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Qualitative Derivation

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Chapter 6

pn Junction Diodes: I-V Characteristics

Majority

carriers

Majority

carriers

Chapter 6

pn Junction Diodes: I-V Characteristics

- When a forward bias (VA > 0) is applied, the potential barrier to diffusion across the junction is reduced.
- Minority carriers are “injected” into the quasi-neutral regions Δnp > 0, Δpn > 0.
- Minority carriers diffuse in the quasi-neutral regions, recombining with majority carriers.

Chapter 6

pn Junction Diodes: I-V Characteristics

- Steady-state conditions.
- Non-degenerately doped step junction.
- One-dimensional diode.
- Low-level injection conditions prevail in the quasi-neutral regions.
- No processes other than drift, diffusion, and thermal R–G take place inside the diode.

Chapter 6

pn Junction Diodes: I-V Characteristics

- Current density J = JN(x) + JP(x)

- JN(x) and JP(x) may vary with position, but J is constant throughout the diode.

Chapter 6

pn Junction Diodes: I-V Characteristics

- Consider the equilibrium carrier concentrations at VA = 0:

p-side

n-side

- If low-level injection conditions prevail in the quasi-neutral regions when VA 0, then:

Chapter 6

pn Junction Diodes: I-V Characteristics

- The voltage VA applied to a pn junction falls mostly across the depletion region (assuming that low-level injection conditions prevail in the quasi-neutral regions).
- Two quasi-Fermi levels is drawn in the depletion region:

Chapter 6

pn Junction Diodes: I-V Characteristics

p-side

n-side

Chapter 6

pn Junction Diodes: I-V Characteristics

- A pn junction has NA=1018 cm–3 and ND=1016 cm–3. The applied voltage is 0.6 V.

- a)What are the minority carrier concentrations at the depletion-region edges?

- b)What are the excess minority carrier concentrations?

Chapter 6

pn Junction Diodes: I-V Characteristics

- From the minority carrier diffusion equation,

- For simplicity, we develop a new coordinate system:

- We have the following boundary conditions:

- Then, the solution is given by:

- LP : hole minority carrier diffusion length

Chapter 6

pn Junction Diodes: I-V Characteristics

- New boundary conditions

- From the x’→ ∞,
- From the x’ →0,

- Therefore

- Similarly,

Chapter 6

pn Junction Diodes: I-V Characteristics

n-side

p-side

Chapter 6

pn Junction Diodes: I-V Characteristics

- Shockley Equation,for ideal diode
- I0 can be viewed as the drift current due to minority carriers generated within the diffusion lengths of the depletion region

Chapter 6

pn Junction Diodes: I-V Characteristics

- I0 can vary by orders of magnitude, depending on the semiconductor material, due to ni2 factor.
- In an asymmetrically doped pn junction, the term associated with the more heavily doped side is negligible.
- If the p side is much more heavily doped,
- If the n side is much more heavily doped,

Chapter 6

pn Junction Diodes: I-V Characteristics

- Total current density is constant inside the diode

- Negligible thermal R-G throughout depletion region dJN/dx = dJP/dx = 0

Chapter 6

pn Junction Diodes: I-V Characteristics

Excess minority

carriers

Excess minority

carriers

- Law of the Junction

- Low level injection conditions

Chapter 6

pn Junction Diodes: I-V Characteristics

- Deficit of minority carriers near the depletion region.
- Depletion region acts like a “sink”, draining carriers from the adjacent quasineutral regions

Chapter 6

pn Junction Diodes: I-V Characteristics

No saturation

“Slope over”

“Breakdown”

Smaller slope

- Si pn-junction Diode, 300 K.

Forward-bias current

Reverse-bias current

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 5

pn Junction Electrostatics

- This time no homework. Prepare well for Quiz 2.