2. Empirical Observations of VBR
Chapter 6
pn Junction Diodes: I-V Characteristics
Empirical Observations of VBR
VBR decreases with increasing N,
VBR decreases with decreasing EG.
Dominant breakdown mechanism is tunneling
VBR : breakdown voltage

3. Chapter 6
pn Junction Diodes: I-V Characteristics
Breakdown Voltage, VBR
If the reverse bias voltage (–VA) is so large that the peak electric field exceeds a critical value ECR, then the junction will “break down” and large reverse current will flow.
At breakdown, VA=–VBR
Thus, the reverse bias at which breakdown occurs is

4. Breakdown Mechanism: Avalanching
Chapter 6
pn Junction Diodes: I-V Characteristics
Breakdown Mechanism: Avalanching
High E-field:
High energy, enabling impact ionization which causing avalanche, at doping level N < 1018 cm–3
Small E-field:
ECR : critical electric field in the depletion region
Low energy, causing lattice vibration and localized heating

5. Breakdown Mechanism: Zener Process
Chapter 6
pn Junction Diodes: I-V Characteristics
Breakdown Mechanism: Zener Process
Zener process is the tunneling mechanism in a reverse-biased diode.
Energy barrier is higher than the kinetic energy of the particle.
The particle energy remains constant during the tunneling process.
Barrier must be thin  dominant breakdown mechanism when both junction sides are heavily doped.
Typically, Zener process dominates when VBR < 4.5V in Si at 300 K and N > 1018 cm–3.

6. Effect of R–G in Depletion Region
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
R–G in the depletion region contributes an additional component of diode current IR–G.
The net generation rate is given by
ET: trap-state energy level

7. Effect of R–G in Depletion Region
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
Continuing,
For reverse bias, with the carrier concentrations n and p being negligible,
Reverse biases with VA< – few kT/q

8. Effect of R–G in Depletion Region
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
Continuing,
For forward bias, the carrier concentrations n and p cannot be neglected,

9. Effect of R–G in Depletion Region
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of R–G in Depletion Region
Diffusion, ideal diode

10. Effect of Series Resistance
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of Series Resistance
Voltage drop, significant for high I
RS can be determined experimentally

11. Effect of High-Level Injection
Chapter 6
pn Junction Diodes: I-V Characteristics
Effect of High-Level Injection
As VA increases and about to reach Vbi, the side of the junction which is more lightly doped will eventually reach high-level injection:
(for a p+n junction)
(for a pn+ junction)
This means that the minority carrier concentration approaches the majority doping concentration.
Then, the majority carrier concentration must increase to maintain the neutrality.
This majority-carrier diffusion current reduces the diode current from the ideal.

12. High-Level Injection Effect
Chapter 6
pn Junction Diodes: I-V Characteristics
High-Level Injection Effect
Perturbation of both minority and majority carrier

13. Summary Deviations from ideal I-V Forward-bias current
Chapter 6
pn Junction Diodes: I-V Characteristics
Summary
Deviations from ideal I-V
Forward-bias current
Reverse-bias current
Due to high-level injection and series resistance in quasineutral regions
Due to thermal generation in depletion region
Due to avalanching and Zener process
Due to thermal recombination in depletion region

14. Minority-Carrier Charge Storage
Chapter 6
pn Junction Diodes: I-V Characteristics
Minority-Carrier Charge Storage
When VA>0, excess minority carriers are stored in the quasineutral regions of a pn junction.

15. Charge Control Approach
Chapter 6
pn Junction Diodes: I-V Characteristics
Charge Control Approach
Consider a forward-biased pn junction.
The total excess hole charge in the n quasineutral region is:
Since the electric field E»0,
Therefore (after all terms multiplied by q),
The minority carrier diffusion equation is (without GL):

16. Charge Control Approach
Chapter 6
pn Junction Diodes: I-V Characteristics
Charge Control Approach
Integrating over the n quasineutral region (after all terms multiplied by Adx), QP QP
Furthermore, in a p+n junction,
So:
In steady state

17. Charge Control Approach
Chapter 6
pn Junction Diodes: I-V Characteristics
Charge Control Approach
In steady state, we can calculate pn junction current in two ways:
From slopes of Δnp(–xp) and Δpn(xn)
From steady-state charges QN and QP stored in each “excess minority charge distribution”
Therefore,
Similarly,

18. Charge Control Approach
Chapter 6
pn Junction Diodes: I-V Characteristics
Charge Control Approach
Moreover, in a p+n junction:
In steady state

19. Chapter 6
pn Junction Diodes: I-V Characteristics
Narrow-Base Diode
Narrow-base diode: a diode where the width of the quasineutral region on the lightly doped side of the junction is on the order of or less than one diffusion length.
n-side contact

20. Narrow-Base Diode I–V We have the following boundary conditions:
Chapter 6
pn Junction Diodes: I-V Characteristics
Narrow-Base Diode I–V
We have the following boundary conditions:
Then, the solution is of the form:
Applying the boundary conditions, we have:

21. Narrow-Base Diode I–V Solving for A1 and A2, and substituting back:
Chapter 6
pn Junction Diodes: I-V Characteristics
Narrow-Base Diode I–V
Solving for A1 and A2, and substituting back:
Note that
The solution can be written more compactly as

22. Narrow-Base Diode I–V With decrease base width, xc’0:
Chapter 6
pn Junction Diodes: I-V Characteristics
Narrow-Base Diode I–V
With decrease base width, xc’0:
Δpn is a linear function of x due to negligible thermal R–G in region much shorter than one diffusion length
 JP is constant
This approximation can be derived using Taylor series approximation

23. Narrow-Base Diode I–V Because , then Then, for a p+n junction:
Chapter 6
pn Junction Diodes: I-V Characteristics
Narrow-Base Diode I–V
Because , then
Then, for a p+n junction:

24. Narrow-Base Diode I–V If xc’ << LP, Resulting
Chapter 6
pn Junction Diodes: I-V Characteristics
Narrow-Base Diode I–V
If xc’ << LP,
Resulting
Increase of reverse bias means
Increase of reverse current
Increase of depletion width
Decrease of quasineutral region xc’=xc–xn

25. Back to ideal diode solution
Chapter 6
pn Junction Diodes: I-V Characteristics
Wide-Base Diode
Rewriting the general solution for carrier excess,
For the case of wide-base diode (xc’>> LP),
Back to ideal diode solution

26. Back to ideal diode solution
Chapter 6
pn Junction Diodes: I-V Characteristics
Wide-Base Diode
Rewriting the general solution for diffusion current,
For the case of wide-base diode (xc’>> LP),
Back to ideal diode solution

27. Chapter 6
pn Junction Diodes: I-V Characteristics
Homework 5
1. (8.14)
The cross-sectional area of a silicon pn junction is 10–3 cm2. The temperature of the diode is 300 K, and the doping concentrations are ND = 1016 cm–3 and NA = 8×1015 cm–3. Assume minority carrier lifetimes of τn0 = 10–6 s and τp0 = 10–7 s.
Calculate the total number of excess electrons in the p region and the total number of excess holes in the n region for (a) VA = 0.3 V, (b) VA = 0.4V, and (c) VA = 0.5 V.
2. (7.2)
Problem 6.11, Pierret’s “Semiconductor Device Fundamentals”.
Deadline: , at 08:30 am.