Empirical observations of v br
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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

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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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