1. Example 5-3
Find an expression for the electron current in the n-type material of a forward-biased p-n junction.

2. 3. 3. Reverse Bias
Physically, extraction occurs because minority carriers at the edges of the depletion region are swept down the barrier at the junction by the E field, and holes in the n region diffuse toward the junction.
Fig. 18. Reverse-biased p-n junction: minority carrier distributions near the reverse-biased junction

3. Example 5-4
Consider a volume of n-type material of area A, with a length of one hole diffusion length Lp. The rate of thermal generation of holes within the volume is
Assume that each thermally generated hole diffuses out of the volume before it can recombine. The resulting hole current is I=qALppn/τp, which is the same as the saturation current for a p+-n junction. We conclude that saturation current is due to the collection of minority carriers thermally generated within a diffusion length of the junction.

4. 4. Reverse-bias Breakdown
< Preface >
If the current is not limited externally, the junction can be damaged by excessive reverse current, which overheats the device as the maximum power rating is exceeded.
It is important to remember, however, that such destruction of the device is not necessarily due to mechanisms unique to reverse breakdown.
The first mechanism, called the Zener effect, is operative at low voltages(up to a few volts reverse bias).
The breakdown occurs at higher voltages(from a few volts to thousands of volts), the mechanism is avalanche breakdown.

5. 4. 1. Zener Breakdown
Heavily doped junction → High electric fields → Tunneling effect occurs
High electric field makes steep energy band, and reverse bias makes narrower width of barrier.
Fig. 20. The Zener effect: (a) heavily doped junction at equilibrium; (b) reverse bias with electron tunneling from p to n; (c) I-V characteristic

6. 4. 2. Avalanche Breakdown Lightly doping
Breakdown mechanism is the impact ionization of host atoms by energetic carriers.
Fig. 21. Electron-hole pairs created by impact ionization : (a) a single ionizing collision by an incoming electron in the depletion region of the junction; (b) primary, and tertiary collisions

7. 4. 2. Avalanche Breakdown
In general, the critical reverse voltage for breakdown increases with the band gap of the material, since more energy is required for an ionizing collision.
Vbr decreases as the doping increases, as Fig. indicates.
Fig. 22. Variation of avalanche breakdown voltage in abrupt p+-n junctions, as a function of donor concentration on the n side, for several semiconductors.

8. 4. 3. Rectifiers
Most forward-biased diodes exhibit an offset voltage E0, which can be approximated in a circuit model by a battery in series with the ideal diode and resister R.
Fig. 23. Piecewise-linear approximations of junction diode characteristics : (a) the ideal diode; (b) ideal diode with an offset voltage; (c) ideal diode with an offset voltage and a resistance to account for slope in the forward characteristic.

9. A short, lightly doped region → The reason of punch-through
4. 3. Rectifiers
A short, lightly doped region → The reason of punch-through
It is possible for W to increase until it fills the entire length of this region.
→ The result of punch-through is a breakdown below the value of Vbr
Fig. 24. Beveled edge and guard ring to prevent edge breakdown under reverse bias : (a) diode with beveled edge; (b) closeup view of edge, showing reduction of depletion region near the bevel; (c) guard ring

10. 4. 4. Breakdown Diode
It is designed for a specific breakdown voltage(higher doping). Such diodes are also called Zener diodes(several hundred voltages).
It can be used as voltage regulators in circuits with varying inputs.
Fig. 26. A breakdown diode : (a) I-V characteristic; (b) application as a voltage regulator

11. 5. Transient and A-C Conditions
< Preface >
Since most solid state devices are used for switching or for processing a-c signals, we cannot claim to understand p-n junctions without knowing at least the basics of time dependent processes.
In this section we investigate the important influence of excess carriers in transient and a-c problems.
The switching of a diode from its forward state to its reverse state is analyzed to illustrate a typical transient problem.

12. 5. 1. Time Variation of Stored Charge
Jp(x)
Jp(x+Δx) Δx
Rate of increase of hole concentra- recombination
Hole buildup tion in ΔxA per unit time rate
Fig. 4-16
Fig Current entering and leaving a volume ΔxA.

13. 5. 1. Time Variation of Stored Charge

14. 5. 1. Time Variation of Stored Charge
Stored charges are
recombination with electrons
Fig. 27. Effects of a step turn-off transient in a p+-n diode: (a) current through the diode; (b) decay of stored charge in the n-region; (c) excess hole distribution in the n-region as a function of time during the transient.

15. 5. 1. Time Variation of Stored Charge

16. 5. 2. Reverse Recovery Transient
= p(xn)-pn
t=0, p-n diode has forward-bias.
Ir=-E/R, when stored charges are totally recombination.
It’s desirable that tsd is small compared with the switching time.
Fig. 28. Stored delay time in a p+-n diode: (a) circuit and input square wave; (b) hole distribution in the n-region as a function of time during the transient; (c) variation of current and voltage with time; (d) sketch of transient current and voltage on the device I-V characteristic

17. 5. 2. Reverse Recovery Transient
Fig. 28. Effects of storage delay time on switching signal: (a) switching voltage; (b) diode current

18. Example 5-5
At the time t=0 the current is switched to –Ir at a forward biased p+-n diode.
Apply appropriate boundary condition and quasi-steady state approximation to find the tsd.

19. 5. 3. Switching Diodes
A diode with fast switching properties → either store very little charge in the neutral regions for steady forward currents, or have a very short carrier lifetime, or both.
The methods to improve the switching speed of a diode.
To add efficient recombination centers to the bulk material. For Si diodes, Au doping is useful for this purpose. The carrier lifetime varies with the reciprocal of the recombination center concentration.
To make the lightly doped neutral region shorter than a minority carrier diffusion length. This is the narrow base diode. In this case the stored charge for forward conduction is very small, since most of the injected carriers diffuse through the lightly doped region to the end contact. → Very little time required to eliminate the stored charge in the narrow neutral region.

20. 5. 4. Capacitance of p-n Junctions
Junction capacitance : dominant under reverse bias
Charge storage capacitance : dominant under forward bias
Junction Capacitance

21. 5. 4. Capacitance of p-n Junctions
xp0
xn0

22. 5. 4. Capacitance of p-n Junctions
Charge Storage Capacitance

23. 5. 4. Capacitance of p-n Junctions
Fig. 30. Depletion capacitance of a junction: (a) p+-n junction showing variation of depletion edge on n side with reverse bias. Electrically, the structure looks like a parallel plate capacitor whose dielectric is the depletion region, and the plates are the space charge neutral regions; (b) variation of depletion capacitance with reverse bias.

24. 5. 4. Capacitance of p-n Junctions
Fig. 31. Diffusion capacitance in p-n junctions. (a) Steady-state minority carrier distribution for a forward bias, V, and reduced forward bias, V-ΔV in a long diode; (b) minority carrier distributions in a short diode; (c) diffusion capacitance as a function of forward bias in long and short diodes.