1. Spring 2007EE130 Lecture 14, Slide 1 Lecture #14 OUTLINE pn junction electrostatics Reading: Chapter 5

2. Spring 2007EE130 Lecture 14, Slide 2 Qualitative Electrostatics Band diagram Electrostatic potential Electric field Charge density

3. Spring 2007EE130 Lecture 14, Slide 3 “Game Plan” for Obtaining  (x),  E (x),  V(x) Find the built-in potential V bi Use the depletion approximation   (x) (depletion-layer widths x p, x n unknown) Integrate  (x) to find E(x) –boundary conditions E(-x p )=0, E(x n )=0 Integrate E(x) to obtain V(x) –boundary conditions V(-x p )=0, V(x n )=V bi For E(x) to be continuous at x=0, N A x p = N D x n  solve for x p, x n

4. Spring 2007EE130 Lecture 14, Slide 4 Built-In Potential V bi For non-degenerately doped material:

5. Spring 2007EE130 Lecture 14, Slide 5 V bi for “One-Sided” pn Junctions p + n junctionn + p junction

6. Spring 2007EE130 Lecture 14, Slide 6 The Depletion Approximation On the p-side,  = –qN A On the n-side,  = qN D s A qN dx d   E )( )( 1 x -qN A Cx qN x s s A    E )( )( s D x xnxn -qN x    E x p

7. Spring 2007EE130 Lecture 14, Slide 7 The electric field is continuous at x = 0  N A x p = N D x n Electric Field in the Depletion Layer

8. Spring 2007EE130 Lecture 14, Slide 8 On the p-side: (arbitrarily choose the voltage at x = x p to be 0) On the n-side: Electrostatic Potential in the Depletion Layer

9. Spring 2007EE130 Lecture 14, Slide 9 At x = 0, expressions for p-side and n-side must be equal: We also know that N A x p = N D x n

10. Spring 2007EE130 Lecture 14, Slide 10 Depletion Layer Width Eliminating x p, we have: Eliminating x n, we have: Summing, we have:

11. Spring 2007EE130 Lecture 14, Slide 11 If N A >> N D as in a p + n junction: What about a n + p junction? where One-Sided Junctions

12. Spring 2007EE130 Lecture 14, Slide 12 A p + n junction has N A =10 20 cm -3 and N D =10 17 cm -3. What is a) its built in potential, b)W, c)x n, and d) x p ? Solution: a) b) c) d) Example

13. Spring 2007EE130 Lecture 14, Slide 13 Summary For a non-degenerately-doped pn junction at equilibrium: –Built-in potential –Depletion-layer width For a one-sided (p+n or pn+) junction at equilibrium: –Built-in potential –Depletion-layer width