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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:

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

EE130/230M Spring 2013

Lecture 9, Slide 2

Idealized pn Junctions

- 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

EE130/230M Spring 2013

Lecture 9, Slide 4

Electrostatics (Step Junction)

Band diagram:

Electrostatic potential:

Electric field:

Charge density:

EE130/230M Spring 2013

Lecture 9, Slide 5

“Game Plan” to obtain r(x),E(x), V(x)

- Find the built-in potential Vbi
- Use the depletion approximation r (x)
(depletion widths xp, xn unknown)

- Integrate r (x) to find E(x)
Apply boundary conditionsE(-xp)=0, E(xn)=0

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

- For E(x) to be continuous at x=0, NAxp = NDxn
Solve for xp, xn

EE130/230M Spring 2013

Lecture 9, Slide 6

Built-In Potential Vbi

For non-degenerately doped material:

EE130/230M Spring 2013

Lecture 9, Slide 7

What if one side is degenerately doped?

p+n junction

n+p junction

EE130/230M Spring 2013

Lecture 9, Slide 8

The Depletion Approximation

In the depletion region on the p side, = –qNA

In the depletion region on the n side, = qND

EE130/230M Spring 2013

Lecture 9, Slide 9

Electric Field Distribution

E(x)

-xp

xn

x

The electric field is continuous at x = 0

NAxp = NDxn

EE130/230M Spring 2013

Lecture 9, Slide 10

Electrostatic Potential Distribution

On the p side:

Choose V(-xp) to be 0

V(xn) = Vbi

On the n side:

EE130/230M Spring 2013

Lecture 9, Slide 11

Derivation of Depletion Width

- At x = 0, expressions for p side and n side must be equal:
- We also know that NAxp = NDxn

EE130/230M Spring 2013

Lecture 9, Slide 12

Depletion Width

- Eliminating xp, we have:
- Eliminating xn, we have:
- Summing, we have:

EE130/230M Spring 2013

Lecture 9, Slide 13

Depletion Width in a One-Sided Junction

If NA >> NDas in a p+njunction:

What about a n+p junction?

where

EE130/230M Spring 2013

Lecture 9, Slide 14

Example: One-Sided pn Junction

A p+n junction has NA=1020 cm-3 and ND =1017cm-3.

Find (a) Vbi (b) W (c) xn and (d) xp.

EE130/230M Spring 2013

Lecture 9, Slide 17

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.

EE130/230M Spring 2013

Lecture 9, Slide 18

Summary

- For a non-degenerately-doped pn junction:
Built-in potential

Depletion width

- For a one-sided junction:
Built-in potential

Depletion width

EE130/230M Spring 2013

Lecture 9, Slide 20

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