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Lecture #14

OUTLINE pn junction electrostatics Reading: Chapter 5. Lecture #14. Qualitative Electrostatics. Band diagram. Electrostatic potential. Electric field. Charge density. “Game Plan” for Obtaining r ( x ) , E ( x ) , V ( x ). Find the built-in potential V bi

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Lecture #14

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

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

  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 x=0, NAxp = NDxn • solve for xp, xn EE130 Lecture 14, Slide 3

  4. Built-In Potential Vbi For non-degenerately doped material: EE130 Lecture 14, Slide 4

  5. Vbi for “One-Sided” pn Junctions p+n junction n+p junction EE130 Lecture 14, Slide 5

  6. x p The Depletion Approximation On the p-side, = –qNA qN d E = - A e dx s qN -qNA = - + = ( x + ) A ( x ) x C E e 1 e s s On then-side,  = qND -qN - = x D ( xn ) ( x ) E e s EE130 Lecture 14, Slide 6

  7. Electric Field in the Depletion Layer • The electric field is continuous at x = 0 • NAxp = NDxn EE130 Lecture 14, Slide 7

  8. Electrostatic Potential in the Depletion Layer On the p-side: (arbitrarily choose the voltage at x = xp to be0) On the n-side: EE130 Lecture 14, Slide 8

  9. At x = 0, expressions for p-side and n-side must be equal: • We also know that NAxp = NDxn EE130 Lecture 14, Slide 9

  10. Eliminating xp, we have: Eliminating xn, we have: Summing, we have: Depletion Layer Width EE130 Lecture 14, Slide 10

  11. One-Sided Junctions If NA >> NDas in a p+njunction: What about a n+p junction? where EE130 Lecture 14, Slide 11

  12. Example • A p+n junction has NA=1020 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) EE130 Lecture 14, Slide 12

  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 EE130 Lecture 14, Slide 13

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