consider only the net dopant concentration on each side of the pn junction:

NA net acceptor doping on the p side: (NA-ND)p-side

ND net donor doping on the n side: (ND-NA)n-side

EE130/230A Fall 2013


Electrostatics (Step Junction)

Band diagram:

Electrostatic potential:

Electric field:

Charge density:

Lecture 9, Slide 5EE130/230A Fall 2013R.F. Pierret, Semiconductor Fundamentals, Figure 5.4

“Game Plan” to obtain (x), E(x), V(x)1. Find the built-in potential Vbi

2. Use the depletion approximation (x)(depletion widths xp, xn unknown)

3. Integrate (x) to find E(x)Apply boundary conditions E(-xp)=0, E(xn)=0

4. Integrate E(x) to obtain V(x)Apply boundary conditions V(-xp)=0, V(xn)=Vbi

5. For E(x) to be continuous at x=0, NAxp = NDxn

Solve for xp, xn Lecture 9, Slide 6EE130/230A Fall 2013

Built-In Potential Vbi

i

A

isidepFi

n

NkT

n

pkTEE

ln

ln)(

sideniFsidepFisiden Ssidep Sbi )()( EEEEqV

i

D

isideniF

n

NkT

n

nkTEE

ln

ln)(

For non-degenerately doped material:


R.F. Pierret, Semiconductor Fundamentals, Figure 5.4a

What if one side is degenerately doped?

sideniFsidepFibi EEEEqV )()(

p+n junction n+p junction


The Depletion ApproximationIn the depletion region on the p side, = –qNA

Lecture 9, Slide 9

ps

A

s

A xxqN

CxqN

x

1)(

In the depletion region on the n side, = qND

xxqN

CxqN

x ns

A

s

D

1)(

EE130/230A Fall 2013


Electric Field Distribution

The electric field is continuous at x = 0

NAxp = NDxn

Lecture 9, Slide 10

xxn-xp

E(x)

EE130/230A Fall 2013

On the p side:

Choose V(-xp) to be 0

On the n side:

12)(

2)( Dxx

qNxV p

s

A

22

2 )(2

)(2

)( xxqN

VDxxqN

xV ns

Dbin

s

D

Lecture 9, Slide 11

Electrostatic Potential Distribution

V(xn) = Vbi

EE130/230A Fall 2013

• At x = 0, expressions for p side and n side must be equal:

• We also know that NAxp = NDxn

Lecture 9, Slide 12

Derivation of Depletion Width

EE130/230A Fall 2013

Depletion Width• Eliminating xp, we have:

• Eliminating xn, we have:

• Summing, we have:

)(

2

DAD

Abisn NNN

N

q

Vx

)(

2

DAA

Dbisp NNN

N

q

Vx

DA

bispn NNq

VWxx

112


Depletion Width in a One-Sided Junction

If NA >> ND as in a p+n junction:

What about a n+p junction?

where density dopantlighter NNN AD

1111

nD

bis xqN

VW

2

0 ADnp NNxx

qNVW bis2


Peak E-Field in a One-Sided Junction

biVWdx )0(2

1

s

bibi qNV

W

V

22

)0(

bis V

qNW

2


V(x) in a One-Sided Junction

Lecture 9, Slide 16

biDA

D VNN

NV

)0(

p side n side2)(

2)( p

s

A xxqN

xV

2)(2

)( xxqN

VxV ns

Dbi

EE130/230A Fall 2013

Example: One-Sided pn JunctionA p+n junction has NA=1020 cm-3 and ND =1017cm-3. Find (a) Vbi (b) W (c) xn and (d) xp .

i

DGbi n

N

q

kT

q

EV ln

2

D

bis

qN

VW

2

Wxn

ADnp NNxx


Voltage Drop across a pn Junction

Note that VA should be significantly smaller than Vbi in order for low-level injection conditions to prevail in the quasi-neutral regions.



Effect of Applied Voltage

Lecture 9, Slide 19

DAAbi

s

NNVV

qW

11)(

2

EE130/230A Fall 2013R.F. Pierret, Semiconductor Fundamentals, Figure 5.11

Summary• For a non-degenerately-doped pn junction:

Built-in potential

Depletion width

• For a one-sided junction:

Built-in potential

Depletion width

2ln

i

ADbi n

NN

q

kTV

DA

Abispn NNq

VVxxW

112

i

Gbi n

N

q

kTEV ln

2

qN

VVW Abis

2

Lecture 9, Slide 20

WNN

Nx

DA

Dp W

NN

Nx

DA

An

EE130/230A Fall 2013

Linearly Graded pn Junction


Lecture 9 OUTLINE pn Junction Diodes – Electrostatics (step junction) Reading: Pierret 5; Hu...

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