lecture #17

EE130 Lecture 17, Slide 1Spring 2007

Lecture #17

OUTLINE

• pn junctions (cont’d)

– Reverse bias current

– Reverse-bias breakdown

Reading: Chapter 6.2


Carrier Concentration Profiles: Forward Bias


Carrier Concentration Profiles: Reverse Bias

– Depletion of minority carriers at edges of depletion region

– The only current which flows is due to drift of minority carriers across the junction. This current is fed by diffusion of minority carriers toward junction (supplied by thermal generation).


Alternative Derivation of Formula for I0

“Depletion approximation”:

• I0 represents the rate at which carriers are thermally generated within a diffusion length of the depletion region:

Pnnp

Di

p

n

ppNn

Ai

n

p

LxxxNnp

t

p

-xx-x-LNnn

t

n

/

/

2

2

p

DiP

n

AiN

NnqAL

NnqALI

// 22

0


A Zener diode is designed to operate in the breakdown mode.

V

I

VBR

P N A

R

Forward Current

Small leakageCurrent

(a)

3.7V

R

(b)

ICZener diode

Junction Breakdown


• If the reverse bias voltage (-VA) is so large that the

peak electric field exceeds a critical value CR, then the junction will “break down” (i.e. large reverse current will flow)

• Thus, the reverse bias at which breakdown occurs is

biCRs

BR VqN

V 2

2

s

BRbiCR

VVqN

2

Breakdown Voltage, VBR


if VBR >> Vbi

CR increases slightly with N:

For 1014 cm-3 < N < 1018 cm-3,

105 V/cm < CR < 106 V/cm

qNV CRs

BR 2

2

Avalanche Breakdown Mechanism

Small E-field:

High E-field:


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

Ec

Ev

VA = 0:

Ev

Ec

Empty StatesFilled States -

Tunneling (Zener) Breakdown Mechanism

VA < 0:

biCRs

BR VqN

V 2

2

V/cm 106CRTypically, VBR < 5 V for Zener breakdown


Empirical Observations of VBR

• VBR decreases with increasing N

• VBR decreases with decreasing EG


Breakdown Temperature Dependence

• For the avalanche mechanism: – VBR increases with increasing T, because

the mean free path decreases

• For the tunneling mechanism: – VBR decreases with increasing T, because

the flux of valence-band electrons available for tunneling increases


Summary• The minority-carrier concentrations at the edges of

the depletion region change with the applied bias VA, by the factor

• The diode saturation current I0 is dominated by the term associated with the more lightly doped side:

p+ n diode:

p n+ diode:

• I0 can be viewed as the drift current due to minority carriers generated within a diffusion length of the depletion region

kTqVAe /

)( 20

DP

PinP NL

DqAnxII

)( 20

AN

NipN NL

DqAnxII


Reverse-bias breakdown:• If the peak electric field in the depletion region exceeds

a critical value CR, then large reverse current will flow.

This happens at a large negative voltage, called the “breakdown voltage”:

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

biCRs

BR VqN

V 2

2


Deviations from the Ideal I-V Behavior

Forward-bias current Reverse-bias current

lecture #17

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