1. 6 pn Junction Diode : I-V Characteristics

2. 6.1 THE IDEAL DIODE EQUATION 6.1.1 Qualitative Derivation

4. 6.1.2 Quantitative Solution Strategy General Considerations (1) The diode is being operation under steady state condition (2) A nondegenerately doped step junction models the doping profile (3) The diode is one-dimensional (4) Low-level injunction prevails in the quasineutral region (5)There are no processes other than drift, diffusion, and thermal recombination-generation taking place inside the diode. Specifically, G L =0

5. (6.2) (6.3) (6.4a) (6.4b) General relationships

6. (6.5a) (6.5b) The condition for the use of the minority carrier diffusion equations

7. Current due to diffusion ( ε ≈0 in the quasineutral regions) Depletion Region Considerations From continuity equations in the depletion regions (6.6a) (6.6b) (6.7a) (6.7b)

8. Carrier current is constant throughout the depletion region Total current in the depletion region Boundary condition - Δn P in the p-side - Δp n in the n-side (6.8a) (6.8b) (6.9)

9. At the Ohmic Contacts - There is no potential drop at p- and n- contact

10. For wide-base diode, the contact is located at x=±∞ At the Depletion Region Edges From quasi-Fermi level formalism - F N -F P ≤ E Fn -E Fp =qV A - law of the junction (6.10a) (6.10b) (6.11) (6.12)

11. at x=-x p or and Similarly (6.13) (6.14) (6.15) (6.16)

12. or (6.17) and (6.18) 6.1.3 Derivation Proper (6.19)

13. From boundary condition where (6.20a) (6.21) (6.22) (6.20b)

14. - x'→∞ : exp(x'/L P )→∞ - A 2 =0 - A 1 =Δp n (x'=0)

15. and - On the quasineutral p-side of the junction and (6.26) (6.25) (6.24) (6.23)

16. At the depletion edge or (6.27a) (6.27b) (6.28) (6.29) (6.30)

17. 6.1.4 Examination of Results Ideal I-V For forward biasing greater then a few KT/q (6.31)

18. The Saturation Current and - As a general rule, the heavily doped side of an asymmetrical junction can be ignored in determining the electrical characteristics of the junction Example 6.1 (6.32a) (6.32b)

19. Carrier Currents

20. Carrier Concentrations

21. Measured I-V plot of p-n diode 6.2 DEVIATIONS FROM THE IDEAL 6.2.1 Ideal Theory Versus Experiment Theory

22. V BR is defined at the reverse voltage for I=1uA or 1mA V BR is dependent on the doping concentration of the bulk (6.33) 6.2.2 Reverse-Bias Breakdown

23. Avalanching - Electron hole pair generation within depletion region by input ionization

24. - Multiplication factor An empirical fit to experimental data gives m=3~6 VBR dependence of doping concentration - From the electric field at x=0 (6.34) (6.35) (6.36)

25. For asymmetrical doped junctions Zener Process - For heavily doped p-n junction - V BR ≃ 4.5V (6.37) (6.38) (6.39)

26. 6.2.3 The R-G Current Extra current arises from thermal carrier recombination- generation in the depletion region The thermal current (6.40) (6.41)

28. and For reverse biases greater than a few kT/q, n→0, p→0 where (6.42) (6.43) (6.44)

29. The combined forward and reverse bias dependence of I R-G The diffusion current under forward biases Total forward bias current (6.45) (6.46) (6.47)

30. 6.2.4 VA→Vbi High-Current Phenomena Series Resistance Resistance in the quasineutral region Small contact resistance Junction voltage

32. (6.48) (6.49)

33. The increased bias voltage gives rise to high-level injection I ∝ exp(q/2KT) Example 6.9 High-Level Injection

34. 6.3.1 Charge Control Approach Minority carrier excess in the n-side quasi-neutral region at given time t and a point x, x n ≤x≤∞ : ∆p n (x,t) Total excess hole charge : Q P The minority carrier diffusion equation with G L = 0 Since in a ≈0 region (6.50) (6.51) 6.3 SPECIAL CONSIDERATIONS

35. we can alternatively write (6.53) (6.54) (6.55) (6.52)

36. i DIFF : Hole current can flow into or out of the region : The excess charge can be modified by recombination-generation within the region In the steady state dQ p /dt =0, i DIFF =I DIFF From approximation of Q P in the diffusion length giving (6.59) (6.58) (6.57) (6.56)