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

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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

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.
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):
charge control approach1

Chapter 6

pn Junction Diodes: I-V Characteristics

Charge Control Approach
  • Integrating over the n quasineutral region (after all terms multiplied byAdx),

QP

QP

  • Furthermore, in a p+n junction,

0

  • So:

In steady state

charge control approach2

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,
charge control approach3

Chapter 6

pn Junction Diodes: I-V Characteristics

Charge Control Approach
  • Moreover, in a p+n junction:

In steady state

narrow base diode

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

narrow base diode i v

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:
narrow base diode i v1

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
narrow base diode i v2

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
  •  JPis constant
  • This approximation can be derived using Taylor series approximation
narrow base diode i v3
Narrow-Base Diode I–V

Chapter 6

pn Junction Diodes: I-V Characteristics

  • Because , then
  • Then, for a p+n junction:
narrow base diode i v4

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
wide base diode

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

wide base diode1

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

homework 5

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: 07.06.2012, at 08:30 am.
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