OUTLINE

1
Lecture 14

• OUTLINE
• pn junction electrostatics
• Reading Chapter 5

2
Qualitative Electrostatics
Band diagram
Electrostatic potential
Electric field
Charge density
3
Game Plan for Obtaining r(x), E(x), V(x)

• Find the built-in potential Vbi
• Use the depletion approximation ? r (x)
• (depletion-layer widths xp, xn unknown)
• Integrate r (x) to find E(x)
• boundary conditions E(-xp)0, E(xn)0
• Integrate E(x) to obtain V(x)
• boundary conditions V(-xp)0, V(xn)Vbi
• For E(x) to be continuous at x0, NAxp NDxn
• solve for xp, xn

4
Built-In Potential Vbi
For non-degenerately doped material
5
Vbi for One-Sided pn Junctions
pn junction
np junction
6
The Depletion Approximation
On the p-side, ? qNA
qN
d
E
-

A
e
dx
s
-qNA
qN
)
(
x



-

)
(
C
x
x
A
E
e
1
e
s
s
On the n-side, ? qND
-qN
-
x

)
(
D
xn
)
(
x
E
e
s
7
Electric Field in the Depletion Layer
The electric field is continuous at x 0 ?
NAxp NDxn
8
Electrostatic Potential in the Depletion Layer
On the p-side
(arbitrarily choose the voltage at x xp to be 0)
On the n-side
9

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

10
Depletion Layer Width

• Eliminating xp, we have
• Eliminating xn, we have
• Summing, we have

11
One-Sided Junctions
If NA gtgt ND as in a pn junction
What about a np junction?
where
12
Example

• A pn junction has NA1020 cm-3 and ND 1017cm-3.
  What is a) its built in potential, b)W , c)xn ,
  and d) xp ?
• Solution
• a)
• b)
• c)
• d)

13
Summary

• For a non-degenerately-doped pn junction at
  equilibrium
• Built-in potential
• Depletion-layer width
• For a one-sided (pn or pn) junction at
  equilibrium
• Built-in potential
• Depletion-layer width