EE130 Lecture 20, Slide 1Spring 2007

Lecture #20

OUTLINE

• pn Junctions (cont’d)

– small-signal model

– transient response• turn-off

Reading: Chapters 7, 8

EE130 Lecture 20, Slide 2Spring 2007

Small-Signal Model of the Diode

kTqVkTqV eIdV

deI

dV

d

dV

dI

RG /

0A

/0

AA

AA )1(1

qkT

IeI

kT

qG DCkTqV

//

0A

CR=1/Gva

i

Small-signal conductance :

dt

dvCGvi a

a

Small signal equivalent circuit:

+

EE130 Lecture 20, Slide 3Spring 2007

Review: Charge Storage in pn-Diode

EE130 Lecture 20, Slide 4Spring 2007

2 types of capacitance associated with a pn junction:1. CJ depletion capacitance

(due to variation of depletion charge)

2. CD diffusion capacitance (due to variation of stored minority charge in the quasi-

neutral regions)

For a one-sided p+n junction, QP >> QN

so Q = QP + QN QP:

qkT

IG

dV

dI

dV

dQC

/

τττ DCp

pA

pA

D

EE130 Lecture 20, Slide 5Spring 2007

What are three ways to reduce Cdep?

WA

dV

dQC s

A

depJ

Depletion Capacitance

np

W

“insulator” conductorconductor

EE130 Lecture 20, Slide 6Spring 2007

Total pn-Junction Capacitance

• CD dominates at moderate to high forward biases

• Cdep dominates at low forward biases, reverse biases

1/

τ /DCD kTqVAe

qkT

IC

WAC s

J

DCCC JR=1/Gva

i

+

EE130 Lecture 20, Slide 7Spring 2007

NqA

VV

A

W

C Ss 2Abi

22

2

2J

)(21

CJ-vs.-VA (Reverse Bias)

EE130 Lecture 20, Slide 8Spring 2007

If the slope of the (1/Cdep)2 vs. VA characteristic is -2x1023

F-2 V-1, the intercept is 0.84V, and A is 1 m2, find the lighter and heavier doping concentrations Nl and Nh. Solution:

ln 2i

lhbi

n

NN

q

kTV 318026.0

84.0

15

202

cm 108.1106

10

eeN

nN kT

qV

l

ih

bi

315

28141923

2

cm 106

)cm101085.812106.1102/(2

)/(2

AqslopeN sl

Example

EE130 Lecture 20, Slide 9Spring 2007

Summary: Small Signal Model

qkT

IG DC

/

qkT

IC

/

τ DCD

W

AC s

J

)1( /0

A kTqVDC eII

DJ CCC

Depletion capacitance

Diffusion capacitance

Conductance

EE130 Lecture 20, Slide 10Spring 2007

Transient Response of pn Diode• Suppose a pn-diode is forward biased, then suddenly

turned off at time t = 0. Because of CD, the voltage across the pn junction depletion region cannot be changed instantaneously.

The delay in switching between the ON and OFF states is due to the time required to change the amount of excess minority carriers stored in the quasi-neutral regions.

EE130 Lecture 20, Slide 11Spring 2007

Turn-Off Transient• In order to turn the diode off, the excess minority

carriers must be removed by net carrier flow out of the quasi-neutral regions and/or recombination– Carrier flow is limited by the switching circuitry

EE130 Lecture 20, Slide 12Spring 2007

Decay of Stored ChargeConsider a p+n diode (Qp >> Qn):

t

i(t)

t

vA(t)

ts

ts0

pxx

n

qAD

i

dx

dp

n

For t > 0:

pn(x)

EE130 Lecture 20, Slide 13Spring 2007

Examples (qualitative)

t

i(t)

ts

Increase IF

t

i(t)

ts

Increase IR

t

i(t)

ts

Decrease p

EE130 Lecture 20, Slide 14Spring 2007

Storage Delay Time ts

• ts is the primary “figure of merit” used to characterize the transient response of pn junction diodes

• By separation of variables and integration from t = 0+ to t = ts, noting that

and making the approximation

We conclude that

sp

pR

p

pp ttQ

IQ

idt

dQ

0

ττ

ppF tQI τ/)0(

0)( sp ttQ

R

Fps I

It 1lnτ