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Empirical Observations of V BR

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Chapter 6

pn Junction Diodes: I-V Characteristics

Dominant breakdown mechanism is tunneling

- VBR decreases with increasing N,

- VBR decreases with decreasing EG.

- VBR : breakdown voltage

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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

Chapter 6

pn Junction Diodes: I-V Characteristics

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

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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.

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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

Chapter 6

pn Junction Diodes: I-V Characteristics

- Continuing,

- For reverse bias, with the carrier concentrations n and p being negligible,

- Reverse biases with VA< – few kT/q

Chapter 6

pn Junction Diodes: I-V Characteristics

- Continuing,

- For forward bias, the carrier concentrations n and p cannot be neglected,

Chapter 6

pn Junction Diodes: I-V Characteristics

Diffusion, ideal diode

Chapter 6

pn Junction Diodes: I-V Characteristics

Voltage drop, significant for high I

RS can be determined experimentally

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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.

Chapter 6

pn Junction Diodes: I-V Characteristics

Perturbation of both minority and majority carrier

Forward-bias current

Chapter 6

pn Junction Diodes: I-V Characteristics

Deviations from ideal I-V

Reverse-bias current

Due to thermal generation in depletion region

Due to high-level injection and series resistance in quasineutral regions

Due to avalanching and Zener process

Due to thermal recombination in depletion region

Chapter 6

pn Junction Diodes: I-V Characteristics

- When VA>0, excess minority carriers are stored in the quasineutral regions of a pn junction.

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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):

Chapter 6

pn Junction Diodes: I-V Characteristics

- Integrating over the n quasineutral region (after all terms multiplied byAdx),

QP

QP

- Furthermore, in a p+n junction,

0

- So:

In steady state

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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,

Chapter 6

pn Junction Diodes: I-V Characteristics

- Moreover, in a p+n junction:

In steady state

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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

Chapter 6

pn Junction Diodes: I-V Characteristics

- We have the following boundary conditions:

- Then, the solution is of the form:

- Applying the boundary conditions, we have:

Chapter 6

pn Junction Diodes: I-V Characteristics

- Solving for A1 and A2, and substituting back:

- Note that

- The solution can be written more compactly as

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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
- JPis constant

- This approximation can be derived using Taylor series approximation

Chapter 6

pn Junction Diodes: I-V Characteristics

- Because , then

- Then, for a p+n junction:

Chapter 6

pn Junction Diodes: I-V Characteristics

- If xc’ << LP,

- Resulting

- Increase of reverse bias means
- Increase of reverse current
- Increase of depletion width
- Decrease of quasineutral region xc’=xc–xn

Chapter 6

pn Junction Diodes: I-V Characteristics

- Rewriting the general solution for carrier excess,

- For the case of wide-base diode (xc’>> LP),

Back to ideal diode solution

Chapter 6

pn Junction Diodes: I-V Characteristics

- Rewriting the general solution for diffusion current,

- For the case of wide-base diode (xc’>> LP),

Back to ideal diode solution

Chapter 6

pn Junction Diodes: I-V Characteristics

- 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: 07.06.2012, at 08:30 am.