1. ECE 663 P-N Junctions – Equilibrium P N W V appl = 0 V bi = (kT/q)ln(N A N D /n i 2 ) W =  2k s  0 V bi (N A +N D )/q(N A N D ) V bi EFEF

2. ECE 663 P-N Junctions – Forward Bias P N W V appl > 0 V bi = (kT/q)ln(N A N D /n i 2 ) W =  2k s  0 (V bi -V appl )N A +N D )/q(N A N D ) V bi -V appl E Fp E Fn - + E Fn - E Fp = qV appl in QNR

3. ECE 663 P-N Junctions – Reverse Bias P N W V appl < 0 V bi = (kT/q)ln(N A N D /n i 2 ) W =  2k s  0 (V bi +V appl )N A +N D )/q(N A N D ) V bi +V appl E Fp E Fn - + E Fn - E Fp = -qV appl in QNR

4. Voltage variation  x E x V x

5. ECE 663 Equilibrium: Forward and Reverse Currents cancel

6. ECE 663 + Forward Bias - Forward Bias: Reverse thermionic flow increases n i e (E Fn -E i )/kT

7. ECE 663 - Reverse Bias + Reverse Bias: Forward currents win

8. ECE 663 I-V Curve for Ideal Diode

9. ECE 663 Ideal P-N Junction Diode Assumptions: Steady-State conditions Non-degenerate doping One-dimensional Low Level Injection Only drift, diffusion,thermal R-G (no photons)

10. ECE 663 Ideal P-N Junction Diode D P - = 0 ∂2pn∂2pn ∂x2∂x2 pnpn PP D N - = 0 ∂2np∂2np ∂ x’ 2 npnp NN x x'

11. ECE 663 Boundary Conditions D P - = 0 ∂2pn∂2pn ∂x2∂x2 pnpn PP x np = n i 2 (e F n -F p ) np = n i 2 e qV/kT in QNR regions

12. ECE 663 Condition in the Depletion Region x x'

13. ECE 663 Condition in the Depletion Region x x' No RG JnJn JnJn JpJp JpJp ≈ -qD P ∂pN∂pN ∂x∂x ≈ qD N ∂nP∂nP ∂x∂x ≈ -qD N ∂nP∂nP ∂ x’

14. ECE 663 Condition in the Depletion Region x x' JnJn JnJn JpJp JpJp J p (x n ) J n (-x p ) = J n (x n ) J = J n (-x p ) + J p (x n ) J

15. ECE 663 Minority Carrier Diffusion Equations – n side QNR Boundary Conditions:

16. ECE 663 Solution Use continuity equation to find current density at edge of depletion x=x n

17. ECE 663 For the p-side Boundary Conditions: Current Density from continuity equation -

18. ECE 663 Total Diode Current Ideal diode equation or Shockley Equation

19. ECE 663 Saturation Current Density

20. ECE 663 Larger by e qV/kT Forward Bias

21. ECE 663 Smaller by e qV/kT Reverse Bias

22. ECE 663 Ideal Diode I-V characteristic

23. ECE 663 Real Diode I-V characteristic