1. ECE 663 Ideal Diode I-V characteristic

2. ECE 663 Real Diode I-V characteristic

3. ECE 663 Real Diode – Forward Bias (semi-log scale)

4. ECE 663 Real Diode – Reverse Bias

5. ECE 663 What’s wrong with this picture? Forward Bias –For V < 0.35 volts slope is kT/2q –For 0.35V < V < 0.7volts, slope is kT/q –For V > 0.7 volts, slope less than kT/q (V~V bi ) –I 0 ~10 -14 A from intercept of semi-log plot in FB

6. ECE 663 What’s wrong with this picture? Reverse Bias –Current ~10 3 times larger than FB I 0 –Reverse current doesn’t saturate –Breakdown – large current above V bd Avalanche breakdown Zener (tunneling) process

7. ECE 663 Reverse Bias Avalanche Breakdown Depletion width larger than mean free path  lots of collisions

8. ECE 663 Avalanching Minority carriers accelerated by electric field in depletion region The average energy lost per collision goes up as E field (voltage) goes up (v =  E ) At some critical field (E c ), the average energy lost per collision will be enough to “ionize” lattice atoms – knock out more carriers Those carriers will also be accelerated by E>E c and make more carriers when they collide, etc……. Many collisions=huge multiplication in number of carriers= avalanche breakdown

9. ECE 663 Max. Field Doping Charge Density Electric Field Electrostatic Potential N A x p = N D x n = W D /(N A -1 + N D -1 ) K s  0 E m = -qN A x p = -qN D x n = -qW D /(N A -1 + N D -1 ) V bi = ½| E m |W D

10. ECE 663 Maximum Field E m =  2qV bi /k s  0 (N A -1 +N D -1 )

11. ECE 663 Avalanching One-sided junctions

12. ECE 663 Experimental Data on V BR

13. ECE 663 Zener Breakdown - Tunneling Barrier must be thin: depletion is narrow  doping on both sides must be large Must have empty states to tunnel into  V bi + V BR > E G /q

14. ECE 663 Zener diode I-V characteristic

15. ECE 663 Reverse bias R-G in the depletion region

16. ECE 663 R-G Current In depletion region we don’t have low level injection because number of carriers is small and injected carriers is large But, in depletion n,p  0

17. ECE 663 But Reverse bias current=lifetime measurement

18. ECE 663 Forward Bias R-G

19. ECE 663 Forward Bias R-G current n and p cannot be neglected in the depletion region in FB so the integral is not so easy as in RB. Estimate value of integral using maximum value of integrand = constant

20. ECE 663 Forward Bias R-G current Integrand maximum when n + p is minimum or n = p W

21. ECE 663 Ideality factor

22. Forward Bias with High Currents: High Level injection np = ni 2 e qV/kT n ~ p ≈ n i e qV/2kT Use in boundary condition

23. ECE 663 Forward Bias with High Currents: Series Resistance I = I 0 [e qV/kT -1] I = I 0 [e q(V-IR s )/kT -1]

24. ECE 663 Real Diode I-V curve summary A.Breakdown (V B ~1/N B ) B.R-G RB (I~  V) C.R-G FB (slope~q/2kT) D.High Level Inj.(slope ~ q/2kT) E.Series Resistance – slope over

25. ECE 663 Narrow Base P-N junction Diode What happens if the diode is smaller than the minority carrier diffusion length(s)? Diffusion lengths can be 20-30 microns

26. ECE 663 Similarly for J n

27. ECE 663 Total diode current Compare to result from wide base ideal diode:  Replace minority carrier diffusion length with diode width

28. ECE 663 Charge control methodology x-xp-xp npnp Analyze by examining injected minority carrier charge: e.g. electrons injected into p side of FB diode Total negative charge on p-side:

29. ECE 663 Charge control method Approximate total charge by diffusion length times charge at boundary of QN-depletion regions: Non-equilibrium injected electrons with average lifetime of  n Recombination Rate=charge/time=current

30. ECE 663 Charge control but Similarly for holes on the n-side:

31. ECE 663 Total current: Same result as before but we didn’t have to solve the minority carrier diffusion equations Stored charge and recombination = current needed to resupply