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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:.

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Lecture 9
Lecture 9

OUTLINE

  • pn Junction Diodes

    • Electrostatics (step junction)

      Reading: Pierret 5; Hu 4.1-4.2


Pn junctions
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


Terminology
Terminology

Doping Profile:

EE130/230M Spring 2013

Lecture 9, Slide 3


Idealized pn junctions
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
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
“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 v bi
Built-In Potential Vbi

For non-degenerately doped material:

EE130/230M Spring 2013

Lecture 9, Slide 7


What if one side is degenerately doped
What if one side is degenerately doped?

p+n junction

n+p junction

EE130/230M Spring 2013

Lecture 9, Slide 8


The depletion approximation
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
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
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
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
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
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


Peak e field in a one sided junction
Peak E-Field in a One-Sided Junction

EE130/230M Spring 2013

Lecture 10, Slide 15


V x in a one sided junction
V(x) in a One-Sided Junction

p side

n side

EE130/230M Spring 2013

Lecture 9, Slide 16


Example one sided pn junction
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
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


Effect of applied voltage
Effect of Applied Voltage

EE130/230M Spring 2013

Lecture 9, Slide 19


Summary
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


Linearly graded pn junction
Linearly Graded pn Junction

EE130/230M Spring 2013

Lecture 9, Slide 21


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