1. Chapter 6. pn Junction Diode
I-V Characteristics
The Ideal Diode Equation
Deviations from the Ideal

2. 6. pn Junction Diode
◆ Ideal Diode Equation

3. 6. pn Junction Diode

4. 6. pn Junction Diode

5. 6. pn Junction Diode

6. 6. pn Junction Diode

7. ◆ Quasi-neutral Region
6. pn Junction Diode
◆ Quasi-neutral Region
Under the assumed steady state conditions with GL = 0 minority carrier diffusion equations for the p and n quasi-neutral regions

8. ◆ Depletion Region 6. pn Junction Diode Continuity equations for E≠0
If thermal R-G is negligible throughout the depletion region

9. 6. pn Junction Diode
→JN, JP : constant independent of position inside the depletion region

10. ◆ Boundary Condition in the n-side quasi-neutral region
6. pn Junction Diode
◆ Boundary Condition
   in the p-side quasi-neutral region
  in the n-side quasi-neutral region
at ⅰ) the Ohmic contacts
ⅱ) the edges of the depletion  region
ⅰ) At the Ohmic contacts : minority carrier → 0 before the contacts

11. ⅱ) At the depletion region edges
6. pn Junction Diode
ⅱ) At the depletion region edges
   (3.72) at the edges of the depletion region,
At all points inside the diode.
Law of the junction
Similarly,

12. 6. pn Junction Diode
◆ Derivation Proper
For Convenience,  
                                                                                                                                                       

13. 6. pn Junction Diode
General solution (1)

14. 6. pn Junction Diode
Similarly,

15. Ideal diode equation (Shockley eq.)
6. pn Junction Diode
Ideal diode equation (Shockley eq.)

16. Examination of Results
6. pn Junction Diode
Examination of Results
◆ Ideal I-V

17. I  I0 for reverse biases > a few kT/q
6. pn Junction Diode
I  I0 for reverse biases > a few kT/q
I  I0exp(qVA/kT) for forward biases > a few kT/q

18. 6. pn Junction Diode
◆ Saturation current
- Heavily doped side of p+-n and n+-p junctions : negligible
         
for p+-n diodes
for n+-p diodes
⇒ Consider only the lightly doped side
⇒ Heavily doped side of an asymmetrical junction can be ignored to determine the electrical characteristics

19. 6. pn Junction Diode
◆ Carrier currents

20. 6. pn Junction Diode

21. Deviations From The Ideal
6. pn Junction Diode
Deviations From The Ideal
◆  Ideal Theory Versus Experiment
Breakdown for a certain reverse bias
        → Large reverse-bias current
R-G current in the depletion regions for the reverse-bias and small forward bias
      → q/2kT for voltages below 0.35V & does not saturate for the reverse bias
VA → Vbi high-current for VA → Vbi
     → High level of current flowing at forward biases over 0.7 volts
      → The slope decreases or “slope over”

22. 6. pn Junction Diode

23. 6. pn Junction Diode

24. ◆ Reverse-Bias Breakdown
6. pn Junction Diode
◆ Reverse-Bias Breakdown
- Large reverse current flows when the reverse voltage exceeds a certain value : reversible process
1. Avalanching process : typical
2. Zener process : Only when both sides of the junction doped heavily
- Breakdown voltage VBR : absolute value of the reverse voltage where the current goes off to infinity
- VBR tends to increase with the band gap of semiconductor
- Doping on the lightly doped side : used to vary  VBR
        
where NB : doping on the lightly doped side of the junction

25. 6. pn Junction Diode

26. 6. pn Junction Diode
◆ Avalanches

27. ◆ Collisions by a carrier in the depletion region
6. pn Junction Diode
◆  Collisions by a carrier in the depletion region
- Energy lost by the carriers at small applied reverse bias : small
    → Cause simply lattice vibrations → localized heating
  - Energy transferred to the semiconductor with increasing reverse bias : large
    → Ionize a semiconductor atom
    → Collision frees a valence electron from the atom or electron from
valence band to conduction band
    → Create EHP : impact ionization
    → Accelerated by the electric field
    → Additional collision as create more carriers : Avalanche

28. ◆ Multiplication factor M
6. pn Junction Diode
◆ Multiplication factor M
- Carrier multiplication before reaching breakdown
   → Because the distance between collisions : random variable
where I0 : current with at any carrier multiplication
                  
(6.35)
where 3≤m≤6
※       
  → Lattice scattering increases as T increases
  → Smaller mean free path
  → Larger critical electric field for avalanching
  → Higher VBR       

29. 6. pn Junction Diode
◆ Zener process

30. 6. pn Junction Diode

31. Requirements for tunneling
6. pn Junction Diode
Requirements for tunneling
  (1) Must be filled states on one site of the barrier and empty states
on the other side of the barrier at the same energy
  (2) Width of the potential energy barrier : very thin < 100 Å
※ Zener process
  Tunneling takes place when the electrons pass through the barrier from the valence band electrons on the p-side to empty states at the same energy in the conduction band on the n-side of the junction.
   → Greater the reverse bias, greater the reverse bias tunneling
current
   → Heavily doped on both side of the junction for the depletion
width < 10-6 cm

32. Tunnel diode operation
6. pn Junction Diode
Tunnel diode operation
      (Heavily doped cases, degenerated)
Type N negative resistance, voltage controlled negative resistance
  → Switching, oscillation, amplification.

33. 6. pn Junction Diode
Ip : peak tunneling current
Iv : valley current

34. 6. pn Junction Diode
Normal diode

35. ◆ Recombination and Generation in transition region
6. pn Junction Diode
◆ Recombination and Generation in transition region
※ Reverse-bias
  → Carrier concentration in the depletion region reduced
  → Causes the thermal generation of EHP : temperature,
     recombination center
※ Forward-bias
  → Carrier concentration in the depletion region increase
  → Carrier recombination for the carriers that can not make it
     over the potential hill being partially eliminated via recombination

36. 6. pn Junction Diode
  → Small for wide band gap, low temperature (small ni) and low
voltage
  → n=2 at low voltage, n=1 at high voltage

37. 6. pn Junction Diode

38. 6. pn Junction Diode

39. 6. pn Junction Diode
Ohmic Losses (VA→Vbi)

40. Punch-through → Current increases → IRS increases → VJ decreases
6. pn Junction Diode
→ Current increases → IRS   increases → VJ  decreases
→ Carrier injection level decreases
→ Current increases slowly with increased bias
⇒ High-level injection → Enhance carrier concentration
                      → Reduce the series resistance
                      ⇒ Conductivity modulation
Punch-through
   Entire device region becomes depleted with increasing reverse bias