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Lecture 11

OUTLINE

- pn Junction Diodes (cont’d)
- Narrow-base diode
- Junction breakdown
Reading: Pierret 6.3.2, 6.2.2; Hu 4.5

Introduction In modern IC devices, however, it is common for one side of a pn junction to be shorter than the minority-carrier diffusion length, so that a significant fraction of the “injected” minority carriers reach the end of the quasi-neutral region, at the metal contact.

- The ideal diode equation was derived assuming that the lengths of the quasi-neutral p-type & n-type regions (WP’ , WN’) are much greater than the minority-carrier diffusion lengths (Ln , Lp) in these regions.
- Excess carrier concentrations decay exponentially to 0.
- Minority carrier diffusion currents decay exponentially to 0.

Recall that Dp = Dn = 0 at an ohmic contact

In this lecture we re-derive the diode I-V equation with the boundary condition that Dp = 0 at a distance xc’ (rather than ) from the edge of the depletion region.

EE130/230A Fall 2013

Lecture 11, Slide 2

Excess Carrier Distribution (n side)

- From the minority carrier diffusion equation:
- For convenience, let’s use the coordinate system:
- So the solution is of the form:
- We have the following boundary conditions:

x’’ 0

0 x’

xc'

EE130/230A Fall 2013

Lecture 11, Slide 3

Applying the boundary conditions, we have:

Therefore

Since this can be rewritten as

We need to take the derivative of Dpn’ to obtain the hole diffusion current within the quasi-neutral n region:

EE130/230A Fall 2013

Lecture 11, Slide 4

Thus, for a one-sided p+n junction (in which the current is dominated by injection of holes into the n-side) with a short n-side:

Evaluate Jp at x=xn (x’=0) to find the injected hole current:

EE130/230A Fall 2013

Lecture 11, Slide 5

Therefore if xc’ << LP:

For a one-sided p+n junction, then:

EE130/230A Fall 2013

Lecture 11, Slide 6

Excess Hole Concentration Profile

If xc’ << LP:

Dpn is a linear function:

- Jp is constant
(No holes are lost due to recombination as they diffuse to the metal contact.)

Dpn(x)

slope is

constant

x'

0

x'c

0

EE130/230A Fall 2013

Lecture 11, Slide 7

General Narrow-Base Diode I-V

- Define WP‘ and WN’ to be the widths of the quasi-neutral regions.
- If both sides of a pn junction are narrow (i.e. much shorter than the minority carrier diffusion lengths in the respective regions):

e.g. if hole injection into the n side is greater than electron injection into the p side:

J

JP

JN

x

xn

-xp

EE130/230A Fall 2013

Lecture 11, Slide 8

Summary: Narrow-Base Diode

- If the length of the quasi-neutral region is much shorter than the minority-carrier diffusion length, then there will be negligible recombination within the quasi-neutral region and hence all of the injected minority carriers will “survive” to reach the metal contact.
- The excess carrier concentration is a linear function of distance.
For example, within a narrow n-type quasi-neutral region:

- The minority-carrier diffusion current is constant within the narrow quasi-neutral region.
Shorter quasi-neutral region steeper concentration gradient higher diffusion current

- The excess carrier concentration is a linear function of distance.

Dpn(x)

location of metal contact

(Dpn=0)

x

0

xn

WN’

EE130/230A Fall 2013

Lecture 11, Slide 9

pn Junction Breakdown

C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 4-10

Breakdown

voltage, VBR

VA

AZener diodeis designed to operate in the breakdown mode:

EE130/230A Fall 2013

Lecture 11, Slide 10

Review: Peak E-Field in a pn Junction

E(x)

-xp

xn

x

E(0)

For a one-sided junction,

where N is the dopant concentration on the lightly doped side

EE130/230A Fall 2013

Lecture 11, Slide 11

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” (i.e. large reverse current will flow)
- Thus, the reverse bias at which breakdown occurs is

EE130/230A Fall 2013

Lecture 11, Slide 12

Avalanche Breakdown Mechanism

R. F. Pierret, Semiconductor Device Fundamentals, Figure 6.12

High E-field:

if VBR >> Vbi

Low E-field:

- ECR increases slightly with N:
- For 1014 cm-3 < N < 1018 cm-3,
- 105 V/cm < ECR < 106 V/cm

EE130/230A Fall 2013

Lecture 11, Slide 13

Tunneling (Zener) Breakdown Mechanism

Dominant breakdown mechanism when both sides of a junction are very heavily doped.

VA = 0

VA < 0

Ec

Ev

Typically, VBR < 5 V for Zener breakdown

C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 4-12

EE130/230A Fall 2013

Lecture 11, Slide 14

Empirical Observations of VBR

R. F. Pierret, Semiconductor Device Fundamentals, Figure 6.11

- VBR decreases with increasing N
- VBR decreases with decreasing EG

EE130/230A Fall 2013

Lecture 11, Slide 15

VBR Temperature Dependence

- For the avalanche mechanism:
- VBR increases with increasing T, because the mean free path decreases

- For the tunneling mechanism:
- VBRdecreases with increasing T, because the flux of valence-band electrons available for tunneling increases

EE130/230A Fall 2013

Lecture 11, Slide 16

Summary: Junction Breakdown

- If the peak electric field in the depletion region exceeds a critical value ECR, then large reverse current will flow.
This occurs at a negative bias voltage called the breakdown voltage, VBR:

where N is the dopant concentration on the more lightly doped side

- The dominant breakdown mechanism is
avalanche, if N < ~1018/cm3

tunneling, if N > ~1018/cm3

EE130/230A Fall 2013

Lecture 11, Slide 17

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