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# Lecture 11 - PowerPoint PPT Presentation

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.

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OUTLINE

• pn Junction Diodes (cont’d)

• Narrow-base diode

• Junction breakdown

Reading: Pierret 6.3.2, 6.2.2; Hu 4.5

• 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.

• 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.

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

• 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

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

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

• 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

• 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

Dpn(x)

location of metal contact

(Dpn=0)

x

0

xn

WN’

EE130/230A Fall 2013

Lecture 11, Slide 9

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

• 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

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

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

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

• 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