Qualitative derivation
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Chapter 6. pn Junction Diodes: I - V Characteristics. M ajority carriers. M ajority carriers. Qualitative Derivation. Chapter 6. pn Junction Diodes: I - V Characteristics. Current Flow in a pn Junction Diode.

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Qualitative Derivation

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Qualitative derivation

Chapter 6

pn Junction Diodes: I-V Characteristics

Majority

carriers

Majority

carriers

Qualitative Derivation


Current flow in a pn junction diode

Chapter 6

pn Junction Diodes: I-V Characteristics

Current Flow in a pn Junction Diode

  • 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.


Ideal diode assumptions

Chapter 6

pn Junction Diodes: I-V Characteristics

Ideal Diode: Assumptions

  • 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.


Current flow in a pn junction diode1

Chapter 6

pn Junction Diodes: I-V Characteristics

Current Flow in a pn Junction Diode

  • Current density J = JN(x) + JP(x)

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


Carrier concentrations at x p x n

Chapter 6

pn Junction Diodes: I-V Characteristics

Carrier Concentrations at –xp, xn

  • 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:


Law of the junction

Chapter 6

pn Junction Diodes: I-V Characteristics

“Law of the Junction”

  • 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:


Excess carrier concentrations at x p x n

Chapter 6

pn Junction Diodes: I-V Characteristics

Excess Carrier Concentrations at –xp, xn

p-side

n-side


Example carrier injection

Chapter 6

pn Junction Diodes: I-V Characteristics

Example: Carrier Injection

  • 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?


Excess carrier distribution

Chapter 6

pn Junction Diodes: I-V Characteristics

Excess Carrier Distribution

  • 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


Excess carrier distribution1

Chapter 6

pn Junction Diodes: I-V Characteristics

Excess Carrier Distribution

  • New boundary conditions

  • From the x’→ ∞,

  • From the x’ →0,

  • Therefore

  • Similarly,


Pn diode i v characteristic

Chapter 6

pn Junction Diodes: I-V Characteristics

pn Diode I–V Characteristic

n-side

p-side


Pn diode i v characteristic1

Chapter 6

pn Junction Diodes: I-V Characteristics

pn Diode I–V Characteristic

  • 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


Diode saturation current i 0

Chapter 6

pn Junction Diodes: I-V Characteristics

Diode Saturation Current I0

  • 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,


Diode carrier currents

Chapter 6

pn Junction Diodes: I-V Characteristics

Diode Carrier Currents

  • Total current density is constant inside the diode

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


Carrier concentration forward bias

Chapter 6

pn Junction Diodes: I-V Characteristics

Excess minority

carriers

Excess minority

carriers

Carrier Concentration: Forward Bias

  • Law of the Junction

  • Low level injection conditions


Carrier concentration reverse bias

Chapter 6

pn Junction Diodes: I-V Characteristics

Carrier Concentration: Reverse Bias

  • Deficit of minority carriers near the depletion region.

  • Depletion region acts like a “sink”, draining carriers from the adjacent quasineutral regions


Deviations from the ideal i v behavior

Chapter 6

pn Junction Diodes: I-V Characteristics

No saturation

“Slope over”

“Breakdown”

Smaller slope

Deviations from the Ideal I-V Behavior

  • Si pn-junction Diode, 300 K.

Forward-bias current

Reverse-bias current


Empirical observations of v br

Chapter 6

pn Junction Diodes: I-V Characteristics

Dominant breakdown mechanism is tunneling

Empirical Observations of VBR

  • VBR decreases with increasing N,

  • VBR decreases with decreasing EG.

  • VBR : breakdown voltage


Breakdown voltage v br

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


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


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.


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


Effect of r g in depletion region1

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


Effect of r g in depletion region2

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,


Effect of r g in depletion region3

Chapter 6

pn Junction Diodes: I-V Characteristics

Effect of R–G in Depletion Region

Diffusion, ideal diode


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


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.


High level injection effect

Chapter 6

pn Junction Diodes: I-V Characteristics

High-Level Injection Effect

Perturbation of both minority and majority carrier


Summary

Forward-bias current

Chapter 6

pn Junction Diodes: I-V Characteristics

Summary

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


Homework

Chapter 5

pn Junction Electrostatics

Homework

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


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