Semiconductor Device Physics Lecture 5 Dr Ing Erwin

Semiconductor Device Physics Lecture 5 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 President University 0 1 9 Erwin Sitompul SDP 5/1

Semiconductor Device Physics Chapter 5 pn Junction Electrostatics President University Erwin Sitompul SDP 5/2

Chapter 5 pn Junction Electrostatics Metallurgical Junction Doping profile Step junction idealization President University Erwin Sitompul SDP 5/3

Chapter 5 pn Junction Electrostatics Poisson’s Equation Poisson’s equation is a well-known relationship in electricity and magnetism. It is now used because it often contains the starting point in obtaining quantitative solutions for the electrostatic variables. In one-dimensional problems, Poisson’s equation simplifies to: President University Erwin Sitompul SDP 5/4

Chapter 5 pn Junction Electrostatics Equilibrium Energy Band Diagram pn-Junction diode President University Erwin Sitompul SDP 5/5

Chapter 5 pn Junction Electrostatics Qualitative Electrostatics Equilibrium condition Band diagram Electrostatic potential President University Erwin Sitompul SDP 5/6

Chapter 5 pn Junction Electrostatics Qualitative Electrostatics Equilibrium condition Electric field Charge density President University Erwin Sitompul SDP 5/7

Chapter 5 pn Junction Electrostatics Formation of pn Junction and Charge Distribution q. NA– President University Erwin Sitompul q. ND+ SDP 5/8

Chapter 5 pn Junction Electrostatics Formation of pn Junction and Charge Distribution President University Erwin Sitompul SDP 5/9

Chapter 5 pn Junction Electrostatics Built-In Potential Vbi • Vbi for several materials: Ge ≤ 0. 66 V Si ≤ 1. 12 V Ge. As ≤ 1. 42 V For non-degenerately doped material, President University Erwin Sitompul SDP 5/10

Chapter 5 pn Junction Electrostatics Relation between ρ(x), E(x), and V(x) 1. Find the profile of the built-in potential Vbi 2. Use the depletion approximation ρ(x) With depletion-layer widths xp, xn unknown 3. Integrate ρ(x) to find E(x) Boundary conditions E(–xp) = 0, E(xn)=0 4. Integrate E(x) to obtain V(x) Boundary conditions V(–xp) = 0, V(xn) = Vbi 5. For E(x) to be continuous at x = 0, NAxp = NDxn Solve for xp, xn President University Erwin Sitompul SDP 5/11

Chapter 5 pn Junction Electrostatics The Depletion Approximation On the p-side, ρ = –q. NA with boundary E(–xp) = 0 On the n-side, ρ = q. ND with boundary E(xn) = 0 President University Erwin Sitompul SDP 5/12

Chapter 5 pn Junction Electrostatics Step Junction with VA = 0 Solution for ρ Solution for E Solution for V President University Erwin Sitompul SDP 5/13

Chapter 5 pn Junction Electrostatics Step Junction with VA=0 At x = 0, expressions for p-side and n-side for the solutions of E and V must be equal: President University Erwin Sitompul SDP 5/14

Chapter 5 pn Junction Electrostatics Depletion Layer Width Eliminating xp, Eliminating xn, Summing Exact solution, try to derive President University Erwin Sitompul SDP 5/15

Chapter 5 pn Junction Electrostatics One-Sided Junctions If NA >> ND as in a p+n junction, If ND >> NA as in a n+p junction, Simplifying, where N denotes the lighter dopant density President University Erwin Sitompul SDP 5/16

Chapter 5 pn Junction Electrostatics Example: Depletion Layer Width A p+n junction has NA = 1020 cm– 3 and ND = 1017 cm– 3, at 300 K. a) What is. Vbi? b) What is W? c) What is xn? d) What is xp? President University Erwin Sitompul SDP 5/17

Chapter 5 pn Junction Electrostatics Step Junction with VA 0 • To ensure low-level injection conditions, reasonable current levels must be maintained VA should be small President University Erwin Sitompul SDP 5/18

Chapter 5 pn Junction Electrostatics Step Junction with VA 0 In the quasineutral, regions extending from the contacts to the edges of the depletion region, minority carrier diffusion equations can be applied since E ≈ 0. In the depletion region, the continuity equations are applied. President University Erwin Sitompul SDP 5/19

Chapter 5 pn Junction Electrostatics Step Junction with VA 0 Built-in potential Vbi (non-degenerate doping): Depletion width W : President University Erwin Sitompul SDP 5/20

Chapter 5 pn Junction Electrostatics Effect of Bias on Electrostatics • If voltage drop â, then depletion width â • If voltage drop á, then depletion width á President University Erwin Sitompul SDP 5/21

Chapter 5 pn Junction Electrostatics Linearly-Graded Junction President University Erwin Sitompul SDP 5/22

Chapter 5 pn Junction Electrostatics Homework 5 1. (6. 4) 2. (7. 6) Consider a silicon pn junction at T = 300 K with a p-side doping concentration of NA = 1018 cm– 3. Determine the n-side doping concentration such that the maximum electric field is |Emax| = 3× 105 V/cm at a reverse bias voltage of (i) VR = 25 V; (ii) VR = 5 V. Problem 5. 4 Pierret’s “Semiconductor Device Fundamentals”. Change ND from 1015 /cm 3 to 3× 1015 /cm 3. Deadline: Wednesday, 16 October 2019, at 10: 30. Next week class will be on Wednesday, 16 October 2019. No class on Friday, 18 October 2019. President University Erwin Sitompul SDP 5/23